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## Related questions in Mathematics

### 78 correct answers out of 100 test questions 39 correct answers out of 50 test questions

### A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.9 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to one decimal place.)

-4 m

____

8 m

the answer to the problem is the subtract by the 8 -4=4 isnt it the work to show

### A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when he is 50 ft from the pole?

the pole with a speed of 5 ft/s along a straight path. How fast is the tip of his shadow moving when

he is 40 ft from the pole?

Solution: USE SIMILAR TRIANGLES. Let d be the distance between the man and the pole and let x be the length of the man's shadow. Then x=(d + x) = 6=15, so 15x = 6x + 6d and 9x = 6d. Then

x = (2=3)d. The problem wants us to find d(d + x)=dt = d(d)=dx + dx=dt, since this is the speed

of the tip of his shadow. We know dx=dt = (2=3)d(d)=dt and we know d(d)=dt = 5 ft/s, from the

problem. Then d(d + x)=dt = (5=3)d(d)=dt = 25=3 ft/s.

### 3-3x6+2= we have 3 answers so far -17 -13 2 any idea's on which is correct

### Amy Is training for a half marathon. In practice, she runs 2 miles in 15 minutes. If she continues at the same rate, how many miles will she run in 1 hour ? Please answer! ❤️️❤️️

2 * 4 = 8.

she will run 8 miles in a hour.

### 15 dollars every lawn he mows. Is the amount of money proportional to the number of lawns mowed

### Please answer those three question

2- Five and two hundred and sixty seven thousandths. Hundredths.

### A square field is to be ploughed ramu gets it ploughed in rupees 34560 at the rate of 15 perm sq find the side of square field.

### Hi everybody! I hope you are doing well. I really need help on these two algebra 1 questions. I've been stuck for a whole day and I would appreciate it if it could be explained.. 1. Bradley has 3 square pieces of cardboard with each side equal to x units. For each piece, he does something different to it according to each part below:Part A: Bradley pasted rectangular strips along two adjacent sides of the cardboard to increase its length and width by y units each. What will be the change in the area of the piece of cardboard? Show your work.Part B: Bradley cut off rectangular strips from two adjacent sides of the cardboard to decrease its length and width by y units each. What will be the change in the area of the piece of cardboard? Show your work. Part C: Bradley cut off a strip from one side of the cardboard and pasted the strip on an adjacent side of the cardboard to increase its length by y units and decrease its width by y units. What will be the change in the area of the cardboard? Show your work. 2. Part A: Divide (10x^4y^3 + 5x^3y^2 - 15x^2y - 25x^2y^4) by -5x^2y. Show your work, and justify each step. Part B: How would your answer in Part A be affected if the x^2 variable in the denominator was just an x? Part C: What is the degree and classification of the polynomial you got in Part A? Even if you only have time to answer one of the questions, it would really help. Thank you so much!

Oh well, let me see what I can do.

#1:

First off. Draw 3 Squares.

Each side will have the length/width of X.

First let's find the area of a normal square.

Because Area is Base * Height we will get this:

x*x = x^2

Part A:

Alright! So we have our square, but now they add 2 strips to both sides of this square. They tell us that the length/width has increased by y. Which means that our new side is equivalent to the following expression:

X + Y

This is due to the fact that we are simply adding a new side. We haven't multiplied our length/width. So, let's examine the new area.

(x+y)*(x+y) = (x+y)^2

Now we will actually square the expression by using the FOIL method.

F - First

O - Outer

I - Inner

L - Last

Multiply the First Terms:

x*x = x^2

Multiply the Outer Terms:

x*y = xy

Multiply the Inner Terms:

y*x = xy (yx is the same as xy)

Multiply the Last Terms:

y*y = y^2

Add them all together and we have our answer!

**Area = x^2 + 2xy + y^2**

(The two xy's add together to form 2xy!)

We are not done here! Now we must find the Change in the Area. To do so we must subtract the new area and the old area. So! Let's get right to it. (Keep in mind the "old area" is the area of a square which has the length/width of X)

(New Area) - (Old Area)

(x^2 + 2xy + y^2) - (x^2)

Cancel out the like terms to get a final answer of... :

**Change in Area = 2xy + y^2**

Part B:

Same situation as the last problem! Except in this case we will be subtracting y. So our sides now look like this:

X - Y

Area = Base*Height

Both are base and height equal x-y. So we just need to multiply them together like before.

Area = (x - y)^2

Area = (x - y)(x - y)

Multiply the First Terms:

x*x = x^2

Multiply the Outer Terms:

x*-y = -xy

Multiply the Inner Terms:

-y*x = -xy

Multiply the Last Terms:

-y*-y = y^2

**Area = x^2 - 2xy + y^2**

Change in Area = x^2 -2xy + y^2 - x^2

Once again the x^2 will cancel out.

**Change in Area = -2xy + y^2**

Part C:

This is where it becomes a bit trickier. Now we have a rectangle instead of a square.

So we have two different sides.

I'll note that it doesn't matter if you say the x-y or x+y are the length or the width. As long as they are both represented it is fine.

Area = L*W

Area = (x - y)(x + y)

Multiply the First Terms:

x*x = x^2

Multiply the Outer Terms:

x*y = xy

Multiply the Inner Terms:

-y*x = -xy

Multiply the Last Terms:

-y*y = -y^2

**Area = x^2 + xy - xy + y^2**

The xy's cancel out.

Change in Area = x^2 + y^2 - x^2

You can probably guess by now, but the x^2's will cancel out once again!

**Change in Area = y^2**

#2: Part A:

(10x^4y^3 + 5x^3y^2 - 15x^2y - 25x^2y^4)/-5x^2y

We need to ask a few questions to get to our answer.

Is the constant in front of the denominator (-5) divisible by all of the constants in front of all the terms in the numerator (10 + 5 - 15 - 25)?

What variables are in the denominator? (x and y are)

Do all of the terms in the numerator have x and y?

If yes, then what is the lowest power of x? (x^2)

If yes, then what is the lowest power of y? (y)

What we have here is what we need to reduce the denominator by.

So we reduce all the constants by -5. (Divide by -5)

10/-5 = -2

5/-5 = -1

-15/-5 = 3

-25/-5 = 5

Next up is the variables.

For these we simply subtract the lowest power from all of them. (In reality we are dividing them by x^2, thus reducing

x^4/x^2 = x^2

x^3/x^2 = x

x^2/x^2 = 1

x^2/x^2 = 1

Lastly the y terms.

Same deal with the x terms.

y^3/y = y^2

y^2/y = y

y/y = 1

y^4/y = y^3

Now put them all together!

**-2x^2 -xy +3 +5y^3**

Part B:

All the x terms would be increased by 1 due to being reduce one less power.

So it'll look like this:

**-2x^3 - x^2y + 3 + 5xy^3**

Part C:

The Degree is 3, because the highest power is 3 (y^3). The classification for this is a Cubic Polynomial.

### Choose the correct solution in roster form. S is the set of prime numbers that are less than 15. A- { 2, 3, 5, 7, 11, 13 } B- { 2, 3, 5, 7, 9, 11, 13 } C- { 1, 3, 5, 7, 9, 11, 13 } D- { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 } ---------------------------------------------------------------------------------- Write the solution to the inquality in set-builder notation. 9t - 4 >32 A- { t | t > 4 } B- { t | t > 6 } C- { t | t > 28 } D- { t | t > 36 }

Mathematically speaking, roster form of a set is a list of elements that are in the set.

Basically, to represent a set in roster form, we simply list the elements of the set, separated by commas, within braces.

as per the question, consider the set, S, described verbally:

S = {all prime numbers less than 15}

To write this in roster form, we would first identify all the elements in the set. Let's see. . . the integers that are strictly greater than 0 and less than or equal to 4 would be the integers that are between 0 and 4, not including 0, but including 4, so 1, 2, 3, and 4.

Now we just write these integers, separated by commas, within braces.

** S = {2, 3, 5, 7, 11, 13}. So answer is option A**

Set notation is a representation of a set of the form {element | properties of that element}.

To represent the inequality in set builder notation, we will first have to solve for the inequality as follows:

9t - 4 >32

**Step 1: Add 4 on LHS(Left hand side) and RHS(right hand side) of the inequality.**

9t > 36

**Step 2: Divide LHS and RHS by 9**

**t > 4**

This means that the inequality holds for all values of t greater than 4 i.e.

**{ t | t > 4 }. so answer is option A**

### 1. Eric has $115 to spend on back to school clothes. So far, he has spent $90. Write an inequality to show how much more money Eric can spend. 2. Sofia has been saving money to buy a new computer. For her birthday. Sofia's mother gave her twice what she had already saved. Now she has $135 a. Using x to represent the money Sofia saved before her mother's present, write an equation that represents the situation. b. How much did Sofia have before her birthday?

115 - 90 = 25

0 >/= x =/< 25

qn2)

a)

135 = x + 2x

135 = 3x

b)

sofia saved x before her birthday:

3x = 135

× = $45

### Find the volume of cubical box . if the cost of painting of outer surface is rs 1440 at the rate rs 15 per mcube

1)We have to calculate the surface of this cubical box.

Rate=cost of painting / surface ⇒surface=cost of painting/rate

Data:

Rate=$15/m²

cost of painting=$1440

Surface=$1440/($15/m²)=96 m²

2)We find out the length of the side:

Surface of a cubical box=6(side²)

Data:

Surface of a cubical box=96 m2

Therefore:

96m²=6 (side²)

side²=96 m²/6

side²=16 m²

side=√(16 m²)=4 m

3) We find the volume of a cubical box.

volume=(side³)

volume=(4 m)³

volume=64 m³

**Answer: the volume of this cubical box would be 64 m³.**

### Jerry says that if a store has a sale for 35% off and the sale price of a stairmaster is $137, then you can figure out what the original price was by taking 35% of 137 and adding it back onto the $137. So the original price should be $184.95. But that answer doesn't check. Why

### How do I solve for x ?X +8=-15

### On an architect's drawing of the floor plan for a house, 1 inch represents 3 feet if a room is represented on the floor plan by a rectangle that has sides of length 3.5 inches and 5 inches, what is the actual floor area of the room in square feet?

5×3=15

15×10.5=157.5 square feet

### Help help help please.....A financial planner wants to invest $8,000, some in high risk stocks earning 15% annually and the rest in safer mutual funds earning 6% annually. How much should be invested at each rate to get a return of $930 annually from the two investment?

### Area and circumference of a circle with a diameter of 2. Use the value 3.14 for pie and do not round your answers.

Given that we know that Pi is the number of times the diameter fits into the circumference, we can come up with the formula that:

Pi = circumference/diameter

Now that we know this we can rearrange and substitute your values like so:

Circumference = Pi x Diameter

Circ. = 3.14 x 2 = 6.28

Therefore 6.28 is the circumference of this circle :)

### Choose the statement that best describes the value of 7 4 √ 74 square root of, 74, end square root. Choose 1 answer. Choose 1 answer. The value of 7 4 √ 74 square root of, 74, end square root is between 8 88 and 8 . 5 8.58, point, 5. The value of 7 4 √ 74 square root of, 74, end square root is between 8 . 5 8.58, point, 5 and 9 99. The value of 7 4 √ 74 square root of, 74, end square root is between 9 99 and 9 . 5 9.59, point, 5. The value of 7 4 √ 74 square root of, 74, end square root is between 9 . 5 9.59, point, 5 and 1 0 1010.

### Find the perimeter of the polygon. 14 ft, 15 ft, 7 ft, and 11 ft.

### Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.96 with a standard deviation of $0.12. Using Chebyshev's Theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.72 and $4.20? Round your answer to one decimal place.

**Answer:**

25%

**Step-by-step explanation:**

Given that prices of a gallon of milk at various stores in one town have a mean of $3.96 with a standard deviation of $0.12.

When sales lie between 3.72 and 4.20 dollars we get

we have 3.72 = 3.96-2 (0.12) and

4.20 = 3.96+2(0.12)

Hence simply we can write

i.e. 25% is the minimum percentage of stores that sell a gallon of milk for between $3.72 and $4.20

### Solve. x-3y+2z=1 -x+4y-4z=1 5x-y+6z=9 Write answer in the form (x,y,z).

-1x + 4y - 4z = 1 → -1x + 4y - 4z = 1

5x - 1y + 6z = 9 → y - 2z = 2

1x - 3y + 2z = 1

-1x + 4y - 4z = 1 → -1x + 4y - 4z = 1 → -5x + 20y - 20z = 5

5x - 1y + 6z = 9 → 5x - 2y + 6z = 9 → 5x - 1y + 6z = 9

19y - 14z = 14

y - 2z = 2 → 19y - 38z = 38

19y - 14z = 14 → 19y - 14z = 14

-24z = 24

-24 -24

z = -1

y - 2z = 2

y - 2(-1) = 2

y + 2 = 2

- 2 - 2

y = 0

x - 3y + 2z = 1

x - 3(0) + 2(-1) = 1

x - 0 - 2 = 1

x - 2 = 1

+ 2 + 2

x = 3

(x, y, z) = (3, 0, -1)

### Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.96 with a standard deviation of $0.12. Using Chebyshev's Theorem what is the minimum percentage of stores that sell a gallon of milk for between $3.72 and $4.20? Round your answer.

Side note that is crazy expensive milk.

### A line passes through (−1, 5) and (1, 3) Which answer is the equation of the line? A.x + 2y = 7 B. x + y = 4 C. x + y = 2 D.x + 2y = 5

### Estimate this plz :52,851+65,601=118452.....Sooo...whats the estimate answer???

### Book covers are brought in for the seventh-grade students. The 180 book covers will be shared equally by 4 classes. If each class has 15 students, how many book covers would each student get?

180/60= 3 (180 book covers divided among 60 students)

Each student gets

**3**covers.

### You are making a banner. You have a sheet of paper that is 2 m wide and want to leave a 35-cm blank margin on either side. How many centimeters can you use for text?

Ok you have 200 cm of paper. Each side needs 35 cm for a margin so:

35 + 35 = 70.

Then subtract 70 from 200 and you are left with 130 cm of space left for text.