Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.

If Twelve out of Sixty students are trying out for the spring musical, the percentage of students trying out for the musical is , 20%.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

In above question, if Twelve out of Sixty students are trying out for the spring musical, we have,

Number of students trying out for the musical = 12

Total number of students = 60

Percentage of students trying out for the musical is , [tex]\frac{12}{60} *100[/tex] = 20%

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now, we're assuming this is some rectangular area, and thus is simply the product of both quantities, let's change all mixed fractions to improper fractions firstly.

[tex]\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{11\frac{3}{4}} \implies \cfrac{11\cdot 4+3}{4} \implies \stackrel{improper}{\cfrac{47}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}\cdot \cfrac{47}{4}\implies \cfrac{1175}{8}\implies 146\frac{7}{8}~ft^2[/tex]

An equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2) is y = 3x - 5.

Mathematically, the standard form of the equation of a straight line (slope-intercept form) is given by this mathematical expression;

y = mx + c

Where:

From the information provided, we have the following points on line g:

Point = (-3, 6)

Point = (0, 5)

Next, we would determine the slope of line g as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (5 - 6)/(0 - (-3))

Slope, m = -1/3

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1/3 × m₂ = -1

m₂ = 3

At point (1, -2), an equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 3(x - 1)

y + 2 = 3x - 3

y = 3x - 3 - 2

y = 3x - 5

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Luca's average trip will be 58 miles per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

In this case, it took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, Luca's average trip will be:

= Distance / Time

= 464 / 8

= 58 miles per hour.

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2 copies of 1/10 can be written as 2/10

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here 2 copies of 1/10 thus 2×1/10=2/10

                                                                =1/5

Hence, 2 copies of 1/10 can be written as 2/10

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Answer:

3.5m(3m + 1.8)

10.5m^2+6.3m

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5x5 = 25

Answer:

25

Step-by-step explanation:

Let's go through our times tables really quick!

5x1 = 5 (5 + 0)

5x2 = 10 (5 + 5)

5x3 = 15 (5 + 5 + 5 [10 + 5])

5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)

As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5

So, 5x5 is 25

Hope this helped!

Answer:

[tex] \sf \: a) \: 1[/tex]

Step-by-step explanation:

Given values of variables,

→ e = 3.2

→ d = 10

→ u = 7

The problem needed to solve is,

[tex] \sf \rightarrow \: \frac{ue}{eu} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{ue}{eu} [/tex]

[tex] \sf \rightarrow \: \frac{(7 \times 3.2)}{(3.2 \times 7)} [/tex]

[tex] \sf \rightarrow \: \frac{22.4}{22.4} [/tex]

[tex] \sf \rightarrow \: \frac{1}{1} = 1[/tex]

Hence, option (a) is correct.

Answer:

Option A ) 1

Step-by-step explanation:

[tex]\frac{ue}{eu} = \frac{3.2X7}{7X3.2} = \frac{22.4}{22.4} = 1[/tex]

Hence , Option A ) is the answer

The required measure of the value of x is given as 2√3. Option A is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Consider the given triangle,

perpendicular = 6
base = x

Applying trigonometric operation,
tan30 = perpendicular/base
tan30 = 6/ x
x = 6/√3
x = 2√3

Thus, the required measure of the value of x is given as 2√3. Option A is correct.

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The value of 10% as a fraction and a decimal will be 1/10 and 0.1.

From the information, we want to write the percentage as a fraction as well as a decimal. A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.

10% as a fraction will be calculated by dividing 10 by 100. This will be:

= 10 / 100

= 1 / 10

10% as a decimal will be calculated by dividing 10 by 100 and giving it in decimal form.

= 1/10

= 0.1

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. Complete question

Write 10% as a fraction and a decimal

Answer:

B. 8 servings

Step-by-step explanation:

1 quart = 4 cups

3x4=12

3 quarts of clam chowder = 12 cups of chowder

1 1/2 cups each

12 divided by 1 1/2 = 12 divided by 3/2 = 12 divided by 2/3 = 8 servings

Answer:

2/15 6/15 8/15 9/15 12/15

Step-by-step explanation:

Answer: 2/15, 6/15, 8/15, 9/15, 12/15.

Step-by-step explanation:

Just treat the denominators like they are not there for now, and treat the numerators like they are whole numbers and then rearrange:

8, 2, 9, 6, 12

Now rearrange from smallest to largest:

2, 6, 8, 9, 12

Now just put the denominators back in under the arranged numbers:

2/15, 6/15, 8/15, 9/15, 12/15

Words and their definitions:

Numerator: Top part of the fraction

Denominator: Bottom part of the fraction

The linear equation y = 15x +100. And the graph and table are given in the attached image.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

Laura gets a job at Costco to make extra money during the holidays and will get paid $15 an hour.

She also gets a $100 bonus for agreeing to start right away.

Let x be an hour, she worked.

And y be the total earnings.

So, the equation,

y = 15x + 100

The table is given in the attached image.

And the graph is also given.

Therefore, the equation is y = 15x + 100

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Answer:

62 degrees.

Step-by-step explanation:

I think this because it appears that ABC makes a 90 degree angle and I would think that you would just subtract 28 from 90 and get 62.

Hope it helps! =D

Answer:

(0.5, 3)

Step-by-step explanation:

Just entered it into a desmos graphing calculator online

Answer: The answer is 29,446,941,856

Step-by-step explanation:

The value of the expression 8x² + 6x - 8 below when x=2 is 36.

The expression can be evaluated by following the steps below:

8x² + 6x - 8 in x = 2 means that the variable x will be replaced by the given number which is 2.

8*2² + 6*2 - 8

8*4 + 12 - 8

32 + 16 - 8 = 36

This therefore means that when x= 2 in 8x² + 6x - 8 , the value gotten will be 36.

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Answer: The answer to your question is the letter B. May want to assess it before answering.

Explanation:

Multiply out the fractions. This is because volume = length*width*height when it comes to rectangular prisms, aka blocks.

(3/8)*(5/8)*(7/8) = (3*5*7)/(8*8*8) = 105/512

This fraction cannot be reduced since 105 and 512 have no factors in common, other than 1. A clue of this is to notice how neither 3, nor 5, nor 7 share any common factors (other than 1) with 8 in the denominator.

Answer:

105/512

Step-by-step explanation:

hope this helps

The perimeter of the rectangle is 19n + 7.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The perimeter of a rectangle is the sum of the whole sides of the rectangle.

Therefore, let's find the perimeter of the rectangle with width of 6n - 3.5 ft and length of 3.5n + 7 ft. Hence,

perimeter of a rectangle = 2(l + w)

where

Therefore,

w = 6n - 3.5

l = 3.5n + 7

Hence,

perimeter of a rectangle = 2(6n - 3.5 +  3.5n + 7)

perimeter of a rectangle = 2(6n + 3.5n - 3.5 + 7)

perimeter of a rectangle = 2(9.5n + 3.5)

perimeter of a rectangle = 19n + 7

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Total amount paid by Donna is $16,689.6 and interest paid is $789.6.

The cash up front paid by the buyer in real estate transactions and other significant purchases is known as a down payment on a house. For a property being used as a primary residence, down payments, which are typically a percentage of the purchase price, can range from as little as 3% to as much as 20%.

According to question:

Given,

Price of car= $15,900

Down Payment=$4800

number of months=12 x 4=48 month

Monthly payment=$245.70

Total amount Donna paid = Down payment+ all monthly installment

Total amount = $4800+ 48 x 247.70 =$16,689.6

Interest Paid = $16,689.6 - $15,900 = $789.6

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Answer:

11

Step-by-step explanation:

29-20= 91

2+9=11

11+9=

Answer:

  To get black from red ...

Step-by-step explanation:

You want the know the transformation that is applied to the red graph to make it be the black graph.

We note that the vertex of the black graph is (-1, 4), which is 1 unit left and 4 units up from the vertex of the red graph.

The black graph opens downward, and has a slope of ±3 compared to the slope of ±1 for the red graph. This means it has been reflected across the x-axis and scaled by a factor of 3.

The reflection and scaling can both be accomplished by multiplying the function by -3. The translation is accomplished by adding 4 to the function value to shift it up 4 units, and adding 1 to the x-value to shift the graph left 1 unit.

The transformations applied to the red graph are ...

The points to be graphed are (6, 0) and (0, 3). The graph of the equation is shown in the attached image

y = - 1/2x + 3

In order to graph the equation of the line:

First, find the value of x when y = 0:

y = - 1/2x + 3 , when y = 0:

0 = - 1/2x + 3

1/2x = 3

x = 3 × 2

x = 6

Also, find the value of y when x = 0:

y = - 1/2x + 3, when x = 0:

y = - 1/2(0) + 3

y = 3

Therefore,  the values to be plotted on our graph are (6, 0) and (0, 3). The image of the graph is attached

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The third term of the geometric sequence will be 8/3.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The equation is given below.

aₙ = (2/3) · (-2)ⁿ⁻¹

The third term of the geometric sequence will be given as,

a₃ = (2/3) · (-2)³⁻¹

a₃ = (2/3) · (-2)²

a₃ = (2/3) · (4)

a₃ = 8 / 3

The third term of the geometric sequence will be 8/3.

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Answer:

Given,eqn is -6x-18y=20

or,-18y=6x+20

or,y=6x+20/-18

or,y=6x/-18 +20/-18

or,y= - X/3 -10/9

Comparing above eqn with y=mx +c,we get

m= -1/3 and y-intercept (c)=-10/9

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Answer:

slope: -1/3  y-int: -10/9

Step-by-step explanation:

first step is to turn the equation into slope intercept form (y=mx+b)

-6x-18y=20

+6x        +6x

-18y=6x+20

divide -18 on both sides

y=-1/3x-10/9

the m is the slope, and the b is the y-intercept

The solution that (4, 10) represents is that Jim purchased 4 iced teas and 10 soft pretzels at a cricket game.

The equation that describes the relationship between the

number of iced teas and the number of soft pretzels purchased is;

3x + 2y = 32

Where;

x represents the iced teas.

y represents soft pretzels at a cricket game

Now, we are told that the ordered pair (4, 10) is a solution of the equation. This means that;

x = 4 and y = 10 is a solution.

What it means is that Jim purchased 4 iced teas and 10 soft pretzels at a cricket game

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Answer: The correct answer is C. Jana has a higher ratio of hits to total attempts, so she has a better batting average. This can be calculated by dividing the number of hits by the number of attempts: Jana's batting average is 7/10 = 0.7, and Tasha's batting average is 10/16 = 0.625. Since 0.7 is greater than 0.625, Jana has a higher batting average.