A rectangular prism has the following dimensions: / = 5a, w =
find the volume of the rectangular prism.
O 10a - 30a + 10a²
O 10a³-3a² + a
O 10a - 30a + 10a³
O 10a -30a³ + 10a²
2a, and h= (a³ - 3a² + a). Use the formula V = 1. w. h to

After adding the expressions (8.5+ 6.25m) and (12 +3.75m) the value is obtained as (20.5 + 10m).

What is an expression?

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

The first expression is - (8.5+ 6.25m)

The second expression is - (12 +3.75m)

Apply the addition operation on the expressions -

= (8.5+ 6.25m) + (12 +3.75m)

= 8.5 + 6.25m + 12 + 3.75m

= 8.5 + 12 + 6.25m + 3.75m

= (20.5 + 10m)

Therefore, the value is obtained as (20.5 + 10m).

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Answer:

[tex]\boxed{y = 4x + 7}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b the y-intercept

To find the slope, take the two points, find the difference in y values and divide by the corresponding difference in x values

Two points are [tex](- 1, 3)[/tex] and [tex](- 2, -1)[/tex]

Difference in y values [tex]= -1 -3 = -4[/tex]

Difference in corresponding x values [tex]= -2 - (-1) = -2 + 1 = -1[/tex]

Slope

 [tex]m = \dfrac{-4}{-1} = 4[/tex]

So the equation of the line is of the form
[tex]y = 4x + b[/tex]

To find b, take the coordinates of any of the two points and plug the x and y values into the above equation and solve for b

Let's take point (-1, 3)

Plug in values:

[tex]3 = -4 + b\\\\3+4 = b\\ \\b = 7[/tex]

Therefore the equation of the line is
[tex]\boxed{y = 4x + 7}[/tex]

The number of fabric used for headband and wristband for each player is 25.8in and 9.3 in

Word problem is a verbal description of a problem situation wherein one or more questions are posed, the answers to which can be obtained by the application of mathematical operations.

Represent the number of fabric used on headband by x and the number of fabric used on wristband by y

Therefore;

31x +3x = 876.52

34x = 876.52

divide both sides by 34

x = 876.52/34

x = 25.8 inches

31y = 288.61

dive both sides by 31

y = 288.61/31

y = 9.3 inches

therefore 25.8 inches of fabrics and 9.3 inches of fabrics are used on headband and wristband of each player

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Answer: Two times a number y would be represented mathematically as 2*y. It means that a number y will be multiplied by 2 to get the result.

Answer:

y = - 3

Step-by-step explanation:

A line parallel to the x- axis is a horizontal line with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (2, - 3 ) with y- coordinate - 3 , then

y = - 3 ← equation of line

Answer:152+n

Step-by-step explanation:

152 for last year, n for this year. Add them together you get the answer for the total of pies in 2 years

Answer: The answer to the computation 348 + 598 is 946.

Step-by-step explanation:

To obtain an estimate for the computation 348 + 598, we can round the two numbers to the nearest ten.

348 rounded to the nearest ten is 350

598 rounded to the nearest ten is 600

So, our estimate for the sum of 348 + 598 is 350 + 600 = 950

Using a calculator, the actual computation is 348 + 598 = 946

Our estimate of 950 is 4 more than the actual answer of 946. This means that our estimate is slightly higher than the actual answer. This is not a big difference and it is reasonable as the numbers are rounded to nearest 10.

Answer:

Nose inglés lo siento xdddddddddddddddddddddd

The representation of the fraction 10/8 as a mixed number is given as follows:

[tex]\frac{10}{8} = 1\frac{1}{5}[/tex]

The fraction in this problem is given as follows:

10/8.

A mixed number is composed by two parts, as follows:

The integer part and the fractional part are defined as follows:

For the division of 10 by 8, we have that:

Then the mixed number is given as follows:

[tex]1\frac{2}{10}[/tex]

The fraction 2/10 can be simplified as 1/5, hence the simplified representation is given as follows:

[tex]1\frac{1}{5}[/tex]

The problem asks to represent the fraction 10/8 as a mixed number

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From the coordinates we can see the rule for this transformation is:

It is a dilation by a scale factor of 2 and reflection in the y-axis.

It means this is a similarity transformation, since the figure has changed its size.

Answer:

Dilation of scale factor 2 centered at the origin, followed by a reflection in the y-axis.

Similarity transformation.

Step-by-step explanation:

Given vertices of ΔABC:

Given vertices of ΔA'B'C':

From observation, the series of transformations the transforms ΔABC to ΔA'B'C' are:

This is a similarity transformation as the two triangles have the same shape but different sizes.

Answer:

x=3

Step-by-step explanation: I'm not 100% if this is it because it's been awhile but I believe that you write 2x+2=4x-4 to solve for x since they're both y=mx+b equations. After solving it you would get 3

The slope-intercept form of the equation of the given line which passes through the point (2, 7) and has a slope of 8 is:

     y = 8x - 9

What is meant by slope-intercept form of the line equation?

The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis) are known, the slope-intercept formula can be used to determine the equation of a line. The equation of a line is the equation that each point on the line fulfils.

Given the line passes through a point  (2,7) and the slope is 8.

When a point on the line and slope are given, the equation of the line is:

y - y₁ = m ( x - x₁)

m = slope  = 8

Substituting,

y - 7 = 8 ( x - 2)

y - 7 = 8x -16

y = 8x - 9

Therefore the slope-intercept form of the equation of the given line is:

     y =  8x - 9

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Answer:

Step-by-step explanation:

a. 47 men

b. 24 men like soda

c. 23 men do not like soda

d. 61 women

e. 26 women like soda

f. 35 women do not like soda

Using cosine law and sine law, the value of angle E and D are 14° and 35° and the length of side d is 19 units

The law of cosines is a mathematical formula used to calculate the measure of a third side of a triangle when two sides and the angle between them are known. It is also used to calculate the angles of a triangle when all three sides are known. The formula is: c² = a² + b² - 2ab cos(C).

In this given problem, triangle DEF can be;

f² = e² + d² - 2(e)(d) cos(F)

But we don't know the length of side d

Using sine law

f / sin F = e / sin E

25 / sin 131 = 8 / sin E

sin E = 8 * sin 131 / 25

E = 13.97°

E = 14°

Using sum of angles in a triangle

D + E + F = 180°

D = 180 - (14 + 131)

D = 180 - 145

D = 35°

Using cosine law;

d² = e² + f² - 2(e)(f)cos(D)

Substituting the values into the formula;

d² = 8² + 25² - 2(8)(25)cos(35)

d = 19

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Answer:

a) 6a+5 b)4

Step-by-step explanation:

a) 3a+3a+5 = 6a+5

b)6a + 5 = 29

6a = 29-5

6a = 24

6 6

a = 4

Answer:

A) The standard formula of the equation of a circle that has a center of (-4,-2) and contains the points (-1,2) is (x + 4)2 + (y + 2)2 = 25.

B) The general formula for the equation of a circle is (x - h)2 + (y - k)2 = r2, where (h,k) is the center of the circle and r is the radius.

Answer:

175 mins

Step-by-step explanation:

LCM of 25 and 35 is 175 which is when the next bell together will happen.

The expression that describes the sequence is 3 + n.

Let's use an expression to describe the sequence as follows:

4, 5, 6, 7....

The sequence follows an arithmetic patterns. Therefore, let's use an arithmetic progression formula to express the sequence.

Hence,

a + (n - 1)d = nth term

where

Therefore,

a = 4

d = 5 - 4 = 1

Hence,

nth term = 4 + (n - 1)1

nth term = 4 + (n - 1)

nth term = 4 + n- 1

nth term = 3 + n

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Answer:

Step-by-step explanation:

1.75?

Answer:

Let's use the same information as above to show how a formula can be used to quickly calculate the break-even output.

Remember contribution per unit? Here is a reminder of this crucial and really useful formula:

Contribution per unit = selling price per unit less variable cost per unit

In our example, contribution per unit = £10 less £4 = £6 per unit

Now apply the classic formula for calculating breakeven output:

Break-even output (units) = Fixed costs (£) / Contribution per unit (£)

So, break-even output = £40,000 divided by £6 = 6,666 units

Note: break-even output is always expressed in terms of units

So break-even output = 6,666 units

If the information is available, it is always quicker and easier to use this formula rather than use a table or draw a chart.

Answer:

It may

Step-by-step explanation:

Vertically shift the graph of f(x) up 7 units.

By:-"||Ziddiboy||"

Answer:

y = 2x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 6 ) and (x₂, y₂ ) = (9, 20 )

m = [tex]\frac{20-6}{9-2}[/tex] = [tex]\frac{14}{7}[/tex] = 2 , then

y = 2x + c ← is the partial equation of the line

to find c substitute either of the 2 points into the partial equation

using (2, 6 ), then

6 = 2(2) + c = 4 + c ( subtract 4 from both sides )

2 = c

y = 2x + 2 ← equation of line

Answer: y= 5x - 9

Hope this will help

Answer:

y=5x-9

Step-by-step explanation:

In y=mx+b, m is the slope and b is the y intercept all you have to do is replace m and b with the numbers associated in the problem this case since 5 is the slope you put it where m is, and b being the y-intercept you put the -9 there!

Answer:

Step-by-step explanation:

The general formula for finding the antiderivative of a polynomial function is to add one to the exponent of each term and divide by that new exponent.

To find the antiderivative of y = 5x -6x² +9x³, we need to integrate each term individually, using the general formula:

∫ (5x) dx = (5/1)x^(1+1) = 5x^2 + C

∫ (-6x²) dx = (-6/2)x^(2+1) = -3x^3 + C

∫ (9x³) dx = (9/4)x^(3+1) = (9/4)x^4 + C

So the antiderivative of y = 5x -6x² +9x³ is:

∫ y dx = 5x^2 - 3x^3 + (9/4)x^4 + C

Where C is the constant of integration, which can take any real value.

Therefore , the solution of the given problem of vectors comes out to

be -25.

An object with both magnitude and direction is referred to as a vector. A vector can be visualised geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

Here,

Given:

lul=3,|v|=4 and |w|=5

Also, u+v+w=0

On squaring both sides, we get

=> u2+v2+w2+2(u.v+v.w+w.u) = 0

=> 32+42+52 +2(u.v+v.w+w.u) = 0

=> 9+16+25+2(u.v+v.w+w.u) = 0

=> u.vv.w+w.u

=> -50 = -25

Therefore , the solution of the given problem of vector comes out to

be -25.

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Answer:

5 combination 3

5 fictorial divided by (5-3)! 3!

by using the above method 10 will be your answer

The multiplicative inverse of 6 + 2i is 3/20 - 1/20i.

When a number is multiplied by its original number, the multiplicative inverse of that number, or x-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2-1 since it fulfills the formula: 2 x 2-1 = 2 x 12 = 1. It is also known as a number's reciprocal.

Use the following method to determine a complex number's multiplicative inverse:

The original complex number is reciprocated to find the inverse. The complex number (6+2i) has a reciprocal of 1/6+2i. Simplify by multiplying the reciprocal's numerator and denominator by the conjugate of the denominator:

1/6+2i × 6 - 2i/6 - 2i

3/20 - 1/20i.

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After transformation, the point (-1,2) in the image would be (-1,-2)

Each transformation applied to the prior image is combined into a composition of transformations. The result of a translation is identical to a composition of reflections across parallel lines (twice the distance between the parallel lines). The composite transformation is carried out by multiplying the matrix in order from the right to the left side if it is represented as a column. The output from the preceding matrix is multiplied by the new matrix that will follow.

First, we must mirror the point (-1, 2) around the line y=-x.

(X, Y) is the rule (-y,-x)

you obtain (-1,2)—>(-2,1) (-2,1)

At this point, you must rotate (-2,1) by 90 degrees.

(X, Y) is the rule ( -y,x)

so (-2,1)—> (-1,-2) (-1,-2)

After transformation, the point (-1,2) in the image would be (-1,-2)

The complete question is,

What is the image point of (-1,2) after the transformation R 90° ry=-x

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Answer: The solution of the equation is x = 48. The equation is 20 = x - 28.

Step-by-step explanation:

-20 is like having -20 dollars, and you want to know how much you have to add to it to get to 28 dollars. So we add 20 to -28 and we get the number x = 48, so 48 dollars is what we need to add to -20 dollars to get to 28 dollars.

The mean number of goals for two seasons is 2.44 goals per match.

When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.

To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.

Given, Last season Rio's football team scored 50 goals in 20 matches.

This season they scored 60 goals in 25 matches.

Therefore, The mean number of goals per match for each season is,

= (50 + 60)/(20 + 25).

= 110/45.

= 2.44 goals per match.

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The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) ,

B ' ( 28, 14 ) and C ' ( -7, -7 ) .

What is a graph ?

Graph can be defined as the visual representation which is used to represent the data.

The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.

For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.

The dilation rule can be written as (x, y) -> (7x, 7y)

As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.

Example: side AB = 7 units, side A'B' = 49 units

Hence, The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) , B ' ( 28, 14 ) and C ' ( -7, -7 ) .

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