It’s algebra it says find each function value here is a picture of the work sheet

Answer:

\(y=\frac{7}{4}x-9\)

Step-by-step explanation:

Question:

Find the equation of the line through the point (4, -2) with slope \(\frac{7}{4}\)

Answer + Step-by-step explanation:

Answer: \(y=\frac{7}{4}x-9\)

Step-by-step explanation:

When trying to find the equation of a line passing through a point and then given the slope, always remember if you're trying to write the equation in slope-intercept form, find the slope and the y-intercept of the equation.

Slope-Intercept form: y = mx + b where m = slope and b = y-intercept

so the slope is already given but we have to find the y-intercept.

so... the equation of the line with a slope of \(\frac{7}{4}\) is:

\(y=\frac{7}{4}x\)

but in addition, we need a y-intercept so...

\(y=\frac{7}{4}x+b\)

now use the given point on the question "(4, -2)" to solve for the y-intercept

so plug in the coordinates of the point in the equation:

\(y=\frac{7}{4}x+b\)

\((-2)=\frac{7}{4}(4)+b\)

\(-2=\frac{28}{4} +b\)

\(-2=7+b\)

\(b=-2-7\)

\(b=-9\)

so the y-intercept of the line is -9

and the equation of the line is \(y=\frac{7}{4}x-9\)

Answer:

the 3 steps

Step-by-step explanation:

1. Rearrange the equation so "y" is on the left and everything else on the right.

2. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

3. Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

For more such questions on center

https://brainly.com/question/1506955

#SPJ8

Answer:

That would be :

4x – 10 = x2 – 5x + 10  ( y = 4x - 10 is substitute for y)

PROOF:        y + 5x = x² + 10

                    (4x - 10) + 5x = x² + 10

                     4x - 10  =  x² -5x + 10

   0 = x2 – 9x + 20  (liked terms are grouped and simplified)

PROOF:      4x - 10  =  x² -5x + 10

                  4x = x² -5x + 10 + 10

                   0  = x² -5x -4x + 20

                   0  = x² - 9x + 20

Solving:

            x² - 9x + 20 = 0

            x² - 5x - 4x + 20 = 0

            (x - 5) (x - 4)  = 0

         ⇒ x = 4  (as question says) OR x = 5

Step-by-step explanation:

hope this helps

Answer:

D,E

Step-by-step explanation:

To find the solution of the compound inequality x − 2 > 4 or 5x ≥ 35, we need to solve each inequality separately and then combine their solutions using the OR operator.

Solving x − 2 > 4, we add 2 to both sides to get x > 6.
Solving 5x ≥ 35, we divide both sides by 5 to get x ≥ 7.

The solution of the compound inequality x − 2 > 4 or 5x ≥ 35 is the set of all values of x that satisfy at least one of the inequalities, which is x > 6 or x ≥ 7.

To graph this solution, we draw a number line and mark the points 6 and 7 with open circles (because they are not included in the solution). Then we shade the region to the right of 6 and/or to the right of 7, as shown below:

<---o---o=========>
6   7

The open circles indicate that 6 and 7 are not included in the solution, because x can be any value greater than 6 or any value greater than or equal to 7, but not both at the same time.

To know more about compound inequality visit:

https://brainly.com/question/20296065

#SPJ11

the problem is x > 6 or x ≥ 7. To explain this solution, we need to solve each inequality separately and then combine the results.

First, we solve x − 2 > 4 by adding 2 to both sides to get x > 6.

Next, we solve 5x ≥ 35 by dividing both sides by 5 to get x ≥ 7.

To combine the results, we take the union of the two solutions, which gives us x > 6 or x ≥ 7. This means that any value of x that is greater than 6 or equal to 7 will satisfy the original compound inequality.

The graph that represents this solution is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

the solution to the compound inequality x − 2 > 4 or 5x ≥ 35 is x > 6 or x ≥ 7, and the graph that represents it is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

To know more about number visit:

https://brainly.com/question/3589540

#SPJ11

The words need not be English language words  142506

What is permutation and combination?

A set of elements can be divided into subsets in two different ways: combination and permutation.

                          The components of the subset may be arranged in any order when combined. The components of the subset are listed in a permutation in a certain order.

If the word has 5 different letters  then it is just 26-choose-5 or (26/5).

If the word has 4 different letters  then it is just 26-choose-4 or (26/4)

have 4 options to choose which letter to duplicate twice.

This gives =  4*(26/4)

If the word has 3 different letters  then it is just 26-choose-3 or (26/3).

you duplicate one of the three letters 3 times - 3 options for that, or you choose 2 letters and duplicate each one twice - again 3 options. In total this gives  = 6*(26/3).

If the word has 2 different letters  then it is just 26-choose-2 or (26/2).

The sets of 2 different letters and duplicate either one of the letters 4 times - 2 options; or duplicate one letter 2 times, and the other 3 times - again 2 options. In total this is  = 4*(26/2).

The word has just 1 distinct letter you have =  (26/1).

we get :

N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) +  (26/1)

= 142506

The words need not be English language words  = 142506

Learn more about  permutation and combination

brainly.com/question/28065038

#SPJ4

a) If all puffins stand together, we can consider them as a single group. Therefore, we have four objects - this group of puffins and the three penguins - that can be arranged in 4! ways. Within the group of puffins, the six puffins can be arranged in 6! ways. Therefore, the total number of ways is 4! * 6! = 172,800.

b) Similarly, if all penguins stand together, we can consider them as a single group. Therefore, we have two groups - this group of penguins and the six puffins - that can be arranged in 2! ways. Within the group of penguins, the three penguins can be arranged in 3! ways. The six puffins can be arranged in 6! ways. Therefore, the total number of ways is 2! * 3! * 6! = 43,200.

To solve the problem, we use the concept of permutations. Permutations are arrangements of objects in a certain order. We use the formula n!/(n-r)! to find the number of permutations when we select r objects from n objects.

In part (a), we treat the group of puffins as a single object. Therefore, we have four objects in total. We can arrange them in 4! ways. Within the group of puffins, there are 6! ways to arrange the puffins themselves. Therefore, we multiply the number of arrangements of the puffins by the number of arrangements of the groups of objects to get the final answer.

In part (b), we treat the group of penguins as a single object. We have two groups of objects, which can be arranged in 2! ways. Within the group of penguins, there are 3! ways to arrange the penguins themselves. We multiply all the possibilities to get the final answer.

In conclusion, there are 172,800 ways for the three penguins and six puffins to stand in a line so that all puffins stand together, and 43,200 ways for all penguins to stand together. We used the formula for permutations to solve the problem.

To know more about permutation visit:

https://brainly.com/question/30649574

#SPJ11

Answer:

225

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

there is no other line

This situation does not contradict Rolle's Theorem because Rolle's Theorem requires the function to be continuous on a closed interval and differentiable on an open interval, which is not satisfied by f(x) = tan x in the interval (0, π).

To show that f(0) = f(π), we evaluate the tangent function at these points. At x = 0, tan(0) = 0, and at x = π, tan(π) = 0. Therefore, f(0) = f(π).

To investigate whether there exists a number c in the interval (0, π) such that f'(c) = 0, we need to find the derivative of f(x). The derivative of tan x is given by f'(x) = sec² x. However, the secant squared function is never equal to zero. Therefore, there is no c in the interval (0, π) where f'(c) = 0.

This situation does not contradict Rolle's Theorem because Rolle's Theorem requires certain conditions to be met. First, the function must be continuous on the closed interval [a, b], which is not satisfied by f(x) = tan x since it is not defined at x = π/2. Second, the function must be differentiable on the open interval (a, b), but f'(x) = sec^2 x is not defined at x = π/2. Thus, the requirements of Rolle's Theorem are not fulfilled, and its conclusion does not apply to f(x) = tan x in the interval (0, π).

Learn more about Interval:

brainly.com/question/11051767

#SPJ11

By using the integrating factor method, we found that the solution to the differential equation xy' - y = x^2 is y = x^2 + Cx.

To solve this differential equation using an integrating factor, we follow the steps below:

Step 1: Rewrite the equation in the standard form.

The given equation can be rewritten as:

y' - (1/x)y = x.

Step 2: Identify the integrating factor.

The integrating factor (IF) is calculated as the exponential of the integral of the coefficient of y. In this case, the coefficient of y is -(1/x), so the integrating factor is IF = e^(-∫(1/x)dx).

Step 3: Evaluate the integrating factor and multiply the entire equation by it.

The integrating factor can be evaluated as IF = e^(-ln|x|) = 1/x. Multiplying the original equation by the integrating factor, we get:

(1/x)y' - (1/x^2)y = 1.

Step 4: Simplify and integrate.

The left side of the equation can be simplified using the product rule for differentiation:

(d/dx)(y/x) = 1.

Integrating both sides with respect to x, we have:

∫(d/dx)(y/x) dx = ∫1 dx.

This simplifies to:

y/x = x + C,

where C is the constant of integration.

Step 5: Solve for y.

Multiplying both sides of the equation by x, we get:

y = x^2 + Cx.

Therefore, the solution to the given differential equation is y = x^2 + Cx, where C is a constant.

In summary, by using the integrating factor method, we found that the solution to the differential equation xy' - y = x^2 is y = x^2 + Cx.

To Know More about multiply  click here

brainly.com/question/25114566

#SPJ11

The assumption that is specific to the repeated measures ANOVA is c. the same participants are tested in each level.

This is because in a repeated measures design, the same participants are tested multiple times under different conditions, and therefore any differences observed between conditions are assumed to be due to the manipulation of the independent variable rather than individual differences between participants.

The other assumptions listed (homogeneity of variance, IV measured on an interval or ratio scale, and sphericity) are also important for conducting a repeated measures ANOVA, but they are not specific to this type of design.

Learn more about ANOVA:

https://brainly.com/question/25800044

#SPJ11

The ball is in the air for 4 seconds.

The maximum height of the ball is 64 feet.

The horizontal distance the ball travels in the air is 443.2 feet.

We have,

a)

The golf ball will land on the ground when y(t) = 0.

Using the given values.

y(t) = 0 = 0 + 128 sin(30) t - 16t²

Simplifying and solving for t.

16t² - 64t = 0

16t(t - 4) = 0

t = 0 or t = 4

The time t = 0 represents when the ball is hit off the tee, so we discard that value. Thus, the ball is in the air for 4 seconds.

b)

The maximum height of the ball occurs at the vertex of the parabolic path. To find the vertex, we need to find the value of t that gives the maximum value of y(t).

This occurs when:

t = -b/2a = -128 sin(30)/(2(-16)) = 2 seconds

So the maximum height is:

y(2) = 0 + 128 sin(30)(2) - 16(2)^2 = 128 - 64 = 64 feet

c)

The horizontal distance the ball travels is given by the formula x(t) = v_0 cos(Ф)t.

Plugging in the given values.

x(t) = 128 cos(30) t = 64√3 t

To find how far the ball travels horizontally, we need to find x(4), since the ball is in the air for 4 seconds.

Thus:

x(4) = 64√3 (4)

= 256√3

= 443.2 feet

Thus,

The ball is in the air for 4 seconds.

The maximum height of the ball is 64 feet.

The horizontal distance the ball travels in the air is 443.2 feet.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

The answer is 8 : 22, 12:33 as they are two equelivant ratios 11 and 4

Answer:

67.5

Step-by-step explanation:

The missing angle measures on the right triangle are given as follows:

First we obtain the measure of angle y. To obtain it, we consider that any angle is supplementary with it's exterior angle, that is, the sum of it's measures is of 180º.

As the exterior angle is of 135º, the measure of angle y is obtained as follows:

y + 135 = 180

y = 180 - 135

y = 45º.

Then we obtain the measure of angle x, considering that the sum of the measures of the three internal angles of a triangle is of 180º. Hence:

x + 45 + 90 = 180

x = 180 - 135

x = 45º.

The right triangle is given by the image shown at the end of the answer.

More can be learned about angle measures at https://brainly.com/question/25716982

#SPJ1

A percentage is a way to describe a part of a whole. The number of French people at the conference is 50.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

As it is given that the total number of people in the conference is 500, while 10% of the participants are french. Therefore, the number of people who are French at the conference can be written as,

Number of French People = 10% of the number of people in the conference

\(\text{Number of French People} = \dfrac{10}{100} \times 500 = 50\)

Hence, the number of French people at the conference is 50.

Learn more about Percentages:

https://brainly.com/question/6972121

Answer:

No, they are not equivalent.

Step-by-step explanation:

The first expression, (3 6) 9, is equal to 9, while the second expression, 3 (6 9), is equal to 3. The two expressions are not equivalent because they do not produce the same result when the operations are carried out. The properties of associativity, commutativity, and identity do not apply to these expressions.

Answer:

no they are not equivalent

Step-by-step explanation:

The two expressions are not equivalent. This is because the distributive property does not apply in this case, as the parentheses on the left side of the expression have precedence over the parentheses on the right side. Therefore, the expression on the left side would be evaluated first, resulting in a different answer than the expression on the right side.

Answer:

_

| x+y(less than or equal to)17

| 11x+8y(greater than or equal to)160

~

Step-by-step explanation:

Answer:

$180

Step-by-step explanation:

First, you have to calculate the amount that Olivia would have paid at the end of the loan which would be the result of multiplying her monthly payment for the number of payments:

Total payment= $308*(12*5)

Total payment= $308*60

Total payment= $18,480

Then, you have to calculate the amount that Garrett would have paid at the end of the loan:

Total payment= $311*(12*5)

Total payment= $311*60

Total payment= $18,660

Now, you have to calculate the difference in the amount Olivia and Garrett would have paid:

$18,660-$18,480= $180

According to this, an $18,000 loan will cost Garrett $180 more than Olivia.

Answer:

18-15

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Plug in: d = 9, e = 5

(9)2 - 3(5)

9 x 2 = 18

-3 x 5 = -15

18 - 15 = 3

Answer:I think its 2x-5/3

Step-by-step explanation:

please let me know if I'm wrong.

Answer:

∠1 = 51

∠2= 51

∠3= 39

∠4= 51

The solution to the system of equation is (14, 6)

1 / 2 x = 10 - 1 / 2 y

8 = x -y

Therefore, let's combine the equation.

1 / 2 x + 1 / 2 y = 10

x - y = 8

x + y = 20

x - y = 8

2y = 12

y = 12 / 2

y = 6

x = 20 - 6

x = 14

Therefore, the solution of the system of equation is (14, 6)

learn more on system of equation here: https://brainly.com/question/8914228?referrer=searchResults

Step-by-step explanation:

What about the table and the information in it that is related to the question? You did not send it!

The required fraction that is greater than −2/3 and less than −1/2 can be written as follows: `(-1/2) + (1/6)` which simplifies to `(-3/6) + (1/6)` which equals `-2/6`.

Therefore, the required fraction is `-2/6`. In order to determine the fraction which is greater than −2/3 and less than −1/2, you need to find a fraction that is smaller than −1/2 and bigger than −2/3. There is a common denominator of 6 for the fractions -2/3 and -1/2. Therefore, you can convert them into similar fractions with the common denominator 6 as -4/6 and -3/6 respectively.The required fraction can be expressed as (-1/2) + (1/6) which equals (-3/6) + (1/6) which equals -2/6.

Therefore, the required fraction is -2/6, which can be simplified as -1/3. Hence, the fraction that is greater than −2/3 and less than −1/2 is -1/3.

To know more about Fraction visit-

https://brainly.com/question/10354322

#SPJ11

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

The phrase "twelve less than the product of three and a number" can be translated into an algebraic expression. To do this, we need to assign a variable to the unknown number and then use multiplication and subtraction to represent the given information.

Let x be the unknown number. The product of three and x is 3x. Twelve less than 3x is 3x - 12. Therefore, the algebraic expression for "twelve less than the product of three and a number" is 3x - 12. This expression represents a value that is 12 less than three times the number x.

For instance, if we know that a number is 7, we can use this expression to find the value of "twelve less than the product of three and 7."3x - 12 = 3(7) - 12= 21 - 12= 9Therefore, the value of "twelve less than the product of three and 7" is 9. We can also use this expression to write an equation and solve for x. For example, if we know that the value of "twelve less than the product of three and a number" is 33, we can write an equation:3x - 12 = 33Then, we can solve for x:3x = 33 + 123x = 45x = 15. Therefore, the unknown number is 15.

To summarize, the phrase "twelve less than the product of three and a number" can be translated into an algebraic expression 3x - 12. We can use this expression to find the value of the expression for a given value of x or to write and solve an equation involving this expression.

Learn more about product from the given link

https://brainly.com/question/20451763

#SPJ11

Answer: The area of Triangle is A = 43.25

Step-by-step explanation:

In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3 \(s^{2}\)* s = √3/4(\(s^{2}\))

Define Area of Triangle:

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4(\(s^{2}\)) . The perimeter of an equilateral triangle is 3s.

So, we can write,

A = √3/4(\(s^{2}\))

It means, A = Area of the Triangle

S = length of Triangle = 10inches.

A = √3/4(\(s^{2}\))

A = √3/4(\(10^{2}\))

A= √3/4*100

A = 1.73/4*100

A = 0.4325*100

A = 43.25

The area of Triangle is A = 43.25

Learn more about event correlation here: brainly.com/question/27713486

#SPJ9

Answer:

35 - 2a

Step-by-step explanation:

The answer would be 35 - 2a because thats the equation you have given us. If it were 35 - 2a = something then I would be able to answer it by a = something but for now based on the info its 35 - 2a

The amount of the annual depreciation has been $90.

The statement provides us with the following data:

The yearly depreciation of the table saw can be calculated by subtracting the depreciated value from the original cost and dividing by the number of years.

Yearly depreciation = (Original cost - Depreciated value) / Number of years

Yearly depreciation = ($810 - $450) / 4

Yearly depreciation = $360 / 4

Yearly depreciation = $90

Therefore, the amount of yearly depreciation for the table saw is $90.

See more about depreciation at https://brainly.com/question/30319999

#SPJ11