For the following, find the length of AB:

(Use \large \pi=3.14 when necessary and round your final answer to the hundredths.)







Arc AB =

Using simplification by factorisation and division

(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3) and (3x² - 9)/(x² - x - 6) = 3x/(x + 2)

To simplify the equations, we shall factorize both the numerator and the denominator, and divide through by a common factor.

for the equation (x² + 6x + 9)/(x² - 9);

the numerator:

x² + 6x + 9 = x² + 3x + 3x + 9

x² + 6x + 9 = x(x + 3) +3(x + 3)

x² + 6x + 9 = (x + 3)(x + 3)

the denominator:

x² - 9 = x² - 3²

x² - 9 = (x + 3)(x - 3) {difference of two squares}

(x² + 6x + 9)/(x² - 9) = (x + 3)(x + 3)/(x + 3)(x - 3)

divide through by the common factor (x + 3)

(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3)

For the equation; (3x² - 9)/(x² - x - 6)

the numerator:

3x² - 9 = 3x(x -3)

the denominator:

x² - x - 6 = x² -3x + 2x - 6

x² - x - 6 = x(x - 3) + 2(x - 3)

x² - x - 6 = (x + 2)(x - 3)

divide through by the common factor (x - 3)

(3x² - 9)/(x² - x - 6) = 3x/(x + 2)

Thus, (x + 3)/(x - 3) and 3x/(x + 2) are the results for simplifying (x² + 6x + 9)/(x² - 9) and (3x² - 9)/(x² - x - 6) respectively using factorization.

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The value of the h is A(2) / b when the formula is A = 1/2bh the formula is area of the triangle.

Given that,

We have a formula A = 1/2bh

We have to find h value from the formula.

We know that,

The variable h should be on one side of the equation, and the rest should be on the other. Divide the two sides in half as a good place to start. In this way, we eliminate the undesirable fraction.

A / 1/2 = 1/2bh / 1/2

Now on the right hand side left the 1/2 cancels out.

A / 1/2 = bh

And when a fraction is divided, the result is the same as multiplying it backwards.

A(2/1) = bh

Now, divide both sides by b.

A(2) / b = bh/b

On the left hand side b cancels out and we are left with the final product.

h = A(2) / b

Therefore, The value of the h is A(2) / b when the formula is A = 1/2bh the formula is area of the triangle.

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Answer:

Step-by-step explanation:

3.9875

The true statement are

Canister A can hold 30 pounds and contains 71% of its capacity

= 0.71 * 30 pounds

canister B can hold 45 pounds and is 10/18 full

= 45 * 10/18 pounds

canister C can hold 60 pounds and it's 8.8 pounds more than half capacity

= 8.8 + 60 * 1/2 pounds

The total amount available

= 0.71 * 30 + 45 * 10/18 + 8.8 + 60 * 1/2

= 85.1 pounds

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The equations for the horizontal line and the vertical line are y = - 3 and x = 4, respectively.

Herein we find the case of a point (x, y) = (a, b), from which we must derive the equations for the horizontal line and the vertical line, whose forms are described below:

Horizontal line

y = b

Vertical line

x = a

If we know that (x, y) = (4, - 3), then the equations for the horizontal and vertical lines are, respectivelly:

Horizontal line

y = - 3

Vertical line

x = 4

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We know that,

By definition, no function is symmetrical about the x-axis (or any other horizontal line). Because the one flipped with respect to the horizontal violates the vertical line test.

On the other hand, functions can be symmetric about a vertical line or a point. In particular, functions symmetric about the y-axis are also "even" functions, and functions symmetric about the origin are also "odd" functions. Because of this correspondence between graph symmetry and function equality or oddness, "symmetry" in algebra is usually applied to the y-axis and the origin.

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Answer:

  yes: f(x) = 0

Step-by-step explanation:

You want to know if a function exists that is symmetrical about the y-axis and the origin.

A graph is symmetrical about the y-axis if and only if ...

  f(-x) = f(x)

A graph is symmetrical about the origin if and only if ...

  f(-x) = -f(x)

For both conditions to be met, we must have ...

  f(x) = -f(x)

  2f(x) = 0 . . . . . add f(x)

  f(x) = 0 . . . . . . . divide by 2

The graph of f(x) = 0 will be symmetrical about the y-axis and the origin. (It is the x-axis.)

The gallons you can afford if you have $40 is 13 gallons.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3x = 18, for instance.

From the information, the local gas station is offering a deal to their customers. If they purchase $8.00 car wash, the cost per gallon of gas is $2.60.

Here, we want to solve a linear equation to find the gallons you can afford if you have $40.

The linear equation to find how many gallons you can afford if you have $40 will be illustrated as x

This would be:

2.60 × (40 / 8) = x

x = 2.60 × 5

x = 13 gallons

The gallons will be 13.

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The equation of each quadratic in the picture of formula and graphs attached is y=-1(x+8)^2 +9 and y=1/4*(x-6)^2 +3

What is Graph Transformation?

When a graph is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply pushing the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is generated. graph transformations are highly useful for graphing functions without having to start from scratch since they allow you to move, extend, compress, or reflect the curve. The graph of the parent function is either "moved," "resized," or "reflected" by a graph transformation. The three primary categories of graph transformations are as follows:

A)

first of all we need to find which type of parabolic graph is it

from the picture give we can clearly see it is a x^2=-4ay type of graph

and using graph transformation formula

i.e. y= a(x-h)^2 + k

where h = -8

k=9

we get y=a(x+8)^2+9

as we know (-5,0) lie on this graph

so,

0=a(-5+8)^2+9

a=-1

so the equation is y=-1(x+8)^2 +9

B)

first of all we need to find which type of parabolic graph is it

from the picture give we can clearly see it is a x^2=-4ay type of graph

and using graph transformation formula

i.e. y= a(x-h)^2 + k

where h = 6

k=3

we get y=a(x-6)^2+3

as we know (0,12) lie on this graph

so,

12=a(0-6)^2+3

a=1/4

so the equation is y=1/4*(x-6)^2 +3

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Answer: 15 days

Step-by-step explanation:

Pasta salad; 5  10  15  

Pretzel salad; 3  6  9  12  15

- The null hypothesis Is: [tex]$H_0: \mu=4.5$[/tex]

- The alternative hypothesis Is: [tex]$H_1: \mu \neq 4.50$[/tex]

- The test statistic is: t=-0.43

- The p-value of the test is of 0.6684.

What is p-value?

The p-value Is of 0.6684>0.05, which means that we can conclude that the population of student course evaluations has a mean equal to [tex]\mathbf{4 . 5 0}$.[/tex]

We are going to test If the mean Is equals to 4.50, thus, the null hypothesis Is:

[tex]H_0: \mu=4.5[/tex]

At the alternative hypothesis, we test If the mean Is different to 4.50, that is:

[tex]H_1: \mu \neq 4.50[/tex]

Since we have the standard devlation for the sample, the t-distribution is used. The value of the test statistic Is:

[tex]t=\frac{\pi-\mu}{\frac{\sqrt{n}}{\sqrt{n}}}$$[/tex]

For this problem:

[tex]$$\begin{aligned}& t=\frac{4.30-1.5}{\frac{2.21}{\sqrt[3]{80}}} \\& t=-0.43\end{aligned}$$[/tex]

We are testing If the mean is dlfferent from a value, thus, the p-value of test is found using a two-talled test, wlth t=-0.43 and [tex]$80-1=79 \mathrm{df}$[/tex].

Using a t-distribution calculator, the [tex]$\mathrm{p}$[/tex]-value is of [tex]$\mathbf{0 . 6 6 8 4}$[/tex].

The p-value is of 0.6684 > 0.05, which means that we can conclude that the population of student course evaluations has a mean equal to 4.50.

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Answer:

12 km

Step-by-step explanation:

4.4 * 2.727 km = 11.9988   ( using a calculator)

              since the smallest factor (4.4)  has only 2 significant digits , your answer should be rounded to only 2 S.D.      so   = 12 km

The domain of the given graph is -∞>x>-2

The range of the given graph is [0,-4]

What is the range and domain of a graph?

The range is the set of possible output values, which are shown on the y-axis.

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.

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The domain as an inequality x<-2 is { -∞>x>-2}.

The range as an inequality is [0,4]

What is the range and domain of a graph?

Functions in mathematics can be compared to the operations of a vending (soda) machine. When you put in a certain amount of money, you can select different types of sodas. Similarly, for functions, we input different numbers and we get new numbers as the result. Domain and range are the main aspects of functions. You can use quarters and one-dollar bills to buy a soda.

The machine will not give you any flavor of the soda if pennies are input. Hence, the domain represents the inputs we can have here, that is, quarters and one-dollar bills. No matter what amount you pay, you won't get a cheeseburger from a soda machine. Thus, the range is the possible outputs we can have here, that is, the flavors of soda in the machine.

The range is the set of possible output values, which are shown on the y-axis. The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.

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Answer: x : x e R and R >

Step-by-step explanation:

Answer:

A.x=-7/6

B.x=-19/9

C.x=-23/14

D.x=-5/3

E.x=-7/5

Step-by-step explanation:

A. 30x+35, 30x=-35 x = -7/6

B. 45x+90, 45x=-90, x=-19/9

C. 28x+46, 28x=-46, x=-23/14

D. 72x+120, 72x=-120, x=-5/3

E.77+55x, 55x=-77, x=-7/5

Answer:

1.) Feeds on dead organisms – Decomposer

2.)obtain energy nutrients from producers – Consumer

3.)Network of interconnected food chains – Food web

4.)Manufactures food using energy from the sun – Producer

5.)Simple model used for showing how energy passes through an ecosystem – Food chain

6.) Relationship between organisms where both members benefit – Mutualism

Step-by-step explanation:

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The serving size of a certain brand of yoghurt has 4.6 grams of protein. The yoghurt is consumed in three portions. They eat 13.8 grams of protein daily.

A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.

Calculations involving numbers are done using arithmetic operators. The numerical results that are produced by arithmetic operators are associated from left to right.

The following are the three properties you should consider: Commutative addition applies to full numbers. Associative math is the addition of whole integers. When adding whole numbers, the number 0 serves as an identity.

In several contexts, including multiplication (repeated addition), division, and other operations, the fundamental operations of addition and subtraction are applied (repeated subtraction). These operations are used to transform the word problems into mathematical expressions.

= 4.6 x 1 = 4.6

= 4.6 x 3 =13.8

Hence the total grams of protein consumed is 13.8

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Answer: 13.8 grams of protein

Step-by-step explanation:

     If there are 4.6 grams of protein in 1 serving, then to find the number of grams in 3 servings we can use multiplication to solve this question.

4.6 grams of protein * 3 servings = 13.8 grams of protein

The  prize of the 4th place is 18

Given:

1. The second-place seller will receive twice as much as the third-place seller

2. The first-place seller will receive $20 more than the second-place seller

3. The profit portion they will share is $200

Let S, T, F and V represent the prize of the second, third, first and fourth  place respectively

Statement 1 can be written as:

S = 2T  --- (1)

Statement 2 can be written as:

F = S + 20  --- (2)

Statement 3 can be written as:

F + S + T = 200  --- (3)

Substitute (1) and (2) into (3):

F + S + T = 200

(S+20) + 2T + T= 200

(2T+20) +2T + T= 200          (Since S = 2T)

2T+20 +2T + T= 200

5T + 20 = 200

5T = 200-20

5T = 180

T = 180/5

T = 36

Thus, the third-place seller prize is 36

Since the 4th place winner received half of what the 3rd place received. Thus:

V = 1/2 × T

V =  1/2 × 36

V = 18

Therefore, the 4th place prize is 18

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The number of seats in each row would be = 271 seats.

An auditorium is defined as the establishment that can be used for various events such as presentation, seminars and celebrations.

The total number of people seated in the auditorium= 2100 seats.

The total number of seats = 2100

The number of seats per row = 8x

That is,

2100 = 8x

make X the subject of formula;

X = 2100/8

X =263 +8

X = 271 seats per row.

Therefore, the number of seats per row would be = 271 seats per row.

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The length of QR in the quadrilateral is 58.7 units.

A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.

Therefore,

KLMN is similar quadrilateral to OPQR.

Hence,

[tex]\frac{KL}{OP} =\frac{KM}{OQ} =\frac{KN}{OR} =\frac{MN}{QR}[/tex]

[tex]\frac{11}{38} =\frac{17}{QR}[/tex]

cross multiply

11QR = 17 × 38

QR = 646 / 11

QR = 58.7272727273

QR = 58.7

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Answer:x=11/14

Step-by-step explanation:

3(2x+7)=8(4-x)

Multiply the first part of the equation

6x+21=
multiply the 2nd half of the equation

32-8x

6x+21=32-8x

Move the -8x to the left side of the equation making it a positive 8x

8x+6x+21=32

Move the 21 to the right side of the equation

8x+6x=32-21

Add the x’s on the left and subtract the 21 from 32 on the right

14x=11

Divide the 14 into the 11

x=11/14

We can find the test statistic and the critical value by the  distributed the test statistic under the assumption that the null hypothesis hold.

It is the study of external and the internal force.

When the first data will be  pretext and the 2nd  the joe will be the first test, the d will be mu joule  -1. The alternative hypothesis to em d is the  smaller than the 0. The first time we need to find the rest  that sticks by the tree is when we were given the question n equal to the 15 and the d p equal to -15.1. The formula with the  werther to the end has a big  square root of 15 points.

times square 15 equal to the 1.399 point, and the next  time we need to find a p value for this, we will use by  left hand test.To  The 14 degree freedom will be smaller than the minus 1.399 point if the value of the d n -1 degree, freedom and equal to the 15 minus 1 is equal. Energy use the t distribution when it is = 14 degree- freedom is smaller = 1.399 point. I going to compare to 918 point.

We're gong to regent the noon because the alpha is smaller than the 11.

Thus,

We can defined The mean difference is  less than 0 points.

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A line's steepness can be determined by looking at its slope. Slope is determined mathematically as increase over run.

According to the slope equation, the slope of a line may be calculated by dividing the rise of the line between any two places by the run of the same line between the same two sites.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Slope of y =f(x)

Slope (m) = ΔY / ΔX = 14 / 1 = 14

y = 14x + 22

When x=0, y = 22

When y=0, x = -1.5714285714286

Slope of y = g(x)

Slope (m) =ΔY / ΔX = 14 / 1 = 14

y = 14x + 24

When x=0, y = 24

When y=0, x = -1.7142857142857

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Answer:25

Step-by-step explanation:

We have the rate: 35 deliveries in 3.5 hours. or 35/3.5

Find the unit rate -> 35/3.5/

                                /3.5/3.5

10/1

10

10 deliveries per hour

in 2.5 hours

10*2.5

25

*Assuming the rate of deliveries is constant*

The equation y= √(x-1) + 3 is a function of radical function.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Type of function:

linear, power, quadratic, polynomial, rational, exponential, logarithmic, radical etc.

Given equation is

y= √(x-1) + 3

In the equation there is a term √(x-1).

A square root presents in the equation.

This means it is a radical function.

The given equation is of a radical function.

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All of the justifications used to demonstrate the following angles, including the alternate interior theorem justification, are valid.

When a transversal intersects two parallel lines, alternate interior angles are created that are equal to the alternate pairs of those pairs.

The angles formed on the opposing sides of the transversal are known as alternate internal angles.

Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.

Angles that alternate are equal: By creating a Z form, we can easily identify interior alternate angles: Alternate angles come in two varieties: alternate internal angles and alternate exterior angles.

All the reasons are given to prove the following angles are correct including the reason for the alternate interior theorem.

Therefore, all of the justifications used to demonstrate the following angles, including the alternate interior theorem justification, are valid.

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Answer:2/1

Step-by-step explanation:

you just have to flip the slope if it is perpendicular.

By ratios ,orange = 15 , apple = 10 , coconut = 20 are needed to make 45 liters of this cocktail.

What does the math ratio mean?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A proportion is an equation that sets two ratios at the same value.

                   As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

orange = 3

apple = 2

coconut = 4

total = 9

orange =  3/9  * 45  = 15

 apple = 2/9  *  45  = 10

coconut = 4/9  * 45  = 20

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The complete question is -

In a fruit cocktail, the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each type is needed to make 45 liters of this cocktail?