A rectangle has a perimeter of 144 inches. The width of the rectangle is 12 inches less than the length. What is the width, in inches, of the rectangle?

Both A and B represent functions, as the same x value is not used twice.

However, with option C, the x value -2 is used twice, and thus it is not a function.

The concept of functions in mathematics is determined by whether each input (or 'x' value) corresponds to exactly one output (or 'y' value). Upon examination, the sets of ordered pairs in option A qualify as functions, while the sets in options B and C do not.

A function in Mathematics is a relation between a set of inputs and a set of outputs where each input is related to exactly one output. In your question, you have three different sets of ordered pairs. Let's examine them.

A. [(-2,3)], [(-1,5)], [(0,7)], [(1,9)]

Here every 'x' value is paired with only one 'y' value, so this one is a function.

B. [(-3,3)], [(3,3)], [(0,0)], [(1,1)], [(-1,1)]

For this one, we see that 'x' values -1 and 1 are both paired with 'y' value 1. This implies that a single 'x' value has more than one 'y' value which is not allowed for a function. So this one is not a function.

C. [(-2,5)], [(-1,4)], [(0,3)], [(-1,2)], [(-2,1)]

This one is similar to the second case where 'x' values -1 and -2 are both paired with multiple 'y' values. So, this one is not a function either.

So, only the first set constitutes a function.

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In Simplest form your answer is: [tex]\frac{57}{20}[/tex] and as a mixed number is 2 [tex]\frac{17}{20}[/tex]

We can use the number line as a model to help us visualize adding and subtracting of signed integers. Just think of addition and subtraction as directions on the number line. There are also several rules and properties that define how to perform these basic operations.

To add integers having the same sign, keep the same sign and add the absolute value of each number.

To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest.

Subtract an integer by adding its opposite.

answer: well i thing subtracting and adding integers are related because they  both can be solved using an number line

Answer:

A) 0 to 100 mph

Step-by-step explanation:

the range would be the mpg, and domain would be speed.

That would be the best presentation.

[tex]\overline{NP}\ ||\ \overline{AB}\\\\\overline{JI}\ ||\ \overline{PN}[/tex]

The slope of a graph is the rate of change of the graph

The slope of the graph is that passes through (0,2) and (1,-2) is (d) -4

Start by selecting any two points on the line of the graph

[tex](x_1,y_1) = (0,2)[/tex]

[tex](x_2,y_2) = (1,-2)[/tex]

The slope (m) of the graph is simply the average rate of change of the graph.

It is calculated as follows:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substitute values for x and y

[tex]m = \frac{-2-2}{1 - 0}[/tex]

Simplify

[tex]m = \frac{-4}{1}[/tex]

Divide

[tex]m = -4[/tex]

Hence, the slope of the graph is -4

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There are 7/4 gallons leaking per hour. This is the same as 1.75 gallons per hour. Hope this helps! :)

Answer:

[tex]1\frac{3}{4}[/tex] gallons of water will be leaked in one hour.

Step-by-step explanation:

An above ground pool is leaking [tex]\frac{7}{8}[/tex] gallon of water in half an hour.

Therefore, amount of water leaked in one hour will be = 2 × (amount of water leaked in half an hour)

= [tex]2\times \frac{7}{8}[/tex]

= [tex]\frac{7}{4}[/tex]

= [tex]1\frac{3}{4}[/tex] gallons

Therefore, [tex]1\frac{3}{4}[/tex] gallons of water will be leaked in one hour.

-2/3(2x-1/2) ≤1/5x-1

Simplify the left side:

-4/3x+1/3 ≤1/5x-1

Subtract 1/5x from each side:

-23/15x + 1/3≤-1

Subtract 1/3 from each side:

-23/15x ≤-4/3

Divide both sides by -23/15:

X = -4/3 / -23/15

X ≥ 20/23

Convert to interval notation:

[ 20/23 , ∞)

Hey there!!

Given equation :

... 5n + 30 - 17n - ( -12n )

... 5n + 30 -17n + 12n

... 5n + 30 - 5n

... 30

The answer is 30...

Hope my answer helps!!

Solving for n, we find that n equals 3.5 or 7/2.

Simplify the equation by removing the parentheses,
5n + 30 - 17n - (-12)

5n + 30 - 17n + 12.

5n - 17n =30 + 12.

-12n + 42 = 0.

-12n = -42.

n = 42 / 12.

n = 7 / 2 or n = 3.5.

Answer:

Part 1) Option C. Same side interior angles

Part 2) Option A. [tex](3x+4)+(2x+11)=180\°[/tex]

Part 3) Option B. [tex]m<5=77\°[/tex]

Step-by-step explanation:

Part 1) we know that

If p and q are parallel

then

m<3 and m<5 are consecutive interior angles or Same side interior angles

and

[tex]m<3+m<5=180\°[/tex]

Part 2) we know that

[tex]m<3+m<5=180\°[/tex] -----> by consecutive interior angles (supplementary angles)

we have that

[tex]m<3=(3x+4)[/tex]

[tex]m<5=(2x+11)[/tex]

so

substitute

[tex](3x+4)+(2x+11)=180\°[/tex]

Part 3) Find the measure of angle 5

we know that

[tex](3x+4)+(2x+11)=180\°[/tex]

Solve for x

[tex]5x+15\°=180\°[/tex]

[tex]5x=180\°-15\°[/tex]

[tex]x=165\°/5\°=33\°[/tex]

[tex]m<5=(2x+11)[/tex]

substitute the value of x

[tex]m<5=(2(33)+11)=77\°[/tex]

Answer: C, A, B

Step-by-step explanation:

Al bought 24 stickers, gave away 11, then bought 8 more. The numerical expression representing this situation is '24 - 11 + 8'.

The word problem describes Al's activity concerning stickers. To turn the words into a numerical expression, each operation performed by him needs to be included. Initially, Al bought 24 stickers. Then, he gave away 11 stickers. Lastly, he bought 8 more stickers. By using these actions as a guide, the equivalent numerical expression would be '24 - 11 + 8'.

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Hello!

Here is how we solve this question.

We know that 2 shoes = 1 pair

So we subtract 2 from 16 until we reach 0, and count how many times we subtracted.

16-2=14

14-2=12

12-2=10

10-2=8

8-2=6

6-2=4

4-2=2

2-2=0

After we do repeated subtraction we find that Abigail has 8 pairs of shoes!

Hope this helps you with your question.

Since shoes comes in pairs, then the number of shoes Abigael has would be obtained by subtracting 2 from 16 until we obtain 0. Hence, the number of shoes she has is 8.

The total number of shoes = 16

Shoes are in pairs ; Hence 1 pair of shoe = 2 shoes

Using repeated subtraction :

1 ; 16 - 2 = 14

2 ; 14 - 2 = 12

3; 12 - 2 = 10

4; 10 - 2 = 8

5; 8 - 2 = 6

6; 6 - 2 = 4

7; 4 - 2 = 2

8; 2 - 2 = 0

Therefore, the Number of shoes Abigael has is 8

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y = 3x + 21  that's the answer

The dimension of dresser is :

Length is 6.0 feet

width is 3.0 feet

The dimension of bed is :

Length is [tex]5\sqrt{2}[/tex] = 7.1 feet

Width is [tex]4\sqrt{2}[/tex]  = 5.7 feet

The dimension of table:

Length is [tex]2\sqrt{2}[/tex] = 2.8 feet

Width is [tex]2\sqrt{2}[/tex] = 2.8 feet

Answer:

A). Dimensions of the bed = 7.1 ft × 5.7 ft

B). Dimensions of table = 2.8 ft × 2.8 ft

C). Dimensions of the dresser = 6ft × 3ft

Step-by-step explanation:

Dimensions of the room are 14 ft by 10 ft.

We have to find the dimensions of each furniture.

First we take the bed.

Length of the bed = [tex]\sqrt{(5)^{2}+(5)^{2}}[/tex]

= [tex]\sqrt{25+25}[/tex]

= [tex]\sqrt{50}[/tex]

= 7.07 ft ≈ 7.1 ft

Width of the bed = [tex]\sqrt{4^{2}+4^{2}}[/tex]

= [tex]\sqrt{16+16}[/tex]

= [tex]\sqrt{32}[/tex]

= 5.7 ft

We take another furniture table which is in the square shape,

Side of the table = [tex]\sqrt{2^{2}+2^{2}}[/tex]

= [tex]\sqrt{8}[/tex]

= 2.8 ft

Therefore, each side of the table is 2.8 ft

Length of the dresser = 6 ft

Width of the dresser = 3 ft

The question is asking for a decimal number between 200 and 300 with '7' in the thousandths place and '2' in the hundredths place. One possible answer is 250.027, but other variations exist based on the whole number part as long as it is between 200 and 300.

The student's question is asking for a specific decimal number between 200 and 300. The conditions set are that the number should have '7' in the thousandths place, and '2' in the hundredths place. Since there are no conditions for the other places, these digits could be any whole number.

One possible answer could be 250.027. We have '2' in the hundredths place (right after the decimal point), '7' in the thousandths place (two spots after the decimal point), and the whole number part is between 200 and 300. Other possibilities exist too, like 267.327 or 280.217.

This question could relate to a topic like Place Value Decomposition where students learn to read, write, and understand the value of each digit in a decimal number.

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As all angles of the triangle have to give 180 ° and, as the triangle is equilateral (all the angles are equal), the three angles have the same amplitude. 180 ÷ 3 = 60

So, the answer is D.

The measure of angle a (x) is 60 degrees when all sides of triangle are equal The correct answer is option D: 60°.

Since all three sides of the triangle ABC have equal lengths (15 units each), we can determine that this is an equilateral triangle. In an equilateral triangle, all three angles are congruent, meaning they have the same measure.

Let's represent the measure of angle a as "x."

In an equilateral triangle, the sum of all three angles is 180 degrees. So, we can write the equation:

x + x + x = 180

Combine like terms:

3x = 180

Now, divide by 3 to solve for x:

x = 180 / 3

x = 60

Therefore, the measure of angle a (x) is 60 degrees.

The correct answer is option D: 60°.

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y = 6x is your answer.  

ANSWER

The vertical asymptotes are

[tex]\Rightarrow x=2\:or\:x=-1[/tex]

EXPLANATION

We have

[tex]f(x)=\frac{x^2+4}{4x^2-4x-8}[/tex]

For vertical asymptotes we set the denominator to zero and solve the quadratic equation;

[tex]4x^2-4x-8=0[/tex]

[tex]\Rightarrow x^2-x-2=0[/tex]

We split the middle term to obtain,

[tex]x^2+x-2x-2=0[/tex]

[tex]\Rightarrow x(x+1)-2(x+1)=0[/tex]

[tex]\Rightarrow (x-2)(x+1)=0[/tex]

[tex]\Rightarrow x=2\:or\:x=-1[/tex]

Therefore the vertical asymptotes are

[tex]x=2\:or\:x=-1[/tex]

The vertical asymptotes are x = 2 and x = -1

[tex]f(x)=\frac{x^2+4}{4x^2-4x-8}[/tex]

Set the denominator to 0

[tex]4x^2-4x-8 = 0[/tex]

Divide through by 4

[tex]x^2-x-2 = 0[/tex]

Expand

[tex]x^2+x-2x-2 = 0[/tex]

Factorize

[tex]x(x+1)-2(x+1) = 0[/tex]

Factor out x + 1

[tex](x-2)(x+1) = 0[/tex]

Solve for x

x = 2 or x = -1

Hence, the vertical asymptotes are x = 2 and x = -1

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26 and 27.

Consecutive numbers are pairs of numbers like 1 and 2 or 5 and 6. One number right after the other to equal the whole number. Subtract 1 from 53 to get 52 then divide 52 by 2 to get 26. Then just add the 1 back on to get 26 and 27 to equal 53.

Hope this helped! :)

The formula for probability is [tex]\frac{number of ideal outcomes}{number of possible outcomes}[/tex]. Because there are 8 $20 bills, there are 8 ideal outcomes and 20 possible outcomes. THis gives us [tex]\frac{8}{20}[/tex] which can be simplified to [tex]\frac{2}{5}[/tex].

The answer is 2/5 or 0.4 or 40%.

Answer:

2/5

Explanation:

There are 5+7+8 = 20 total bills.

Out of these, 8 are twenty-dollar bills.

The probability of choosing 1 twenty-dollar bill is then 8/20, which simplifies to 2/5.

He is paid 180 dollars for that day

[tex]\$62\cdot0.2=\$12.40[/tex]

[tex]\$62-\$12.40=$49.60[/tex]

Answer:

175 %

Step-by-step explanation:

7/4 = (7/4)* 100

= 700 / 4

=  175 %

The answer is 175% I think

The answer is

3 + i √21 all divided by 3

3 + i √21/3

Hope I helped! :)

Mark brainliest

Answer,

- 1 1/4

Hope this helps :-)

1) The solution of expression is, x = - 6

2) The solution is, - 26

We have to give that,

1) An expression is,

3x - 6 = 7x + 18

2) An expression,

65 - 4² (10 - 2) + 37

Now, Simplify the expressions as,

1) 3x - 6 = 7x + 18

Add 6 on both sides,

3x - 6 + 6 = 7x + 18 + 6

3x = 7x + 24

Subtract 7x on both sides,

3x - 7x = 24

- 4x = 24

Divide both sides by - 4,

x = - 24/4

x = - 6

Hence, Solution is, x = - 6

2) 65 - 4² (10 - 2) + 37

Apply the BODMAS rule,

65 - 16 (8) + 37

65 - 128 + 37

65 + 37 - 128

102 - 128

- 26

Therefore, the Solution is, - 26

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This means it has infinite solutions congrats. When solving algebraic equations you can find one solution, no solutions. When you have infinite solutions that means that equations has multiple things that can equal it.

If the equation 0=0, then its solution is that x can take any real value.

The given equation is 0=0.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

We obtain 0=0, this means the equation is in fact an identity which is true for all values of x. As an equation, its solution is that x can take any real value (assuming we are supposed to be finding real solutions).

Therefore, if the equation 0=0, then its solution is that x can take any real value.

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If a page costs 3.50 and there are 500 pages, all you have to do to get your answer is multiply these 2 numbers,

The answer is 1750