Factor 24j-1624j−1624, j, minus, 16 to identify the equivalent expressions.
Choose 2 answers:
Choose 2 answers:

(Choice A)
A
8(3j-2)8(3j−2)8, left parenthesis, 3, j, minus, 2, right parenthesis

(Choice B)
B
6(4j-2j)6(4j−2j)6, left parenthesis, 4, j, minus, 2, j, right parenthesis

(Choice C, Checked)
C
4(6j-4)4(6j−4)4, left parenthesis, 6, j, minus, 4, right parenthesis

(Choice D)
D
2(12-8)2(12−8)

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer: I think it’s skewed right

Step-by-step explanation:

The model variables the relationship between the strikes (s) and the number of points scored (p)

To determine the number of strikes made, so that 140 points where scored, you have to replace the model with p=140 and solve for s

The first step is to pass "40" to the others side of the equal sing, by performing the inverse operation "-40" to both sides of the expression

Then you have to divide both sides of the expression by 25 to determine the value of s

The bowler made s=4 strikes, the correct choice is A.

Answer:

to figure out x, divide 5x by 5

to figure out 5x, times x by 5,

to figure out 5x-1 take away 1 from the answer in the middle column

Answer:

x > 35

Step-by-step explanation:

Let's denote the width of the picture frame as "x" inches.

According to the problem, the length of the picture frame is 7 inches more than the width, so it can be expressed as "x + 7" inches.

The perimeter of the picture frame can be found by adding up the lengths of all four sides, which is given by:

Perimeter = 2*(length + width)

Substituting the values of length and width in terms of x, we get:

Perimeter = 2*(x + 7 + x)

Perimeter = 4x + 14

Now we can set up an inequality to find the values of x for which the perimeter is greater than 154 inches:

4x + 14 > 154

Subtracting 14 from both sides, we get:

4x > 140

Dividing both sides by 4, we get:

x > 35

Therefore, the values of x for which the perimeter of the picture frame is greater than 154 inches are x > 35.

Answer: 22 /5

-3+7y=5x+2y

Step-by-step explanation:

Subtract 2y from each side

-3+7y-2y=5x+2y-2y

-3 +5y = 5x

Add 5 to each side

5y = 5x+3

Divide each side by 5

y = 5x/5 +3/5

y = x +3/5

Let x = -5

y = -5 + 3/5

y = -25/5 +3/5

y = -22/5

Step-by-step explanation:

f(x) is a linear function, so both the domain and the range are the set of real numbers.

Answer:

Infinite Solutions

Step-by-step explanation:

Both sides of equations are the same when solved.

Step-by-step explanation:

\(a + 3 + 2a = - 1 + 3a + 4\)

\(a - 3a + 2a = 4 - 1 - 3\)

\(3a - 3a = 4 - 4\)

One way its verified

\(0 = 0\)

Hence, no solution.

Consider the provided phrase.

Four times the sum of five and a number

Let the number is n and the sum of five and a number can be written as:

\(n+5\)

Thus, four times the sum of five and a number can be written as:

\(4(n+5)\)

Hence, the required expression is \(4(n+5)\).

What is phrase in math?

In mathematics, we may use a phrase to describe an expression. When we describe an expression in words that incorporates a variable, we are doing so by using an algebraic expression. An example of this may be the phrase "greater than" (an expression with a variable).

run the numbers. to conduct a rational analysis of an issue. You can do the math because I was the last person to depart yesterday night and the first person to arrive this morning, and since only the overweight security guy was present. on April 7, 2005, by Dave L. Flag.

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Answer:

All of them

Step-by-step explanation:

The graph of the function f(x) = 4(2/3)^x is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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The volume of the cube shown can be found to be 132. 65 inch ³ .

To ascertain the volume of a cube , knowledge of one edge's length is mandatory . This side would correspond to all other sides; therefore , multiplying it by three inversely gauges its complete space as a cubic structure.

The formula for the volume of a cube is:

= Side x Side x Side

The side is 5. 1 inch so the volume is:

= 5. 1 x 5 .1  x 5. 1

= 132. 65 inch ³

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Answer:

Step-by-step explanation:

970

Answer:

< - 1.0638. Hope this helps!

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

a) The correct null and alternative hypotheses are: given in option A:
H₀: Pkids = Padults

Ha: Pkids < Padults

b) the p-value is 0.004 (rounded to three significant figures).

a) The correct null and alternative hypotheses are:

H₀: Pkids = Padults (The proportion of kids who eat cereal for breakfast is equal to the proportion of adults who eat cereal for breakfast)

Ha: Pkids < Padults (The proportion of kids who eat cereal for breakfast is less than the proportion of adults who eat cereal for breakfast)

b) To test this claim, we can use a two-sample z-test for proportions. We calculate the test statistic as follows:

z = (phat1 - phat2) / √(p*(1-p)*(1/n1 + 1/n2))

where phat1 and phat2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled proportion. The pooled proportion is calculated as:

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of successes in each sample.

Using the given data, we have:

phat1 = 70/95 = 0.737

phat2 = 35/58 = 0.603

n1 = 95

n2 = 58

x1 = 70

x2 = 35

p = (70 + 35) / (95 + 58)

= 0.680

Then, the test statistic is:

z = (0.737 - 0.603) / √(0.680*(1-0.680)*(1/95 + 1/58))

= 2.62

Using a standard normal distribution table or calculator, we find the p-value associated with a z-score of 2.62 is approximately 0.004.

Therefore, the p-value is 0.004 (rounded to three significant figures).

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the proportion of kids who eat cereal for breakfast is less than the proportion of adults who eat cereal for breakfast.

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Full Question:

Cereal for Breakfast. A parent claims that kids eat cereal for breakfast more often than adults. A statistics-loving friend of the parent does some internet research and finds the following polling data. Of 95 kids polled, 70 of them say cereal is their most common breakfast. Of 58 adults polled, 35 of them say cereal is their most common breakfast. Test the parent's claim using these data.

a) Select the correct null and alternative hypotheses

H₀: Pkids = Padults

Ha: Pkids < Padults

H₀: Pkids = Padults

Hat Pkids ≠ Padults

H₀: Pkids = Padults

Ha: Pkids > Padults

b) Find the p-value (round to three significant figures).

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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The question given above will require a good understanding of surd operation in order to arrive at the best answer. Thus, the answer to the question is:

\(\frac{7\sqrt{14} }{\sqrt{7}} = 7\sqrt{2}\)

To solve this problem, we shall simply rationalise the denominator. This can be obtained as illustrated below:

\(\frac{7\sqrt{14}}{\sqrt{7}}\\\\Rationalise\\\\\frac{7\sqrt{14}}{\sqrt{7}} * \frac{\sqrt{7} }{\sqrt{7}}\\\\\frac{7\sqrt{14*7}}{\sqrt{7*7}}\\\\\frac{7\sqrt{98}}{\sqrt{49}}\\\\\frac{7\sqrt{98}}{7}\\\\\sqrt{98}\\\\\sqrt{98} = \sqrt{49*2} \\\sqrt{98} = \sqrt{49} * \sqrt{2} \\\sqrt{98} = 7\sqrt{2} \\\\Thus, \\\\\frac{7\sqrt{14}}{\sqrt{7}} = 7\sqrt{2}\)

Therefore, from the calculations made above, the solution to the question is  7√2

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Answer: The answer is D. the last option

Step-by-step explanation:

The correct answer is option d) The graph is the radical function, y = √x shifted right 1 unit and up 4 units.

The original function is y = √(x - 1) + 4, which represents a radical function.

This function involves taking the square root of the quantity (x - 1) and then adding 4 to the result.

By shifting the function right 1 unit, we are replacing x with (x - 1). This means that the graph will be shifted horizontally by 1 unit to the right compared to the standard square root function.

By shifting the function up 4 units, we are adding 4 to the output of the square root function.

This means that the graph will be shifted vertically by 4 units compared to the standard square root function.

Therefore, the graph of the function y = √(x - 1) + 4 is the radical function y = √x shifted right 1 unit and up 4 units.

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The total cost of rents is $180.

In the given table,

The cost of skis per day  = $48

The cost of pole per day = $12

Now since given that,

Alveres rents for 3 days

Therefore,

The cost of skis for 3 days  = $48 x 3

                                             =  $144

The cost of pole for 3 days = $12 x 3

                                             = $36

To find the total cost of rental,

Adding the cost of 3 days of skis and cost of 3 days of poles,

Hence,

Total cost of rents = $144 + $36

                               = $180

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Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

The best way to solve these sorts of problems that involve two factors of unknown quantities but with certain properties is to use equations:

Let's set some variables

Now based on the information given by the question, let's set up some equations:

              ⇒ \(s + h = 166\)

             ⇒ h = s - 54

Now lets put the equation together

  s + h = 166 -- equation 1

  h = s - 54   -- equation 2

Solve:

  Plug the value of h from equation 2 into equation 1

      s + (s - 54) = 166

        2s - 54 = 166

           2s = 220

             s = 110 -- equation 3

   Plug the value of s from equation 3 into equation 2

      h = 110 - 54 = 56

            h = 56

Therefore:

Hope that helps!

Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (11, - 17) and (x₂, y₂ ) = (2, 1) ← 2 ordered pairs from the table

m = \(\frac{1-(-17)}{2-11}\) = \(\frac{1+17}{-9}\) = \(\frac{18}{-9}\) = - 2

To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

We have,

To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

This will result in the y-terms canceling out, and we will be left with only x-terms on one side of the equation, which we can then solve for x.

So, multiplying the second equation by 2, we get:

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

6x + 8y = 10

Now, adding this to the first equation, we get:

4x - 8y + 6x + 8y = 20 + 10

10x = 30

Dividing both sides by 10, we get:

x = 3

Now, we can substitute this value of x back into either of the original equations to solve for y.

4x - 8y = 2

So,

4(3) - 8y = 20

12 - 8y = 20

-8y = 8

y = -1

Therefore,

The solution to the system of equations is (x, y) = (3, -1).

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Based on the angle relationships formed by the parallel lines, the statements that are true are:

B. m∠3 = 100°

C. m∠2 + m∠4 = 80°

Some of the angle relationship that applies when two parallel lines are crossed by a transversal are:

Given the image attached below, where m and n are parallel lines, we can deduce the following measures of the numbered angles based on the angle relationships:

Measure of angle 1 = 60° [vertical angles]

Measure of angle 2 = 20° [corresponding angles]

Using the triangle sum theorem, we also have:

Measure of angle 3 = 180 - m∠CAB - m∠1

Measure of angle 3 = 180 - 20 - 60 = 100°

m∠4 = 60° [corresponding angles]

m∠2 + m∠4 = 20 + 60 = 80°

From the above, we can conclude that the statements are:

B. m∠3 = 100°

C. m∠2 + m∠4 = 80°

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Parallel lines are those straight lines that are always the same distance apart from each other.

B m∠3 = 100°

C. m∠2 + m∠4 = 80° are true

Parallel lines are those straight lines that are always the same distance apart from each other. · Parallel lines never meet no matter how much they are extended.

Given that, n||m

Point B is lies on line m.

Point A and C are lies on line n.

There are two lines started from point B and one line passes through point A and one line passes through point B forms a triangle ABC.

∠ACB=1

∠ABC=2

There is an angle with line m and line AB is denoted by 2.

Using the triangle sum theorem, we also have:

Measure of angle 3 = 180 - m∠CAB - m∠1

Measure of angle 3 = 180 - 20 - 60 = 100°

m∠4 = 60° [corresponding angles]

m∠2 + m∠4 = 20 + 60 = 80°

Hence From the above, we can conclude that the statements are:

B. m∠3 = 100°

C. m∠2 + m∠4 = 80°

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Answer:

b, d, and e

Step-by-step explanation:

those are the three answers

Answer:

I would say b d and e to

Step-by-step explanation:

hope that helps

Answer:

\(B)~ 3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }\)

Step-by-step explanation:

\(3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }\\\\\\= 3\sqrt{\dfrac 75} + i\sqrt{\dfrac 95 }\\\\\text{It is now in the standard form of a complex number (a+bi).}\)

Answer:

Answer is 12

Step-by-step explanation:

I hope it's helpful!