I believe the answer to be c but I'm not the best at word problems this is a practice study guide.

In order to determine which is the equivalent equation, simplify the given expression:

-2x + 5 - 3x = 5x + 25 simplify like terms left side

-2x - 3x + 5 = 5x + 25

-5x + 5 = 5x + 25 subtract 5x both sides and subtract 5 both sides

-5x - 5x = 25 - 5 simplify both sides

-10x = 20

Hence,the equivalent expression is -10x = 20

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

Let the rate of change of  the edge length x, y, and z of a closed rectangular box are:

dx/dt= 1m/s

dy/dt= -2 m/s

dz/dt= 0.5 m/s

a) The volume of the box

From the formula of the volume,

V=xyz

Then,

differentiate w.r.t t

[tex]\frac{dV}{dt} = xy\frac{dz}{dt} + yz\frac{dx}{dt} +xz\frac{dy}{dt}[/tex]

[tex]\frac{dV}{dt} = xy(0.5)+ yz(1)+xz(-2)[/tex]

put the value of x, y, z , then we get

[tex]\frac{dV}{dt} = 2.3.(0.5)+ 3.5.(1)+2.5.(-2)[/tex]

[tex]\frac{dV}{dt} = 3+ 15 - 10[/tex]

[tex]\frac{dV}{dt} = 8m^3/s[/tex]

The rate of change of the volume of the box is 8m³/s.

b) surface area of the box

surface area of the rectangular box is

s = 2xy + 2yz + 2zx

differentiate w.r.t t

[tex]\frac{ds}{dt} = 2(y + z)\frac{dx}{dt} + 2(z + x)\frac{dy}{dt} +2(x + y)\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 2(y + z)(1) + 2(z + x)(-2)+2(x + y)(0.5)[/tex]

[tex]\frac{ds}{dt} = 2(3 + 5)(1) + 2(5 + 2)(-2)+2(2 + 3)(0.5)[/tex]

[tex]\frac{ds}{dt} = 16 -40 + 5[/tex]

[tex]\frac{ds}{dt} = -19m^2/s[/tex]

The rate of change of the surface area of the box is -19m²/s.

c) diagonal of the box

lengths of  the boxes for the diagonal is

s = 2x² + y² + z²

differentiate equation w.r.t t

[tex]\frac{ds}{dt} = 4x\frac{dx}{dt} + 2y\frac{dy}{dt} +2z\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 4.2.1+ 2.3.(-2) +2.5.(0.5)[/tex]

[tex]\frac{ds}{dt} = 8 -12 + 5[/tex]

[tex]\frac{ds}{dt} =1m/s[/tex]

The rate of change of the diagonal of the box is 1m/s.

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

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Average rate is f(a+266)-f(a))/266

so f(a+266) equals (0.16 x 266) + f(a)

f (a+266)= (0.16 x 266) + 92.39

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.

We need to solve the next expressions:

17. 19yd. 28in.- 16yd. 31in

We need to solve subtract each expression.

Then:

19yd. 28in.- 16yd. 31in =

19yd - 16yd and 28in-31in

3yd -3in

Then, we have the next equivalent.

1 yard = 36 in

So:

36 in - 3 in = 33 in

Therefore

19yd. 28in.- 16yd. 31in = 2 yard 33

18 61wk. 4da.- 18wk. 6da.

We need to subtract both expression:

Then

61wk - 18wk = 43kw

4da-6da = -2da

Where 1 week = 7 days

Then

7 da - 2da = 5 da

Hence, 43kw -1 wk = 42 wk.

The result is:

42 wk 5 da

21. 8tbsp. 2tsp. * 15

We need to convert 2ts into tbsp and then multiply the result by 15.

If

1 tsp ------- 0.333tbsp

Then

2tp ------ 2(0.333tbsp)= 0.66666 tbsp

Now

(8tbsp + 0.6666 ) * 15 = 130 tbsp

The Pythagorean theorem states:

where a and b are the legs and c is the hypotenuse of a right triangle.

Substituting with c = 9 and a = 5, we get:

Given:

The original selling price of 1 swimsuit = $44.95

The selling price of 1 marked down swimsuit = $16.90

Using the provided formula:

Where,

M is the markdown

S is the original selling price

N is the reduced price

Substituting we have:

Solving for N:

Hence, the reduced price is $28.05

Answer:

$28.05

Paul is the oldest and Fred is the youngest of the three.

Younger is a comparative adjective that generally indicates more youthful.

Similar to old, elder simply indicates older in age. It is a comparative version of old.

Given that x is a natural number, let Bill's age equal x years.

Paul's age is thus calculated as (x + a) Years, where an is any positive integer.

Fred is also younger than Bill.

So, Fred's age is equal to x - k, where k is any positive integer.

As a result, if we arranged Fred, Bill, and Paul's ages, they would be

Bill, Fred, and Paul

x-k < x < x+a

As a result, we can conclude that Paul is the oldest and Fred is the youngest of the three.

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The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;

The river is "actually" 137.5 miles long

the median is 25, because:

the mean value is :

1. Quadratic curve

2. Odd degree function

3. TWO REAL ZEROS

The most appropriate choice for profit will be given by-

Profit percent after selling a bag of garri is 25%

What is profit?

If the selling price of an article is more than the cost price of the article, then the difference between selling price and the cost price of the article gives the profit

Profit = SP - CP

Here,

Cost price of a bag of Garri = N320

Selling price of a bag of Garri = N400

Profit = N(400 - 320)

         = N80

Profit Percent = [tex]\frac{80}{320} \times 100[/tex]

                       = 25%

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We have to graph the function F(x) defined as:

We can graph it as:

To see the complete graph we have to show the horizontal axis from x = -30 to x = 30 and the vertical axis from y = -80 to y = 80.

Answer: Option B

The most appropriate choice for geometric series will be given by

The equation is [tex]y = 80 (1.2)^x[/tex] and it is a geometric function.

What is geometric series ?

The series in which the ratio between consecutive terms of the series are same is called geometric series

For example, 2, 4, 8, 16, ... is a geometric series in which ratio between two consecutive terms is 2.

Number of pieces of art in 2004 = 80

Number of pieces of art  in 2005 = [tex]80 \times 1.2[/tex]

Number of pieces of art in 2006 =  [tex]80\times (1.2)^2[/tex]

Number of pieces of art after x years from 2004 = [tex]80 \times (1.2)^x[/tex]

The equation is [tex]y = 80 (1.2)^x[/tex]

This is a geometric function

The graph has been attached here.

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Given:

Required:

To find the correct one.

Explanation:

The given quation is:

4 + x +8 =24

Subtract 8 on both sides

4 + x +8 - 8 = 24 -8

4 + x = 16

Final Answer:

Thus the first option is the correct answer.

Anisha used the substitution method to solve the system of equations.

She is missing the value of y.

To find it we plut the value of x in the first equation, then:

Therefore the solution is (4,-1)

Given the picture, we have:

Enclosed area: A = x*y

Fence Length: F= 2x+y

Answer: Fanuela walked 2.808 miles.

Step-by-step explanation:

If 3.9 = 100 and we need to work out what 72 is we can do this/

3.9 ÷ 10 = 0.39 which = 10

0.39 ÷ 10 = 0.039 which = 1

so with these calculations we can solve the problem.

To get the 70 in 72 we can do 0.39 x 7 (10 x 7) which = 2.73.

To get the remaining 2 in 72 we can do 0.039 x 2 (1 x 2) which = 0.078.

2.73 + 0.078 = 2.808.

Fanuela walked 2.808 miles.

Hope this helps! Feel free to ask any questions if you're still unsure.

To find the step where the error was made, we are going to correctly solve the equation:

We need to solve for x, first we subtract 3 from each side:

We divide by 2 each side:

The first step that shows an error in the solution of the equation is the Step 2, because when we have two negative numbers, we add them, we do not subtract them.

Answer: B. Step 2

The probability of picking a heart or an ace is 17/52

Here, we want to get the probability

The number of cards in a standard deck is 52 cards

Now, we need to know the number of hearts and the number of ace

There are 13 hearts, and 4 aces

The probability of picking a heart is;

The probability of picking an ace is;

The probability of picking an ace or a heart is the sum of both which is;

Answer:

Yes, because if you divide the two numbers, you get a whole number which means it is. Also, since the last numbers are 56, 8 can go into 56 so yes.

Step-by-step explanation:

Given in the scenario:

a.) Helen ran 15 1/4 kilometers last week.

b.) Riley ran 4 1/12 less kilometers than Helen.

c.) Derrick ran 7 3/8 more kilometers than Riley.

d.) Their goal is to run 60 kilometers in total.

To be able to determine how much further do they need to run to get 60 kilometers in total, we must first determine how many kilometers did Riley and Derrick run.

We get,

A.)

Recall: To be able to subtract mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.

The LCM of 4 and 12 is 12. We get,

Let's now proceed with the subtraction,

Conclusion: Riley ran 11 1/6 kilometers.

B.)

Recall: To be able to add mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.

The LCM of 6 and 8 is 24. We get,

Let's now proceed with the addition,

Conclusion: Derrick ran 18 13/24 kilometers.

C.) To be able to determine how much further do they need to run to get 60 kilometers in total, we subtract 60 by the sum of distance the three people ran.

We get,

The same process that we did, convert all numbers into similar fractions.

The LCM of 4, 6 and 24 is 24. We get,

Let's proceed with the operation,

Therefore, they need to run a total of 361/24 kilometers to be able to meet their goal.

Note that if plane N and plane M intersects each other in two points (say A and B) it follows that they intersects each other in the line that contains A and B. So they cannot intersect exactly in only two points. Postulate number 10

We know that a function has a unique value of y for each value in x so the correct statement is:

c. it is not a function because there are multiple y values for a given x value

This is a simple question to solve when we use the calculator (as the question allows us to use it).

For this problem when we have :

It can be read as "log base 10 of pi", and using a calculator we find:

And that is the final answer.

NOTE: this result means that:

.

-11 is an integer number

Answer:

C 109

Step-by-step explanation:

First add all the known angles inside the triangle first to get 109°

Then since all angles in a triangle add to 180°

you take away 109 from 180 so

180-109 which equals 71

Then since all angles on a straight line add up to 180°

you take 71 from 180 so

180-71 = 109

so x = 109°

The net loss from accepting the special order at a discount of 25% from the regular price, without the existence of excess capacity is $38,700.

Since Coronado Co. lacks the excess capacity for special orders, it implies that it will incur fixed costs per unit of the special order in addition to the variable costs.

Therefore, the company will incur a per unit cost of $40 ($16 + $12 + $9 + $3) while generating a revenue of $39 per unit.

This results in a loss of $1 per unit.

Selling price per unit = $52

Unit Costs:

Direct Materials = $16

Direct Labor = $12

Variable Overhead = $9 (75% of $12)

Total variable cost per unit = $37

Fixed Overhead = $3 (25% of $12)

Special order price per unit = $39 ($52 x 1 - 75%)

Contribution margin per unit = $2 ($39 - $37)

Total contribution margin = $77,400 ($2 x 38,700)

Fixed Overhead without excess capacity = $116,100 ($3 x 38,700)

Net loss = $38,700 ($77,400 - $116,100)

Thus, without excess capacity, it is inadvisable for Coronado to accept the special order at a total loss of $38,700.

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Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e

The formula to find the equation of straight line is

Substitute the values into the formula of the equation of a straight line

Solve for y i.e make y the subject

Thus, the answer is

Thus, the answer is the last option.