HELPPPPPPPPPPP , witch should I pick .

Answer:

Reflection across the x-axis: y = − f ( x ) y = -f(x) y=−f(x) The concept behind the reflections about the x-axis is basically the same as the reflections about the y-axis. The only difference is that, rather than the y-axis, the points are reflected from above the x-axis to below the x-axis, and vice versa.

the equation for g(x) after reflected over x axis and translated 4 units left

\(g(x)=-(x+4)^2\)

Given :

Parent function is \(f(x)=x^2\)

When a graph is reflected over x-axis then f(x)=-f(x)

When a graph is translated 'a' units left then we add 'a' with

f(x) becomes f(x+a)

Parent function f(x) is reflected over x-axis , multiply -1 with f(x)

so , \(f(x)=-x^2\)

Now we translate 4 units to the left, add 4 with x

\(g(x)=-x^2\\g(x)=-(x+4)^2\)

The final equation of g(x) is

\(g(x)=-(x+4)^2\)

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Answer:

They are zeroes when y=0

Step-by-step explanation:

For a function \(f(x)\), if \(f(x)=0\), the values of x that make the function true are known as roots, or x-intercepts, or zeroes.

The greater number is \($n^3+8$\)

Let x be the greater number and y be the smaller number. We know that x-y=8.

We are also given that the smaller number is n³.

So we can set up the equation:

x = y + 8

x = n³ + 8

Therefore, the greater number is \($n^3+8$\).

The greater number is given as n³ + 8. If the smaller number we get is represented by the n³,  then by adding 8 to that value gives the greater number. The difference between the two numbers is always going to be 8, regardless of the value of n.

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Step-by-step explanation:

The answer is a - (-b) = (-b) - a

for example if we take;

a = 4

b = 2

c = 2

and we replace;

4 - ( -2) = (-2) - 4

6 = -6

which is not true....

All the remaining are true....

even u can just use the values of abc and check if its true....

Answer:

Q___R___S

QR = RS

8x - 51 = 3x - 6

8x - 3x = 51 - 6

5x = 45

x = 45/5

x = 9

I hope I helped you^_^

No, translation does not affect the slope of a line.

The slope of a line is determined by the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. This ratio remains the same regardless of where the line is located in the coordinate plane.

Translation, on the other hand, involves moving the entire line horizontally and/or vertically without changing its shape or orientation. Translation only affects the position of the line in the coordinate plane, but does not alter its slope.

The picture shows two lines that are converging at the down right end tis means the point lines are not parallel and the slope is altered

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Answer:

The school's total goal was 600 cans, and the school collected 270 canned vegetables.

Step-by-step explanation:

To find the school's collection goal, divide the amount collected by the percentage of the goal (as a decimal):

450/0.75

= 600

So, the goal was 600 cans.

To find how many canned vegetables they collected, multiply the number of cans by the percentage of canned vegetables (as a decimal):

450(0.6)

= 270

So, the school collected 270 canned vegetables.

The school's total goal was 600 cans, and the school collected 270 canned vegetables.

Answer:

1.565

2. 250

Step-by-step explanation:

To calculate the volume of the bucket, we need to use the formula for the volume of a frustum of a cone. The frustum is the part of the cone that remains after the top has been cut off. In this case, the bucket has the shape of a frustum. The formula for the volume of a frustum of a cone is:

V = 1/3πh (R² + r² + Rr)

Where V is the volume, h is the height of the frustum, R and r are the radii of the top and bottom circles, respectively.

In this case, we have:

h = 4 cm
R = 6 cm (radius of the top circle, which is half the diameter)
r = 4 cm (radius of the bottom circle, which is half the diameter)

So, plugging in the values we get:

V = 1/3π(4) (6² + 4² + 6×4)
V = 1/3π(4) (36 + 16 + 24)
V = 1/3π(4) (76)
V = 100.53 cm³

Therefore, the volume of the bucket is 100.53 cm³.
To find the volume of the bucket, we can use the formula for the volume of a frustum of a cone:

Volume = (1/3)πh(R² + r² + Rr)

Here, R is the radius of the top, r is the radius of the bottom, and h is the height (or depth) of the bucket.

1. Convert the diameters to radii: R = 12 cm / 2 = 6 cm, r = 8 cm / 2 = 4 cm
2. Substitute the values into the formula: Volume = (1/3)π(4)(6² + 4² + 6×4)
3. Calculate the volume: Volume ≈ 248.37 cm³

So, the volume of the bucket is approximately 248.37 cm³.

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Answer:

14

Step-by-step explanation:

8/9 = 0.888888888......

<5 round down

\(\geq\)5 round up

8/9 = 0.888888888....

larger than 0.5

the answer is 14

Answer:

First blank is >=

Second blank is <=

Step-by-step explanation:

At least means the sign is greater than or equal to

No more than means the sign is less than or equal to

To determine the area of a region, we need to know the specific shape and dimensions of the region in question. The process for finding the area varies depending on the shape. P(Y - X < 1) = Area of region below y - x = 1 within the given constraints= 1/6 sq. units.

Given, f(x, y) = x + y, where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2 We are to find P(Y - X < 1)

Now, Y - X < 1 is the equation of the line in the XY plane. We have to find the area of the region below this line within the given constraints. To find this, we have to integrate over the region below the line,

i.e.,y - x = 1 implies x = y - 1∫∫R (x + y)dA = ∫₀² ∫₀^(y-1) (x + y) dx dy= ∫₀² [(y²/2) - y + (1/2)] dy= 1/6 sq. units.

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Answer:

Step-by-step explanation:

Given function f(x, y) = x + y, where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2. The probability of P(Y - X < 1) is 1/4.

Now we have to find P(Y - X < 1).

The probability of (Y - X < 1) is given by:

P(Y - X < 1) = Area of the region {(x, y): y - x < 1} / Area of the region R.

Here R is the region bounded by 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2.

We know that the function f(x, y) = x + y is a plane with slope 1, and intersects the y-axis at (0, 0) and the x-axis at (0, 0).

Now the line y - x = 1 intersects the plane at x = 0 and y = 1, so the intersection point is (0, 1).

Now the area of the region {(x, y): y - x < 1} can be found by finding the area of the triangle ABC as shown below: \(A=\frac{1}{2}Base×Height\), Where base BC is of length 1 and height AB is of length 2 - 1 = 1.

Therefore, the area of the triangle ABC is:

Area of the triangle ABC = 1/2 × 1 × 1

= 1/2

The area of the region R can be found by finding the area of the rectangle with sides of length 1 and 2.

Therefore, the area of R is:

Area of R = 1 × 2

= 2

P(Y - X < 1) = Area of the region {(x, y): y - x < 1} / Area of the region RP(Y - X < 1)

= (1/2) / 2P(Y - X < 1)

= 1/4

Therefore, P(Y - X < 1) = 1/4.

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Answer:

$138

Step-by-step explanation:

%15 -> .15

120×.15=18

$120 + $18 = $138

In the given parallelogram vwxy: x = 3; m∠Y = 65° and ∠YVX = 61° by (alternate interior angle).

A quadrilateral with the opposing sides parallel is called a parallelogram (and thus opposite angles equal).

In the given parallelogram vwxy:

Parallel sides are equal.

So, 2x = 6

x = 6/2 = 3

Opposite pair of angles are also equal.

So,

∠W = ∠Y = 65°

Now,

∠YVX = 61° (alternate interior angle).

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The given points, only the point (4, -9, -8) lies on line 1.

To determine whether certain points lie on the line 1, which is perpendicular to the plane x - 2y - 4z = 5 and contains the point (2, -5, 0), we can check if the coordinates of those points satisfy the equation of the line.

The direction vector of the line 1 is perpendicular to the plane and can be determined from the coefficients of x, y, and z in the plane equation. In this case, the direction vector of the line is (1, -2, -4).

Now, we can write the parametric equation of the line l as:

x = 2 + t * 1

y = -5 + t * (-2)

z = 0 + t * (-4)

To check if a point (x₀, y₀, z₀) lies on the line 1, we need to find a value of t that satisfies the parametric equations.

Let's consider the following points and determine if they lie on line 1:

Point (3, -6, -4)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (3, -6, -4) into the parametric equations:

x₀ = 2 + t * 1 --> 3 = 2 + t --> t = 1

y₀ = -5 + t * (-2) --> -6 = -5 - 2 --> t = -1

z₀ = 0 + t * (-4) --> -4 = 0 - 4t --> t = 1

The value of t is not consistent across all equations, so the point (3, -6, -4) does not lie on line 1.

Point (2, -5, 0)

This point is given as the point that line 1 contains. Therefore, it lies on line 1.

Point (4, -9, -8)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (4, -9, -8) into the parametric equations:

x₀ = 2 + t * 1 --> 4 = 2 + t --> t = 2

y₀ = -5 + t * (-2) --> -9 = -5 - 2t --> t = 2

z₀ = 0 + t * (-4) --> -8 = 0 - 8t --> t = 1

The value of t is consistent across all equations, so the point (4, -9, -8) lies on line 1.

Therefore, among the given points, only the point (4, -9, -8) lies on line 1.

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The complete question is:

Let l be the line perpendicular to the plane x - 2y - 4z = 5 and containing the point (2, -5, 0). determine whether the following points lie on line l.

Answer:

1111111111111111111111111111111111111111

Step-by-step explanation:

The probability distribution for the number of odd dice appearing on the three dice is:0   1/81   3/82   3/83   1/8.To produce a probability distribution, calculate the probability of each possible outcome by finding the sum of the probabilities of the individual outcomes that lead to that result. This problem is based on three standard dice being rolled and the number of odd values that appear is used to advance the game piece.

The total number of possible outcomes is 6³ = 216.

The sum of all the probabilities of the individual outcomes that have one odd die is

(3/6)²(3/6) = 27/216 = 1/8.

The sum of all the probabilities of the individual outcomes that have two odd dice is

(3/6)(3/6)(3/6) × 3 = 27/216.

The multiplication by 3 reflects the 3 possible positions for the pair of odd dice.

Finally, the sum of all the probabilities of the individual outcomes that have three odd dice is

(3/6)³ = 27/216.

Therefore, the probability distribution for the number of odd dice appearing on the three dice is:

Number of odd dice P(Dice)
0                 1/8
1                 3/8
2                 3/8
3                 1/8

The probability distribution of a game is the distribution of probabilities of all possible outcomes of the game. It is a mathematical function that calculates the probability of each possible outcome by finding the sum of the probabilities of the individual outcomes that lead to that result.

In this problem, three standard dice are rolled, and the number of odd values that appear is used to advance the game piece. We can produce the probability distribution for this experiment as follows:

Since there are three dice, the total number of possible outcomes is 6³ = 216.

The number of odd dice on the three dice can range from 0 to 3.

The sum of all the probabilities of the individual outcomes that have one odd die is

(3/6)²(3/6) = 27/216 = 1/8.

The sum of all the probabilities of the individual outcomes that have two odd dice is (3/6)(3/6)(3/6) × 3 = 27/216.

The multiplication by 3 reflects the 3 possible positions for the pair of odd dice.

Finally, the sum of all the probabilities of the individual outcomes that have three odd dice is (3/6)³ = 27/216.

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Answer:

2.92

Step-by-step explanation:

Answer:

2.92

Step-by-step explanation:

12×.59=7.08 10-7.08=2.92

Answer:

A bag of chips costs $1

A pickle costs $1.25

Step-by-step explanation:

P + 2c = 3.25                            Start with these two equations

3p + 4c = 7.25

p = -2c + 3.25                           Solve for one variable

3(-2c +3.25) + 4c = 7.25           Substitute

-6c + 9.75 + 4c = 7.25

-2c = -2

c = 1

p + 2(1) = 3.25                           Substitute

p + 2 = 3.25

p = 1.25

The causes of variation that can be identified and eliminated are called; Assignable Causes.

There are two primary causes of variation in the quality of a product or process. These two primary causes are called;

Now, Common causes of variation are defined as random causes that we cannot identify. However, Assignable causes of variation are those that can be identified and eliminated.

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the measure of angle A is 96° when A and B are vertical angles.

We are given the two vertical angles as:

A = (4x − 4)° and B = (5x – 29)°

We know that, vertical angles are equal to each other.

So, we get that:

4 x - 4 = 5 x - 29

5 x - 4 x = 29 - 4

x = 25

A = 4 x - 4

A = 4 ( 25 ) - 4

A = 100 - 4

A = 96°

Therefore, the measure of angle A is 96° when A and B are vertical angles.

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Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

To find an explicit formula for the sequence, we first need to solve the recurrence relation. We can do this by finding the roots of the characteristic equation r^2 - 4r + 3 = 0, which are r = 1 and r = 3. Therefore, the general solution to the recurrence relation is ak = A(1)^k + B(3)^k, where A and B are constants determined by the initial conditions. Plugging in a0 = 1 and a1 = 2, we get the system of equations A + B = 1 and A + 3B = 2. Solving for A and B, we get A = 1/2 and B = 1/2. Therefore, the explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

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An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters, and the length of the path is 5 meters more than the width.

The equation that can be used to find the dimensions of the patio is x2 (x + 5)2 = 841.

Step-by-step explanation:

Let us say that the length of the patio is l, then we have that;l = x + 5We are to find the dimensions of the patio which is its length and width

.The diagonal of a rectangle can be obtained from its width and length.Using Pythagoras theorem, we can get the diagonal of the rectangle;diagonal2 = width2 + length2d2 = x2 + (x + 5)2d2 = x2 + x2 + 10x + 25d2 = 2x2 + 10x + 25d = √(2x2 + 10x + 25)

But we are given that the diagonal of the patio is 29 meters long,d = 29Putting this value into our diagonal equation;d = √(2x2 + 10x + 25)29 = √(2x2 + 10x + 25)

Squaring both sides of the equation;29² = (2x² + 10x + 25)841 = 2x² + 10x + 25

Next, we simplify the equation by bringing all the terms to one side of the equation.

841 = 2x² + 10x + 250 = 2x² + 10x - 8160 = x² + 5x - 168x² + 40x - 672 = 0We factorize the quadratic equation;x² + 5x - 84 = 0(x + 12)(x - 7) = 0

The width cannot be negative,x - 7 = 0x = 7mTherefore, the width of the patio is 7 meters.

The length of the patio is;length = width + 5length = 7 + 5length = 12mThe dimensions of the patio are;Width = 7mLength = 12m

Check;diagonal2 = width2 + length2d2 = 7² + 12²d2 = 49 + 144d2 = 193d ≈ 13.89m

Given that the diagonal of the patio is 29 meters long, we are to check if it's approximately equal to 29 meters.diagonal ≈ 13.89m

The value of the diagonal is not equal to 29m, however, it's approximately equal to 29m.

Therefore, the values we have calculated are correct.The equation that can be used to find the dimensions of the patio is x2 (x + 5)2 = 841.

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The width of a graph is determined by the coefficient in front of the x² term. The larger the absolute value of the coefficient, the narrower the graph.

Therefore, the order from narrowest to widest graph is:
c. r(x) = −13x², p(x) = 7x², q(x) = 0.4x²
To order the functions from the narrowest graph to the widest graph for p(x) = 7x2, q(x) = 0.4x2, and r(x) = -13x2, consider the coefficients of each quadratic function. A higher absolute value of the coefficient results in a narrower graph, while a smaller absolute value results in a wider graph.
1. For p(x) = 7x2, the coefficient is 7.
2. For q(x) = 0.4x2, the coefficient is 0.4.
3. For r(x) = -13x2, the coefficient is -13 (with an absolute value of 13).
Ordering the functions by their coefficients' absolute values (from highest to lowest) gives:
r(x) = -13x2, p(x) = 7x2, q(x) = 0.4x2
Therefore, the correct answer is:
d. r(x) = -13x2, q(x) = 0.4x2, p(x) = 7x2

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The problem states that a can of tomato sauce contains 8 oz of sauce and a case contains 12 cans. We are trying to find out how many cases of tomato sauce Chef Hugo orders and we know that he gets a total of 480 oz of sauce.

What in mathematics is a linear equation?

According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We can use the formula 12(8)x = 480 to find out the number of cases of tomato sauce that Chef Hugo orders.

Here's the calculation:

12(8)x = 480

96x = 480

x = 5

Therefore, Chef Hugo orders 5 cases of tomato sauce.

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The formula for logistic growth can be expressed as P(t) = K / (1 + A * e^(-rt)), where P(t) is the population at time t, K is the carrying capacity, r is the growth rate, A is the initial population.

Logistic growth is a type of population growth that considers a carrying capacity, which is the maximum population size that an environment can sustain. The formula for logistic growth takes into account the carrying capacity (K), the growth rate (r), and the initial population (A) to describe how the population changes over time.

In this case, the carrying capacity is given as 1500, and the growth rate is 0.25 per year. Let's denote the population at time t as P(t).

The formula for logistic growth can be written as:

P(t) = K / (1 + A * e^(-rt))

Plugging in the given values, we have:

P(t) = 1500 / (1 + A * e^(-0.25t))

The value of A is not explicitly given, so it represents the initial population. If the initial population is known, it can be substituted into the formula. If not, A can be left as a variable.

The term e^(-0.25t) represents the exponential decay component, which approaches 0 as t increases. It is multiplied by A, allowing the population to approach the carrying capacity over time.

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Answer:

option 2

Step-by-step explanation:

√8^2+(22/2)^2=√64+121=√185≈13.6

The derivative of the given function f(x) = 2ln x - x is f'(x) = (2/x) - 1

Here are the derivatives of the given functions along with the approximations:

1. Given function: f(x) = x² + 4x + ln x

The derivative of the given function f(x) = x² + 4x + ln x is:

f'(x) = 2x + 4 + (1/x)

Approximation: We need to approximate ln 2 using five decimal approximations. ln 2 is the same as loge 2.

Hence, we can use the linear approximation formula using the values a = 1 and h = 1. x = 2 is slightly greater than 1.

Hence, we will use a positive value for h.

Linear approximation of ln 2 = ln a + [(1/a)(x - a)]

= ln 1 + [(1/1)(2 - 1)]

= 0 + 1 = 1

Hence, ln 2 is approximately 1 using the linear approximation method.

2. Given function: f(t) = 2t² - 3ln i

The derivative of the given function f(t) = 2t² - 3ln i is:

f'(t) = 4t

Approximation: We need to approximate ln 2.01 and ln 1.9 using linear approximations.

ln 2.01 is the same as loge 2.01.

Using the linear approximation formula, we can write:

ln 2.01 ≈ ln 2 + [(1/2)(0.01)]

= 0.693147 + 0.005

= 0.698147

Similarly, we can approximate ln 1.9:

ln 1.9 ≈ ln 2 - [(1/2)(0.1)]

= 0.693147 - 0.05

= 0.643147

Hence, ln 2.01 is approximately 0.698147 and ln 1.9 is approximately 0.643147 using linear approximations.

3. Given function: f(x) = 10 - ln x

The derivative of the given function f(x) = 10 - ln x is:

f'(x) = -(1/x)

Approximation: We need to approximate ln 2. We can use the linear approximation formula:

ln 2 ≈ ln 1 + [(1/1)(2 - 1)]

= 0 + 1

= 1

Hence, ln 2 is approximately 1 using the linear approximation method.

4. Given function: f(x) = 2ln x - x

The derivative of the given function f(x) = 2ln x - x is:

f'(x) = (2/x) - 1

Approximation: We do not need to make any approximations for this function.

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A function assigns the value of each element of one set to the other specific element of another set.

A function assigns the value of each element of one set to the other specific element of another set.

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

In keeping with the remarks, the simple answer is that all polynomials are functions, but not all functions are polynomials. A function is essentially a rule that allocates a codomain value to every domain value.

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Answer:

7 nickels

20 dimes

5 quarters

Step-by-step explanation:

n=nickels. d=dimes. q=quarters

n+d+q=32

0.05n+0.1d+0.25q=3.60

d=8+n+q

Solve for number of dimes:

d-8=8-8+n+q

d-8=n+q

d-d-8=n+q-d

-8=n+q-d

  32=n+q+d

-  (-8=n+q-d)

32 - (-8) = n-n + q-q + d-(-d)

32 + 8 = d + d

40 = 2d

d = 20  => simplify

20=8+n+q  ==> substitute 20 for d (d=8+n+q)

20-8 = 8-8+n+q

n+q = 12

0.05n+0.1(20)+0.25q=3.60  ==> substitute 20 for d

0.05n + 2 + 0.25q = 3.60

(0.05n + 2 + 0.25q = 3.60)*100 ->remove the decimals by multiplying by 100

5n + 200 + 25q = 360

5n + 200 - 200 + 25q = 360 - 200

5n + 25q = 160

Solve for number of quarters:

(5n + 25q)/5 = 160/5  ==> simplify the equation

  n + 5q = 32

- (n + q = 12)

n-n + 5q-q = 32-12

0 + 4q = 20

4q = 20

q = 5  ==> simplify

Solve for number of nickels:

n+20+5=32  ==> plug in 20 for d and 5 for q  (n+d+q=32)

n+25=32

n+25-25=32-25  ==> solve for n

n=7 ==> simplify

n=7: 7 nickels

d = 20: 20 dimes

q = 5: 5 quarters

Answer:

360 degrees and 2pi radians is one revelation

Step-by-step explanation: