Write equivalent expressions.
-4y+8

Select all that apply.

A: -4(y-2)
B: -4(-2+4y)
C: (2-y)4
D: 4(-y+8)

Answer:

c = 8

Step-by-step explanation:

4x³ + cx² + x + 2 ÷ x + 2 = ...

first we divide

4x³ + cx² by x + 2

and that is by doing 4x³/x = 4x².

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

now we need to find the remainder, as with regular number divisions :

4x² × (x + 2) = 4x³ + 8x²

which we need to subtract from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

----------------

0 cx² - 8x²

now we pull down the next position (x) and divide that by x + 2

4x³ + cx² + x + 2 ÷ x + 2 = 4x² + 1

- 4x³ + 8x²

----------------

0 cx² - 8x² + x

and the same again, to find the remainder, we have to subtract 1×(x + 2) = x + 2 from the left side

4x³ + cx² + x + 2 ÷ x + 2 = 4x² ...

- 4x³ + 8x²

----------------

0 cx² - 8x² + x

- x + 2

-----------------------------

cx² - 8x² 0 0

the polynomial is divisible by x + 2, if the remainder is 0.

so,

cx² - 8x² = 0

cx² = 8x²

c = 8

Answer:

x(f)- this is the correct answer

The value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².

In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a composite function is essentially applied to the output of another function.

Given that,

s(x)=x²

t(x) = 4x³

The value of the composite functions is given as:

(t + s)(x) = t(x) + s(x) = 4x³ + x²

(t.s)(x) = (4x³)x² = [tex]4x^5[/tex]

(t - s)(x) = t(x) - s(x) = 4x³ - x²

Hence, the value of the functions defined for all real numbers is (t + s)(x) = 4x³ + x², (t.s)(x) = (4x³)x² = [tex]4x^5[/tex], (t - s)(x) = 4x³ - x².

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Answer: 68.82

Step-by-step explanation:

74 * (1- 7%) and solve

= 68.82

The equation Distance = Speed × Time can be used to calculate the time spent in both city and highway. The sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

Distance is a numerical measurement of the distance between two objects in physical space. It is commonly measured in meters, kilometers, or miles. Angles, such as degrees of longitude and latitude, can also be used to calculate distance.

Distance may be estimated mathematically using methods such as the Pythagorean theorem. When studying the movement of things, such as in physics and engineering, and estimating the speed of objects in motion, distance is a significant component.

Since you know the total distance traveled and the average speed of the vehicle in both city and highway, you can use the equation

Distance = Speed × Time

to solve for the time spent in both city and highway.

For time spent in city:

35 mph × C = 995 miles

C = 995 miles/35 mph = 28.43 hours

For time spent in highway:

60 mph × H = 995 miles

H = 995 miles/60 mph = 16.58 hours

Therefore, the sum of C + H = 28.43 hours + 16.58 hours = 45.01 hours.

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Answer:

(a)

smaller value = 125 ft

larger value = 250 ft

(b)

31250 ft²

Step-by-step explanation:

(a)

In total, the farmer used 875ft worth of fencing.

In terms of x, the total fencing used is: 2x + x + x + x + 2x = 7x

This means 7x=875ft. Dividing both sides by 7, we find x=125ft

The dimensions of the rectangular enclosure in terms of x are "x and 2x". Subbing in 125ft for x, these dimensions become "125ft and 2(125ft)" or "125ft and 250ft".

(b)

Since we know the enclosure is 125ft long and 250ft wide, and since the area of a rectangle is its length times its width, the are of the enclosure is:

125ft * 250ft = 31250 ft²

Answer:

(a)

smaller value =125 ft

larger value = 250 ft

(b)

31250 ft?

Using Chebyshev's Theorem, it is found that at least 89% of days have a high temperature between 6.6ºF and 51ºF.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

Considering k = 3, the percentage is of at least 89% and the bounds are given as follows:

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Answer:

-$48.39

Step-by-step explanation:

Answer:

y=b+5+k/2

Step-by-step explanation:

2y-k=b+5

2y=b+5+k

2y/2=b+5+k/2

y=b+5+k/2

Answer:

y = b+ 5 + k/2.

Step-by-step explanation:

2y - k = b + 5

the subject for y

[tex]2y - k = b + 5 \\ 2y = b + 5 + k \\ \frac{2y}{2} = \frac{b + 5 + k}{2} \\ y = \frac{b + 5 + k}{2}. [/tex]

No, because each item does not have an equal chance of being selected. That is option D.

A simple random sample is defined as the type of random sampling where by a particular amount of data (subset) is being selected from the total population of data that is under study.

The simple random sampling method which is used by researchers has the following disadvantages such as:

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To find the area of the prism we must identify the area of each of the faces of the prism and then add them. So, the surface would be: 312 ft²

To find the surface of the prism we must find the area of each of the faces and then add them as shown below:

Based on the above, the correct answer would be 312 ft² is the total area of this prism.

Note: This question is incomplete. Here is the complete information:

Image attached.

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Step-by-step explanation:

the volume of such a regular cylinder is (as for any regular object) :

base area × height

and for a cylinder the base area is a circle, and its area is

pi×r²

so, combined, the volume of our cylinder is

pi×r²×height = pi×9²×26.5 = pi×81×26.5 =

= 6,743.428631... cm³

≈ 6,743 cm³

Work Shown:

4.5% of 125 = 0.045*125 = 5.625

That rounds to 5.63

Answer:

5.625

Step-by-step explanation:

By using the substitution method, the value of x is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2y - 4x = 8                 .......equation 1.

3(x + 4) - 2y = 5          .......equation 2.

From equation 1, we have:

y = 2x + 4         .......equation 3.

By using the substitution method to substitute equation 3 into equation 2, we have the following:

3(x + 4) - 2(2x + 4) = 5

3x + 12 - 4x - 8 = 5

-x + 4 = 5

x = 4 - 5

x = -1.

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The value of angle ABE is 52°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.

The sum of interior angle in a triangle is 180°

Angle EBD = 180-(90+27)

= 180-117

= 63°

angle ABE + EBD = ABD

ABE = ABD - EBD

ABE = 115-63

= 52°

Therefore the value of angle ABE is 52°

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Answer:

b. B, C, and E

Step-by-step explanation:

The lateral surface area is the sum of the areas of all the faces except for the base.

In the function, f(x) = a(b)ˣ the value of a and b is

The function defined by f(x) = a(b)ˣ is a exponential function

Where

a is the starting function

b is the base function

The starting function from (0,24)

24 = a(b)ˣ

a = 24

using (1, 18), we solve for the base

18 = 24(b)

b = 0.75

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Answer: To find the monthly rent during the 11th year, we need to calculate the total increase in rent over the course of 10 years and then add that to the original monthly rent of $900.

The total increase in rent over 10 years is $120 per year * 10 years = $1200.

So, the monthly rent during the 11th year would be $900 + $1200 = $2100.

Therefore, the monthly rent during the 11th year would be $2100.

Step-by-step explanation:

The volume of the irregular figure is solved to be

The volume of the irregular figure is solved by the formula

= area of the figure * thickness

The area of the figure is solved by dividing the firue into regular shapes and this will result to two rectangles

Area of the first rectangle

= length x width

= 4 * (12 - 5)

= 4 * 7

= 28 square centimeters

Area of the second rectangle

= 10 * 5

= 50 square centimeters

Total area = 50 + 28 = 78

volume = 78 * 1 = 78 cubic centimeters

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The required trigonometric ratios are as follows: sin t = 1/2 and cos t = √3/2.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

According to the given figure, we have a right triangle ΔABC which has:

AB = 1/2

BC = √3/2

CA = AB² + BC²

CA = √(1/2)² + (√3/2)²

CA = √1/4 + 3/4

CA = √4/4 = 1

As we know that the trigonometric ratios are as follows:

sin (180°- t) = AB/CA

sin t = (1/2)/1

sin t = 1/2

cos (180°- t) = BC/CA

cos t = (√3/2)/1

cos t = √3/2

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Answer:

[tex]y=\pm2\sqrt{5}[/tex]

Step-by-step explanation:

[tex]4y^2=80\\y^2=20\\y=\pm\sqrt{20}\\y=\pm2\sqrt{5}[/tex]

The square root method for solving a quadratic equation involves isolating the squared term, and then taking the square root of both sides of the equation.

Starting with the equation 4y^2 = 80, we can isolate the squared term by dividing both sides of the equation by 4:

y^2 = 20

Next, we take the square root of both sides of the equation:

y = ±√20

The solution in radical form is y = ±√20. To simplify the radical, we can factor 20 into 2 * 10. Then, we can simplify the square root as follows:

y = ±√2 * √10 = ±2√10

So, the simplified solution is y = ±2√10.

Answer: a) Mean and standard deviation of the sampling distribution:

The mean of the sampling distribution, also known as the expected value or the population mean, is equal to the proportion of U.S. residents who receive a jury summons each year, which is 15%. So, the mean of the sampling distribution is:

µ = 0.15

The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:

σ = √(p(1 - p) / n)

where p is the population proportion of U.S. residents who receive a jury summons each year (0.15), and n is the sample size (500).

σ = √(0.15 * (1 - 0.15) / 500)

σ ≈ 0.03

So, the standard deviation of the sampling distribution is approximately equal to 0.03.

b) Interpretation of the standard deviation:

The standard deviation measures the spread of the sampling distribution, or how much the sample proportions deviate from the population proportion. A smaller standard deviation indicates that the sample proportions are more likely to be close to the population proportion, while a larger standard deviation indicates that the sample proportions are more likely to be further from the population proportion.

In this case, the standard deviation of 0.03 indicates that the sample proportions are expected to be within 0.03 of the population proportion (0.15) about 68% of the time.

c) Justification for the approximate normality of the sampling distribution:

According to the central limit theorem, the distribution of the sample proportions will be approximately normal as long as the sample size is large enough. In this case, with a sample size of 500, we can assume that the sampling distribution is approximately normal.

Step-by-step explanation:

The answer choice which is true about the given equation; y = -2x as required to be determined is; It is a linear function because its graph is a straight line.

It follows from the task content that the given function y = -2x as required be identified as being a linear equation or not and why?

On this note, since the graph of the equation is such that g

it yields a straight line, it follows that the given function; is a linear function because its graph is a straight line.

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Answer:

21.7% to win $3, thats ~1/5

Step-by-step explanation:

100/6 = 10.(6) % to roll for each number (let it be just ~10.7)

for rolling a 3 or a 1 u will get $3

10.7 + 10.7 = 21.7% to win $3, thats 1/5

Answer:

add wtwo numbers x by 3? I am sorry don't understand question

Step-by-step explanation:

The distance between the point P and the plane through the points Q, R, and S is 60/23.

The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:

d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|

Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:

n = (Q-R) x (Q-S)

The coefficients of the normal vector can be found using the following equations:

A = n1

B = n2

C = n3

D = -(A * x2 + B * y2 + C * z2)

Substituting the values of Q, R, and S, we have:

Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)

Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)

The cross product of Q-R and Q-S is:

n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)

So,

A = -23

B = 29

C = 17

D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109

Finally, substituting the values of x1, y1, and z1:

d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|

= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|

= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|

= |60 / √(-23^2 + 29^2 + 17^2)|

= |60 / √(529)|

= 60 / 23

So the distance between the point P and the plane through the points Q, R, and S is 60/23.

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The equation for v is ±√k/m

Two or more expressions with an Equal sign is called as Equation.

The given equation is k=mv²

k equal to m times of v square.

Where k is a formula of kinetic energy.

We need to solve for v

To do this we have to isolate the variable v

To isolate the variable v we have to Divide both sides by m

v²=k/m

v square equal to k by m.

Square root on both sides.

v=±√k/m

v equal to plus or minus square root of k by m.

Hence, the equation for v is ±√k/m

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Answer:

Step-by-step explanation:

To find the number of solutions for a system of linear equations, we can use the method of substitution or elimination. Here, we'll use the method of substitution.

We'll start by solving for x in one of the equations and then substitute that expression into the other equation. If the resulting equation has a unique solution, then the system has a unique solution. If the resulting equation has no solution, then the system has no solution. If the resulting equation has infinitely many solutions, then the system has infinitely many solutions.

Let's start by solving the first equation for x:

y = -7/2 x + 11

To solve for x, we'll isolate x by subtracting 11 from both sides of the equation:

y - 11 = -7/2 x + 11 - 11

y - 11 = -7/2 x

Next, we'll multiply both sides of the equation by -2/7 to cancel out the fraction on the right side:

-2/7 (y - 11) = -2/7 (-7/2 x)

-2/7 y + 22/7 = 7/2 x

Now, we have an expression for x in terms of y. We can substitute this expression into the second equation:

7x + 2y = 20

7 (-2/7 y + 22/7) + 2y = 20

Substituting -2/7 y + 22/7 for x, we get:

7 (-2/7 y + 22/7) + 2y = 20

Expanding the left side of the equation, we get:

-2y + 22 + 2y = 20

0y = -2

Since 0y is never equal to -2, this equation has no solution.

Therefore, the system of equations has no solution, and there are no values of x and y that satisfy both equations simultaneously.

So, the system of equations y = -7/2 x + 11 and 7x + 2y = 20 has no solutions.