On a coordinate plane, a parabola opens up. It goes through (negative 7, 5), has a vertex at (negative 4, negative 4), and goes through (negative 1, 5).
The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.

The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).

Answer:

its "a" your welocome

Step-by-step explanation:

i did the test

number 9 is 36  12x3 is 36

The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval  (4, −∞).

What is an increasing and decreasing functions?

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We have,

[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]

[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 4, 4i, −4i, 10, 8

∴ f′(x) = 0  

   x = 4,

Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)

In interval (−∞, 4),  f′(x) < 0

Hence, the given function (f) is strictly decreasing in interval (−∞, 4)

​

In interval (4, −∞),  f′(x) > 0

Hence, the given function (f) is strictly increasing in interval  (4, −∞)

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​

3x²-2x+5 is the other factor of the above polynomial (6x³-x²+8x+5) other than (2x+1).

In mathematics, a polynomial is an equation made up of coefficients and indeterminates, also referred to as variables. Only addition, subtraction, multiplication, and powers of positive-integer variables may be utilized to solve it. An example of a polynomial with one uncertain x is x² + 4x + 7.

Polynomials are commonly used in calculations in both mathematics and science. For instance, in the fundamental sciences of chemistry, physics, economics, and social science, they are used to define polynomial functions. They are also used in numerical analysis and calculus to approximate other functions. Simple word problems to complex scientific conundrums are all represented by polynomial equations. Polynomials are used in advanced mathematics.

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Coppinger Corp is using Scenario Analysis.

Given, that Coppinger Corp is considering the use of a computer to assign probability distributions to the input variables used in the analysis.

The computer would then randomly select input variables from their distributions and calculate npvs based on those selections

Now, A scenario analysis consists of multiple inputs. For eg. a Company may consider how an increase in available fuel can impact their number of goods sold etc.

Here, also Coppinger Corp is assigning multiple values to the computer and getting outputs.

So, this can be the Scenario Analysis.

Hence, Coppinger Corp is using Scenario Analysis.

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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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Answer:

-8

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

Answer:

it's 50 g

Step-by-step explanation:

it's like a multiplying assberry kehe

1. The linear function .f(2) = 79.4, therefore, test average for maths class after 2 test is: 79.4

2. Using the function table, the test average for science class is after the second test is: 84.

3. f(4) = 79.8

4. g(4) = 80

5. Science class was higher.

The equation of a linear function is given as .f(x) = mx + b, given that m represents the slope/unit rate, and b is the y-intercept or starting value.

The linear function for average test score in maths class is given as, .f(x) = 0.2x + 79

Write the linear function for science class;

Slope (m) = change in y/change in x = (84 - 82)/(2 - 3) = 2/-1

Slope (m) = -2

Substitute m = -2 and (x, y) = (3, 82) into y = mx + b:

82 = -2(3) + b

82 = -6 + b

82 + 6 = b

88 = b

b = 88

Substitute m = -2 and b = 88 into g(x) = mx + b:

g(x) = -2x + 88

Part 1:

Substitute x = 2 into .f(x) = 0.2x + 79

.f(2) = 0.2(2) + 79

.f(2) = 79.4

Test average for maths class after 2 test is: 79.4

Part 2:

Using the function table, when x = 2, the test average for science class is: 84.

Part 3:

Substitute x = 4 into  .f(x) = 0.2x + 79

.f(4) = 0.2(4)+ 79

.f(4) = 79.8

Part 4:

Substitute x = 4 into g(x) = -2x + 88

g(4) = -2(4) + 88

g(x) = 80

Part 5:

Science class had a higher test 4 average of 80.

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Answer:

b & d

Step-by-step explanation:

Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.

Proportion refers to the quantity of a value or variable contained in another value.

Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.

Proportions are depicted using fractions, decimals, or percentages.

The number of avocados required for 4 orders of guacamole = 6.5

The total number of orders of guacamole required = 14

The number of avocados to make 1 order = 6.5/4

The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)

Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.

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Answer: -5,5 = B

Step-by-step explanation:

Kelly fill 200 sacks with the weight of 2000 kg potatoes and in each sack, she can fill up to 12.5 kg of potatoes.

The gravitational attraction of an item near the Earth or another celestial body toward the center of the body. The weight of an item is determined by its mass and the strength of the gravitational force. We use the following generic formula to compute weight: W = mg. Where 'W' is the object's weight,'m' is the object's mass, and 'g' is the acceleration due to gravity. The value of g on Earth is 9.8 m/s2. The most frequent definition of weight is the force imposed by gravity on a body.

Here,

weight of potatoes she has=2500 kg

weight of each sack that contain the potatoes=12.5 kg

with this, she can fill,

=2500/12.5

=200 sacks

Kelly fills 200 sacks with 2000 kg of potatoes, and each sack can hold up to 12.5 kg of potatoes.

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The perimeter of rectangle ABDC is 61.24 units.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The rectangle ABDC is given in the question which has:

AB = 8 and AC = 24

Here AC is the diagonal of the rectangle which is the hypotenuse in a right triangle.

As per Pythagoras's theorem,

AC² = AB² + BC²

24² = 8² + BC²

576 = 64 + BC²

BC² = 512

BC = 22.62

The perimeter of rectangle ABDC = 2(AB + BC)

The perimeter of rectangle ABDC = 2(8 + 22.62)

The perimeter of rectangle ABDC = 2(30.62)

The perimeter of rectangle ABDC = 61.24 units

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The amount that Charlotte earn per hour on the weekends than she earns during the week is: C. $2.30.

Number of dollars earn per hour during the week = x

Number of dollars earn per hour on the weekend =y

Formulate an equation

13x + 14y = 250.90  Equation 1

15x + 8y = 204.70 Equation 2

Solving  for x and y by multiply equation 1  by -8 and equation 2 by 14 -104x - 112y = -2007.20

210x +112y = 2865.80

106x             = 858.60

Divide both sides by 106x

x = 858.60/106

x =  $8.10

Substitute x into eq 1 so as to solve for y

13(8.10) + 14y = 250.90

105.30 + 14y = 250.90

Subtract 105.30 from both sides

14y = 145.60

Divide both side by 14y

y = 145.60 /14

y  = 10.40

Hence,

Additional earning per hour = y-x

Additional earning per hour = $10.40 - $8.10

Additional earning per hour=$2.30 per hours

Therefore the correct option is C.

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The different-sized groups are three groups of each size (35), five groups of each size (21), and seven groups of each size (15).

Given that;

A landscaper must plant 105 little bushes on a park's grounds. He intends to divide the bushes into equal groups.

We are asked to find what different-sized groups could a landscaper can make.

Here, we use Prime factorization;

Let,

∴ 105 = 3 * 5 * 7

From the above factors, we can find different groups as;

3 groups of each sized 35.

5 groups of each sized 21.

7 groups of each sized 15.

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Answer: ___________________________________________

58/15

a) The margin of error for an 80% confidence interval in Arkansas is 0.1041

b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

n = 3600

standard deviation = 399.876

Confidence Interval = 80%

a) α = 0.20

The margin of error = Zα/2 (σ / √n)

Zα/2 = 1.4395 --- (From the tabular value)

The margin of Error = 1.4395 + 399.876 / √3600

Therefore, the Margin of Error = 8.1041

b) Margin of Error = 0.07 = 7%

α = 0.20

Critical Value = 1.2816

Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²

n = [(1.2816 * 399.876) / 0.07]²

n = 53599358.98

Therefore, Sample size, n = 53599359

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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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Answer:

[tex]g(x) + h(x) = x^3 + 6x + 5[/tex]

Step-by-step explanation:

We are told that:

[tex]g(x) = x^3 + 5x[/tex]

[tex]h(x) = x + 5[/tex],

and we are asked to find an expression for [tex]g(x) + h(x)[/tex].

In order to find the expression for  [tex]g(x) + h(x)[/tex], we have to simply add the expressions of [tex]g(x)[/tex] and [tex]h(x)[/tex] together:

[tex]g(x) + h(x)[/tex]

= [tex]x^3 + 5x + x + 5[/tex]

= [tex]x^3 + 6x + 5[/tex]

Answer:

41 pounds of raspberries and 25 pounds of grapes

Step-by-step explanation:

x = pounds of raspberries
y = pounds of grapes

1.50x + 2.75y = 130.25
x + y = 66 --> y = -x + 66

Substitute and solve for x:
 1.50x +2.75(-x +66) = 130.25
1.50x - 2.75x + 181.5 = 130.25
150x - 275x + 18150 = 13025
           -125x +18150 = 13025
                       -125x = -5125
                              x = 41

Substitute x to find y:
41 + y = 66
y = 25

Answer:

There were 41 pounds of raspberries sold and 25 pounds of grapes sold.

Step-by-step explanation:

The solution for the expression is X =87/ 48 or 1.812

To solve  for x in the equation we follow the step below:

Step 1: Open the bracket by multiply 4

= 4x +4x/3 = 9 2/3

= 4x +  4x /3 = 29/3

Step 2: Evaluate for X

= [tex]\frac{12x + 4x}{3}[/tex] = [tex]\frac{29}{3}[/tex]

= [tex]\frac{16x}{3}[/tex] =[tex]\frac{29}{3}[/tex]

Step 3: Cross multiply

: 3 (16x) = 3(29)

48x = 87

Step 3: Divide both sides by 48

=[tex]\frac{48x}{48}[/tex] =[tex]\frac{87}{48}[/tex]

x = [tex]\frac{87}{48}[/tex] = 1.812

Therefore, the solution for the expression is X =87/ 48 or 1.812

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The radius of each of the smaller balls is R = 2r.

You can use a tape measure, for instance, to directly measure the distance around the sphere's widest point. The radius of this circle, which serves as the sphere's circumference, is one. A circle's circumference is computed as 2 x x radius. Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We can use the following formula to get the volume of a sphere whose radius is "r": A sphere's volume is equal to 4/3r³.

Given,

A steel ball is melted down to make eight smaller identical balls. If the radius of the original steel ball was 20 cm:

Let the spherical ball's radius be R.

And with r being the radius of 8 similar balls,

According to the inquiry,

Volume of 8 similar balls = the volume of a larger sphere

3/4πR³ = 8 × 3/4πr³

R³ = 8r³

R = 2r

The radius of each of the smaller balls is R = 2r.

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Answer:

to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

Step-by-step explanation:

No, we cannot find a unique price for an apple and an orange

Let the price of an apple be $x and that of orange be $y.

Condition 1.

They need $10 for 4 apples and 4 oranges.

Then, 4x + 4y = 10

or, 2x + 2y = 5 .....(1)

Condition 2.

They need $12 for 6 apples and 6 oranges.

Then, 6x + 6y = 12

or, 2x + 2y = 5 .....(2)

Two identical linear equations have been discovered.

They do, however, create a system of dependent linear equations that reduces to:

2x + 2y = 5

There are infinite possible solutions to this linear equation.

Thus, we get the conclusion that an apple and an orange cannot have different prices.

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The runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.

We need to select all the runners whose speeds are in a proportional relationship with each other.

We find the speed using formula, speed = distance / time

Name         Time (seconds)           Distance (miles)              Speed(mps)

Liam                   306.6                           0.5                      0.5/306.6 = 0.0016    

Taylor                756.36                          1.2                      1.2/756.36 = 0.0016

Sarah                 504.35                         0.7                     0.7/504.35 = 0.0014

Ashley               459.9                          0.75                    0.75/459.9 = 0.0016

Connor              600.5                              1                          1/600.5 = 0.0017

Nathan               942.75                         1.5                     1.5/942.75 = 0.0016

Juan                   827.82                         1.35                  1.35/827.82 = 0.0016

Katie                   429.48                          0.6                   0.6/429.48 = 0.0014

Therefore, the runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

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Answer:

y+1=-4(x+5)

Step-by-step explanation:

it changed to point slope form so now it’s different

the equation is y-y1=m(X-x1)

y-(-1)=m(x-(-5)

y+1=m(x+5)

Now to find slope y2-y1/x2-x1

-5+1/-4+5

-4/1

-4 is the slope so we just fill it in

y+1=-4(x+5)

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The test statistic is -2.60 as a sample of 380 patients found that 95 were uninsured.

A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. For instance, the Z-statistic, which has the typical normal distribution under the null hypothesis, is the test statistic for a Z-test. Here,

n=380

x=95

p=95/380

p=0.25

test=(0.25-0.31)/√(0.28(1-0.28)/380)

test=-2.60

The test statistic is -2.60 because 95 out of 380 patients in the sample did not have insurance.

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