Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.

f(x)=

The area of the circle is  [tex]225\pi \ in.[/tex]

Hence, Option A is the correct answer.

A circle is a round-shaped figure that has no corners or edges. The Diameter is the longest chord of the circle. It divides the circle into two equal halves.

Diameter of the circle (d)= 30 in.

The radius of a circle is the distance from the center of the circle to any point on its circumference. The diameter is twice the radius of the circle.

The radius of the circle will be =d/2

                                             = [tex]\frac{30}{2}[/tex]

                                             = 15 in.

So, the radius of the circle is 15 in.

The area of the circle is given by [tex]A = \pi r^2[/tex]

So we have,

[tex]A = \pi r^2[/tex]

[tex]A = \pi 15^2[/tex]

[tex]A =225\pi \ in.[/tex]

Hence, the area of the circle is [tex]225\pi \ in.[/tex]

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Investment in the share of stock in xyzzy corporation is not a good investment.

In order to determine if the investment is a good investment, the present value of the cash flows from the investment has to be determined. The investment is a good investment if the present value of the cash flows is equal or greater than the cost of the stock.

Present value is the sum of the discounted cash flows from a project.

Present value = 5 / 1.08 + 5 / 1.08² + 5 / 1.08³ + 120 / 1.08³ = 108.15

The present value of the cash flows is less than the cost of the stock today. This means that the stock is not a good investment.

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30% of the area under the normal curve lies to the left of -0.52 z - score.

What is z - score?

The relationship between a value and the mean of a group of values is quantified by a Z-score. The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has the same score as the mean.

To find the z - score, divide your data point by your standard deviation after taking your data point and subtracting the mean from it.

Here, 30% = 0.30

So,

P(Z < z) = 0.30

From z - table, z - score for the probability 0.30 is -0.5244

-0.5244 ≈ -0.52

Hence, 30% of the area under the normal curve lies to the left of -0.52

z - score.

The option (c) is the correct answer.

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Answer:

$3.96

Step-by-step explanation:

Use the formula:
[tex]p(1+\frac{r}{n} )^{nt}[/tex]

p is our initial investment

r is the interest rate

n is the term

t is time

doing this we get

[tex]200(1+\frac{.04}{1})^{0.5}[/tex]

where t = 0.5 because the term is 6 months or half a year

We get a value of 203.96 which is the amount of money being paid after 6 months.

The interest is then our initial value of $200 subtracted from our final value.

[tex]203.96-200= 3.96[/tex]

The equations that have a true solution include the following:

8⋅72−12=22−2⋅3 fraction numerator 8 times 7 over denominator 2 end fraction minus 12 equals 22 minus 2 times 3.

48 ÷ 8 + 2³ = 5 + 3²

In this exercise, we have to determine the equations that are true and this would  be done by simplifying and evaluating each of the equations as follows:

(8 × 7)/2 - 12 = 22 - (2 × 3)

Opening the bracket on both sides of the equation, we have:

56/2 - 12 = 22 - 6

28 - 12 = 16

16 = 16 (True).

48 ÷ 8 + 2³ = 5 + 3²

Next, we would evaluate the exponents as follows:

48 ÷ 8 + 8 = 5 + 9

6 + 8 = 14

14 = 14 (True).

150/5² = 30 - 4² - 12

By evaluating the exponents, we have the following:

150/25 = 30 - 16 - 12

6 = 2 (False).

9² - 7² = 20 ÷ (7 - 2)

Opening the bracket, we have the following:

9² - 7² = 20 ÷ 5

By evaluating the exponents, we have the following:

81 - 49 = 4

32 = 4 (False).

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The school dance committee can be chosen in 1,86,70,176 ways.

Given, that  7 freshmen, 8 sophomores, 9 juniors, and 9 seniors are eligible to be on the committee.

Also, the school dance committee consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors

So, the number of ways in which the committee can be chosen are

C(7 , 2)×C(8 , 3)×C(9 , 4)×C(9 , 5)

On solving C(7 , 2), we get

C(7 , 2) = (7×6)/2 = 21

On solving C(8 , 3), we get

C(8 , 3) = (8×7×6)/(3×2) = 56

On solving C(9 , 4), we get

C(8 , 3) = (9×8×7×6)/(4×3×2) = 126

On solving C(9 , 5), we get

C(9 , 5) = (9×8×7×6×5)/(5×4×3×2) = 126

So, C(7 , 2)×C(8 , 3)×C(9 , 4)×C(9 , 5) = 21×56×126×126

= 1,86,70,176

The committee can be chosen in 1,86,70,176 ways.

Hence, the school dance committee can be chosen in 1,86,70,176 ways.

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The equation of line that passes through the given point is y = 4.

Given line : y = 7​

So, the slope (m₁ = 0 )

Let's consider the slope of the line perpendicular to the given line as m₂,

m₁ * m₂ = -1

m₂ = 0

Now,

The equation of the line perpendicular to the given line and passing through the point (−8,4) will be

y−y₁ = m(x−x₁)

y−4 =  0(x−(−8)

y-4 = (0)(x+8)

y -4 = 0

y = 4

Thus, the equation of the required line is y = 4.

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The number of the books sold that were Mystery books is 201.

From the information, there were 750 books sold last week at Sid's Bookstore. and the central angle for the Mystery slice is 96.48°.

In this case, it should be noted a circle graph has total angle of 360°.

This will be:

= 96.48/360 × 750

= 201

The number of books is 201.

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The depreciation expenses foe each year is 4375.

Given,

In the question;

The cost of the truck is $20,000 with an estimated life of four years.

The residual value of the truck is $2,500.

To find the depreciation expenses for each year.

Now, According to the question:

Based on the given condition:

Formulate:

(20,000-2,500) ÷ 4

= 17500/4

Cross out the common factor:

= 4375

Hence, The depreciation expenses foe each year is 4375.

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Answer:

see explanation

Step-by-step explanation:

80 and 11x + 1 are a linear pair and sum to 180° , that is

80 + 11x + 1 = 180

81 + 11x = 180 ( subtract 81 from both sides )

11x = 99 ( divide both sides by 11 )

x = 9

Answer:

x=60° y=15° m∠c=45° ∠DBC=105° ∠CBA=75°

Step-by-step explanation:

Since it shows that 7y and 5y make 180 degrees, 12y=180 and y=15

So m∠c=45 degrees and ∠CBA is 75 degrees.

180-(45+75)=60 degrees.

So ∠DBC is 105 degrees.

Val's margin of error is of 10 pounds rounded to the nearest whole number.

In statistics, a confidence interval is a range to estimate for unknown terms. The most common level is the 95% confidence interval.

It can be calculated by

CI = Mean ± margin of error.

Margin of error can be calculated by the following equation:

M = 1.96 s /√n

where s is the standard deviation. n is the sample size.

In this problem:

The standard deviation is 50, hence s = 50

Val weighed 100 cows. n = 100

Then:

M = 1.96 s /√n

M = 1.96 x 50 /√100

M = 1.96 x 50 /10

M = 9.8

Therefore, Val's margin of error is of 10 pounds rounded to the nearest whole number.

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Answer:

2x^3+x^2-23x-4

Step-by-step explanation:

x^2(2x+1)-5x(2x+1)-4(2x+1)

2x^3+x^2-10x-5x-8x-4

=2x^3+x^2-23x-4

Answer:

A = {1,2,3,4,5}

B = {5,6,7,8,9}

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

Explanation:

Consider the set

A = {1,2,3,4,5}

The mean is found by adding up all the values to get 15, then divide by the number of values (5) to get 15/5 = 3

The standard deviation is a bit more complicated, and it depends which version you select (sample vs population). Let's say we go for the population standard deviation. Using a calculator gets us a population standard deviation of roughly 1.414; this value tells us how spread out the data set is. The higher the value, the more spread out the data set will be.

Now consider adding some fixed value to each item in set A. Let's add 4 to each value

We go from A = {1,2,3,4,5} to B = {5,6,7,8,9}

If you were to use a calculator, then the population standard deviation is still roughly 1.414 but the mean is now 7. The standard deviation hasn't changed because the values are still spread out the same way.

Note: infinitely many answers are possible for sets A and B.

Answer:

x=11

Step-by-step explanation:

we know these 2 angles added together is equal to 180 so we can make these 2 equations equal to 180

(6x+12)+(10x-8)=180

16x+4=180

16x=176

x=11

Hopes this helps please mark brainliest

Answer:

SAS Congruence Postulate Theorem (Side-Angle-Side Postulate Theorem)

Step-by-step explanation:

The following pictures shows that 2 pairs of sides are equal between the 2 triangles and a single pair of angles are equal. Thus we know that SAS Congruence Postulate Theorem proves that these triangles are congruent.

Answer:

aprox 57 days

Step-by-step explanation:

2560-1934=626

626/14=44.7142857143

2560/44.7142857143=57.25 days

After two years, compound interest increases your wealth. By the end of two years, compound interest has generated more money than simple interest.

The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money. Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.

As per the given information provided in the question,

[tex]M = s(1+\frac{i}{c_p} )c_p*y[/tex]

Where,

M represents the amount of money,

s represents the initial amount that is $300,

cp represents the compounding period.

Number of years, y = 2

M = 318,479 for Patrick's investment.

M = 331,482 for Brooklyn

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The slope of the line will be;

⇒ m = - 11/8

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

11x + 8y = 176

Now,

We know that;

The standard form of equation of line with slope m and y - intercept at b is,

⇒ y = mx + b

First way;

The  equation of line is,

⇒ 11x + 8y = 176

We can change it into standard form of equation of line as;

⇒ 11x + 8y = 176

⇒ 8y = - 11x + 176

⇒ y = - 11/8x + 22

By compare, We get;

Slope (m) = - 11/8

Second way;

The  equation of line is,

⇒ 11x + 8y = 176

⇒ y = - 11/8x + 22

Differentiate with respect to x,

⇒ dy/dx = - 11/8

⇒ m = - 11/8

Thus, The slope of the line will be;

⇒ m = - 11/8

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I did not understand part A but the answer for part B is OB. $80. hope this helps!

The probability for the given case is 1/3.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The probability of an event cannot be negative.

A spinner has numbers indicated on it from one to six.

Suppose A be the event spinner lannds on 1.

And, B be the event the spinner land on 4.

Now, the probability of any event is the ratio of number of favorable outcome to the total number of outcomes which is given as,

P(A) = 1/6

And, P(B) = 1/6

Thus, the probability of event A or B is given as,

P(A or B) = P(A) + P(B)

              = 1/6 + 1/6

              = 1/3

Hence, the probability that the spinner lands on 1 or 4 is 1/3.

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Answer: its 2/5 + 1/10

Step-by-step explanation: iready got it right

Answer:

x = -1

Step-by-step explanation:

Rewrite the equation as 6x + 8 = 2

Subtract  8 from both sides of the equation.
6x = 2 − 8

Subtract 8 from 2.

6x = −6

Divide each term in 6x = −6 by 6 and simplify.

Divide each term in 6x = −6 by 6.
[tex]\frac{6x}{6} = \frac{-6}{6}[/tex]

Simplify the left side.
[tex]x=\frac{-6}{6}[/tex]
Simplify the right side.

Divide -6 by 6

x = -1

Answer:

See below

Step-by-step explanation:

NOT SURE WHY MY PREVIOUS ANSWER GOT DELETED

(1 + .07/12)^12 = 1.07229     WHICH IS   7.229 %   a.p.y.

           ( same answer....less detail)

The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 100 inches will be 4.55.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The longest line which can be drawn inside the circle will be the diameter.

The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation.

Distance traveled in one rotation = Perimeter of the wheel.

⇒ 2π(3.5) = 21.99

The number of rotations = 100/21.99 = 4.55

Hence "The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 100 inches will be 4.55".

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The correct option is A . 12(3+2+4) shows the greatest common factor of these three values using the distributive property

A factor is an integer in mathematics that, when multiplied by other integers, produces the desired results. The resultant total is also known as the factors. The numbers can often be combined in a broad variety of ways. If you are familiar with the multiplication tables, it will be simple for you to determine the factors.

When two or more numbers are combined, the largest number is the greatest common factor (GCF). They are divided by the biggest number, which yields a natural number (factor). There are a few things that both share once all the variables that effect the number have been identified. The term "largest common factor" refers to the common factor among the others having the highest number.

The product of the common prime factors of 2 or more numbers is the greatest common factor(GCF) of the numbers.

Using the distributive property, it can be written that  .a(b+c) = ab + ac

Step 2

Write each number as the product of its prime factors. The product of the common factors is the greatest common factor(GCF) of the numbers.

The numbers,36 , 24 , 48  can be factored as follows.

36 = 2 * 2 * 3 * 3

24 = 2 * 2 * 3 * 2

48 = 2 * 2 * 3 * 2 * 2

Hence, the greatest common factor(GCF) of these numbers is equal to  

2 * 2 * 3  or 12 .

Take out the greatest common factor(GCF), 12 from the expression,  36+24+48 using the distributive property to obtain the result.

36+24+48 = 12 * 3 + 12 * 2 + 12 * 4

                 = 12 ( 3 + 2 + 4 )

Hence, the correct option is A .

Option B is incorrect as the factored out term is 6, which is not the greatest common factor(GCF) .

Option C is incorrect as the factored out term is 4, which is not the greatest common factor(GCF) .

Option D is incorrect as the factored out term is 3, which is not the greatest common factor(GCF) .

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Answer:

I notice the x intercepts affects the slope of the equation

Step-by-step explanation:

Answer:

Given: The equation of the rainbow has a shape of a parabola:

In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points

We will draw a line that will be intersected with the parabole at two points and one of them has x = 4

See the following picture:

As shown in the figure, the plane takes off from the point (-18, 0)

And it makes a slanted line that cuts through the rainbow at two points.

The equation of the linear function will be: y = 0.5x + 9

The table of the linear function will be as follows:

2. What is the domain and range of the rainbow?

Domain = all the possible value of x = ( -∞, ∞ )

Range = all the possible value of y = ( -∞ , 27 )

3. Explain what the domain and range represent in context.

The domain is all the possible values of x that can be substituted into the function

So, as we have a polynomial function, the domain will be all real numbers

The range is all the possible values of y that will be results when we have substituted with the x-values

As we have a parabola, the range will be ( -∞ , 27 )

What are the X- and y-intercepts of the rainbow?

As shown in the figure:

There are two points:

Step-by-step explanation:

The equivalent ratios are 6:3, 24:12 and 18:9.

According to the question,

We have the following information:

We have a table where number of people and  benches are given.

(Note that equivalent ratios mean that when we simplify it then the ratio should be equal to the original ratio.)

Now, we will find the equivalent ratios column-wise:

In first column, we have 6 and 3.

6:3

Now, in second column, we have:

_:12

Now, dividing 12 by 3, we have 4.

Multiplying 4 into 6:

24:12

Now, in third column, we have:

18:_

Dividing 18 by 6:

18/6 = 3

Multiplying 3 by 3:

18:9

Hence, the equivalent ratios are 6:3, 24:12 and 18:9.

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