Write the equation of the graph shown below in factored form.

a graph that starts at the top left and continues down through the x axis at negative one to a minimum around y equals negative twelve point two five and goes up to touch the x axis at two and the goes back down to a minimum around y equals negative one half and goes back up through the x axis at two.

f(x) = (x − 2)2(x + 1)(x − 3)
f(x) = (x + 2)2(x − 1)(x + 3)
f(x) = (x + 2)2(x + 1)(x + 3)
f(x) = (x − 2)2(x − 1)(x − 3)

The measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

According to the question,

We have the following information:

We have a figure where angle MCJ is 130°.

Now, we can extend the two given lines as imaginary lines. After extending the lines, we will find that these lines are parallel and the lines are being cut by another line.

We know that in this case the alternate interior opposite angles are equal and the sum of consecutive alternate interior angles is 180°.

Now, ∠MCJ and ∠CMB are alternate interior opposite angles and thus they are equal.

Hence, the measure of ∠MCJ is 130° because ∠MCJ and ∠CMB are alternate interior opposite angles.

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Answer:

Step-by-step explanation:

Ok;

1. Area is base times height.

Here shown, the base is 18cm and the height is 11cm. Don't be fooled by the 14cm for it is just the leg of a triangle not full height!!

18*11=198cm^2

2. Divide by two. We just caculated the area of the rectangle. Now we know a triangle is half of a rectangle's area so divide by 2!

198/2= 98cm^2

Answer:

(f+g)(x) = x - 7

Step-by-step explanation:

(f+g)(x) tells you to add the functions together. It means

f(x) + g(x)

= -3x - 5 + 4x - 2

combine like terms.

= 4x-3x - 5 - 2

= x - 5 - 2

simplify.

= x - 7

(f+g)(x) means

f(x) + g(x)

= x - 7

Answer:

16 and 12

Step-by-step explanation:

A.1 IN=2FT

8IN =2(8)FT

= 16

B.1 IN=2FT

6IN=2(6)FT

=12 FT

Answer:

11.6666666 (infinitely)

Answer:

1200

Step-by-step explanation:

1,500-300=1200

The transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

The given functions are f(x)=-1/4 x-2 and r(x)=4f(x).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

r(x)=4f(x)

So, r(x)=4(-1/4 x-2)

⇒ r(x)=-x-2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Vertical: stretch

The graph of the functions is given below.

Therefore, the transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

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It will take 6 days for the sister to earn as much as the brother.

Two or more expressions with an equal sign are defined as an equation.

Given that, the sister earns $30 per day and pays a $60 license fee and the brother earns$20 per day.

The income of the sister in x days is:

30x - 60

The income of the brother in x days is:

20x

The income of the sister and the brother is equal when:

30x - 60 = 20x

30x - 20x = 60

10x = 60

x = 6

Hence, It will take 6 days for the sister to earn as much as the brother.

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The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

a)

The given condition makes a right-angle triangle as shown below,

The tan function,

tanθ = 6/25

θ = 14.50°

b)

When a player is 5 feet closer means (20 feet far)

tanθ = 6/20

θ = 16.70°

c)

As the player gets closer the angle becomes more and more.

Hence "The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases".

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Answer:

the slope of the line is undefined

Answer:

x = 1

Step-by-step explanation:

Given exponential equation:

[tex]3^{2x}-9=0[/tex]

Add 9 to both sides of the equation:

[tex]\implies 3^{2x}-9+9=0+9[/tex]

[tex]\implies 3^{2x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left(3^2\right)^{x}=9[/tex]

[tex]\implies9^{x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]

[tex]\implies9^{x}=9^1[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x=1[/tex]

The value of the algebraic expression 2/5g + 3h - 6 if evaluated when g = 10 and h = 6 is 16.

2/5g + 3h - 6

When g = 10 and h = 6

2/5g + 3h - 6

2/5(10) + 3(6) - 6

20/5 + 18 - 6

4 + 18 - 6

16

In conclusion, the value of the expression 2/5g + 3h - 6 when evaluated is given by 16

Complete question:

Evaluate 2/5g + 2h - 6 start fraction, 2, divided by, 5, end fraction, g, plus, 3, h, minus, 6 when g=10 g, equals, 10 and h=6 h, equals, 6

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Answer:

c = 11.46 yd

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

The probability of selecting a blonde is 0.40

Probability is the likelihood that something will occur.

In this case, from the twenty students, it should be noted that the number of blondes are 8.

Black hair = 5

Blonde hair = 8

Brown hair = 5

Red hair = 2

Therefore, the probability of choosing a blonde will be:

= Number of blonde / Total students

= 8/20

= 0.40

The probability is 0.40

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Complete question

Of the 20 students in Kendra's class 5 have black hair eight have blonde hair 5 have brown hair 2 have red hair.kendra used the spinner to blonde hair. What's the experimental probability that the student will have blonde hair?

The expression that represents the statement "the product of a number and eight" is 8x.

Expression:

Expression means the mathematical statement that consists of  minimum of two numbers/variables and at least one math operation(addition, subtraction, multiplication and division) in it.

Given,

The given statement is "the product of a number and eight".

Now, we have to find the suitable expression for this statement.

In order to find the suitable expression, we have to divide the given statement and then we have to identify the keyword in it.

By using those keywords, we have to solve it.

In the given statement we have identify the following:

product

number

eight

Here the product refers the multiplication

number is any unknown number that is x.

eight refers the number 8.

When we combine these keywords we can get the expression 8x.

Therefore, the resulting expression is 8x.

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Answer:

10

Step-by-step explanation:

(2w + 4) - (2w - 6)

2w + 4 - 2w + 6

2w - 2w + 4 + 6

10

I hope this helps!

The standard error for the sample was 0.13 when "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89."

The standard deviation of a statistic's sampling distribution, or an estimate of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean. By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.

Here,

The standard error=standard deviation/√number of samples

=0.65/√25

=0.65/5

=0.13

When "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89," the standard error for the sample was 0.13.

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To get the answer go to desmos

Answer:

2.2360679775 or 2.24

Answer:

Step-by-step explanation:

     I am going to transform this equation into slope-intercept form, as it is usually easier to graph it that way.

  Given:

-8 + x = 4y - 16

  Add 16 to both sides of the equation:

-8 + x + 16 = 4y

  Divide both sides of the equation by 4:

-2 + [tex]\frac{1}{4}[/tex]x + 4 = y

  Reflexive property and combine like terms:

y = [tex]\frac{1}{4}[/tex]x + 2

  Now, we will graph. The 2 is our y-intercept and the  [tex]\frac{1}{4}[/tex] is our slope, graphed as "rise over run." This means we will rise one unit up and run four units right.

      See attached.

The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that a figure with side length of 12 units is being dilated in a figure with side length of 4.

In this case, the scale factor = 4/12 = 1/3

Hence, The scale factor of a figure with a shape with a side length of 12 and is dilated to a shape with 4 is 1/3.

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The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

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From the properties of a right triangle is found that the missing length x= [tex]5\sqrt{3}[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The sum of the internal angles of a right triangle also is equal to 180°.

The question gives a figure which is compound for two right triangles.

For each triangle is informed two angles, then:

       45+90+ x = 180

       135 + x =180

        x=180-135

        x=45°

       60+90+ y = 180

       150+ y =180

        y=180-150

        y=30°

Thus, the angles for the given triangle are:

From the trigonometric ratio sinФ, you can find the hypotenuse the triangle 2. See below.

[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 45 =\frac{hypotenuse \ triangle 2 }{hypotenuse \ triangle 1} \\ \\ \frac{\sqrt{2} }{2}=\frac{hypotenuse \ triangle 2 }{10\sqrt{2} }\\ \\ 2*hypotenuse \ triangle 2 = 10*2\\ \\ hypotenuse \ triangle 2 = \frac{10*2}{2} \\ \\ hypotenuse \ triangle 2 =10[/tex]

If the hypotenuse of triangle 2 is 10, you can apply again the trigonometric ratio sinФ for finding x

[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 60=\frac{x }{hypotenuse \ triangle 2} \\ \\ \frac{\sqrt{3} }{2}=\frac{x }{10}\\ \\2x=10 \sqrt3\\ \\ x=5\sqrt3[/tex]

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The equation that could be used to solve for the time t in hours that she drove before her stop is 80t + 100(8/3 - t) = 250.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let t = time she drove before her stop

If the total trip time is 3 hours including the stop, which took 20 minutes, then the time she drove after the stop is 3 - t - 1/3 or 8/3 - t.

If altogether she drove a distance of 250 km, then the sum of the products of the rate of speed and time each drive is equal to 250.

(80 km/h)(t) + (100 km/h)(8/3 - t) = 250

Simplify the equation.

80t + 100(8/3 - t) = 250

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432 ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a different color from each of its proper divisors.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It claims that if there are n ways to do something and m ways to do something else after that, then there are n m n*m methods to do both of these acts.

Here,

(1) All prime number can take any of three colors, except one of 2 or 3 as both are connected via 6..

so 2, 5, 7 can have 3 ways each - 3*3*3 = 27 ways

(2) Let us take the multiples of 2..

4 can take any of the remaining 2 colors, while 8 would take the remaining colour. As like 4, 6 can also take any of 2 colors other than the colour of integer 2.

Thus 2*2*1=4

3 is restricted because of 6, so it cannot have the same color as 6 and therefore 3 can have any of the remaining 2 colors.

We could also have taken 3 colors for 6, and then 2 and 3 would have 2 colors each and overall 2*2*3.. We are still getting the same

Only integer left is 9, so it will take any of the 2 colors other than that of 3, so 2 ways..

Total 2*2=4

Combined way of  integers = 27∗4∗4=432 ways

There are 432 different methods to paint the numerals 2, 3,..., 9 red, green, or blue so that each number has a different hue from each of its suitable divisors.

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Answer:

to find the max number of guests:

25x-400 = 50

25x = 50 + 400

25x + 450

then divide

x = 450/25

x = 18

to find the min number of guests:

25x = 400 - 50

25x = 350

then divide

x = 350/25

x = 14

Minimum number of tables reserved:

is dividing the max/7 per table

x = 18/7

x = 3

Step-by-step explanation:

An example of experiment is B. Researchers working for a company test their new sneaker design to see if it helps athletes run faster.

An experiment simply means a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. It should be noted that experiments provide insight into cause-and-effect as they demonstrate what outcome occurs when a particular factor is manipulated

Experiments have a vital place in the development of science because experiments are used to test the reality of a thought, an axiom, or a phenomenon with a theoretical basis and to turn it into a law or a theorem.

In this case, testing the new sneakers is an experiment.

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Answer:

see explanation

Step-by-step explanation:

(a)

given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation

to find k use any ordered pair from the table

using (2, 4 ) , then

4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

16 = k

y = [tex]\frac{16}{x^2}[/tex] ← equation of variation

(b)

when y = 25 , that is

25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]

the positive value of x is then [tex]\frac{4}{5}[/tex]

Amount of water after x minutes is more in pool B.

Two or more expressions with an Equal sign is called as Equation.

Given,

Pool A started with 5000 liters of water, and 50 liters per minute are being.

Pool B started with 4800 liters of water, and 30 liters per minute are being.

5000-50x=4800-30x

Add 30x on both sides

5000-50x+30x=4800-30x+30x

5000-20x=4800

5000-4800=20x

200=20x

Divide both sides by 20

20=x

Now substitute x in pool A equation

5000-50x

5000-50(20)=5000-1000

Pool A =4000

Now substitute x in pool B equation

4800-30x

4800-30(20)

4800-600

Pool B =4200

4200>4000

Pool B> Pool A

Hence amount of water after x minutes is more in pool B.

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The domain is x [tex]\geq[/tex] 0. interval notation:  [0,[tex]\infty[/tex])

the range is f(x)≤0, interval notation:  (-[tex]\infty[/tex],0 ]

What are the domain and range of a function?

The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.

A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)

Find domain:

Set the term under the square root [tex]\geq[/tex]0

So, the domain is x [tex]\geq[/tex] 0. interval notation:  [0,[tex]\infty[/tex])

Find range:

The range of a radical function of the form -c√(ax+b) +k is f(x)≤k

So, the range is f(x)≤0

interval notation:  (-[tex]\infty[/tex],0 ]

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