Write the domain for the following piecewise-defined function using intervalnotation,2 if x < 1f(x) =1 2 – x2 if x > 1

The quadratic function that models the path of the second kick is given by:

y = -2/125(x - 25)² + 10.

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which the coefficients are explained as follows:

For the first kick, the equation is:

y = -1/40(x - 25)² + 15.

Meaning that the ball reached a maximum height of yards after an horizontal distance of 25 yards.

For the second kick, the horizontal distance is the same, but the maximum height if 5 yards less, that is, of 10 yards, hence the vertex is:

(h,k) = (25, 10).

Hence the equation is:

y = a(x - 25)² + 10.

After 50 yards, the ball hits the ground, hence the leading coefficient a is found as follows:

0 = a(50 - 25)² + 10

625a = -10

a = -10/625

a = -2/125

Hence:

y = -2/125(x - 25)² + 10.

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The number of minor damaged books in 73500 book collection is 8,673 books.

Given that, 661 books had no damage, 78 books had minor damage, and 26 books had major damage.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the minor damaged books be x.

Now, 78 : 661 :: x : 73,500

⇒ 661x = 73500 × 78

⇒ 661x = 57,33,000

⇒ x = 57,33,000 ÷ 661

⇒ x = 8,673.22

≈ 8,673

Therefore, the number of minor damaged books in 73500 book collection is 8,673 books.

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Answer: Sara is 51 and madison 19

Step-by-step explanation: Yes

Answer:

12.56$

Step-by-step explanation:

12 / 3=4

4 × 3.14 = 12.56

Answer:

y = 4x -80

Step-by-step explanation:

We need the slope and the y intercept.

The y intercept is -80.  This is where the line crosses the y axis.

The slope is the change in y over the change in x.  

Let's go from point (0,-80) the y intercept the the point that cross the x axis (20,0)  Start at -80, how many units to you go up until you are at the same level as point (20,0)? 80 units.  Now, from (0,0) how many units do you go right to get to (20,0)? 20.

We end up go 80 unit up and 20 units right, this would be written [tex]\frac{80}{20}[/tex] Which simplifies to 4.  This is our slope.

Slope (m) = 4

y intercept (b)= -80  Plug those into

y = mx + b

y = 4x -80

The sum of the internal angles of a triangle is 180°

Since AD is parallel to BC and DC is parallel to AB, the angle ADC must be equal to the angle ABC, which is 123°

Then, the angle CAB is 180° - 24° - 123° = 33°

well, let's move like the crab, backwards, and start off with

3)

Check the picture below.

[tex]tan(A )=\cfrac{\stackrel{opposite}{BC}}{\underset{adjacent}{AC}}\implies tan(A)=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{4}}\qquad \textit{now let's find the \underline{hypotenuse}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ AB=\sqrt{(AC)^2 + (BC)^2}\implies AB=\sqrt{4^2 + 3^2}\implies \underline{AB=5} \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\hspace{5em} cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}}[/tex]

2)

well, Graciella said they couldn't just using the tangent they were given, well, she needs stop playing Angry Birds too much.

1)

well, from what I read, Angelica thought it was possible, so she was correct all along, I don't see any mistakes in her statements, all we did in 3) was what Angelica suggested.

Answer:

7cd(ab-3be+2ef)

Step-by-step explanation:

they all have the number 7 In common so you take that out and you take out whatever letters they have in common

Answer:

7cd(ab - 3be + 2ef

Step-by-step explanation:

Simplify:

    7abcd = 7 * a * b* c * d

  21bcde = 7 * 3 * b * c * d * e

   14cdef = 7 * 2 * c * d * e * f

GCF = 7 cd

7abcd - 21bcde + 14cdef = 7cd*( ab  - 3be + 2ef)

Explanation.

The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)

To do this, we can use the formula:

In our case, we have

We will simply put all the values above into the formula to get the equation of the line

Simplifying further

Cross multiplying

Therefore, the equation of the line is

The value of x are 4 and 2.4 after simplifying and applying the quadratic formula.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The equation is:

4/(x - 2) + 3/(x - 3) = 5

4(x - 3) + 3(x - 2) = 5(x -2)(x - 3)

4x - 12 + 3x - 6 = 5x² - 25x + 30

5x² - 32x + 48 = 0

After solving the above quadratic equation by the formula:

[tex]\rm x = \dfrac{-(-32) \pm\sqrt{(-32)^2-4(5)(48)}}{2(5)}[/tex]

x = 4

x = 2.4

Thus, the value of x are 4 and 2.4 after simplifying and applying the quadratic formula.

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Answer:

⚠️⚠️⚠️⚠️⚠️⚠️♀️

Step-by-step explanation:

⚠️⚠️⚠️♀️

Answer:

2x=108

Step-by-step explanation: This is the equation because when it says twice a number, you are multiplying a number two times. In this case, the number is not given, so x is the variable being multiplied two times. If the number was 8, it would look like this: 2(8)=108. Of course this isn't true, but to find the actual answer you would divide two on both sides of the equation. This is so that both of the two's cancel out on the left side of the equation. and the variable is left on that side. Our goal is to isolate the variable. In these types of equations, our goal is to isolate the variable and find what the variable is worth. If we do 108 divided by 2 that gives us 54. Since there was x left on the left side of the equation and there is 108 left on the right side we have our equation. x=54

Number explanation below

2x=108

2x/2=108/2

x=54

If there is no solution to a compound inequality, it can involve AND.

A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the equal validity of both statements in the compound sentence. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true.

The term "OR" can help us find more solutions, whereas the phrase "AND" can help us find less solutions. As a result, we can create a compound inequality with no solution by using "AND."

Therefore, if there is no solution in compound inequality, it may involve AND.

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The measure of x, m∠DEG, m∠GEF  and m∠DEF will be 5,112°,68°and 180° respectively.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that,

m∠DEG = (23x-3)°

m∠GEF = (12x+8)°

As m∠DEF is a straight angle its angle measurement is 180

As a result,

m∠DEF=m∠DEG+m∠GEF

180°=m∠DEG+m∠GEF

Put the given values

180°=(23x-3)°+(12x+8)°

180=35x+5

35x=180-5

35x=175

x=5

Substitute the value of x to obtain all the angles as

m∠DEG=(23x-3)°

m∠DEG=(23(5)-3)°

m∠DEG=112°

For m∠GEF,

m∠GEF=(12x+8)°

substitute the value of x

m∠GEF=(12(5)+8)°

m∠GEF=68°

Thus, the measure of x, m∠DEG, m∠GEF  and m∠DEF will be 5,112°,68°and 180° respectively.

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The given percentage cannot be represented on the grid.

What is percentage?

A percentage (from Latin: per centum, "by a hundred") is a quantity or ratio stated as a fraction of 100 in mathematics. The percent symbol, "%," is commonly used, however the abbreviations "pct.", "pct," and sometimes "pc" are also used. A % is a non - dimensional (pure) quantity; it does not have a unit of measurement. In the context of sports statistics, the term "%" is frequently used incorrectly since the referred figure is stated as a decimal proportion, not a percentage. Similarly, a team's winning percentage, or the fraction of matches won, is commonly reported as a decimal proportion; a team with a.500 winning percentage has won 50% of its matches.

The given percentage cannot be represented on the grid.

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Answer:

40 feet

Step-by-step explanation:

-10 -30

The equation of the line parallel to 3x-6y=3 and passes through (-2, 3) is y = 1 / 2 x + 4

The equation of the line passes through (-2, 3) and it is parallel to the equation 3x - 6y = 3.

Therefore, the equation of a line can be represented as follows:

y = mx + b

where

Parallel lines have the same slope.

Hence,

3x - 6y = 3

3x - 3 = 6y

y = 1 / 2 x - 1 / 2

Therefore, the slope of the equation is 1 / 2.

Let's find the y-intercept using (-2, 3).

3 = 1 / 2 (-2) + b

3 + 1 = b

b = 4

Therefore, the equation is y = 1 / 2 x + 4

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We can conclude that the mode of the following data are 4 and 5.

As the given data set is:

Mode is calculated when in the given data set the number appears most often.

So, count each number as we get the result:

Therefore, the modes are 4 and 5.

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Answer: a13=310.7

Step-by-step explanation:

Formula= an=a1r^n-1

a13=1100(0.9)13-1

a13=310.7

Answer: 5x + 15 = y

Step-by-step explanation:

mx+b = y

find rise over run

(y_2-y_1)/(x_2-x_1) = m

(-5-5)/(-4+2)

simplify

-10/-2

10/2

5 = m

plug in a point and find b

5(-2) + b = 5

-10 + b = 5

b = 15

5x + 15 = y

The image of the function f(x) = x , after the translation is g(x) = x -2 .

In the question

it is given that

the function f(x) = x ,

and f(x) has to be translated 2 units to the right means subtract 2 from the function .

which means g(x) = f(x) - 2

substituting f(x) = x , we get

g(x) = x - 2

the answer in the form of mx+b is g(x) = x - 2

(can refer to the graph given below)

Therefore , The image of the function f(x) = x , after the translation is g(x) = x - 2 .

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Question Should look like

determine the distance between (-4,-7) and (-8,-13)

A. [tex]\sqrt{10}[/tex]

B. [tex]\sqrt{82}[/tex]

C. [tex]\sqrt{544}[/tex]

D. [tex]\sqrt{52}[/tex]

Answer: D. [tex]\sqrt{52}[/tex]

Step-by-step explanation:

[tex]a^{2}+b^{2}= c^{2}[/tex]

a =(8-4)... b=(13-7)

a=4, b=6

therefore...

[tex]a^{2}+b^{2}= c^{2}\\4^{2}+6^{2}=c^{2}\\16+36=c^{2}\\52=c^{2}\\c=\sqrt{52}[/tex]

Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.

We need to define the angle.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

Parts of an Angle

There are two main parts related to an angle - the arms and the vertex.

Arms of the Angle

The two rays which join at a common point to form the angle are called the arms of the angle.

Vertex of the angle

Vertex is a common endpoint that is shared by the two rays.

Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.

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Answer:

A

Step-by-step explanation:

Proportions can be any number so other statements can't be always true

Answer:

A. Class X has a greater proportion of boys than Class Y

Step-by-step explanation:

- Before choosing any objective, first relate the two proportions.

Multiply class Y by 2:

[tex]{ \rm{y = 2(4 : 5)}} \\ { \rm{y= 8:10}}[/tex]

- So it can be related with class X as the ratios have a common proportion of girls; 10

[tex]{ \rm{x= 9:{ \green{10}}}} \\ { \rm{y = 8:{ \green{10}}}}[/tex]

- By observation, we see that class X has a greater number of boys than in class Y

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: ...creed}}}[/tex]

Proportionately, based on Marvin's initial deposit, Victor invested Php 40,000 in the partnership.

Proportion is like a ratio that shows a numerical relationship between two variables.

Proportions equate one ratio to a value.

For instance, we can equate Marvin's investment ratio to his investment.

This equation helps us to calculate the total investment made by the four partners in the small business.

                               Jamie   Ralph   Marvin          Victor   Sum of Ratio

Investment ratio         8:         3:           12:                2           25

Investment amount    ?           ?     Php 240,000    ?            ?

Marvin investment = Php 240,000 = 12/25

Total investment by the partners = Php 500,000 (Php 240,000/12 x 25)

Victor's investment = Php 40,000 (Php 500,000 x 2/25)

Profit for the year = Php 150,000

Thus, based on proportional contributions of Marvin, Victor's investment is Php 40,000.

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10 pounds of food each chicken eat last week.

This is a problem from an algebraic equation. We can solve this problem by following a few steps.

Each chicken eats the same amount of food, as per the question. Let's assume there is x number of chickens.

Therefore, if each chicken eats the same amount of food then the total food required for all chickens is, (x × x) = x² pound.

Again, Mrs. Rollins bought 100 pounds of chicken food.

Hence x² is equivalent to 100 pounds. We can generate an equation from this. Which is,

x² = 100

Or, √x² = √100         [ root both sides ]

Or, x = 10

Now, we can conclude that there are 10 chickens and each chicken eats 10 pounds of food in a week.

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Answer:

x- intercept = - 3

Step-by-step explanation:

to find the x- intercept , where the line crosses the x- axis, let y = 0 in the equation and solve for x

2x - 0 + 6 = 0

2x + 6 = 0 ( subtract 6 from both sides )

2x = - 6 ( divide both sides by 2 )

x = - 3 ← x- intercept

Based on the weight of the plastic to the weight of the paper, the ratio of plastic to paper in the simplest form is 6 : 1

To find the ratio of plastic to paper, there is a need to convert the weights such that they have the same units.

Assuming we convert the plastics to grams, the number of grams of plastic would be:

= 3 kg x 1,000 grams per kg

= 3,000 grams

The ratio then would be:

3,000 grams of plastic   : 500 grams of paper

To get to the simplest form, divide both sides by 500:

3,000 / 500 : 500 / 500

6 : 1

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Answer: -19/8

What is an improper fraction?

  An improper fraction is where the numerator is greater than the denominator. To turn -2 3/8 into an improper fraction, we will "combine" -2 and 3/8.

First, we will find what -2 becomes. -2 is the same as two wholes:

     -2 * 8 = -16

Next, we will subtract this into the numerator of the fraction:

     -16 - 3 = -19

Lastly, we will put this new numerator over the denominator:

     -2 3/8 = -19/8