Graph h(x) = (x - 2)(x - 4)

Answer:

\(P(x)=2x^3-2x^2-49x+48\)

Step-by-step explanation:

Let the original polynomial be \(P(x)\).

We know that when it is divided by \((x-5)\), the quotient is \(2x^2+8x-9\) and we get a remainder of 3.

Therefore, this means that:

\(\frac{P(x)}{x-5}=2x^2+8x-9+\frac{3}{x-5}\)

Remember what it means when we have a remainder. Say we have 13 divided by 3. Our quotient will be 4 R1, or 4 1 over 3. We put the remainder over the divisor. This is the same thing for polynomials.

So, to find our original polynomial, multiply both sides by \((x-5)\):

\((x-5)\frac{P(x)}{x-5}=(x-5)(2x^2+8x-9+\frac{3}{x-5})\)

The left side will cancel. Distribute the right:

\(P(x)=2x^2(x-5)+8x(x-5)-9(x-5)+\frac{3}{(x-5)}(x-5)\)

Distribute:

\(P(x)=(2x^3-10x^2)+(8x^2-40x)+(-9x+45)+(3)\)

Combine like terms:

\(P(x)=(2x^3)+(-10x^2+8x^2)+(-40x-9x)+(45+3)\)

Evaluate:

\(P(x)=2x^3-2x^2-49x+48\)

And we're done!

The answer is there the same

Answer:they taste the same

Step-by-step explanation:

Answer:

$1,830.6

Step-by-step explanation:

$1,830.6 is your answer!This is because; 30 × 9 ≈ 270 + 1,560.60≈1,830.6

We can Long Division method to solve quotients step by step

What is long division method and its steps ?

When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

We need to comprehend a few stages in order to divide. A vinculum or right parenthesis separates the dividend from the quotient, while a vertical bar separates the divisor from the dividend. Let's now go through the long division stages listed below to comprehend the procedure.

1. Take the dividend's first digit starting from the left . Verify if this digit exceeds or is equal to the divisor.

2. Next, divide it by the divisor, and write the result as the quotient on top.

3. Subtract the outcome from the digit, and then put the difference below.

Step 4: Decrease the dividend's subsequent digit (if present).

Step 5: Carry out Step 4 again.

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Answer:

x=1

Step-by-step explanation:

6x+2=9x-1

2=3x-1

3=3x

1=x

Answer:

1

To find:

x

Step-by-step explanation:

6x + 2 = 9x - 1

6x - 9x = -1 -2

-3x = -3

x = -3/-3

x = 1

hope it helps you!!

The surface area of the pyramid is 126. 22 in²

The formula for calculating the surface area of a triangular pyramid is expressed as;

SA = BA + 1/2(P + s)

Such that the parameters are;

From the information

Perimeter = 3(15.75) = 47. 25 in

Base area = 1/2 × 12.25 × 15.75 = 96. 47 in²

Substitute the values

Surface area =  96. 47 + 1/2 (47. 25 + 12.25)

add the values

Surface area = 96. 47 + 1/2 (59.5)

divide the values

Surface area = 126. 22 in²

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Answer:

225

Step-by-step explanation:

(- 15)² = - 15 × - 15 = 225

Answer: 3x-2x or (3x)-(2x)

Write an expression that best represents the difference between triple and double a number?

Step-by-step explanation: HOPE THIS HELPS!

Answer:

3x-2x

Step-by-step explanation:

I hope you this is it

Answer:

2 and 3

Step-by-step explanation:

In equation 3, if you move the 3x to the other side, 5y = -1 + 3x then it's would be the same as equation 2

the indentation diagonal length is approximately 0.0686 units.

What is Intention Diagonal Length?

The indentation diagonal d is determined by the mean value of the two diagonals d 1 and d 2 at right angles to each other: To avoid the risk of bulging of the material on the opposite side of the sample, the thickness should not fall below a certain minimum value. value. The minimum thickness depends on the expected hardness of the material and the test load.

To calculate the indentation diagonal length using the Vickers hardness value, you need to know the applied load and the hardness number. The Vickers hardness test measures the resistance of a material to indentation using a diamond indenter.

In this case, you have the following information:

Load: 0.700 kg

Vickers HV: 650

The Vickers hardness number (HV) is defined as the applied load divided by the surface area of the indentation.

The formula to calculate the indentation diagonal length (d) is:

d = 1.854 * sqrt(L / HV)

Where:

d = indentation diagonal length

L = applied load in kg

HV = Vickers hardness number

Plugging in the values:

d = 1.854 * sqrt(0.700 / 650)

Calculating the square root and performing the division:

d ≈ 1.854 * 0.0370262

d ≈ 0.0686

Therefore, the indentation diagonal length is approximately 0.0686 units. Please note that the specific unit (e.g., millimeters) was not provided in the question, so the answer is given in relative units.

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Ryan = 28 years

Tara = 30 years

Ryan is over 28 years old.

T = R + 2

T + R = 58

Replace T

(R + 2) + R = 58

2R = 56

R = 56 : 2

R = 28 years

T = 30 years

Answer:

The answer is A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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Answer:

Thus, the blanks should be completed with 1;0 respectively

Step-by-step explanation:

Cosine of the sum of angles

The formula for the cosine of angles \alpha and \beta is shown below:

\(cos(\alpha+\beta)=cos\alpha*cos\beta-sin\alpha*sin\beta\)

For the expression given in the question:

\(cos(x+2\pi)=cosx*cos2\pi-sinx*sin2\pi\)

Since

\(cos 2\pi=1, sin2\pi=0:\)

\(cos(x+2\pi)=cosx*1-sinx*0\)

Thus, the blanks should be completed with 1;0 respectively

Answer:

A. 1;0

Step-by-step explanation:

did on edge

Answer:

18.5

Step-by-step explanation:

Just add 18.5 and 55.50 and repeat with the other numbers

Answer:

x is 18.5

Step-by-step explanation:

3/55.50=18.5

same as all the others

Answer:

18

Step-by-step explanation:

To determine the value of -24x + 30y, we can rearrange the original equation -8x + 10y = 6 and solve for y in terms of x. Dividing both sides of the equation by 10 gives us -0.8x + y = 0.6. Rearranging this equation, we find y = 0.8x + 0.6.

Now, substituting this value of y into -24x + 30y, we get:

-24x + 30(0.8x + 0.6)

= -24x + 24x + 18

= 18

Therefore, the value of -24x + 30y, given the true equation -8x + 10y = 6, is 18.

Answer:

To solve for the value of -24x + 30y, we need to manipulate the given equation to get either x or y in terms of the other variable.

Starting with If-8x+10y=6, we can isolate x by subtracting 10y from both sides:

-8x = -10y + 6

Then, divide both sides by -8:

x = (5/4)y - (3/4)

Now that we have x in terms of y, we can substitute this expression into -24x + 30y:

-24((5/4)y - (3/4)) + 30y

Simplifying this expression:

-30y + 18 + 30y

The y terms cancel out, leaving us with:

-24x + 30y = 18

Therefore, the value of -24x + 30y is 18.

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Answer:

A. \((x-3)^{2}\)

Step-by-step explanation:

Find 2 numbers who's sum is -6 and product is 9

-3 and -3

sum = -6

(-3) * (-3) = 9

product = 9

You can also calculate each option individually

A.

\((x -3)^{2} = (x-3)(x-3)\)

Use FOIL... then

\(x^{2} -6x+9\)

Answer:

Step-by-step explanation: The answer to this problem would be A . You would first see if the first and third numbers were perfect squares and if they were you would put the value of the perfect squares in parentheses and add a 2 at the top of the answer after the parentheses

Answer:

No Solutions

Step-by-step explanation:

If you simplify the equation, you would get 30x + 30 = 30x + 40, which if you subtract 30x, you would get 30 = 40, which means that there are no solutions, because no amount for x would balance this equation.

The other friend was riding at a speed of 4 miles per hour.

First we can start by using the formula:

distance = rate × time

Let's call the distance between the two friends "d" and the rate (or speed) of one of the friends "r". We know that they both started at 8:00 am and met up at 8:30 am, which means they each rode for 0.5 hours.

The total distance traveled by both friends is equal to the distance between them:

d = 7 miles

We also know that one of the friends was riding at a rate of 10 miles per hour. Let's call the rate of the other friend "x".

Using the formula, we can write two equations:

distance = rate × time

For the friend riding at 10 miles per hour

d = 10 × 0.5

d = 5 miles

For the friend riding at "x" miles per hour:

d = x × 0.5

d = 0.5x

Since both friends covered the same distance (7 miles), we can set these two equations equal to each other:

5 + 0.5x = 7

Subtracting 5 from both sides, we get:

0.5x = 2

Dividing both sides by 0.5, we get:

x = 4

Therefore, the other friend was riding at a speed of 4 miles per hour.

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The area of the triangle is:

Area = 1/2 * |AB x AC| = 1/2 * |48k| = 24 square units.

Let A = (-4, -2), B = (2, 0), and C = (-2, 6) be the vertices of the triangle. Then the vectors AB and AC are:

AB = B - A = (2, 0) - (-4, -2) = (6, 2)

AC = C - A = (-2, 6) - (-4, -2) = (2, 8)

The area of the triangle is half the magnitude of the cross product of AB and AC:

Area = 1/2 * |AB x AC|

We can find the cross product by taking the determinant of the following matrix:

| \(i\) j k |

| 6 2 0 |

| 2 8 0 |

Expanding the determinant along the first row, we get:

| \(i\) j k |

|6 2 0 |

|2 8 0 |

= \(i\) * (20 - 80) - j * (60 - 20) + k * (68 - 22)

= 48k

Therefore, the area of the triangle is:

Area = 1/2 * |AB x AC| = 1/2 * |48k| = 24 square units.

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Complete question :

Cheddar Cheese

$3/lb

Swiss Cheese

$5/lb

Keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses?

What linear equation in standard form can she use to model the situation?

Answer:

10 lbs of cheddar cheese

6 lbs of Swiss cheese

$3a + $5b = $30

Step-by-step explanation:

Given that :

Cheddar cheese = $3/lb

Swiss cheese = $5/lb

Total amount budgeted for cheese = $30

How many pounds of cheese can Keisha get if she buys only Cheddar cheese?

Pounds of cheedar cheese obtainable with $30

Total budget / cost per pound of cheddar cheese

$30 / 3 = 10 pounds of cheedar cheese

Only Swiss cheese?

Pounds of cheedar cheese obtainable with $30

Total budget / cost per pound of Swiss cheese

$30 / 5 = 6 pounds of Swiss cheese

A mixture of both cheeses?

What linear equation in standard form can she use to model the situation?

Let amount of cheddar cheese she can get = a

Let amount of Swiss cheese she can get = b

Hence,

(Cost per pound of cheddar cheese * number of pounds of cheddar) + (Cost per pound of Swiss cheese * number of pounds of Swiss cheese) = total budgeted amount

(3 * a) + (5 * b) = $30

$3a + $5b = $30

Answer:

38 students

Step-by-step explanation:

100+(16x6)=196

800-196=631

4.50+12=16.5

Hi there! :)

\(\large\boxed{z = 1.764}\)

\(10x^{(2z/3)} = 15\)

Rewrite as a logarithmic equation using this format:

\(a^{b} = c \\\\log_{a}c = b\)

In this instance:

a = 10 (log is by default base 10)

b = 2z / 3

c = 15

Rewrite as the log equation:

\(log 15 = 2z/3\)

Evaluate log (15):

\(1.176 = 2z / 3\)

Multiply both sides by 3:

\(3.528 = 2z\)

Divide both sides by 2:

\(z = 1.764\)

Answer:

z= 3log(15)/2

z= 1.764

Based on the calculations on this arithmetic sequence, the value of the first term is equal to -8.

An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Given the following data:

Tenth term (a₁₀) = 30.

Common difference = 2.

Substituting the given parameters into the formula, we have;

10 =  a₁ + (10 - 1)2

10 =  a₁ + (9)2

10 =  a₁ + 18

a₁ = 10 - 18

First term, a₁ = -8.

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We have the set of values: 98 87 86 100 79 92 88 95 89 86 96.

We have to calculate the IQR:

where Q3 is the third quartile and Q1 is the first quartile.

The first step is to sort the values in ascendent order:

The work done by the force field F is 0.

Given: The force field F(x,y) = y3i + (x3 + 3xy2)j; A particle travels once around the circle of radius 3.

Using Green's Theorem, we need to find the work done by the force field F.

Since we need to calculate the work done on a circular path, we will integrate using polar coordinates. We have r = 3.

Then, dA = r dr dθ

We have∂Q/∂x = 3xy² and ∂P/∂y = 3y²

.∴ ∂Q/∂x - ∂P/∂y = 3xy² - 3y² = 3y (x - y).

By Green's Theorem, we have:

∫∫ (R) (∂Q/∂x - ∂P/∂y) dA = ∫ (C) P(x, y) dx + Q(x, y) dy, where P = y³, Q = (x³+ 3xy²), and C is the positively oriented circle of radius 3.

Substituting polar coordinates for x and y, we have: x = r cosθ, y = r sinθ and dx dy = r dr dθ

∫∫ (R) (∂Q/∂x - ∂P/∂y) dA

= ∫ (C) P(x, y) dx + Q(x, y) dy

= ∫(θ = 0 to 2π) ∫(r = 0 to 3) (3r sinθ) (r dr dθ)

= ∫(θ = 0 to 2π) ∫(r = 0 to 3) 3r2 sinθ dr dθ

= ∫(θ = 0 to 2π) (1/3)(3)3 sinθ dθ

= (3/3)[(-cosθ)2π0]

= (3/3)[(cos0 - cos2π)]

= (3/3)[(1 - 1)]

= (3/3)(0)

= 0

Therefore, the work done by the force field F is 0.

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Take into consideration the solid that results from rotating the area enclosed by the provided curves about the x-axis. y = 2/7 x^2, y = 9/7 - x^2 . the volume of the solid is approximately 1.412 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 2/7 \(x^{2}\) and y = 9/7 - \(x^{2}\) about the x-axis, we can use the method of disks or washers.

First, we need to find the limits of integration. The curves intersect when:

2/7\(x^{2}\) = 9/7 - \(x^{2}\)

Multiplying both sides by 7, we get:

2\(x^{2}\) = 9 - 7\(x^{2}\)

9\(x^{2}\) = 9

\(x^{2}\) = 1

x = ±1

Therefore, the limits of integration are x = -1 and x = 1.

Next, we need to express the curves in terms of y. Solving for x in each equation, we get:

x = ±√(7/2 y)

x = ±√(9/7 - y)

Using the method of disks, we can find the volume of the solid by integrating the areas of circular disks with radius y from y = 0 to y = 9/7.

The radius of each disk is given by the difference between the upper and lower curves evaluated at y:

r = √(9/7 - y) - √(7/2 y)

The area of each disk is given by:

A = π\(r^{2}\)

Substituting for r, we get:

A = π [√(9/7 - y) - √(7/2 y)]

Expanding and simplifying, we get:

A = π [9/7 - y + 7/2 y - 2√(9/7 y)]

A = π [9/7 + 3/2 y - 2√(9/7 y)]

Integrating with respect to y, we get:

V = ∫[0, 9/7] π [9/7 + 3/2 y - 2√(9/7 y)] dy

V = π [(9/7) y + (3/4) - (4/9) \(9/7^{3/2}\) \(y^{3/2}\)] [0, 9/7]

V = π [81/28 - (64/81)  \(9/7^{3/2}\)]

V ≈ 1.412

Therefore, the volume of the solid is approximately 1.412 cubic units.

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