Identify the x-coordinate for the solution to the system of equations. Solve the system using substitution.



x=4y+5

7x - 2y = 35

Answer:

4^3 = 4x4x4

Step-by-step explanation:

its just a shortened version of 4x4 3 times

Answer:

a. the sign is interchange

it should be = x^2 - 3x + 4 - x^3 - 7x + 2

Answer:

see explanation

Step-by-step explanation:

(a)

The student has distributed the second parenthesis by 1 instead of - 1

(b)

Given

(x² - 3x + 4) - (x³ + 7x - 2)

distribute the first parenthesis by 1 and the second by - 1, that is

= x² - 3x + 4 - x³ - 7x + 2 ← collect like terms

= - x³ + x² - 10x + 6

Answer:

N550

N4960

Step-by-step explanation:

10 days

First day: N10

Second day: N20

Third day: N30

...

Tenth day: N100

Sum of sequence: 10 + 20 + 30 + 40 + ... + 80 + 90 + 100

sum = (n/2)[2a+(n−1)d]

a = 10; n = 10; d = 10

sum = (10/2) × [2(10) + (10 - 1)(10)]

sum = 5[20 + 9(10)]

sum = 5[110]

sum = 550

Answer: N550

31 days

First day: N10

Second day: N20

Third day: N30

...

Thirty-first day: N100

Sum of sequence: 10 + 20 + 30 + 40 + ... + 290 + 300 + 310

sum = (n/2)[2a+(n−1)d]

a = 10; n = 31; d = 10

sum = (31/2) × [2(10) + (31 - 1)(10)]

sum = 15.5[20 + 30(10)]

sum = 15.5[320]

sum = 4960

Answer: N4960

The required rate of return is 9.375%.

The value of the perpetuity can be found by dividing the annual cash flow by the discount rate.

The discount rate is the rate at which future cash flows are discounted to find their present value.

We need to calculate the present value of the perpetual cash flow stream. The formula for the present value of a perpetuity is:

PV of a perpetuity = C / r

Where, PV = present value C = annual cash flow r = discount rate PV of the perpetuity

= $12,000/0.05= $240,000

Therefore, the value of this perpetuity today with 5% of annual interest rate is $240,000.

If you are willing to pay $32,000 today to receive $3000 per year forever, then your required rate of return must be 9.375%.

The formula for the required rate of return of a perpetuity is: r = C / PV Putting the values, r = $3000 / $32,000 = 0.09375 or 9.375%

Therefore, the required rate of return is 9.375%.

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Circle parametric equations are equations that define the coordinates of points on a circle in terms of a parameter, such as the angle of rotation. The equations are often written in the form x = r cos(theta) and y = r sin(theta), where r is the radius of the circle and theta is the parameter.

These equations can be used to graph circles and to solve problems involving circles, such as finding the intersection of two circles or the area of a sector of a circle. Circle parametric equations are commonly used in mathematics, physics, and engineering.

Given the circle equation (x−9)²+(y−6)²=4, we can find the parametric equations to represent the circle being traced clockwise as the parameter increases.

Step 1: Rewrite the circle equation in terms of radius
The circle equation can be written as (x−h)²+(y−k)²=r², where (h, k) is the center of the circle and r is the radius. In this case, h=9, k=6, and r=√4 = 2.

Step 2: Write the parametric equations for x and y
Since the circle is traced clockwise, we use negative sine for the y-coordinate. The parametric equations for the circle are:
x = h + rcos(t) = 9 + 2cos(t)
y = k - rsin(t) = 6 - 2sin(t)

As given, x = 9 + 2cos(t). The parametric equations representing the circle being traced clockwise are:
x = 9 + 2cos(t)
y = 6 - 2sin(t)

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Answer:

last one

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

GOOD LUCK!!!

The value of sin ß in simplest radical form is -√(1 - \(cos^2\) ß) = -√(1 - \((-3/7)^2\)) = -2√10/7. In the third quadrant, the cosine value is negative. Given that cos ß = -3/7, we can use the Pythagorean identity to find sin ß.

The Pythagorean identity states that \(sin^2\) ß + \(cos^2\) ß = 1.

Substituting the given value of cos ß, we have:

\(sin^2\) ß + (-3/7)^2 = 1

\(sin^2\) ß + 9/49 = 1

\(sin^2\) ß = 1 - 9/49

\(sin^2\) ß = 40/49

To find sin ß, we take the square root of both sides:

sin ß = ±√(40/49)

Since ß is in the third quadrant, where the sine value is negative, we take the negative square root:

sin ß = -√(40/49)

We can simplify this expression by rationalizing the denominator:

sin ß = -√(40/49) * (√49/√49)

sin ß = -√(40)/7

Further simplifying the radical, we have:

sin ß = -√(4 * 10)/7

sin ß = -2√10/7

Therefore, the value of sin ß in simplest radical form is -2√10/7.

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Answer:

There are 108° in each interior angle of a regular pentagon. This process can be generalized into a formula for finding each interior angle of a REGULAR polygon Each interior angle of a “regular” polygon is given by where n = the number of sides in the polygon.

Step-by-step explanation:

Answer:

It should be 21.1

Step-by-step explanation:

The statement suggesting that larger groups are more effective than smaller groups is false. Smaller groups tend to have better communication, efficiency, and individual participation.

The statement suggests that larger groups, specifically groups of twenty to thirty people with representatives from multiple subgroups, are more effective than smaller groups of six to eight people. However, this statement is generally considered false for several reasons:

Larger groups can face challenges in communication and coordination. With more members, it becomes more difficult to ensure effective information sharing, active participation, and clear decision-making. Small groups often have better communication and coordination due to fewer individuals involved.

Smaller groups tend to be more efficient and productive. In larger groups, there can be increased time spent on managing diverse opinions and reaching consensus, which can slow down the decision-making process and hinder productivity. Smaller groups can often make quicker decisions and accomplish tasks more efficiently.

Larger groups may result in reduced individual participation. Some members may feel less inclined to contribute or may be overshadowed by more dominant personalities. In smaller groups, each member can have a more significant impact and be actively engaged in the group's work.

Smaller groups tend to foster better group dynamics and cohesion. It is easier for members to develop strong relationships, trust, and a shared sense of purpose in smaller groups. Larger groups can struggle with maintaining cohesiveness and a sense of belonging.

While larger groups may have certain advantages, such as a broader range of perspectives and resources, the statement disregards the potential drawbacks of managing larger groups effectively. Overall, smaller groups often exhibit better communication, efficiency, and individual participation, making the statement false in general.

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Explanation

We can find the differences in the table below.

The first differences are the values gotten from subtracting the values in the f(x) column. While the second differences are the values gotten from subtracting the values in the first differences column.

The table can be seen below

Answer A

1) False

2) True

3) False

Answer B: Quadratic function

Reason: A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant. Since the second difference being a constant implies a quadratic difference, modeling the values will ultimately give a quadratic function

Answer:

277.46

Step-by-step explanation:

Answer:

After taking cubes from each corner,no edge will

Six Sigma provides a continuous improvement framework and it has two methodologies.

DMAIC - Define, Measure, Analyze, Improve and Control.

DMADV - Define, Measure, Analyze, Design and verify

What is Six Sigma ?

According to the Six Sigma philosophies, every work can be broken down into discrete processes that may be measured, evaluated, improved, and managed.

                     Processes result in outputs after requiring inputs (x) (y). You can manage the outputs if you manage the inputs. This is typically written as y = f. (x).

What is a fundamental principle of Six Sigma?

The management practice known as "six sigma" aims to reduce errors. It is based on the idea that reducing defects is essential for improving margins, that costs can be cut, and that increasing customer loyalty can help because it is expensive to harbor defects.

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Hope u like it

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Answer:

y-1=-3(x+2)

Step-by-step explanation:

Answer:

-2.05

Step-by-step explanation:

You can just simply type this into your search bar, and when you do that, you get -2.05.

Answer:

Step-by-step explanation:

3²-4(2+3) can be simplified as follows:

3²-4(2+3) = 9 - 4(5) (using the order of operations to first evaluate the expression inside the parentheses)

= 9 - 20

= -11

So, 3²-4(2+3) simplifies to -11.

However, the expression 3-2 (3²-2) can be further simplified using the order of operations:

3-2 (3²-2) = 3 - 2(9-2)

= 3 - 2(7)

= 3 - 14

= -11

So, the simplified expression is -11 in both cases.

The expression can be simplified as 1.

If we take a look at the expression

We can simplify by applying the mathematical operation rule BODMAS and first simplify and calculate the contents inside the brackets hence the expression can be solved as :

\(\frac{3^{2}-4(5)}{3-2(9-2)} \\\)

\(\frac{3^{2}-4(5) }{3-2(7)}\)

\(\frac{3^{2}-20 }{3-14}\)

\(\frac{9-20}{3-14}\)

\(\frac{-11}{-11}\)

1

Thus, on simplification, the expression comes out to be 1.

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The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

Solving for x, we have

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

Describes the following triangle

Using the Pythagorean Theorem again, we have

Solving for h, we have

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

To calculate the sine and cosine of the sum

We can use the following identities

Using those identities in our problem, we're going to have

Angles in 59 non-similar triangles having degree measures that are integers via arithmetic progression.

Let the summation of the angle values be: Using arithmetic progression & triangle knowledge, letting the sum of the angle values be:

∑degree = 180

For an odd arithmetic progression with a strange number of words, the median term is equivalent to the average of both the sum of all terms:

An arithmetic sequence's nth term,

Let the initial triangle angle =a

Let d be a common difference.

Because the angles' measurements follow an arithmetic progression \(T_{n}\) = a + (n - 1) × d

a + (a + d) + (a + 2d) = 180

3a+3d=180

a+d=60

Because an or d cannot be identical to zero, the minimum and maximum possible values for a and d are 1 and 59, respectively.

As a result, there are 59 distinct triangles.

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By applying the concept of Vector function, it can be concluded that the vector function is r(t) = 9 cos(t) i + 9 sin(t) j + (81 cos(t).sin(t)) k

Vector function is a function whose origin is a set of real numbers and whose result area is a set of vectors.

A vector function r(t) is represented as:

r(t) = \(x_{t} i\) + \(y_{t} j\) + \(z_{t} k\)

Cylinder : x² + y² = 81

Surface : z = xy

Now we look at the cylinder equation:

x² + y² = 81

x² + y² = 9²

We multiply each side by 1:

1 * (x² + y²) = 1 * 9²

If we recall the trigonometry function cos²(t) + sin²(t) = 1, then we have:

x² + y² = (cos²(t) + sin²(t)) * 9²

           = 9²cos²(t) + 9²sin²(t)

           = (9 cos(t))² + (9 sin(t))²

Lets assume x² = (9 cos(t))² and y² = (9 sin(t))², then we get :

x = 9 cos(t)

y = 9 sin(t)

Now we substitute the value of x and y into z equation:

z = xy

  = 9 cos(t) x 9 sin(t)

  = 81 cos(t).sin(t)

As we know the value of x, y, and z, we can get the vector function r(t):

r(t) = \(x_{t} i\) + \(y_{t} j\) + \(z_{t} k\)

    = 9 cos(t) i + 9 sin(t) j + (81 cos(t).sin(t)) k

Thus the vector function is r(t) = 9 cos(t) i + 9 sin(t) j + (81 cos(t).sin(t)) k

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Answer:

The value of k for which the equation has two negative roots is k < 1.

Step-by-step explanation:

To find the value of k for which the equation has two negative roots, we need to use the discriminant of the quadratic equation. The discriminant is the expression under the square root sign in the quadratic formula, and it determines the number and nature of the roots of the quadratic equation.

The quadratic equation in the picture is:

x^2 - 2(k - 3)x + 4k = 0

The discriminant of this equation is:

D = b^2 - 4ac

= (-2(k-3))^2 - 4(1)(4k)

= 4(k^2 - 10k + 9) - 16k

= 4k^2 - 56k + 36

For the equation to have two negative roots, the discriminant must be greater than zero and the coefficient of x^2 must be positive (since the leading coefficient is 1). So we have:

D > 0 and 4 > 0

Solving for k, we get:

4k^2 - 56k + 36 > 0

Dividing by 4 and simplifying, we get:

k^2 - 14k + 9 > 0

Factorizing the quadratic expression, we get:

(k - 1)(k - 13) > 0

The inequality is satisfied when either both factors are positive or both factors are negative. So we have two cases:

Case 1: (k - 1) > 0 and (k - 13) > 0

This gives us k > 13, which does not satisfy the condition that the roots should be negative.

Case 2: (k - 1) < 0 and (k - 13) < 0

This gives us k < 1, which satisfies the condition that the roots should be negative.

Therefore, the value of k for which the equation has two negative roots is k < 1.

Answer:Is A

Step-by-step explanation:

I am Really bad at explaining

In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

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The maximum height the golf ball reached before landing back on the ground is 3.75 yards.

To find the maximum height the golf ball reached before landing back on the ground, we need to find the vertex of the quadratic function\(h(t) = -0.6t^2 + 3t.\) The vertex of a quadratic function in the form of\(f(x) = ax^2 + bx + c\) is given by the formula x = -b/(2a).

In this case, a = -0.6 and b = 3. Plugging these values into the formula:

t = -3 / (2 * -0.6) = 3 / 1.2 = 2.5

Now that we have the time at which the ball reaches its maximum height, we can plug this value back into the height function to find the maximum height:

\(h(2.5) = -0.6(2.5)^2 + 3(2.5) = -0.6(6.25) + 7.5 = -3.75 + 7.5 = 3.75\)

So, the maximum height the golf ball reached before landing back on the ground is 3.75 yards.

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Answer:

To solve the equation 3(x+2)=17, we start by simplifying the expression on the left side by distributing the 3:

3(x+2) = 17

3x + 6 = 17

Next, we isolate the variable term by subtracting 6 from both sides:

3x + 6 - 6 = 17 - 6

3x = 11

Finally, we solve for x by dividing both sides by 3:

3x/3 = 11/3

x = 11/3

Therefore, the solution to the equation 3(x+2)=17 is x = 11/3.

To solve the equation 4x+3=2x+15, we start by simplifying the expression by combining like terms:

4x + 3 = 2x + 15

2x + 3 = 15

Next, we isolate the variable term by subtracting 3 from both sides:

2x + 3 - 3 = 15 - 3

2x = 12

Finally, we solve for x by dividing both sides by 2:

2x/2 = 12/2

x = 6

Therefore, the solution to the equation 4x+3=2x+15 is x = 6.

Step-by-step explanation:

WE are givent the functions

and

We want to calculate the following

This operation is the function composition. What it means is that first we are going to input -4 into g. Then, the value we get, we input it into f.

So first we calculate

Now, we calculate

So we have that

65+28H≤250

Step-by-step explanation:

Anand can afford at most 6 hours.

Step-by-step explanation:

The value of the x is 8.33 under the given condition that  RZ is given as 2x + 5 and TW is given as 5x - 20.

From the given question and illustrative diagram we can clearly see that
RZ = 2x + 5
TW = 5x - 20
Now, we have to find the value of 'x' if RZ = 2x + 5 and TW = 5x - 20.
Then, from the given rectangle figure, we can say  that RZ is equal to TW.
Hence equating both the equation we can  evaluate that the value of x  and the equation can be expressed in the forms of
RZ = TW
2x + 5 = 5x - 20
20 + 5 = 5x - 2x
25 = 3x
x = 25/3
x = 8.33
Then, the value of the x is 8.33.
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