The given lengths are two sides of a right triangle. All three sides of the triangle form a Pythagorean Triple. Find the length of the third side and tell whether it is a leg or the hypotenuse. 9 and 41

We know that:

                      x = 10 + y

In the next equation {-3x + y = -28}  x is the same as the first, so:

-3(10 + y) + y = -28

-30 - 3y + y = -28

-30 - 2y = -28            

We add 30 to both sides:

-2y = 2

and divide both sides by (-2):

y = -1

Now we can put y = -1 to the first equation:

  x = 10 + y

  x = 10 - 1

   x = 9

So,

The inverse of the given function is (f^-1)(x) = (1/2)×(√x  - 1) for x ≥ 0.

We are given a function f(x). The function f(x) is defined as (2x + 1)². The domain of the given function f(x) is x ≥ -1/2. We need to find the inverse of the function f(x).

Let us suppose that the function f(x) is represented by the variable "y".

y = f(x)

y = (2x + 1)²

Now we will take the square root on both sides of the equation.

√y = √[(2x + 1)²]

When we cancel out the even powers, we need to take the absolute value using modulus.

√y = |2x + 1|

We already know that x ≥ -1/2, so, modulus will open with a positive sign.

√y = +(2x + 1)

√y = 2x + 1

√y  - 1 = 2x

x = (1/2)×(√y  - 1)

At last, we replace the variables y and x by x and (f^-1)(x).

(f^-1)(x) = (1/2)×(√x  - 1) for x ≥ 0

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12x³ - 39x² -   111x + 30 is polynomial in standard form .

What in mathematics is a polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents.

standard form g(x) = 3(x + 2)(4x - 1)(x - 5)

                      g(X) = 3[ 4x² - x + 8x - 2 )( x - 5 ) ]

                             = 3[ ( 4x² + 7x - 2 ) ( x - 5 )]

                             = 3 [ 4x³ + 7x² - 2x - 20x² - 35x + 10 )]

                             = 3[ 4x³ - 13x² - 37x + 10 ]

                             = 12x³ - 39x² -   111x + 30

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The price of one sweater - x

The price of one shirt - y

From what the problem states, we can assume:

x + 4y = 55

4x + 5y = 110

Multiply both sides of x +4y = 55 by four. This results in 4x + 16y = 220. We then subtract 16y on both sides, resulting in 4x = 220 - 16y. We then insert this into the other equation, which, as a reminder, is 4x + 5y = 110. We replace 4x with 220 - 16y, which results in 220 - 16y + 5y = 110. Now, we can solve it.

Now that we have found out the value of y, we can replace all instances of y in the first equation.

Answer:

Step-by-step explanation

TS=13 as opp sides in an isosceles triangle are equal

AngleT=60

as 60+60+T=180

According to the Pythagoras theorem, the value of the slope of the ramp is 10.44

Pythagoras theorem

Pythagoras theorem states that the sum of squares of the sides equal to the square of the hypotenuse.

The general form of the Pythagoras theorem is,

c² =  a² + b²

where

c refers the hypotenuse

a and b refers the sides of the triangle.

Given,

Here we have the ramp with the side values 3 and 10.

Now, we have to find the value of the slope.

Let us consider x be the hypotenuse or slope of the ramp.

We know that the Pythagoras theorem states that the square of the hypotenuse is equal to the sum of square of the sides.

So, it can be written based on these,

x² = 3² + 10²

x² = 9 + 100

x² = 109

x = √109

When we simplify this one then we get the value of slope as 10.44.

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Answer:

100%

Step-by-step explanation:

If all 27 votes for hunger relief, that would be 100% or all of them.

Answer:

0.3144654088

Step-by-step explanation:

6/19.08=0.3144654088

To determine what satisfying assumptions 1-3 would mean by considering the variable under consideration.

The regression-inference Assumptions 1-3 must be satisfied if β°, β¹ and σ are constants, which ensures the x dimensions and price of every custom home to be normal, with β° + β¹ and a σ standard deviation.

The residuals should not be linear if the normal probability plot is followed.

In the diagram above, the assumptions for regression inferences appear to be unsatisfactory.

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Answer:

9:5

5:14

Step-by-step explanation:

Answer:

5u - 4u = 1u

1u = 15

9u = 135

∴ Both girls have 135 yo-yos together.

Answer:

======================

Sum of interior angles of 6-sides polygon is:

Set equation for the sum of interior angles and solve for x:

Find the measure of angle L:

Correct choice is C.

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\[-0.35em] ~\dotfill\\\\ (120)+(8x)+(6x-7)+\stackrel{\measuredangle L}{(7x-3)}+(5x)+\stackrel{\measuredangle O}{(90)}=720\implies 26x+200=720 \\\\\\ 26x=520\implies x=\cfrac{520}{26}\implies x=20~\hfill \underset{\measuredangle L}{\stackrel{7(20)~~ - ~~3}{\text{\LARGE 137}}}[/tex]

Answer:

8

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

[tex]\frac{A'B'}{12}=\frac{4}{6} \implies A'B'=8[/tex]

We must combine 3 servings of Ta-sty Pocket, 2 serving of P-ita Roll, and 1 serving of In-sta Pancake to get 754 calories, 19.2 g of f-at, and 78.9 g of carbohydrates.

According to the question,

Three brands of breakfast food represents the calories , f-at, and carbohydrates.

To get 754 calories, we should combine

= 450 + 238 + 66

= 3 (150) + 2 ( 119) + 1 (66)

= 3 serving of Ta-sty Pocket + 2 serving of P-ita Roll + 1 serving of In-sta Pancake

To get 19.2g of f-at, we should combine

= 14.4 + 4.6 + 0.2

= 3(4.8) + 2( 2.3) + 1(0.2)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

To get 78.9 g of carbohydrates, we should combine

= 29.4 + 28 + 21.5

= 3(9.8) + 2( 14) + 1 (21.5)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

Hence, we should combine 3 serving of Tasty Pocket, 2 serving of P-ita Roll, 1 serving of In-sta Pancake

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Answer:

[tex]\frac{13}{4}[/tex]

(Decimal: 3.25)

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

5.25

Step-by-step explanation:

1/4+1/3(10-1)

*do what's in parenthesis first!*

10 - 1 = 9

1/4 + 1/3 = 7/12

then you multiply 7/12 x 9 = 5.25

DONT FORGET!

Please Excuse My Dear Aunt Sally

P  E M D A S

The total number of votes which is reduced by the ratios of yes and no votes will be: 4580; + 6412 = 10992;

What are Ratios?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the part to the whole is 5: 10, meaning that 5 out of every 10 people enjoy reading.

In the given question, we have:

The ratio of yes votes to no votes was 7 to 5.

Total Number of Yes votes = 6412;

So, Let us assume the total number of no votes be x;

So, according to the question,

[tex]\frac{7}{5} = \frac{6412}{x}[/tex]

Cross Multiplying the terms:

⇒7 × x = 6412 ×5

⇒x = 4580;

So, The total number of no votes is 4580;

So, The total number of votes will be: 4580; + 6412 = 10992;

Hence,

The total number of votes will be: 4580; + 6412 = 10992;

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If the dimensions of a right rectangular prism are (8)/(5)cm,(10)/(3)cm, and (7)/(4)cm. Then volume of the prism is 401/60 cm³

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases

The dimensions of a right rectangular prism are width is 8/5 cm, Length is 10/3cm and Height is 7/4cm

Volume=Width×Height×Length

=8/5×10/3×7/4

=96+200+105/60

=401/60 cm³

Hence volume of the right rectangular prism is 401/60 cm³

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The equation to show the net effect of these transactions is x - 45 + 150.

The equation is x + 105.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the customer withdrew $45 from a bank account and the customer then deposited $150 into the bank account the next day.

Let the initial amount in the account be x. The amount after the transaction will be:

= x - 45 + 150

= x + 105

The equation is x + 105.

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Answer:

540= 2x2x3x3x3x5

       or

540= [tex]2^{2}[/tex]x[tex]3^{3}[/tex]x5

Step-by-step explanation:

Answer: 16\/729

Step-by-step explanation:

Answer:

six raised to the fourth power divided by three raised to the tenth power

Step-by-step explanation:

(6^−2 • 3^5)^−2 = 6^(-2*-2) * 3^(5*-2) = 6^4 * 3^(-10) = 6^4 / 3^10

The values of x and y will be 10 and 4 respectively, using congruent of the triangle.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Here, ΔRWS ≅ ΔTUV

Here 2y + 10 = 30

2y = 30-10

y=20/2

y=10.

Agian ∠R = ∠T

Here ∠T = 90 -32 =58°

So 8x+26 = 58°

8x = 58-26

x = 32/8

x = 4.

Hence the values of x and y will be 10 and 4 respectively.

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Solving for f(-2) in the function f(x) = 3x^2 + 2x + 4 gave the solution

From the given function f(x) = 3x^2 + 2x + 4 we substitute for x = -2  which is same as function of -2

f(x) = 3x^2 + 2x + 4

pugging in x = -2

f(-2) = 3(-2)^2 + 2(-2) + 4

solving the squared and opening the parentheses

f(-2) = 3 * 4 + -4 + 4

f(-2) = 12 - 4 + 4

f(-2) = 12

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Answer:

36 = 2x + y

x = y

x = 12

y = 12

Step-by-step explanation:

Answer:A=12 C=24

Step-by-step explanation:

there are 3 shares[2x and theunknown]

36=3shares so 1 share=36divided by3=12

ad=12

ch=12x2=24

12+24=36

Answer:

2/3

Step-by-step explanation:

Since 6 *6 = 36 , the square root of 36 is 6

In other words:

[tex]\sqrt{36} \\= 6\\[/tex]

Since 9*9 = 81, the square root of 81 is 9

[tex]\\\/\sqrt{81}\\ = 9[/tex]

Now we have the fraction [tex]\frac{6}{9}[/tex]

Now we reduce [tex]\frac{6}{9}[/tex] to lowest terms:

[tex]\frac{6}{9 } = \frac{2}{3}[/tex]

Therefore, the answer is  [tex]\frac{2}{3}[/tex]

Hope this helps :)

The y-intercept in the equation is 10. This is the initial height of the flower.

An exponential equation can be described as an equation with exponents. The exponent is usually a variable. When an exponential function is drawn on a coordinate graph, it is usually nonlinear because the slope is not constant.

The general form of exponential equation is f(x) = [tex]e^{x}[/tex]

Where:

The y-intercept of an exponential function is the value of y when x is zero. It is the point where the graph intersects the y-axis. The y-intercept represents the initial height of the flower.

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Answer:

x= 134 ± 2

Step-by-step explanation:

The ± symbol is used to mark the range of values that should be expected from the first number, 134.

The growth rates in 1950, 1988 and 2010 are 13.9%, 23.4 and 29.8% respectively

The function of the growth rate equation is given as:

y = -0.0000081x^3+0.00267x^2+8.231

Rewrite properly

So, we have

y = -0.0000081x³ + 0.00267x² + 8.231

From the question, we have

x represents the number of years after 1900

In 1950, x = 50

So, we have

Growth rate in 1950, y = -0.0000081 x 50³ + 0.00267 x 50² + 8.231

Growth rate in 1950, y = 13.9

In 1988, x = 88

So, we have

Growth rate in 1988, y = -0.0000081 x 88³ + 0.00267 x 88² + 8.231

Growth rate in 1988, y = 23.4

In 2010, x = 110

So, we have

Growth rate in 2010, y = -0.0000081 x 110³ + 0.00267 x 110² + 8.231

Growth rate in 2010, y = 29.8

Hence, the growth rate in 2010 is 29.8%

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slope = m = (8 - (-6)) / (8 - 6) = 7

y = mx + b

y = 2x + b

plug in (8, 8) to find b

8 = 2(8) + b

b = -8

y = 2x - 8