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Answer:

3

Step-by-step explanation:

A quarter is equal to four and since 12 divided by 4 = 3, 3 months is a quarter of a year

Have a great day!

Answer:

[tex]\sqrt{x^2+y^2}-x[/tex]

Step-by-step explanation:

[tex]\textsf{Mulitply by}\quad\dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}:[/tex]

[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]

[tex]\textsf{Cancel the common factor}\:y^2:[/tex]

[tex]\implies \sqrt{x^2+y^2}-x[/tex]

Rationalising the denominator of the given fraction means we need to multiply both the numerator and the denominator of the fraction by the conjugate of the expression in the denominator. For example:

[tex]\;\longrightarrow\dfrac{1}{a+b}[/tex]

Here the conjugate of denominator of the expression is a - b. So we need to multiply both the numerator and denominator with the fraction.

[tex]\;\longrightarrow \dfrac{1}{a+b} \times \dfrac{a-b}{a-b}[/tex]

Hence, this is what the rationalization means.

We have been given and equation and we have been asked to rationalise the equation.

The conjugate of the denominator of the given equation is √(x² + y²) - x. Therefore;

[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]

[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]

[tex]\implies \boxed{\sqrt{x^2+y^2}}[/tex]

Hence, this is our required solution for this question.

For the given arithmetic sequence we have:

We know that we have 20 seats on the front row, and then we add 3 more on each row, so the formula will be:

[tex]A_n = 20 + (n - 1)*3[/tex]

This gives the number of seats on the n-th row.

B) The last row has 83 seats, then we need to solve:

[tex]A_n = 20 + (n - 1)*3 = 83\\\\(n - 1)*3 = 83 - 20 = 63\\\\n - 1 = 63/3 = 21\\\\n = 21 + 1 = 22[/tex]

So we conclude that there are 22 rows.

C) The total number of seats will be:

[tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]

D) Instead of using the sum above (we should add 22 terms) we use the general formula for the sum of N terms in an arithmetic sequence:

[tex]S_N = (N/2)*(2A_1 + (N - 1)*d)[/tex]

In this case, we replace N by 22, and d is the common difference of the sequence, which we know is equal to 3, so we wil have:

[tex]S_{22} = (22/2)*(2*20+ (22 - 1)*3) = 11*(40 + 21*3) = 1,133[/tex]

There are 1,133 seats in total.

If you want to learn more about sequences, you can read:

https://brainly.com/question/7882626

Answer:

[tex]\huge\boxed{\sf Slope = m = 5}[/tex]

Step-by-step explanation:

Given slope equation:

y = 5x + 4

Comparing it with the standard form of slope equation

y = mx + b

Where m is slope and b is y-intercept

Hence,

by comparing both equation, we get:

Slope = m = 5

[tex]\rule[225]{225}{2}[/tex]

[tex]f(x) = 3 \sqrt[3]{x} [/tex]

[tex]lim f(x) = 3 \sqrt[3]{ - \infty } = - \infty \\ x = > - \infty [/tex]

[tex]limf(x) = 3 \sqrt[3]{ \infty } = \infty \\ x = > \infty [/tex]

Answer:

As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.

Step-by-step explanation:

I got it right on the test.

Answer:

b

Step-by-step explanation:

Answer:

V = 56.52

Step-by-step explanation:

Formiula

V = (1/3) * pi * r^2 * h

Givens

pi = 3.14

r = 3 yard

h = 6 yards

Solution

V = (1/3) * 3.14 * 3^2 * 6          Multiply 1/3 * 6

V = 2 * 3.14 * 9

V = 56.52

The inequality that represents the scenario is x > 8

From the question, we understand that:

Abel ran more than 8 miles this week

Let the number of miles be x.

The text "more than" means that we make use of the greater than inequality symbol

So, the inequality that determines the steps is:

x > 8

Read more about inequality at:

https://brainly.com/question/11234618

Answer:

m

Step-by-step explanation:

Answer:

Step-by-step explanation:

I did this before. I'm 14 :D

E-

y=20x

Eli ironed 2 more hours and got 400 shirts.

S-

y=35x

Let x be the number of shirts ironed.

400/20x = 20.

20-2=18.

That means she ironed 360 shirts prior.

If both of them were at the same speed of 18 by (let x represent). Then Samantha ironed 630 shirts while Eli ironed 360 shirts, but ironed 2 more hours which got him to get 400 shirts.

Answer:

x = 1.5 or 3/2

Step-by-step explanation:

First, expand the equation.

(2x - 3)² = 0

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

In similar equations, we would solve for both pairs of parenthesis. However, since the equations inside both are the same, we only need to solve for ONE of them, bringing one correct answer.

2x - 3 = 0

Add 3 to both sides.

2x = 3

Divide both sides by 2.

x = 3/2 or 1.5.

Step-by-step explanation:

Answer: Move terms to the left side−52+3=−9−5x2+3x=−9−52+3−(−9)=0−

Common factor−52+3+9=0−5x2+3x+9=0−(52−3−9)=0

Divide both sides by the same factor−(52−3−9)=0−(5x2−3x−9)=052−3−9=0

Solution=3±321 over 10

Step-by-step explanation:

Answer: 1/3 as an equation

Step-by-step explanation: file attached

Answer:

3 1/3 yd^3

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

ft. = 1/3 yd.

3/3 = 1 yd.

6/3 = 2 yd.

5/3 = 1 2/3 yd.

1*2*1 2/3

=2* 1 2/3

=2 4/3

= 3 1/3 yd.^3

Answer:

what does a this mean? .54 is a decimal

Answer:

11² = 121

Step-by-step explanation:

When you divide powers with the same base, subtract the exponents.

[tex] \dfrac{11^6}{11^4} = 11^{6 - 4} = 11^2 = 121 [/tex]

Answer:

121

Step-by-step explanation:

11 to the 6 power = 1771561

11 to the 4 power = 14641

1771561/14641 = 121

Answer:

Step-by-step explanation:

When you square a number, whether it's positive or negative, the square is always positive.  That is, a2 is positive whether a is positive or negative.  Examples:

12 = 1 x 1 = 1

(-1)2 = (-1) x (-1) = 1

52 = 5 x 5 = 25

(-5)2 = (-5) x (-5) = 25

Since the answer is always positive, you don't need the absolute value signs: |a2| = a2.

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Explanation:

The tickmarks tell us that sides HG and FG are the same length. The triangle is isosceles. Directly from this, we know that the opposite angles F and H are congruent. Both are 4y-7 degrees.

Angle G is 90 degrees because of Thales' Theorem. This is because HF is the diameter of the circle. It's also the hypotenuse of the right triangle.

For any triangle, the three interior angles always add to 180 degrees.

F+G+H = 180

(4y-7) + (90) + (4y-7) = 180

8y + 76 = 180

8y = 180-76

8y = 104

y = 104/8

y = 13

Answer:a pair of elements a, b having the property that (a, b) = (u, v) if and only if a = u, b = v.

Answer:

9

Step-by-step explanation:

Given equation:

[tex]5 = \dfrac{x}{3} + 2[/tex]

To determine the solution (x) of the equation, we need to isolate it.  To do this, we can subtract 2 both sides of the equation.

[tex]\implies 5 - 2 = \dfrac{x}{3} + 2 - 2[/tex]

[tex]\implies 3 = \dfrac{x}{3}[/tex]

To further isolate "x", we can use cross multiplication.

[tex]\implies 3 \times 3 = x[/tex]

Finally, simplify the expression on the left-hand-side to obtain the value of x.

[tex]\implies \boxed{9 = x}[/tex]

Answer: 30%

Explanation: Every day is 30%.

- Jackson

Answer:

2/3=More

1/4=less

7/8=more

2/6=less

2/4=equal

Step-by-step explanation:

Look at each model that shows each fraction and also look at the denominators and the numerators of each fraction.

#1

Greater than 1/2

#2

Less than 1/2

#3

Greater than 1/2

#4

Less than 1/2

#5

Equal to 1/2

A fraction is equavalent to the top number divided by the bottom number.

5/8 is equivalent to 5 ÷ 8

Answer: C.  5 ÷ 8

Distance formula: sqrt((x2-x1)^2 + (y2-y1)^2)

distance = sqrt((-1 -2)^2 + (-5-5)^2)
distance = sqrt(109)

Distance = 10.44

Step-by-step explanation:

9x+5x+71+139+92=540

14x+302=540

14x=540-302=238

x=238/14

x=17

Answer:

17

Step-by-step explanation:

let the two numbers be X and Y

let larger number = Y

from the first statement

Y - X = 9 equation (1)

from the second statement

Y = 1+ 2X equation (2)

substitute equation (2) into (1)

1+2X-X = 9

1+X= 9

X = 9-1 = 8

X= 8

put X = 8 into equation (2)

Y= 1+2X

Y= 1+2(8)

Y= 1+16 = 17

larger number = 17.

Answer: 20%

Step-by-step explanation:

98 - 78.40 = $19.6

Discount is 19.6/98 = 0.2

Percentage = 0.2 × 100/ 1

The number of video games in Matthew’s collection is 12

To solve the problem, we need to know what simultaneous equations are

These are a pair of equations which contain two variables.

Now, let

Given that the number of video games in Anthony’s collection is 5 times the number in Matthew’s collection, we have that y = 5x (1)

Also, the total number of video games in both collections is 72.

So, x + y = 72 (2)

Substituting equation (1) into (2), we have

x + 5x = 72

6x = 72

x = 72/6

x = 12

So,  the number of video games in Matthew’s collection is 12

Learn more about number of video games here:

https://brainly.com/question/12452860

Answer:

2x² + 4

Step-by-step explanation:

Check out the attached photo

Answer: 17160 feet

Step-by-step explanation: Convert 3.25miles to feet. Multiply by 5280