The question is which of these statements are true about radicals exponents and rational exponents

The equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)

The given equation of the perpendicular line

y = (1/4)x -7

The equation is in the slope intercept form of the line

y = mx+b

Where m is the slope of the line

By comparing the given equation with the slope intercept form

The slope of  the line m = 1/4

The slope of its perpendicular line = -1/m

= -4

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

The point is given that (-2,-6)

Substitute these values in the equation

(y-(-6) = -4(x-(-2)

y+6 = -4(x+2)

Hence, the equation in the point slope form for the line perpendicular to y = (1/4)x-7 that passes through the point (-2,-6) is y+6 = -4(x+2)

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Answer:

3/8

Explanation:

Let the number be x.

A number multiplied by 2/5 = (2/5)x

Therefore:

To solve for x, first, we cross-multiply.

Next, we divide both sides of the equation by 40.

The number is 3/8.

Givens.

• The total number of laps is 14.

• The total distance is 30.8 miles.

First, divide the total distance by the number of laps.

Each lap length is 2.2 miles.

Let's transform it to yards using the conversion factor 1 mile = 1760 yards.

Therefore, each lap length is 3872 yards.

The amount that he owed the bank and paid is $520.

The simple interest is calculated as:

= Principal × Rate × Time / 100

Principal = $500

Rate = 8%

Time = 6 months = 6/12 = 0.5 years

The interest will be:

= PRT / 100

= (500 × 8 × 0.5)/100

= 2000/100

= $20

The amount paid back will be:

= Principal + Interest

= $500 + $20

= $520

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The shaded portions for the first three circles are a total of 15 while for the fourth one is 1. As a fraction it is therefore,

As mixed numbers it is;

Okay, here we have this:

Considering the provided graph, we are going to find the measure of the angle "3", so we obtain the following:

Since angle 3 and 4 form a straight angle, that is to say that these two angles are supplementary, then we have:

Finally we obtain that the correct answer is the option C.

Explanation:

The equation is given as:

3x + 2 = 11

The first step is to collect like terms ( Note that if 2 crosses to the other side of the equality sign, it becomes -2)

3x = 11 - 2

3x = 9

The next step is to divide both sides by 3:

3x/3 = 9/3

x = 3

Given

A manufacturing plant packages tissues in boxes and each box contains 250 tissues.

Required

We need to find an algebraic expression that illustrates the number of tissues packed per day.

Explanation

Let x be the number of boxes manufactured in one day

Then total number of tissues manufactured on that day is 250x

This answers our first part.

Now in one hour 87500 tissues are manufactured

Let the number of boxes packed in one hour be y

Then

So the answer to second part is 350 boxes.

hello

the question here relates to trionometric identies and we can easily solve this once we know some of the identities

for example

The amount by which the cost of 1 liter of permimum gasoline is greater is $0.43.

The first step is to determine the cost of 1 liter of each type of gasoline. In order to determine the cost of 1 liter, divide the total cost by the number of liters of gasoline bought.

Cost of 1 liter of gasoline = total cost / total liters bought

Cost of 1 liter of regular gasoline = $58.98 / 25 = $2.36

Cost of 1 liter of permimum gasoline = $69.73 / 25 = $2.79

Difference in price = $2.79  - $2.36 = $0.43

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Answer:

Aveage Rate of cCanege = 40

Explanation:

The line segment is drawn in the function below:

Using the line segment:

Therefore, the average rate of change will be:

The average rate of change is 40.

To answer this question, we need to know that the standard form of an equation of this type is written as follows:

We have that the polynomial given is:

In the standard form, we need to write it as follows:

Therefore, the correct answer is option C. This is the standard form for this fourth-degree polynomial.

The ___ in the in the hundreds place has a value _____ times as great as the____in the ____ place.​

• We have 440

• 400 + 40

• Four hundreds + four tens

The relationship between the values of these two digits is that they are the same, but the four in the hundreds place has a value ten times as great as the four in the tens place.

Answer

5/136

Step-by-step explanation

Events

• A: a blue marble is drawn

• B: without replacing the first marble, a green marble is drawn

There are 17 (= 3 + 2 + 5 + 7) marbles in total in the bag. Two of them are blue, then the probability of drawing a blue marble is:

After a blue marble is drawn, 16 marbles are left in the bag. Five of them are green, then the probability of drawing a green marble is:

Finally, the probability of drawing a blue marble and then a green marble without replacement is:

The slope of the line passing through the coordinates (9, 9) and (6, 7) is 2/3.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( 9, 9 )

Point 2( 6, 7 )

To determine the slope, plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 7 - 9 )/( 6 - 9 )

Slope m = ( -2 )/( -3 )

Slope m = ( 2 )/( 3 )

Slope m = 2/3

Therefore, the slope of the line is 2/3.

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The slope of the required line is 2/3 which passes through points (9, 9) and (6, 7).

The slope is simply expressed as an inclination of the line in the coordinate system.

Slope m = (y₂ - y₁) / (x₂ - x₁)

Given that the line that passes through two points (9, 9) and (6, 7)

Let x₁ = 9, y₁ = 9 and x₂ = 6, y₂ = 7

The slope of the required line is

m = (y₂ - y₁ )/( x₂ - x₁ )

Substitute the values in the formula to get the slope of the line,

m = ( 7 - 9 )/( 6 - 9 )

m = ( -2 )/( -3 )

m = ( 2 )/( 3 )

m = 2/3

Therefore, the slope of the line would be 2/3.

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The givenn equation can be written as

Hence only (1,4) satisfies the given equation.

So the correct option is the first one (1,4).

Answer/Step-by-step explanation:

y = mx + b

Slope = m

 y₂ - y₁

---------- = m

 x₂ - x₁

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

y - intercept = b

y - y₁ = m(x - x₁)

If there's an equation I can solve it, but I hope this helps!

When looking at a graph of a line, there are two things you should look for straight off the bat. First, the y-intercept. And second, the slope.

The equation of a line is y = mx + b, where m is the slope, b is the y-intercept, and x is the input.

What is slope?
Slope is a number that determines how the line changes. It is often referred to as the "rate of change" because it represents how much the y-value of the line changes when the input (x) changes. The formula for slope is:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Breakdown: This formula represents the change in the line, typically left to right. It shows the change in x-value over the change in corresponding y-value. This is also known as "rise over run," because the y-value is how much the line changes vertically, while the x-value is how much it changes horizontally.

Example: Let's say our line has a slope of 4, or m = 4/1. This means the y-value will change 4 units when the x-value changes by 1.

What is y-intercept?
Y-intercept is a value that determines the location of the line. When x = 0, the value of b will be the y-value. Essentially, when the line crosses the y-axis, that will be the y-value of the line.

Answer:

1 ½ feet

Step-by-step explanation:

The shortest lizard is ½ a feet

The longest lizard is 2 feet

To find the difference in length:

2-½ = 1½ feet

Answer:

x = 1

Step-by-step explanation:

4(2x-1)+8-14= -8x+ 4+ 2x

Answer:

The point from C goes straight until it reaches A and stull continues till it gets ti B and stops. The angle is then given as 180°

Parallel lines are lines that have the same direction and there is always the same distance between them

Skew lines are lines that are not on the same plane (they are not coplanar) and also they do not intersect.

Intersecting lines are lines that cross at a point, they can be on the same plane or on different planes.

Let's analyze the parts of this problem.

DE and AB.

These two lines are shown in red and blue in the following diagram:

These are not parallel lines because one line is vertical and the other line is horizontal. They are also not intersecting lines because they do not cross at any point. Lines DE and AB are skew lines because they do not intersect and they are on different planes.

--> DE and AB --> skew

CB and

Answer:

yes

we are need multiple the exponents in (x^4y)^(2/3).

[tex]x \frac{8y}{3} [/tex]

so hope it help

Answer:

[tex]x^\frac{8}{3} y^\frac{2}{3}[/tex]

Step-by-step explanation:

I'm not sure if you mean

[tex](x^4y)^\frac{2}{3}[/tex]

or

[tex](x^{4y})^\frac{2}{3}[/tex]

but I'll go with the first one

[tex](x^4y)^\frac{2}{3}[/tex]

(distribute the 2/3) (if the y is by it self, it basically is [tex]y^1[/tex])

[tex]x^\frac{8}{3} y^\frac{2}{3}[/tex]

done

EXPLANATION:

-We must first identify the points that correspond to the x-axis and the points that correspond to the y-axis.

-To calculate the slope, then we apply the formula of the slope or rate of change which is the following:

-now we must correctly locate the points in the formula.

-

This is a hypothesis test for the population mean.

The claim is that on weekends the average wait time for emergency room visits is more than 11 minutes.

Then, the null and alternative hypothesis are:

The significance level is 0.05.

The sample has a size n=28.

The sample mean is M=12.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.5.

The estimated standard error of the mean is computed using the formula:

Then, we can calculate the t-statistic as:

The degrees of freedom for this sample size are:

This test is a right-tailed test, with 27 degrees of freedom and t=2.117, so the P-value for this test is calculated as (using a t-table):

As the P-value (0.0218) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

Conclusion: at a significance level of 0.05, there is enough evidence to support the claim that, on weekends, the average wait time for emergency room visits is more than 11 minutes.

The growth or decay of an original quantity C that increases or decreases in a p% per year after t years is given by the following equation:

If the quantity increases (i.e. it growths) we use the + symbol inside the parenthesis. If the quantity decreases we use the - symbol. This implies that for a growth the term that is raised to t is greater than 1 and for a decay that term is smaller than 1.

Now let's compare that generic equation with the function given by the question:

One of the first things you can notice is that C=3000 which means that the initial price was $3000. Just to be sure that this is correct we can evaluate p(t) at t=0:

So the initial price was $3000.

Now let's compare the terms inside parenthesis that are raised to t:

As I stated before, if the term raised to t is greater than 1 then we are talking about a growth. 1.019 is greater than 1 so this function represents a growth. What's more, in the right side of the equation we must use the + symbol. This way we have an equation for the yearly percentage of change of the price:

We can substract 1 from both sides of this equation:

And we multiply both sides by 100:

So each year the price increases in a 1.9%.

Then the answers in order are:

$3000

growth

1.9%

From the figure, we have the coordinates of the vertices:

ABC ==> A(2, 1), B(5, 1), C(1, 5)

A'B'C' ==> A'(-2, 1), B'(-5, 1), C(-1, 5)

Let's determine the type of transformation that occured here.

Apply the rules of rotation.

For a rotation acorss the y-axis, only the x-coordinates of the points will change to the opposite. i.e from negative to positive or from positive to negative.

For a rotation across the y-axis, we have:

(x, y) ==> (-x, y)

From the given graph, we can see that the only the x-coordinates changed from positive to negative.

Therefore, the transformation that occured here is the reflection across the y-axis.

ANSWER:

B) Reflection across the y-axis.

The most appropriate choice for equation of line in slope intercept form will be given by-

[tex]y = -\frac{1}{2}x - 4[/tex]  is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

The given equation of line is y = 2x-5

Slope of this line = 2

Slope of the line perpendicular to this line = [tex]-\frac{1}{2}[/tex]

The line passes through (2 , -5)

Equation of the required line = [tex]y - (-5) = \frac{1}{2}(x - 2)[/tex]

                                                    [tex]y +5=-\frac{1}{2}x+1\\y = -\frac{1}{2}x +1 -5\\y = -\frac{1}{2}x -4[/tex]

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Given: An arithmetic sequaence has the following parameters

To Determine: The sum of the first 31st term.

Please note that the sum of the first 31st term is represented as

The formula for the finding the n-term of an arithmetic sequence (AP) is

Since, we are given the 9th term as 17, we can calculate the first term a, as shown below:

Calculate the sum of the first 31st term.

The formula for finding the first n-terms of an arithmetic series is given as

We are given the following:

Substitute the given into the formula:

Hence, the sum of the first 31st term of the A.P is 71.3, OPTION D

The base area of the prism is 2x² + 5x - 18

From the question, the given parameters are

Volume = 2 x cubed + 9 x squared minus 8 x minus 36

Height =  x + 2

Rewrite properly as

Volume = 2x³ + 9x² - 8x - 36

Height =  x + 2

The base area is calculated as

Base area = Volume/Height

Using the synthetic division, we have

Set the divisor to 0

x + 2 = 0

This gives

x = -2

So, we have the representation to be

-2 | 2   9  - 8  - 36

Write out 2

So, we have

-2 | 2   9  - 8  - 36

     2

Multiply 2 and -2

This gives

-2 | 2   9  - 8  - 36

          -4

     2

So, we have

-2 | 2   9  - 8  - 36

          -4

     2    5

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10

     2    5   -18

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10   36

     2    5   -18    0

This means that

Base area = 2x² + 5x - 18

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