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## Related questions in Mathematics

### Write the ratio 42 inches to 9 feet as a fraction in simplest form

**42 : 9**

42/9 as a fraction is simplest form:

**14/3**

### Write to explain two ways you can find the sum of 3+4+5.

way 2: draw 3 tally marks then 4 more then 5 more then count them all together to get the sum 12

hope this helped:)

### A BASKETBALL STAR SHOT AT THE HOOP 388 TIMES THE BALL WENT IN 311 TIMES . WRITE A FRACTION THAT DESCRIBES THE PART OF THE TIME THAT HIS SHOTS WENT IN

### EXERCISE A one-year membership to a gym costs $725. The registration fee is $125, and the remaining amount is paid monthly. Define a variable. Then write and solve an equation to find how much new members pay each month.

### 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

### Dante is buying 5 presents at a cost of p each for his relatives. If Dante cannot spend more than $45, write an inequality that best represents this situation?

### The area of rectangle is 1936m sq. if the length is 4 times its breadth. find the dimension of the rectangle.

So, length = 4x m.

Area of the rectangle = 1936m sq.

So,

4x × x = 1936

4x^2 = 1936

x^2 = 1936/4

x^2 = 484

x = √484

x = √22×22

x = 22

Hence, breadth = 22m.

Length = (4×22)m = 88m.

### The value of Sara's new car decreases at a rate of 8% each year 1. write an exponential function to model the decrease in the car's value each month. 2. write an exponential function to model the decrease in the car's value each week. 3. write an exponential function to model the decrease in the car's value each day. 4. what relationship is there between the amount of decrease and the time interval measured

The *correct answers* are:

#1) y=(0.08/12)ˣ = 0.0067ˣ

#2) y=(0.08/52)ˣ = 0.0015ˣ

#3) y=(0.08/365.25)ˣ = 0.0002ˣ

#4) As the number for the time interval increases (more weeks than months per year, more days than weeks per year), the amount of decrease in value of the car decreases inversely.

**Explanation**:

The formula for the amount of decrease in the car is y=(r/n)ˣ, where r is the percent (written as a decimal) of decrease per year and n is the number of time periods per year.

For months, there are 12 months per year, so n = 12. The rate is 8%; 8% = 8/100 = 0.08. This gives us y=(0.08/12)ˣ. Dividing, we get y=(0.0067)ˣ.

For weeks, there are 52 weeks per year, so n = 52. The rate is still 0.08; this gives us y=(0.08/52)ˣ. Dividing, we get y=(0.0015)ˣ.

For days, there are 365.25 days per year, so n = 365.25. The rate is still 0.08; this gives us y=(0.08/365.25)ˣ. Dividing, we get y=(0.0002)ˣ.

Comparing the number of weeks to the number of months, 52/12 = 4.3. There are 4.3 times more weeks in a year than there are days. The amount of decrease from months to weeks went from 0.0067ˣ to 0.0015ˣ; 0.0015/0.0067 = 0.2234, which is close to 1/4.3.

Comparing the number of days to the number of weeks, 365.25/52 = 7.02. There are 7.02 times more days in a year than there are weeks. The amount of decrease from weeks to days went from 0.0015ˣ to 0.0002ˣ/ 0.0002/0.0015 = 0.1333, which is close to 1/7.02.

### A petting zoo has 5 lambs 11 rabbits 4 goats and 4 piglets. find the ratio of goats to the total number of animals. write the ratio in the simplest form then explain its meaning

5+11+4+4=24

Then, find the number of goats and put that into a ratio with 24

4:24

1:6

This ratio means that for every 6 animals there is 1 goat

Hope this helps :D

### 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

### 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 :)

### Jane has a checkbook balance of $68.00. She then writes two checks one for $5.00 and one for $62.50. She also deposits $75.00 then uses a. Calculator to determine her new balance which is the correct series of keys she should press

### 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)

### Write an equation that models the line that passes through the points (4,6) and (-4,8)

-4 - 4 = -8

8 - 6 = 2

Therefore the gradient of the line is -8/2 which equals -4. Now using the formula y = mx + c as a base we can substitute in one of the given points to solve for c given that we have just determined m to be -4:

y = mx + c = -4x + c

6 = -4(4) + c

6 = -16 + c

22 = c

Therefore the equation of this line is:

y = -4x + 22

### HELP MEH PLEASE =) CLICK IF U DARE! Which words in the following create bias do you want to talk to that nice salesperson or that sly salesperson A. Talk; salesperson B. nice; sly C.you;want D.This;that

A) Talk

B)nice

C) want

D) that

the statement "do you want to talk to that nice salesperson" is much more biased. it is purposely making that particular salesperson seem better than the other in a way. hope this helped! :)

### Write a numerical expression.Then write words to match the expression

Three times the sum of six plus four equals thirty

### Ages of sylvans daughters are consecutive even integers. The sum of their ages is 60. Write an equation representing and find age of each daughter.

they are

x,x+2,x+4

total sum is 60

x+x+2+x+4=60

3x+6=60

minus 6 both sides

3x=54

divide both sides by 3

x=18

x+2=20

x+4=22

the ages are

18,20,22

### Which words in the following create bias do you want to talk to that nice salesperson or that sly salesperson A. Talk; salesperson B. nice; sly C.you;want D.This;that

### At the carnival alana gave away 26 ride tickets ti her friends. She now has 57 tickets left. Let x be the number of tickets that alana started with. Write an equation describing this situation that could be used to find the value of x

Explanation: X represents your total in the problem. Then since Alana gave away 26 ride tickets that would be -26. Which means the total (x) minus the amount given away equals how many tickets she has left.

Solve:

x - 26 = 57

+ 26 +26

x = 83

Instructions:

1) You want x alone so you do the opposite of the symbol. So if it's subtracting you add, if you divide you multiply, if you multiply you divide, and if you add you subtract.

2) When you do one thing on one side you must do it to the other side.

3) So -26+26 cancel out which = 0. Add 26 with 57, 57+26=83 so on one side of the equal sign you have x and on the other side, you have 83. So

**x = 83.**

**Equation:**x - 26 = 83

I hope this was understandable. :)

### During a 10 day period the balance of Marta's checking account dropped by $290.Write a division problem during that 10-day period

### The value of the solid's surface area is equal to the value of the solid's volume. Find the value of x. (Cylinder with a radius of 2.5 cm and height of x)

V=hpir^2

SA=2pir^2+2hpir

then r=2.5 and x=? and V=SA then

xpi2.5^2=2pi2.5^2+2xpi2.5

xpi2.5^2=(2.5pi)(2*2.5+2x)

divide both sides by 2.5pi

2.5x=5+2x

minus 2x from both sides

0.5x=5

divide oth sides by 0.5

x=10

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

-x+2y=3

Multiply the second by one:

3x-4y=-5

-2x+4y=6

Combine the equations:

x = 1

Substitute x and solve for y:

-2*1+4y=6

-2+4y=6

4y=8

y=2

Answer:

(1,2)