PPPPPLLLLZZZZ HELPPPP
Use the function f(x) = -16x² + 60x + 16 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph

Answers

Answer 1

Here we have the quadratic function:

f(x) = -16*x^2 + 60*x + 16

We can see that it is in standard form:

y = a*x^2 + b*x + c

a) First we want to completely factorize the function f(x).

To do it, we first need to find the roots of f(x).

Remember that for a generic quadratic equation:

a*x^2 + b*x + c = 0

whit roots x₁ and x₂, the factorized form is:

a*(x - x₁)*(x - x₂)

And the roots are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

Then for the case of f(x) = -16*x^2 + 60*x + 16, the roots are:

[tex]x = \frac{-60 \pm \sqrt{60^2 - 4*(-16)*16} }{2*(-16)} = \frac{-60 \pm 68}{-32}[/tex]

So the two roots are:

x₁ = (-60 + 68)/-32 = -0.25

x₂ = (-60 - 68)/-32 = 4

Then the factorized form is:

f(x) = -16*(x - 4)*(x + 0.25)

B) We already found the roots, which are:

x₁ =  -0.25

x₂ =  4

These are the x-intercepts:

(-0.25, 0) and (4, 0)

C) We can see that the leading coefficient is negative.

This means that the arms of the graph go downwards, so as |x| increases, the value of f(x) tends to negative infinity.

D) To graph f(x) we can find some of the points of the graph (like the x-intercepts and some more of them) and then connect them with a parabola curve, the graph that you will get is the one that you can see below.

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PPPPPLLLLZZZZ HELPPPPUse The Function F(x) = -16x + 60x + 16 To Answer The Questions.Part A: Completely

Related Questions

Write the equation of the line perpendicular to y = 8 - 5z that contains the point (0, 0) . Fill in the slope and y-intercept

Answers

The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.

8y=-5x+16

y=-5/8x+2.

To be perpendicular, the slope has to be 8/5.

What is the slope-intercept form of the line?

The slope-intercept form is y=mx+c

Where m is the slope and c is the y-intercept.

So y=8/5x+b.

We can plug in the given coordinates to get

7=8/5*-5+b

7=-8+b

b=15.

So eqn is y=8/5x+15 or in point-slope form, y=8/5x+15

5y=8x+75

5y-8x=75

The equation of the line perpendicular to y = 8 - 5z is 5x+8y=16.

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please help!! easy but i don't understand <3

Answers

in essence it's just asking on getting the equation of that line in more or less slope-intercept form, hmmm well, it's a line, so all we need is two points to get it, hmmm let's see let's use the starting point and terminal point, so we know it goes through the origin, (0,0) and also goes through (1, 0.7), let's change 0.7 to a fraction, so its 7/10, ok, let's use those two points from it.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{\frac{7}{10}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{7}{10}}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{~~ \frac{7}{10}~~}{1}\implies \cfrac{7}{10}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{\cfrac{7}{10}}(x-\stackrel{x_1}{0})\implies y = \cfrac{7}{10}x[/tex]

Find the equation of the line that is parallel to x=5y-8 and pass through (6, -5) in slope intercept form

Answers

Answer:

y=1/5x-31/5 (or y=0.2x-6.2 in decimals)

Step-by-step explanation:

x=5y-8     (original equation)

x+8=5y (Addition Property of Equality)

1/5x+8/5=y (Division Property of Equality, slope of original equation is 1/5)

y-y1=m(x-x1)    (point-slope formula)

y-(-5))=1/5(x-(6)) (plug in the slope that was found earlier and the point given in the question)

y+5=1/5(x-6)

y+5=1/5x-6/5   (Distributive Property of Multiplication)   Note:  5 = 25/5

y=1/5x-31/5 (Subtraction Property of Equality, and there's your answer)

y=0.2x-6.2 (This is the same answer, but written with decimals)


Round 4.789443 to the nearest whole number

Answers

Answer:

5

Step-by-step explanation:

I don't think I should have to explain this but if it's in between 4.5 and 5 it will be 5 and if it's 4.5-4 it would be 4

5. 7 is above 5 so you round the number higher

A county has constructed a conical building to store sand. The cone has a height of 101 m and a diameter of 330 m. Find the volume of this building to the nearest hundredth. Use 3.14 for π.

Answers

Answer:

2878045.500 cubed metres

Step-by-step explanation:

volume = 1/3* pie* r*r*h

= 1/3 *3.14*165*165*101

=2878045.5 cubed metres

i hope it's helpful

Three friends live in three different states. Monica lives in Rhode Island, Anthony lives in Ohio, and Thomas lives in Colorado.
a.) Determine the sales tax rate in each state.

Answers

Sales tax in Colorado is 2.85%, in Ohio is 5.50%, and in Rhode Island is 7%.

Colorado: 3.50 = 1003.60 = X3.60 x 100 / 3.50 = X360 / 3.5 = X102.85 = X2.85% = Sales tax

Ohio: Y = 1.055X10 x 1.055 = Y10.55 = Y10 = 10010.55 = X10.55 x 100 / 10 = X1055 / 10 = X105.5 = X5.5% = Sales tax

Rhode Island: 10 = 10010.70 = X10.70 x 100 / 10 = X1070 / 100 = X107 = X7% = Sales tax

Therefore, sales tax in Colorado is 2.85%, in Ohio is 5.50%, and in Rhode Island is 7%.

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Over a lengh of 101 inches the hight changes 5" what is the angle?

Answers

Answer:

  2.83°

Step-by-step explanation:

The tangent of an angle is the ratio of rise to run.

 θ = arctan(5/101) ≈ 2.83°

_____

We assume the length is referring to the horizontal distance.

If it is the distance along the path, then the angle is ...

  θ = arcsin(5/101) ≈ 2.84°

What is the slope of the line?
1/2 2 1 -2

Answers

Answer:

the slope of the line is 2

Step-by-step explanation:

Answer:

The slope of the line is 2.

Step-by-step explanation:

The point where the line crosses the y-axis, also known as the y-intercept, is (0,1). The next clear point is (1,3).

We can use the formula for finding slope here.

[tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]

If we plug in the points, with (0,1) being the first and (1,3) being the second, we'll get this:

[tex]\frac{3-1}{1-0} --> \frac{2}{1} --> 2[/tex]

Therefore, the slope is 2.

Below the function h (x) ang g (x) are graphes. At which values of x is true that h (x) > g (x)? Select all that apply.

Answers

Answer:

25

Step-by-step explanation:

At x = 10 and 31 the value of the function h(x) is greater than g(x) thus options (A) and (D) are correct.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given graph of the function,

At x = 10 the h(x) > g(x)

At x = 31 the h(x) > g(x)

Hence "The value of the function h(x) is bigger than g(x) at x = 10 and 31".

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Solve for the value of x

Answers

Answer:

x=9

Step-by-step explanation:

To solve for x, you can set up a proportion between the 2 triangles we see.

The small triangle can be written as [tex]\frac{16}{20}[/tex], and the large triangle can be written as [tex]\frac{16+12}{20+2x-3} = \frac{28}{2x+17}[/tex].

Set both proportions equal to each other.

[tex]\frac{16}{20}=\frac{28}{2x+17}[/tex]

Cross multiply and solve for x.

[tex]16(2x+17)=(28)(20)[/tex]

32x+272=560

32x=288

x=9

What is the mathematical formula of ligma

Answers

Who's Joe? I am in dire need of therapy.

At​ noon, a tank contained 8 in. of water. After several​ hours, it contained 6 in. of water. What is the percent decrease of water in the​ tank?

Answers

Answer:

25%

Step-by-step explanation:

8-6=2

2/8=0.25

0.25×100=25%

Expand and simplify: (x - 7)(x+7)

Answers

Answer:

[tex]x^{2} -49[/tex]

Step-by-step explanation:

Answer:

[tex](x-7)(x+7) =x^2 -7^2 = x^2 -49[/tex]

Step-by-step explanation:

Write an equation in slope-intercept form for the line with y-intercept −8 and slope 1/3

Answers

Answer:

y=1/3x-8

Step-by-step explanation:

The slope intercept form of a line is y=mx+b

m stands for slope and b stands for y intercept

So ... simply put 1/3 in for m and -8 in for b

whats 3-6h if h = -1

Answers

Answer:

9 is the answer.

Step-by-step explanation:

Given:

h = -1

=> 3-6h

=> 3 - 6(-1)

=> 3 + 6

=> 9

Therefore, 9 is the answer.

Hoped this helped.

A bag of mixed nuts has 18 almonds, 8 cashews, and 14 peanuts. If one nut is selected, what is the probability that a peanut is chosen?

Provide the answer as a simplified fraction.

Answers

Answer:

7/20

Step-by-step explanation:

Answer:

ok so here is answer option no1

1/8 + 1/4 = 3/8

or you could do

18 plus 14 equals 32divided into 8 equals 4

Step-by-step explanation:

if this is wrong I'm very very very really really really sorry.

7. A boutique is offering a 25% discount on purchase made in cash. Calculate the cash price Janelle paid for articles totaled to $465.​

Answers

Answer:

$348.75

Step-by-step explanation:

$465 * 25%= 116.25

465-116.25 = $348.75

A certain function multiplies Each input number by three to produce an output number given that X represents the input numbers and Y represents the output numbers which graph represents the function.

Please answer
No links
Picture is included

Answers

Answer:

The answer is A. Hope this helped!!!!!!

Answer:

answer C because is x is input and is multiplied by 3 so the function would have been y=3x so that is C

Line f is parallel to line g.which statements about line f and g is true

Answers

Answer:

Step-by-step explanation:

They have different y intercepts.

They have the same slope.

Here are 2 examples

y = 3x + 5

y = 3x + 19

The slopes are both three. The y intercepts are 5 for the top equation and 19 for the bottom equation.

They are both lines. That means their  domain is -infinity <x < + infinity

Their range is - infinity <y < + infinity.

We are excluding  examples like x = 3 and x = 5 and y = 1 and y = 3.

It is true that they both are parallel in both cases, but the discussion for each pair is a little different.

Simplify the expression
3+4·10 – 8

Answers

Answer:

35

Step-by-step explanation:

one word: PEMDAS. technically they are all a bunch of words but whatever...

P: parentheses

e: exponents

m: multiply

d: divide

a: add

s: subtract

first we multiply 4*10 since that's first on the list

4*10=40

we have

3+40-8

then we add

3+40

which is 43

then we subtract 8 from it as we have 43-8

which is in the end:

35

35

Step by step equation

Help help help help math math

Answers

Since the two lines are parallel the interior angles,
Angle 53 and angle 5, are supplementary angles therefore
53 + 5 = 180
5 = 127

Simplify completely

(192x^12/3x^3)^1/3

Show all work for full credit

Answers

Answer and Explanation: The answer and explanation is in the image.

Nam
20. Carol bought 5 pork chops and 3 steaks.
Each pork chop weighed 0.32 pound
and each steak weighed 0.8 pound. How
Temand
many pounds of meat did Carol buy in
telall?

Answers

Answer: Carol bought 4 pounds(lb) of meat.

Explanation: 0.32 x 5 = 1.60, and 0.8 x 3 = 2.40, and 1.60 + 2.40 = 4.

The weight of the meat bought by Carol is 4 pounds.

What is an expression?

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that Carol bought 5 pork chops and 3 steaks. Each pork chop weighed 0.32 pounds and each steak weighed 0.8 pounds.

The weight of the meat will be calculated as:-

0.32 x 5 = 1.60,

0.8 x 3 = 2.40,

Total weight,

1.60 + 2.40 = 4 pounds

Therefore, the weight of the meat bought by Carol will be 4 pounds.

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What is the value of x and y?

Answers

Answer:

x = 90y = 43

Step-by-step explanation:

The angle bisector in this isosceles triangle is also its altitude. It meets the base segment at right angles.

  x° = 90°

__

The acute angles in a right triangle are complementary.

  y° = 90° -47°

  y° = 43°

Evaluate the expression.
3x + 2y for x = 4.2, y = 2.7

Answers

Answer:

18

Step-by-step explanation:

4.2 • 3= 12.60

2.7 • 2= 5.4

12.6+ 5.4=

18.0

Explain how to find the distance between two integers using the difference.

Answers

Answer:

read explanation for answer

Step-by-step explanation:    Finding the distance between any two integers is obtained by;

Taking the absolute value of the difference between the two integer values.

For instance :

Point A = - 10

Point B = 5

The distance between the two integer points is :

Difference = Point A - Point B = - 10 - 5 = - 15

Absolute value = |-15| = 15

Therefore, This procedure works for any pair of integer distances.

Answer:Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them.

Step-by-step explanation:

The vertices of a triangle are A(0,0),B(3,8) and C(9,0). What is the area of this triangle?

Answers

Answer:

9

Step-by-step explanation:

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Fill in the numbers for each corresponding letter combination within the formula.

Fill in your formula like this: 0(8-10) + 3(0-0) + 9(0-8).

Subtract the numbers within the parentheses.

0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.

Multiply that result by the number to the left of the parentheses.

0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.

Add the three products together.

0 + 0 + 18 = 18

Divide the sum of the three products by 2.

18 ÷ 2 = 9

Answer:36

Step-by-step explanation:

16. Use the vertical line test to determine whether the relation is a function.

Answers

Answer:

neither of them are

Step-by-step explanation:

Find the results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

Answers

Answer:

[tex]\huge\boxed{\overrightarrow{u}-\overrightarrow{v}=\left<-10;\ -3\right>}[/tex]

Step-by-step explanation:

[tex]\overrightarrow{u}=\left<-8;\ 4\right>;\ \overrightarrow{v}=\left<2;\ 7\right>\\\\\overrightarrow{u}-\overrightarrow{v}=\left<-8;\ 4\right>-\left<2;\ 7\right>=\left<-8-2;\ 4-7\right>=\left<-10;\ -3\right>[/tex]

Answer:

Step-by-step explanation:

-u-v = 6,-11

u-v = -10,-3

v-u = 10,3

There is a group of 5 turtles near the playground. More turtles joined. Now there are 13 turtles. How many turtles joined the group?

Answers

Answer:

8 turtles joined the group

Step-by-step explanation:

13-5=8

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