solve using substitution: y=4-2x and 3x+2y=7

Answers

Answer 1

Answer:

(1,2 )

Step-by-step explanation:

use m a t h w a y, it gives you the right answers every time

Answer 2

Answer:

The solution is (1, 2)

Step-by-step explanation:

The expression 4 - 2x is equivalent to y.  Thus, we can eliminate y by substituting 4 - 2x for y in 3x + 2y = 7:

3x + 2(4 - 2x) = 7, or

3x + 8 - 4x = 7

Combining like terms, we get:

-x = - 1, or x = 1.  If x = 1, then (from y = 4 - 2x)  y = 4 - 2(1) = 2

The solution is (1, 2)


Related Questions

on a business retreat, your company of 32 businessmen and businesswomen go golfing. you need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. how many ways can you do this?

Answers

There are 4,845 ways to divide a group of 20 people into foursomes, and there are 1,800 ways to form foursomes with at least one Board member in each.

(a) The number of ways to divide a group of 20 people into foursomes can be calculated using the combination formula:

C(20,4) * C(16,4) * C(12,4) * C(8,4) * C(4,4)

where C(n,r) represents the number of ways to choose r items from a set of n items.

Plugging in the values, we get:

[C(20,4)]  [C(16,4)]  [C(12,4)]  [C(8,4)]  [C(4,4)] = 4,845,120

Therefore, there are 4,845,120 ways to divide the 20 people into foursomes.

(b) If we want to include one of the five Board members in each foursome, we can first choose the Board member for the first foursome (5 ways to do this), then choose the Board member for the second foursome (4 ways to do this), and so on. After choosing the Board members, we can then assign the remaining people to the foursomes in the same way as in part (a).

Therefore, the total number of ways to form the foursomes with one Board member in each foursome is:

5  [C(16,3)]  [C(12,3)]  [C(8,3)]  [C(4,3)] = 1,254,720

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Complete question:

On a business retreat, your company of 20 businessmen and businesswomen go golfing.

(a) You need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. How many ways can you do this?

(b) After all your hard work, you realize that in fact, you want each foursome to include one of the five Board members. How many ways can you do this?

The distance between the point (- 5 ,-2) and y-axis is
length unit.
(a) - 5
(b) – 2
(c) 2
(d) 5​

Answers

Using our x coordinate to find the distance. It is because D distance is always positive.

an amusement park ride consists of a large vertical wheel of radius r that rotates

Answers

The best description of the passenger's linear and angular velocity while passing point A is option d) Linear Velocity Constant, Angular Velocity Constant.

When the passenger is at point A, which is the highest point of the ride, the seat exerts a normal force with a magnitude of 0.8F, where F represents the person's weight. This normal force provides the necessary centripetal force to keep the person moving in a circular path. At this point, the passenger's linear velocity remains constant, as there is no change in speed.

Since the passenger releases a small rock without hitting anything, there are no external torques acting on the system. Therefore, according to the law of conservation of angular momentum, the passenger's angular velocity remains constant as well. The angular velocity is determined by the rotational motion of the wheel and does not change as the passenger passes point A.

Therefore, the passenger's linear velocity is constant, and their angular velocity is also constant while passing point A, resulting in the most accurate description being d) Linear Velocity Constant, Angular Velocity Constant.

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(Equivalent Algebraic Expressions LC)

Simplify this please!!

(Equivalent Algebraic Expressions LC)Simplify this please!!

Answers

Answer:

\(\frac{x^3}{y^7}\)

Step-by-step explanation:

The key to answering this question is the exponential law that says \(a^{-n} = \frac1{a^n}$\) :

\(\frac{y^{-7}}{x^{-3}} \\ \\\to \frac{\frac1{y^7}}{\frac1{x^3}} \\ \\\to \frac1{y^7} \times \frac{x^3}1 \\ \\\to \frac{x^3}{y^7}\)

Im just wasting points :) Ignore this

Answers

why? how much points do you have to spare?

Which transformations are nonrigid transformations?
a. rotation
b. dilation
c. reflection
d. translation
e. stretch

Answers

Dilation and Stretch are non-rigid transformations.

Non - Rigid transformation:

Non-rigid transformations can change the size or shape of the archetype, or both size and shape. The two transformations Strain and Shear are not rigid. The resulting image of the transform is changed in size, shape, or both.

A non-rigid transformation is a transformation that changes the length or angle of a shape's sides. Nonrigid transformations are dilation and stretching.

All types of transformations except dilation are rigid transformations.

Dilation transformations are divided into two types

StretchingCompression

Therefore non-rigid transformations are Dilation and Stretching

Dilation:

Dilation (usually denoted by ⊕) is one of the fundamental operations in mathematical morphology. Originally developed for binary images, it was expanded first to grayscale images and then to full meshes. Stretch operations typically use a structuring element to examine and expand the shapes contained in the input image.

Strechting:

A non-rigid transformation changes the size or shape of an object. Resizing (stretching horizontally, vertically, or both) is a non-rigid transformation.

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1.) Solve the equation for y.
4x-5y=9
A.y= -4x-9
B.y= 5/4x+9/4
C.y= -5/4x-5/9
D.y= 4/5x-9/5

2. Which ordered pair in the form (a,b) is a solution of this equation?
7a-5b=28
A.(-3,-2)
B.(-2,-3)
C.(4,0)
D.(0,4)

3.Which of the ordered pairs in the form (x,y) is a solution of this equation?
5x-y/3=13 (2,-9),(3,-6)
A.Neither is a solution
B.The first is a solution, but the second is not
C. Both are solution
D. The first is not a solution, but the second is

4. Which ordered pair in the form (x,y) is a solution of this equation?
(x+3)y=14
A.(5,2)
B.(11,1)
C.(7,2)
D.(3,2)

5.)Which pair are solutions to the equation?
4xy+8=36
A.(1,7) and (7,1)
B.(7,1) and (3,2)
C.(4,9) and (3,2)
D.(1,7) and (4,9)

Answers

1. Correct option D. y= 4/5x-9/5

2. option C. (4, 0) is a solution.

3. option B, is the correct answer.

4. option B. (11, 1), is a solution.

5. option A, "(1,7) and (7,1)" is a correct answer.

Define the term equation?

A statement proving the equality of two mathematical expressions is known as an equation.

1. Solve the equation for y:  4x - 5y = 9  

⇒ 5y = 4x - 9

⇒ y = 4/5 x - 9/5  (correct option D)

2. Solution of this equation:  7a - 5b = 28

from the given options we simply substitute the values of a and b into the equation and check if the equation holds true.

option C. (4, 0);

Substituting a=4 and b=0 into the equation 7a-5b=28, we get:

7(4) - 5(0) = 28, which is equal to 28. So (4, 0) is a solution.

3. we simply substitute the values of x and y into the equation and check if the equation holds true.

Substituting x=2 and y=-9 into the equation 5x-y/3=13, we get:

5(2) - (-9)/3 = 10 + 3 = 13, which is equal to 13. So (2,-9) is a solution.

Substituting x=3 and y=-6 into the equation 5x-y/3=13, we get:

5(3) - (-6)/3 = 15 + 2 = 17, which is not equal to 13. So (3,-6) is not a solution.

Therefore, option B, "The first is a solution, but the second is not" is the correct answer.

4. we simply substitute the values of x and y into the equation and check if the equation holds true.

option B. (11, 1), Substituting x=11 and y=1 into the equation (x+3)y=14, we get: (11+3)(1) = 14(1) = 14, which is equal to 14. So (11,1) is a solution.

5. we substitute each pair into the equation and check if it holds true.

option A. (1,7) and (7,1); Substituting x=1 and y=7 into the equation 4xy+8=36, we get: 4(1)(7) + 8 = 28 + 8 = 36, which is equal to 36. So (1,7) is a solution.

Substituting x=7 and y=1 into the equation 4xy+8=36, we get:

4(7)(1) + 8 = 28 + 8 = 36, which is equal to 36. So (7,1) is also a solution.

Therefore, option A, "(1,7) and (7,1)" is a correct answer.

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The answers of the given equations are

1. option D

2.option C

3. option B

4.option B

5.option A.

What is equation?

Equation is basically a mathematical statement where two expressions are connected by a equal sign. It contains atleast one variable that has be determined.

1) Given equation is 4x- 5y= 9

To solve this equation at first we subtract 4x from both sides

                         -5y= 9-4x

Multiplying by '-' sign to the both sides of the equation we get,

                         5y= 4x-9

Dividing by 5 on the both sides of equation we get,

                      y= (4/5)x - (9/5)

Hence option D is correct.

2) Given equation is 7a-5b = 28----------(1)

putting a=4 and b=0  in equation (1) we get,

                  7× 4- 5×0=28

Hence the ordered pair ( 4,0) is the solution of the equation as the value of a and b satisfies the right side of equation (1). option C.

3) Given equation is 5x- y/3= 13-----------(2)

Putting (2,-9) in equation (2) we get,

  10+3=13 which is the RHS of equation (2)

Putting (3,-6) in equation (2) we get,

  15+2=17 which is not the RHS of equation (2)

So the first is a solution of the equation but the second is not.

Option B.

4) Given equation is (x+3)y=14---------(3)

Putting the values (11,1) in equation (3) we get,

(11+3)×1= 14 which is the RHS of the equation (3).

So the ordered pair is (11,1).

Option B.

5) Given equation is 4xy+8=36

It can be deduced to,

                      4xy+8=36

                       4xy= 36-8

                        4xy= 28

                           x y= 7-------(4)

Putting (1,7) and (7,1) in equation (4) we get,

                      1×7=7×1=7 which is the RHS of equation (4)

So the pair is (1,7) and (7,1). Option A.

Hence, the answers are

1. option D

2.option C

3. option B

4.option B

5.option A.

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Train A runs back and forth on an east-west section of railroad track. Train A’s velocity, measured in meters per minute, is given by a differentiable function vA(t) where time t is measured in minutes. Selected values for vA(t) are given in the table below.t (Minutes) 0 2 5 8 12vA(t)(meters/minute) 0 100 40 -120 -150Find the average acceleration of train A over the interval 2 ≤ t ≤ 8.

Answers

The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

Explanation:

The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.

To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:

Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute

To find the time interval, we can subtract 2 from 8:

Δt = 8 - 2 = 6 minutes

Now we can use the formula for average acceleration:

a = Δv/Δt = (-220)/6 = -40 meters per minute squared

Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

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ASAP HELP
Find the variance and standard deviation of the data set below:
0 0.107
1 0.352
2 0.400
3 0.141

Answers

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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asap please help for brain list

If a+b = c which of the following statements is true?

b-c=a

a-c=b

c-a=b

c+b= a

Answers

Answer:

c-a=B

Step-by-step explanation:

if A+B=c then you subtract a from c and you get b

Answer:

C. c - a = b

Step-by-step explanation:

a + b = c

There are many ways to rearrange this equation. This can be done through addition and subtraction.

First, let's handle a. a is positive; therefore, we should subtract it.

a + b = c

b = c - a

Next, let's handle b. b is also positive; therefore, we should subtract it.

a + b = c

a = c - b

Finally, we will handle c. c is once again positive; therefore we should subtract it. However, it is the only variable on the right side, which would leave 0. This is not an option, so we will not look at this.

From our options, we can see that we have produced: b = c - a

This is an option, which has been written as c - a = b.

Therefore, your answer is C. c - a = b

Hope this helps!

Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=

Answers

There is a maximum value of 6 located at (x, y) = (1, 6).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 12.

Rearranging the constraint, we get:

6x + y = 12,

or, y = 12 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(12 - 6x) = 12x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 12 - 12x ... (i)

Equating to 0, we get:

12 - 12x = 0,

or, 12x = 12,

or, x = 1.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 1.

The value of y, when x = 1 is,

y = 12 - 6x,

or, y = 12 - 6*1 = 6.

The value of f(x, y) when (x, y) = (1, 6) is,

f(x, y) = xy,

or, f(x, y) = 1*6 = 6.

Thus, there is a maximum value of 6 located at (x, y) = (1, 6).

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The provided question is incomplete. The complete question is:

"Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y)=xy; 6x+y=12.

Find the total surface area of this triangular prism.
10cm
6 cm
4cm
8 cm

Find the total surface area of this triangular prism. 10cm 6 cm 4cm 8 cm

Answers

Method:

Front: 6x8 = 48/2 = 24

Back: Also 24

Base: 8x4 = 32

Left: 6x4=24

Add your answers:

24 + 24 + 24 + 32 + 40

Answer:

TSA is 144 cm²

How do you write 2 more than 3 times?.

Answers

The correct equation to write 2 more than 3 times is 3x + 2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Let us assume that, the number is 17 .

So,

Three time of x = 3 * x = 3x

then,

→ 2 more than three time of x = (3x + 2)

given that, 2 more than three time of x is equal to 17 .

therefore,

→ 3x + 2 = 17

→ 3x = 17 - 2

→ 3x = 15

→ x = 5 (Ans.)

Hence, the required number is 5 .

Verification :-

→ 2 more than three times of 5 = 17

→ 3 * 5 + 2 = 17

→ 15 + 2 = 17

→ 17 = 17 .

hence, the correct equation to write 2 more than 3 times is 3x + 2.

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flx) = 1
g(x) = x-4
Can you evaluate (g o (0)? Explain why or why
not.

Answers

No because it is a -4

sat scores in one state is normally distributed with a mean of 1403 and a standard deviation of 200. Suppose we randomly pick 32 SAT scores from that state. a) Find the probability that one of the scores in the sample is greater than 1484. P(X > 1484) = b) Find the probability that the average of the scores for the sample of 48 scores is greater than 1484 P(X > 1484) = Round each answer to at least 4 decimal places.

Answers

The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

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Three tennis balls are stacked tightly inside of a cylindrical container, as shown below. The radius of each ball is 7 centimeters.
Calculate the volume of the empty space left inside of the container. Round to the nearest hundredth.
Volume of Empty Space =
cm?

Three tennis balls are stacked tightly inside of a cylindrical container, as shown below. The radius

Answers

Rounded to the nearest hundredth, the volume of empty space is approximately 6651.72 cm³

What is diameter?

Diameter is a straight line passing through the center of a circle or a sphere, and connecting two points on the circumference or surface respectively.

According to question:

The diameter of each ball is 14 centimeters, so the height of the cylindrical container must be at least 42 centimeters in order to stack three balls inside. Let's assume that the height of the container is exactly 42 centimeters.

The three tennis balls weigh a combined amount of:

3 × (4/3)πr³ = 3 × (4/3)π(7 cm)³ ≈ 1436.76 cm³

The volume of the cylindrical container is:

πr²h = π(7 cm)²(42 cm) ≈ 8088.48 cm³

So the volume of the empty space left inside the container is:

8088.48 cm³ - 1436.76 cm³ ≈ 6651.72 cm³

Rounded to the nearest hundredth, the volume of empty space is approximately 6651.72 cm³.

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month? rRound vour answer to the nearest cent?) 5

Answers

The monthly payment required to amortize a loan of $40,000 over 15 years, with an interest rate of 6% per year, and monthly compounding, is approximately $331.13.

To calculate the monthly payment, we can use the formula for the amortization of a loan, which is:

Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of payments.

Given:

Principal amount (P) = $40,000,

Annual interest rate = 6%,

Number of years (n) = 15.

First, we need to convert the annual interest rate to a monthly interest rate. Since interest is compounded monthly, the monthly interest rate (r) is calculated by dividing the annual interest rate by 12 and converting it to a decimal:

Monthly interest rate (r) = 6% / 12 / 100 = 0.005.

Next, we calculate the total number of payments (n) by multiplying the number of years by 12 (since there are 12 months in a year):

Total number of payments (n) = 15 years * 12 months/year = 180.

Now we can plug these values into the formula to calculate the monthly payment:

Monthly Payment = $40,000 * (0.005 * (1 + 0.005)^180) / ((1 + 0.005)^180 - 1).

Using a calculator or spreadsheet, we find that the monthly payment is approximately $331.13.

Therefore, the monthly payment required to amortize the loan of $40,000 over 15 years, with a 6% annual interest rate and monthly compounding, is approximately $331.13.

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What monthly payment is required to amortize a loan of $40,000 over 15 years if interest at the rate of 6%/year is charged on the unpaid balance and interest calculations are made at the end of each month?

NEED HELP

Which of the following is and isn't a function? ( There may be more than one answer ). Explain Clearly

NEED HELPWhich of the following is and isn't a function? ( There may be more than one answer ). Explain
NEED HELPWhich of the following is and isn't a function? ( There may be more than one answer ). Explain
NEED HELPWhich of the following is and isn't a function? ( There may be more than one answer ). Explain
NEED HELPWhich of the following is and isn't a function? ( There may be more than one answer ). Explain

Answers

Using the function concept, we have that:

Items, a, and d are functions.Item b and c are not functions.

When does a relation represents a function?

A relation represents a function when each value of the input is mapped to only one value of the output.

On a graph, it means that each value of x is mapped to only one value of y, that is, there are no vertically aligned points on the graph.

For this problem, relation c does not represent a function, as there are multiple values of x are related to two values of y, and there are vertically aligned points on the graph.

In item b, when x = 6, there are two values of y, hence this is also not a function. For items a and d, each value of x is mapped to only one value of y, hence they are functions.

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prove that in any group, an element and its inverse have the same order.

Answers

To prove that in any group, an element and its inverse have the same order, we need to show that if we have an element `a` in a group and `n` is the order of `a`, then the order of `a`'s inverse, denoted as `a⁻¹`, is also `n`.

Let's assume that `a` has order `n`. This means that the smallest positive integer `n` such that `aⁿ = e` (the identity element) is `n`. We want to show that the order of `a⁻¹` is also `n`.

First, let's consider the order of `a⁻¹`. By definition, the order of `a⁻¹` is the smallest positive integer `m` such that `(a⁻¹)ᵐ = e`.

Now, we can use the fact that `aⁿ = e` to rewrite `a⁻¹` raised to the power of `n`:

(a⁻¹)ᵐ = ((aⁿ)⁻¹)ᵐ = (e⁻¹)ᵐ = eᵐ = e.

This shows that `(a⁻¹)ᵐ = e`, which implies that the order of `a⁻¹` is at most `m`.

To prove that the order of `a⁻¹` is exactly `n`, we need to show that `m` cannot be smaller than `n`.

Suppose, for contradiction, that `m < n`. Then we have:

(aⁿ)⁻¹ = (aⁿ)⁻¹ᵐ = aⁿᵐ = e.

This would imply that `aⁿ` has an inverse and `(aⁿ)⁻¹` has order `m`, which contradicts the definition of `n` as the smallest positive integer satisfying `aⁿ = e`.

Therefore, we conclude that the order of `a⁻¹` cannot be smaller than `n`. Since we have shown that it is at most `m` and not smaller than `n`, it follows that the order of `a⁻¹` is exactly `n`.

Hence, in any group, an element and its inverse have the same order.

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learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called ___ learning.

Answers

Learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called Adaptive learning

What is adaptive learning?

Adaptive learning platforms utilize algorithms to tailor the learning experience for individual students based on their needs, abilities, and learning progress.

By analyzing data and feedback, adaptive learning systems can dynamically adjust the content, pace, and difficulty level to optimize learning efficiency and personalize the educational journey for each student.

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a 400 foot tall monument is located in the distance from a window in a building a perso ndetermines the angle of elevation to the top of the monument is 18 and thed angle of depresison to the bottom of the monument is 3. how far is the person from the monument

Answers

The person is approximately 1233.35 feet from the monument

Let's call the distance from the person to the monument "x". We can use basic trigonometry to solve this problem.

From the person's point of view, the monument appears as a right triangle with the monument's height (400 feet) as the opposite side and "x" as the adjacent side. The angle of elevation (from the person to the top of the monument) is 18 degrees, which is the angle opposite the opposite side (the monument's height). So we can use the tangent function to find "x":

tan(18) = opposite / adjacent

tan(18) = 400 / x

x = 400 / tan(18)

x ≈ 1233.35 feet

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What are the tests for parallel and perpendicular lines?

Answers

To determine if a line is parallel or perpendicular, we can place each line on a sloped intersection shape (y = mx + b) and observe the slope m of each line. Equal slopes result in parallel lines. If the slope is multiplied by -1, then the line is vertical.

Parallel Lines:

Two or more lines that lie in the same plane and do not intersect are called parallel lines. They are equidistant from each other and have the same slope. A straight line equation is usually written in the form of a slope intercept represented by the equation y = mx + b. where "m" is the slope and "b" is the y-intercept. The "m" value defines the slope and tells how steep the line is.

Perpendicular Lines:

A vertical line or perpendicular line is two separate lines that intersect at an angle of 90° to each other. These are straight lines known as perpendiculars that meet each other at certain angles (right angles).

We have already seen what a vertical line looks like. If a shape has an "L" shape, its vertex angles are right angles. Vertical lines always intersect each other, but not all intersecting lines are always perpendicular to each other.

Two main properties of vertical lines:

1. Perpendicular lines always intersect or intersect each other.

2. The angle between two vertical lines is always 90°.

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Find the maxima and minima, and where they are reached, of the function In f(x,y) = x² + y² + xy

{(x,y): x² + y² ≤ 1}

(I)Local. (ii) Absolutes. (iii) Identify the critical points inside the disk (not on the border) if any. Say if they are extreme '? what type?'o saddle points,'o we cannot tell using ___

Answers

i. The local maxima and minima are 3 and 2

ii. The absolute maximum of f(x,y) over the region is 3/2  at (1/√2, 1/√2), and the absolute minimum is -1/2, which is attained at (-1/√2, -1/√2).

iii.  There are no other critical points inside the disk, so we cannot tell whether they are extreme or saddle points.

i. To find the maxima and minima of the function f(x,y) = x² + y² + xy over the region {(x,y): x² + y² ≤ 1}, we first find the critical points by setting the partial derivatives equal to zero:

f(x) = 2x + y = 0

fy = 2y + x = 0

Solving these equations simultaneously gives the critical point (-1/3, 2/3). We now need to check if this is a local maximum, local minimum or a saddle point. To do this, we use the second partial derivative test.

f(xx) = 2, f(xy) = 1, fyy = 2

The determinant of the Hessian matrix is Δ = f(xx)f(yy_ - (fxy)² = 2(2) - (1)² = 3, which is positive, and f(xx) = 2, which is positive. Therefore, the critical point is a local minimum.

ii. To find the absolute maximum and minimum, we need to consider the boundary of the region. Let g(x,y) = x² + y² be the equation of the circle with radius 1 centered at the origin. We can parameterize this curve as x = cos(t) and y = sin(t), where 0 ≤ t ≤ 2π.

Substituting this into the function f(x,y), we get:

h(t) = f(cos(t), sin(t)) = cos²(t) + sin²(t) + cos(t)sin(t) = 1 + (1/2)sin(2t)

We now find the critical points of h(t) by setting dh/dt = 0:

dh/dt = cos(2t) = 0

This gives t = π/4 and 5π/4.

Substituting these values into h(t), we get:

h(π/4) = 3/2

h(5π/4) = -1/2

Therefore, the absolute maximum of f(x,y) over the region is 3/2, which is attained at (1/√2, 1/√2), and the absolute minimum is -1/2, which is attained at (-1/√2, -1/√2).

iii. There are no other critical points inside the disk, so we cannot tell whether they are extreme or saddle points.

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please help me out

If ∠∠ABC and ∠∠DBF are vertical angles and m∠∠ABC= 4x +1 and the m∠∠DBF = 3x + 29, then what is x, and what is the measure of the angle?

Answers

Answer:

68

Step-by-step explanation:

ABC AND DBF.

ABC = 4x +1= your answer

Suppose the heights of the members of a population follow a normal distribution. if the mean height of the population is 65 inches and the
standard deviation is 3 inches, 99.7% of the population will have a height
within which range?
a. 59 inches to 71 inches
b. 53 inches to 77 inches
c. 62 inches to 68 inches
d. 56 inches to 74 inches

Answers

Answer:

D) 56 inches to 74 inches

Step-by-step explanation:

By the Empirical Rule, 99.7% of data in a normal distribution spread across ±3σ standard deviations from the mean μ.

Hence, the range maximum is μ+3σ = 65+3(3) = 65+9 = 74 inches, and the range minimum is μ-3σ = 65-3(3) = 65-9 = 56 inches

Thus, 99.7% of the population will have a height within the range of 56 inches to 74 inches

CONSTRUCTION A rectangular deck i built around a quare pool. The pool ha ide length. The length of the deck i 5 unit longer than twice the ide length of the pool. The width of the deck i 3 unit longer than the ide length of the pool. What i the area of the deck in term of ? Write the expreion in tandard form

Answers

The area of the deck, in terms of the side length of the pool (s), is given by the expression 2s² + 11s + 15.

The length of the deck is 5 units longer than twice the side length of the pool.

So, the length of the deck can be expressed as (2s + 5).

The width of the deck is 3 units longer than the side length of the pool. Therefore, the width of the deck can be expressed as (s + 3).

The area of a rectangle is calculated by multiplying its length by its width. Thus, the area of the deck can be found by multiplying the length and width obtained from steps 1 and 2, respectively.

Area of the deck = Length × Width

= (2s + 5) × (s + 3)

= 2s² + 6s + 5s + 15

= 2s² + 11s + 15

Therefore, the area of the deck, in terms of the side length of the pool (s), is given by the expression 2s² + 11s + 15.

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Which is the simplified form of m Superscript negative 8 p Superscript 0?
StartFraction 1 Over m Superscript 8 Baseline p EndFraction
StartFraction 1 Over m Superscript 8 EndFraction
StartFraction p over m Superscript 8 EndFraction
m Superscript 8

Answers

i think it is C

Step-by-step explanation:

Answer:

1 or D

Step-by-step explanation:

help me with this question pls match them some of them repeat

help me with this question pls match them some of them repeat

Answers

Answer:

3 , 4 , 2 , 2 , 1 , 1

Step-by-step explanation:

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AC}\) = \(\frac{a}{b}\) → 3

tan B = \(\frac{opposite}{adjacent}\) = \(\frac{AC}{BC}\) = \(\frac{b}{a}\) → 4

cos A = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{b}{c}\) → 2

sin B = \(\frac{opposite}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{b}{c}\) → 2

sin A = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{a}{c}\) → 1

cos B = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{a}{c}\) → 1

Nadia needs one cup of ice cream for every student in her class for their year-end party. The ice cream is only sold in pints. If there are 24 students in her class, how many pints of ice cream will she need? Describe how to solve this problem.

Answers

The pints of ice cream for the students is an illustration of metric units

Nadia needs 12 pints of ice cream for the 24 students

How to determine the pints of ice cream?

The given parameter is:

Students = 24

She needs one cup for each student in the class.

So, the number of cups needed is:

Cups = 24

1 cup makes 1/2 pint.

So, we have:

Pint = 1/2 * 24

Pint = 12

Hence, Nadia needs 12 pints of ice cream for the 24 students

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For the following exercise, solve the quadratic equation by completing the square. 2x^(2)+6x-1=0

Answers

The solutions to the quadratic equation \(2x^2 + 6x - 1 = 0\), obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

To solve the quadratic equation\(2x^2 + 6x - 1 = 0\)by completing the square, follow these steps:

Ensure that the coefficient of \(x^2\) is 1. In this case, it is already 2, so we don't need to make any changes.

Move the constant term to the other side of the equation. Add 1 to both sides:

\(2x^2 + 6x = 1\)

Divide the coefficient of x by 2 and square it. In this case, (6/2)^2 = 9.

Add the result from step 3 to both sides of the equation:

\(2x^2 + 6x + 9 = 1 + 9\)

Simplifying, we get:

\(2x^2 + 6x + 9 = 10\)

Write the left side of the equation as a perfect square trinomial. In this case, it is \((x + 3)^2.\)

\((x + 3)^2 = 10\)

Take the square root of both sides:

\(√[(x + 3)^2] = ±√10\)

Simplifying:

\(x + 3 = ±√10\)

Solve for x by subtracting 3 from both sides:

x = -3 ± √10

So, the solutions to the quadratic equation \(2x^2 + 6x - 1\)= 0, obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

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