Write the equation of the line in fully simplified slope-intercept form.

Answer:

120960

Multiply the numbers together, Hope this helps :)

Answer:

120,960

Step-by-step explanation:

Answer:

18 cubic units

Step-by-step explanation:

The volume of prism is equal to:

base area x height

therefore;

V = 1.33333 x 13.5

   = 17.999955 ≈ 18

Answer:

The volume of a prism is given by the formula:

V = Bh

Where V is the volume, B is the area of the base, and h is the height of the prism.

Given the height of 1.33333 and an area of the base of 13.5, the volume can be calculated as:

V = 13.5 * 1.33333

V = 18.08332

So the volume of the prism is 18.08332 cubic units.

Step-by-step explanation:

Answer:

A) 3.6 meters

B) 3.24 meters

C) 13 Times

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

I think it would  it  be a) because (-2 b - 12 c)

i might be wrong but i hope it helps

The value of g(-2) is 0 and the value of g(4) is -4.

The function g is defined as a piecewise function that assigns a specific value to the input x depending on the range of x.

For x between -8 and -2 (not including -2) the function g assigns 6 as the output, for x between -2 and 4 (not including 4) the function g assigns 0 as the output, and for x between 4 and 10 (not including 10) the function g assigns -4 as the output. Therefore, for input x = -2, the function g assigns 0 as the output and for input x = 4, the function g assigns -4 as the output.

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Complete question :

consider a function g.

given

g(x) = 6    if  -8 ≤ x < -2

g(x) = 0     if  -2 ≤ x < 4

g(x) = -4     if  -4 ≤ x < 10

find the value of g(-2) and g(4)

The values of x when solved;

a. x≥ 3. 44

b. x≥3. 44

c. x ≤ 8. 8

Inequalities are simply described as relations that makes a non-equal comparison between two numbers, variable or other mathematical expressions.

They are used to compare numbers on the number line on the basis of size

From the information given, we have to determine the value of x in the inequality given;

a. 5 1/2≥1.6x

convert to improper fraction

11/2 ≥1.6x

divide both sides by 1. 6

x≥ 3. 44

b. x≥3 7/16

convert to improper fraction

x≥ 55/ 16

x≥3. 44

c. x≤8 4/5

convert to improper fraction

x≤ 44/ 5

x ≤ 8. 8

Hence, the value are  x≥ 3. 44, x≥3. 44 and x ≤ 8. 8

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Answer:

so here you have given four point if you find slope be between A and B and then another slope between C and D so according to the formula Slopem1 × slopem2 = -1

if this condition fulfil then it's perpendicular

A. The number of red balls he had was 8  at the beginning.

Duke's starting red ball total can be found by setting up a system of equations. First, let x represent the number of red balls and y represent the number of blue balls.

After 5 days, the equation is x-15=y+10. This equation states that after 5 days, the number of red balls (x) minus 15 will equal the number of blue balls (y) plus 10. After 9 days, the equation is x-27=2y+20.

This equation states that after 9 days, the number of red balls (x) minus 27 will equal twice the number of blue balls (y) plus 20. To solve for x, both equations can be set equal to each other and solved. This results in x=8. Therefore, Duke had 8 red balls at the beginning.

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Considering the expression of a line, the equation of the line that passes through the pair of points (-4,1) and (4, -1) is y=-1/4x +2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a line, the value of the ordinate to the origin b can be obtained.

In this case, being (x₁, y₁)=  (-4, 1) and (x₂, y₂)= (4, -1), the slope m can be calculated as:

m= (-1 -1)÷ (4 - (-4))

m= (-1 -1)÷ (4 +4)

m= (-2)÷ 8

m= -1/4

Considering point 1 and the slope m, you obtain:

1= (-1/4)× (-4) + b

1= -1 +b

1 +1= b

2= b

Finally, the equation of the line is y=-1/4x +2.

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Solutions for the given graph can be be given as function  [tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

A relation called a "function" is one in which each input has just one Solution.

In the relationship, y is a function of x because there is only one solution y for each input x (1, 2, 3, or 0). Since y = 3 has multiple solution (x = 1 and x = 2), x is not a function of y.

As we can see, f(x) has two inequalities

in first case x ≤ -1.5

And equation is

[tex]$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

m = -2

Line equation

y - 0 =  -2(x - (-1.5))

y = −2x − 3

in second case x ≤ -1.5

And equation is

[tex]$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

m = 0.75

Line equation

y - 0 =  0.75(x - (-4))

y = 0.75x + 3

[tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

Thus, Solutions for the given graph can be be given as function  [tex]$ f(y) \left \{ {{y < -2x - 3} \atop {y < 0.75x + 3}} \right.[/tex]

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The balance in your account after 5 years, given the annual simple interest rate and the amount deposited, is $ 1, 612. 50

To find the balance on the account after 5 years, you first need to find the simple interest on the account every year ;

= Amount deposited x Simple interest rate

= 1, 500 x 1. 5 %

= $ 22. 50

The interest over 5 years is :

= 22. 50 x 5

= $ 112. 50

The balance is therefore:

= 1, 500 + 112. 50

= $ 1, 612. 50

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Full question is:

A savings account pays an annual simple interest rate of 1.5%. What would be the balance in your account after 5 years, if you deposited $ 1, 500?

Answer:

60

Step-by-step explanation:

Total angle of triangle= 180

so 4x + 5x + 3x = 180

12x = 180

x = 180/12

x = 15

E = 5x = 5×12 = 60

Answer:

A dodecahedron is a solid shape that has exactly five planes of symmetry.

Step-by-step explanation:

A plane of symmetry is a plane that divides a shape into two identical halves, such that if a line were drawn along the plane, the resulting image would be an exact mirror image of the original shape.

A dodecahedron is a regular solid shape with 12 congruent regular pentagons as its faces. Each of these faces can serve as a plane of symmetry, and the center of each face also serves as a point of symmetry.

The dodecahedron has five planes of symmetry that pass through the centers of its faces. Each of these planes is perpendicular to one of the five faces that share a common vertex. The solid shape has no other plane of symmetry passing through its edges or through its vertices because there are not enough edges or vertices that are equidistant from the center of the solid.

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Answer:

3n³-19n²+20n

Step-by-step explanation:

(g×f)(n)= g(n) × f(n)

= (n²-5n)(3n-4)

=3n³-4n²-15n²+20n

=3n³-19n²+20n

Answer:

No

Step-by-step explanation:

outliers are numbers in a line that exceed out from the range.

Answer:

its 45

Step-by-step explanation:

Answer:

[tex]\boxed{22}.[/tex]

Step-by-step explanation:

In June, the camp had 325 campers and 26 counselors, for a ratio of 325/26=<<325/26=12.5>>12.5 campers per counselor.

In July, there are 325-265=<<325-265=60>>60 remaining campers from June, and 215 new campers arrive, for a total of 60+215=<<60+215=275>>275 campers in July.

To maintain the same ratio of campers to counselors as in June, the camp would need 275/12.5=<<275/12.5=22>>22 counselors in July.

Answer: -7x+2x+5-4x=-9x+6

The equation -7x+2x+5-4x=-9x+6 is an example of an equation that has no solution. This is because the left side of the equation, -7x+2x+5-4x, is not equal to the right side, -9x+6.

When we simplify the left side of the equation, we get -7x+2x+5-4x = -9x. We can see that the left side and right side of the equation are not equal and thus have no solution.

In general, an equation has no solution when the two sides of the equation are not equal, and there is no value of the variable that can make them equal.

Step-by-step explanation:

The pattern of the two charts and fill in the missing numbers is as follows:

For time 1,2, 3, 4, 5, 6, 7,8,9, and 10 the distance is 4, 8, 12, 16, 20, 24,28,32, 36, and 40 respectively.

When the time is increased by one(1) the corresponding distance is increased by 4.

Hence the pattern of increase in distance is:

T₁ = 4

T₂ = (4+ 4)

T₂ = 8

T₃ = (8 + 4)

T₃ = 12

T₄ = (12 + 4)

T₄ = 16

T₅ = (16 + 4)

T₅ = 20

T₆ = (20 + 4)

T₆ = 24

T₇ = (24 + 4)

T₇ = 28

T₈ = (28 + 4)

T₈ = 32

T₉ =  (32 + 4)

T₉ = 36

T₁₀ =  (36 + 4)

T₁₀ = 40

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The area of the rectangle is x(14-x).

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc. You can use the formula of the area of a rectangle to find the space occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches.

Yes, the expression a(x) = x(14-x) represents the area of a rectangle with width x. The expression is a function that takes the width of the rectangle as input and returns the area of the rectangle as output. The area of a rectangle is given by the formula A = lw, where A is the area, l is the length of the rectangle, and w is the width of the rectangle. In this case, the length of the rectangle is 14 and the width is x, so the area of the rectangle can be expressed as a(x) = x(14-x).

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The perimeter of the rectangle is fixed at P(x) =28

Now, According to the question:

Let's Know:

Area and Perimeter of Rectangle

Areas and perimeters are the most basic parameters involved in shapes, with the former being the space that can be covered by a shape and the latter being the measure of the outline of the shape.

A rectangle has dimensions defined by the length, l, and the width, w, which can be used in determining its area and perimeter. These are obtained using the following formulas.

A = l × w

P = 2l+ 2w

We are given the area of a rectangle as a function of x, which is

a(x) = x(14−x) We are asked to determine the perimeter of the rectangle.

the area of a rectangle is given by:

A = l × w

l is the length and w is the width. We may notice that in this formula, the two dimensions or components are simply multiplied together. Going back to the given function, we can see that the components on the right side of the equation also have this relation. If we look closely, we can see that we have two factors, x  and (14 − x), and that they are multiplied to each other. We can assume that x is the length of the rectangle and (14−x)  is the width of the rectangle. The product of these two expressions gives the area function.

Now, let's apply these to the perimeter of a rectangle. Generally, the perimeter of a rectangle is given by

            P = 2l + 2w

Since, for our case, the length is x and the width is (14− x), substituting these into the formula for the perimeter gives us

P(x) = 2x + 2(14 - x)

P(x) = 2x + 28 - 2x

P(x) = 28

Therefore, the perimeter of the rectangle is fixed at P(x) =28.

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If Polygon q is a scaled copy of polygon p the value of x is 6 value of y would be 2/9

Here, the idea of scale factor is used.

A figure's scale factor determines how much larger or smaller it is compared to the other figure. The scale factor refers to the amount by which a figure would indeed be increased or decreased.

In mathematics, a scale factor is the ratio between similar measurements of an object as well as a representation of this same object.

Polygon Q is a scaled copy of Polygon P.

The value of x is 6

Therefore, From the given statement,

4/3 = x/y

When x = 6 then

4/3 = x/ y

4/3 = 6/y

y = 4/3 (1/6)

y = 2/9

here, the scale factor would be:

k = y/x

k = 3/4

so, if Polygon q is a scaled copy of polygon p the value of x is 6 value of y would be 2/9

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It is not possible to answer this question  for polygon without additional information.

In order to answer this question, we need to know the value of y in the original polygon p. Without knowing this value, it is impossible to calculate the corresponding value in polygon q. For example, if polygon p has a side length of 10 units, and polygon q has a side length of 60 units, then the value of y in polygon q would be 6 times the value of y in polygon p. However, without knowing the value of y in polygon p, we cannot calculate the value of y in polygon q.

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Answer:

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 7 : a₁ = 2

Step-by-step explanation:

An explicit formula has the form

[tex]a_{n}[/tex] = a₁ + d(n - 1)

compare with [tex]a_{n}[/tex] = 2 + 7(n - 1)

then a₁ = 2 and common difference d = 7

the recursive rule allows a term to be found by adding d to the previous term, that is

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 7 : with a₁ = 2

Therefore  $6,440 money will Grayson have to retire.

We must first determine the entire number of months Grayson will be saving for in order to determine how much money he would need to retire. Since there are 12 months in a year and he plans to retire in 20 years, he will be saving for 20 * 12 to equal 240. 30 years.

Next, we can figure out how much money Grayson will need to retire using the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A is the total amount Grayson will need to retire, and P represents the monthly saving goal ($1,000).

Since interest is compounded monthly, r represents the annual interest rate of nine percent and n represents the number of times interest is compounded annually.

The number of years Grayson will be setting up money is t. (20)

With these values entered into the formula, we obtain:

A = $1,000(1 + 0.09/12)^(12*20)

A = $1,000(1.0075)^(240) (240)

A = $1,000(6.44) (6.44)

A = $6,440

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The range of the ordered pairs  {(4, -2), (3, 2), (-1, 0), (-3, 4)} is {-2, 2, 0, 4}

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

{(4, -2), (3, 2), (-1, 0), (-3, 4)}

This means that

Ordered pairs =  {(4, -2), (3, 2), (-1, 0), (-3, 4)}

Rewrite as

(x, y) =  {(4, -2), (3, 2), (-1, 0), (-3, 4)}

The domain is the set of the x values

So, we have the following representation

x = {4, 3, -1, -3}

Remove repeated entries

x = {4, 3, -1, -3}

So, the domain is x = {4, 3, -1, -3}

On the other hand, the range of the ordered pairs is the set of the y values

So, we have

Range = {-2, 2, 0, 4}

So, the range is {-2, 2, 0, 4}

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The expression 2(m - 4) is equivalent to 2m - 8.

In the expression 2(m - 4), the term inside the parentheses is m - 4. When you multiply this term by 2, you get 2(m - 4) = 2m - 8.

So, the expression 2(m - 4) is equivalent to 2m - 8.

Of the five options given, the only one that is equivalent to 2(m - 4) is 2m - 8. The other options are not equivalent because they do not have the same value as 2(m - 4) when you plug in different values for m.

For example, if you plug in m = 6, the expression 2(m - 4) becomes 2(6 - 4) = 2(2) = 4.

On the other hand, the other options do not give the same result when you plug in the same value for m:

2m - 7: 2(6) - 7 = 12 - 7 = 5

2m - 3: 2(6) - 3 = 12 - 3 = 9

2m: 2(6) = 12

2m + 10: 2(6) + 10 = 12 + 10 = 22

Since none of these options gives the same result as 2(m - 4) when you plug in the same value for m, they are not equivalent to 2(m - 4).

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The equivalent expression of 2(m − 4) + 1 is 2m − 7. So the option a is corect.

In the given question, we have to find which expression is equivalent to 2(m − 4) + 1.

The given expression is 2(m − 4) + 1.

To solve this expression we firstly solve the small bracket. To solve the small bracket we use distributive property. In this property:

a(b+c) = ab + bc

Now solving the expression.

2(m − 4) + 1 = 2m − 2*4 + 1

2(m − 4) + 1 = 2m − 8 + 1

2(m − 4) + 1 = 2m − 7

Hence, the equivalent expression of 2(m − 4) + 1 is 2m − 7. So the option a is corect.

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The complete question is:

Which expression is equivalent to 2(m − 4) + 1?

(1) 2m − 7

(2) 2m − 3

(3) 2m − 9

(4) 2m − 10

Answer:

Step-by-step explanation:

the squares of consecutive odd numbers are always divisible by 8

The minimum sample size required for the estimate is given as follows:

385.

The bounds of a z-distribution confidence interval, which is used as we have the standard deviation for the population, are given as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which the parameters are given as follows:

Hence the equation for the margin of error is given as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The variance is known to be 3.61, hence the standard deviation is given as follows:

[tex]\sigma = \sqrt{3.61} = 1.9[/tex]

The critical value for a 95% confidence interval is given as follows:

z = 1.96.

Hence the required sample size for a margin of error of M = 0.19 is calculated as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.19 = 1.96\frac{1.9}{\sqrt{n}}[/tex]

[tex]0.19\sqrt{n} = 1.96 \times 1.9[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 1.9}{0.19}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 1.9}{0.19}\right)^2[/tex]

n = 385.

(rounding up, as for a sample size of 384, the margin of error would be slightly above 0.19).

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A convex polygon is a polygon which has all its interior angles as less than 180° . The correct option is B

Convex polygon is a closed figure where all its interior angles are less than 180° and the vertices are pointing outwards. convex is used to refer to a shape that has a curve.

Therefore from visual inspection of all four options only option B seems to fulfill the criteria mentioned . A convex shape is a shape where all of its parts point outwards. No part of it points inwards,

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The absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

To find the absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4), we can find the critical points of the function within the interval and check the endpoints of the interval. A critical point is a value of x where the first derivative of the function is equal to zero or is undefined.

First we will find the first derivative of the function:

f'(x) = 3x^2 - 6x

The critical points occur when the first derivative is equal to zero:

3x^2 - 6x = 0

x(3x - 6) = 0

x = 0, x = 2

We now need to check if these critical points are maximum or minimum points. For this we need to calculate the second derivative of the function:

f''(x) = 6x - 6

If the second derivative at a critical point is positive, the critical point is a local minimum. If the second derivative at a critical point is negative, the critical point is a local maximum.

f''(0) = 60 - 6 = -6

f''(2) = 62 - 6 = 6

We can see that the second derivative at x = 2 is positive and the second derivative at x = 0 is negative, therefore x = 2 is a local minimum and x = 0 is a local maximum.

Now we need to check the endpoints of the interval to see if they are the absolute maximum or minimum

(-2)^3 - 3(-2)^2 + 12 = -2 - 12 + 12 = -2

(4)^3 - 3(4)^2 + 12 = 64 - 48 + 12 = 28

We can see that the maximum value of the function is 28 at x = 4 and the minimum value of the function is -2 at x = -2, so the absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

Therefore, The absolute maximum value of the function f(x) = x^3 - 3x^2 + 12 on the closed interval (-2, 4) occurs at x = 4.

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1a) The number of pictures per second taken by the first camera is 7.

1b) The number of pictures per second taken by the second camera is 6.

1c) The number of pictures per second taken by the third camera is 5.

2) The camera that takes pictures the fastest is the First Camera.

The rate of speed is the quotient of the total number of pictures taken per camera and the time used.

Using division operation, the number of pictures is divided by the time to determine the speed of each camera per second.

                                        First        Second        Third

                                     Camera     Camera     Camera

Number of pictures         49             24               25

Time (seconds)                  7               4                 5

Pictures per second         7 (49/7)      6 (24/4)     5 (25/5)

Thus, we can conclude that the First Camera is the fastest since it takes 7 pictures per second unlike the second and third cameras.

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