11. Tom borrowed some money from his father seven months ago. Every month,
he pays back $400 to his father. Currently, he owes $2,500.
a) How much will he owe his father three months from now?
b) How much money did he borrow from his father?

Answer:

A = 15

B = 3

Step-by-step explanation:

Since Team A has 12 more points than team B, then,

A - 12 = B

A = B + 12 ( equation 1 )

team A has 5 times as many points as team B, so,

5B = A. ( equation 2 )

Substitute equation 1 into equation 2

A = B + 12

5B = B + 12

5B - B = 12

4B = 12

B = 3

we'll substitute the answer into equation 2

5B = A

5(3) = A

A = 15

I hope this helps :D

have a nice day dear...

Answer:

1 4/10

Step-by-step explanation:

3 1/2 turns into 3 5/10 minus 4 9/10 blah blah blah anyways yeah

Answer:

1000-0=1/2(2000-0)

y= 1/2x

-1x + 2y = 0

If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank is; $937,500.

This is about the concept of compound interest which is defined as the interest on savings that is calculated on both the initial principal and the accumulated interest from previous periods.

From the question, let us make x to represent the amount of cash.

Now, we are told that one portion of it pays 0.5%and as such this will be 0.005x.

Now, the other portion pays 3.5% and as such this is 0.035x.

Combining both knowing that the total the company earned in the last year was $37,500 and we have;

0.005x + 0.035x = 37500

0.040x = 37500

Solve for x to get;

x = (37500)/(0.04)

x = 937500

Therefore, the company started with $937,500.

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Answer:

Option F

Step-by-step explanation:

According to given information

1) You had F fruits and took 4 pieces out of a bag, it is:

2) Then you have 12 pieces of fruit remained:

This equation matches the answer choice F.

answer: 3 to 5 = 6 to 10 = 9 to 15

so the answer would be 6 raisins

Answer:

3x+4x=10x=10/7=1.42

Step-by-step explanation:

3x+4x=10x

7x=10x

10/7=

1.42

Answer: Around 10 sixth graders would get free lunch.

Step-by-step explanation: first, divide 500/25 to find the percentage of students receiving free lunches. You should get 0.05, or 5%. Then, multiply the number of sixth graders (203) by 5%. Your answer is 10.15, rounded down to 10. (Because it is impossible to have 0.15 of a student)

The rate of change in enrollment from 2010 to 2020 is -53 students per year.

Interpretation:

A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.

Here, we have,

To find the rate of change in enrollment from 2010 to 2020, we can use the formula for calculating the rate of change:

Rate of change = (Change in enrollment) / (Time interval)

Where:

Change in enrollment = Enrollment in 2020 - Enrollment in 2010

Time interval = Year in 2020 - Year in 2010

Let's calculate the rate of change:

Change in enrollment = 715 - 1245 = -530

Time interval = 2020 - 2010 = 10 years

Rate of change = (-530) / 10 = -53

The rate of change in enrollment from 2010 to 2020 is -53 students per year.

Interpretation:

A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.

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The first number in the range of the function is 7

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The function is given as

f(x) = -2x - 3

Also, we have the domain to be

(-5,-1,3,5)

The first value in this domain is

x = -5

So, we have

f(-5) = -2 x -5 - 3

Evaluate

f(-5) = 7

This represents the first number in the range

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The formula for the volume of a sphere is 4/3πr³. The formula for r is d/2. We know d, so we can substitute this for r.

4/3(3.14)(32/2)^3
4/3(3.14)(16)^3
4/3(3.14)4096
4.19(4096
17612.24 cm^3

[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ the\ diameter\ to\ radius\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Finding\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]

price change: 125 - 200 = -75 coins

percent of change = price change/original price *100 = -75/200*100 = -37.5%

that is, a discount of 37.5%

Answer:

Step-by-step explanation:

Find the volume of the metal as following:

Find the mass:

Answer:

3619.1 grams (nearest tenth)

Step-by-step explanation:

Volume of a cylinder

[tex]V=\pi r^2 h[/tex]

where:

The radius of a circle is half its diameter.

Find the volumes of the external and internal cylinders by substituting the given values into the formula for volume of a cylinder:

[tex]\implies \textsf{Volume of the external cylinder}&=\pi \cdot 5^2 \cdot 16=400 \pi \; \sf cm^3[/tex]

[tex]\implies \textsf{Volume of the internal cylinder}&=\pi \cdot 4^2 \cdot 16=256 \pi \; \sf cm^3[/tex]

Find the volume of the cylindrical hollow metal pipe by subtracting the volume of the internal cylinder from the volume of the external cylinder:

[tex]\begin{aligned}\implies \textsf{Volume of the metal pipe}&=\sf Volume_{external}-Volume_{internal}\\&=400 \pi - 256 \pi\\& = 144 \pi \sf \; cm^3\end{aligned}[/tex]

Density formula

[tex]\rho=\dfrac{m}{V}[/tex]

where:

Given:

Substitute the given values of density and the found volume into the density formula and solve for m:

[tex]\begin{aligned}\implies \rho&=\dfrac{m}{V}\\8&=\dfrac{m}{144 \pi}\\m&=8 \cdot 144\pi\\m&=1152 \pi \\m&=3619.11473...\\m&=3619.1\; \sf g \;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the mass of the pipe is 3619.1 grams (nearest tenth).

Note: I have used the exact value of π (not a rounded value).

The number of seats in Section A is 26000 ,The number of seats in Section B is 14800 and, The number of seats in Section C is 11200.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Let the number of seats in Section A is "a".

Let the number of seats in Section B is "b".

and, Let the number of seats in Section C is "c".

Now using the statement "stadium has 52,000 seats"

we can make equation: a + b + c = 52000  

Now using the statement "Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C" and "stadium takes in$1,307,200 from each sold out event".

we can make equation: 28a + 24b + 20c = $1,307,200

Now using the statement "he number of seats in Section A equals the total number of seats in Sections b and C"

we can make equation: a = b + c

Solving these three equations. We get,

a = 26000 , b = 14800 and c = 11200

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i solved it

you graph it :)

Answer:

x^3

Step-by-step explanation:

Because they are the same base in a division question, you subtract the exponents.

5-2=3.

Answer = x^3

Hope this helps!

Btw, if this is right, please give me brainliest, thanks!

Answer:

x^3

Cancel the common factor of x^5 and x^2.

Hope you have a wonderful day :)

Answer:

A. 3

Step-by-step explanation:

45 + 15 + 25 = 85

There are 85 flowers.

There are 25 roses, 45 tulips, an 15 roses.

What are all 3 of these divisible by?

5!

That means that there will be 5 bouquets.

Let's divide each number by 5 to find out how many of each type of flower is in each bouquet.

25/5 = 5

5 roses in each bouquet

45/5 = 9

9 tulips in each bouquet

15/5 = 3

3 snapdragons in each bouquet

5 + 9 + 3 = 17

There are a total of 17 flowers in each bouquet.

Out of those 17 flowers, 3 are snapdragons.

A. 3

Answer:

x = 6

Step-by-step explanation:

5x - 9 = 3x + 3 ( subtract 3x from both sides )

2x - 9 = 3 ( add 9 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

The standard equation is 7x + y = 9

layoff Ax + By = C is the usual form for two-variable direct equations. A standard form direct equation is, for case, 2x + 3y = 5. When an equation is given in this format, chancing both intercepts is rather simple( x and y). When trying to break systems involving two direct equations, this form is also relatively helpful.

Given

7x + 3 = 5 and y - 1 = 6

Add the bottoms from the two given equations to produce a single standard-form equation.

By shifting the constant fromR.H.S. toL.H.S., the equations are reset to zero.

7x + 3 - 5 = 0

7x - 2 = 0----( 1)

y - 1 = 6

y - 1 - 6 = 0

y - 7 = 0-----( 2)

Equation 1 and equation 2 must be combined.

7x - 2 + y - 7 = 0

7x + y - 9 = 0

layoff Ax + By = C is the equation's conventional form.

A, B, and C are integers and x and y are variables in this type of equation.

Accordingly, the common equation is

7x + y - 9 = 0

7x + y = 9

therefore the standard equation is 7x + y = 9

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Answer:

x = 10

Step-by-step explanation:

The internal angles of a triangle sum 180°

74° + 45°+ (8x-19)° = 180°

119 + 8x - 19 = 180

119 - 19 + 8x = 180

100 + 8x = 180

8x = 180 - 100

8x = 80

x = 80/8

x = 10

Check:

74 + 45 + (8x-19) = 180

1100 + 8*10 = 180

100 + 80 = 180

The relation that represents a function is the mapping in: B.

A relation is defined as a function if each of the x-value (domain element of input) in the relation corresponds to exactly one y-value (range element of output).

The relation in option A is not a function because it has two different y-values, 7 and 5 that corresponds to an x-value, 6. The relations in option C and D do not represent a function also.

The mapping in option B shows a relation where each x-value (domain element) is related or corresponds to only one y-value (range element). Therefore, it is a function.

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Answer:

x=4

Step-by-step explanation:

first, you have to add all of the sides up:

x+2x+x+3x+7+5x-4=12x+7-4=12x+3

12x+3=51. now, we can subtract 3 from both sides, so that we can isolate x.

     -3  -3

12x=48

x=4

By multiplying 2 on both the numerator and denominator of  [tex]\frac{-3}{5}[/tex] .

The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as

[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]

A fraction is written with a numerator and a denominator where the numerator is less than the denominator.

Example: 1/3 is a fraction

We have,

[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex]

We have different denominators and we need to make the denominator the same.

We will multiply 2 on both the numerator and denominator of  [tex]\frac{-3}{5}[/tex].

= [tex]\frac{2 \times -3}{2 \times 5}[/tex]

= [tex]\frac{-6}{10}[/tex]

We see that,

The denominator in [tex]\frac{-6}{10}[/tex]  and [tex]\frac{-7}{10}[/tex]  is the same.

i.e 10.

Now,

[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] can be written as [tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]

Thus,

By multiplying 2 on both the numerator and denominator of  [tex]\frac{-3}{5}[/tex] .

The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as

[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]

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The statement that is true about what D’Neese said is (d) D’Neese is incorrect because a^-n = a/-n

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation statement is given as

1/10^5 is equivalent to 10^5

The above statement can be rewritten in another way

So, we have the following equation

1/10^5 = 10^5

As a general rule of indices, we have the following exponent rule

So, we have the following equation

1/a^n = a^-n

This means that the equation statement is false

This is so because

1/10^5 is not equivalent to 10^5, instead 1/10^5 is equivalent to 10^-5

Hence, the true option about the statement is (d)

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Answer:

x = 1 ± √3

Step-by-step explanation:

    x² - 2x - 2

Co-efficient of x² = a = 1

Co-efficient of x = b = -2

Constant = c = -2

 D = b² - 4ac

     = (-2)² - 4 *1*(-2)

     = 4 + 8

     = 12

       [tex]\sf x = \dfrac{-b \ \± \sqrt{D}}{2a}[/tex]

           [tex]\sf = \dfrac{2 \ \± \sqrt{12}}{2*1}\\\\\\=\dfrac{2 \± \sqrt{2*2*3}}{2}\\\\\\= \dfrac{2 \±2\sqrt{3}}{2}\\\\\\= \dfrac{2}{2} \± \dfrac{2\sqrt{3}}{2}\\\\\\= 1 \± \sqrt{3}[/tex]

[tex]\sf x = 1 + \sqrt{3} ; \ ; or \ x = 1 - \sqrt{3}[/tex]

The amount of interest would be $8.4 Charis received at the end of two years.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

We have been given data as:

Principal (P) = $140

Rate of Interest (R) = 3% = 3/100 = 0.03

Time (T) = 2 years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

⇒ Simple interest = 140 × 0.03 × 2

⇒ Simple interest = $8.4

Therefore, the amount of interest would be $8.4 Charis received at the end of two years.

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The missing co-ordinate r = 8

(6,9) and (r,-1) are two points on a line whose slope is given as -5.

Slope of a line is the change of y co-ordinates divided by the change in x co-ordinates between two points on a line.

Take (x₁, y₁) = (6,9) and (x₂, y₂) = (r, -1).

The slope of a line is given by,

Slope, m = (y₂-y₁)/ (x₂-x₁)

⇒  -5 = (-1-9)/(r-6)

⇒ -5 = -10/(r-6)

⇒ 1 = 2/(r-6)

⇒ r-6 = 2

⇒ r = 2+6

⇒ r = 8

So the points are (6,9) and (8,-1).

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Answer:

1. False, 2. False, 3. False

Step-by-step explanation:

Answer: 9, 144, 225, 10,000

Step-by-step explanation:

9=3x3

144=12x12

225=15x15

10,000=100x100