1. Use the function f (x) to answer the questions:

f(x) = 2x^2 − 3x − 5

Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

2. The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company: (picture of graph attached below)

Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)

Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (3 points)

Part C: Describe the constraints of the domain. (3 points)

I promise to give braInliest to the correct answer.

Step-by-step explanation:

product=× three=3 a number is unknown =x plus=+ five=5 is=equals to 20

3×x +5=20

3x+5=20

Subtract 5 from both sides

3x+5-5=20-5

3x=15

3x/3=15/3

x=5

The integral of [tex]\int {x(25x^2 + 1)} \, dx[/tex] is [tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]

The integral expression is given as:

[tex]\int {x(25x^2 + 1)} \, dx[/tex]

Start by expanding the bracket

[tex]\int {25x^3 + x} \, dx[/tex]

Next, we integrate each term in the expression

[tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]

Hence, the integral of [tex]\int {x(25x^2 + 1)} \, dx[/tex] is [tex]\frac{25}{4}x^4 + \frac{x^2}{2} + C[/tex]

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[tex]\text{Given that,}~ p(x) = x^2 +3 ~ \text{and}~ h(x) = \sqrt{x-3} \\\\(p \circ h)(x)\\\\=p(h(x))\\\\=p\left(\sqrt{x-3}\right)\\\\=\left(\sqrt{x-3} \right)^2 +3\\\\=x-3 +3\\\\=x[/tex]

Answer:

C. 1/3

Step-by-step explanation:

there are 48 possible outcomes, and out of those 16 of them have a sum of 3.

16/48

simplify

1/3

Answer:

Step-by-step explanation:

12*6.5%=0.72

12+15%=13.8

0.72+13.8=14.52

For the horizontal segment, the value of the ordinate will not change. Then the second point will be (x, 3.5).

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

The point is given as (3, 3.5).

Then name a second point so that the two points form a horizontal segment.

For the horizontal segment, the value of the ordinate will not change.

Let x be the abscissa.

Then the point will be given as (x, 3.5).

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Answer: Choice B

It is not a valid sample because it is not a random sample of the population.

Explanation:

The researcher should have randomly selected the participants, either by picking names out of a hat, using a random number table, or some kind of computer software to pick the names. Letting the first 8 people form the sample is very likely not representative of the population at large. We have a lot of bias here. Therefore, this is not a valid sample.

Answer:

2.5 seconds.

Step-by-step explanation:

h(t) = -4t^2 + 20t

= -4(t^2 - 5t)

Convert to vertex form by completing the square:

h(t) = -4[(t - 2.5t)^2 - 6.25]

     = -4(t - 2.5)^2 + 25    <--------- vertex form

So the vertex is at the point (2.5, 25).

So the athlete reaches the maximum height ( of 25 feet), after 2.5 seconds.

The graph is shown below. Then the linear system crosses each other at (1.5, 5).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear equations are given below.

y = 5 ...1

2x + y = 8 ...2

The graph is shown below.

By equations 1 and 2. Then we have

2x + 5 = 8

     2x = 3

       x = 1.5

Then the lines cross each other at (1.5, 5).

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Answer: The mean of the data is 278.

Step-by-step explanation:

To the the mean of the data, we’ll have to add all the numbers up and divide it by the amount of data.

275+279+279+276+278+277+280+282+284+270=2780

2780/10=278

The sequence converges to 5 as n goes to ∞. We can prove this rigorously:

The claim is that, for [tex]n\in\Bbb N[/tex],

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = 5[/tex]

By definition of the limit, this means for any ε > 0, there exists some N such that for any n larger than N, we have

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| < \varepsilon[/tex]

In order to ensure this inequality, we work backwards to find N in terms of ε :

[tex]\left| \dfrac{5n-1}{n+1} - 5 \right| = \left| \dfrac{5n-1 - 5(n+1)}{n+1} \right| = \dfrac4{|n+1|} < \varepsilon[/tex]

n is a natural number, so n + 1 > 0 and |n + 1| = n + 1. Then

[tex]\dfrac4{n+1} < \varepsilon \implies \dfrac{n+1}4 > \dfrac1\varepsilon \implies n+1 > \dfrac4\varepsilon \implies n > \dfrac4\varepsilon - 1[/tex]

Let N be the smallest natural number greater than or equal to 4/ε - 1, i.e.

[tex]N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then the proof follows: suppose

[tex]n \ge N = \left\lceil \dfrac4\varepsilon - 1 \right\rceil[/tex]

Then

[tex]n \ge \left\lceil\dfrac4\varepsilon - 1\right\rceil \implies n > \dfrac4\varepsilon - 1 \\\\ \implies n+1 > \dfrac4\varepsilon \\\\ \implies \dfrac4{n+1} < \varepsilon \\\\\implies \left|\dfrac{5n-1}{n+1}-5\right| < \varepsilon[/tex]

as required.

Or we can avoid the rigor and use some facts we know about limits:

[tex]\displaystyle \lim_{n\to\infty} \frac{5n-1}{n+1} = \lim_{n\to\infty} \frac{5-\frac1n}{1+\frac1n} = 5[/tex]

since 1/n converges to 0 as n goes to ∞.

Answer:

23.5

Step-by-step explanation:

let's take the number as X

2X+20=66.3

2X=66.3-20

X=23.15

Builder can build 7 one bedroom houses and 5 two bedroom houses.

What is consistent Equation?

A linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.

Let x represents the number of one-bedroom houses and y represents the number of two bedroom houses.

According to Question,

Total number of houses is 12 i.e. x + y = 12..........(i)

Total we have 88 windows in which 6 windows can be use in one bedroom house and 9 windows can be used in two bedroom house so,

6x + 9y = 88 ..................(ii)

From Equation (i) and (ii), we get

x = 7 and y = 5

Thus, Builder can build 7 one bedroom houses and 5 two bedroom houses.

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Answer:

Step-by-step explanation:

A scientist is working with 12 meters of gold wire. How long is the wire in millimeters?

12 meters = 12000 mm

(1m = 1000 mm)

12 * 1000 = 12000

Answer:

Table B

Step-by-step explanation:

A function is present when x-value can only have a single y-value.

Answer: The answer to your first question is b^2+2b-8. You second answer is y^2-4y+3.

Step-by-step explanation: Now, these questions deal with the FOIL method commonly taught in schools. The FOIL method is to turn factored binomials back into quadratics. Let's first go over what FOIL means.
F - First. So you multiply the first terms in each set of parenthesis, so b times b and y times y make b squared and y squared.
O - Outer. Multiply the two outer terms together, so b times -2 and y times -3. Remeber to pay attention to your signs when you multiply during these probelms!
I- Inner. Multiply the two inner terms together. so 4 times b and -1 times y. Again, make sure the signs are incorporated!
L - Last. Multiply the last terms in the binomials. So 4 times -2 and -1 times -3.

Now that we have our numbers, we have expanded quadratics that look like these:
b^2 -2b+4b-8 and y^2-3y-y+3

Now combine the two middle terms into +2b and -4y, and your answers are b^2+2b-8 and y^2-4y+3.

Answer:

2 pounds.

Step-by-step explanation:

We have been given that Luke bought 256 ounces of strawberries. He divided them evenly between 8 different pies. We are asked to find the pounds of strawberries that Luke put on each pie.

First of all, we will convert 256 ounces into pounds.

We know that 1 pound equals 16 ounces. To convert 256 ounces into pounds, we need to divide 256 by 16.

[tex]256[/tex] [tex]ounces=\frac{256}{16}[/tex] [tex]pounds=16[/tex] [tex]pounds[/tex]

Now we will divide 16 pounds by 8 to find number of strawberries put on each pie.

[tex]Pounds[/tex] [tex]of[/tex] [tex]strawberries[/tex] [tex]on[/tex] [tex]each[/tex] [tex]pie=\frac{16}{8}[/tex]

[tex]Pounds[/tex] [tex]of[/tex] [tex]strawberries[/tex] [tex]on[/tex] [tex]each[/tex] [tex]pie=2[/tex]

Therefore, Luke put 2 pounds strawberries on each pie.

Answer:

x = 4/7, 5

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Answer:

x = 4/7 or x = 5

Step-by-step explanation:

Step 1: Add to 3 to both sides

Step 2: Factor by grouping

This equation is in the form ax² + bx + c = 0. Since there are no terms that multiply to 20 and add to -39, we have to find terms that multiply to a (7) * (20) and add to -39.

Now, we split -39x into -35x and -4.

Next, we factor each expression in the parentheses. After that, we put the terms outside the parentheses together. Reminder, the terms inside the parentheses should be the same.

Step 3: Solve for x using 7x - 4 = 0 and x - 5 = 0.

or

Answer:

The amplitude is the highest point that the curve reached

Which is in your case = 2

The correct probability expression is (a) P(a) = three-fifths

Using the data in the complete question, we have:

n(A) = 3

n(U) = 5

The probability of A is then calculated using:

P(A) = n(A)/n(U)

This becomes

P(A) = 3/5

Hence, the correct probability expression is (a) P(a) = three-fifths

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Answer:

It’s A my friend

Step-by-step explanation:

i did the quiz

yw :)

hope i helped/ made life easier

Answer + Step-by-step explanation:

a) GE = r = GM

Then GEO is an isosceles triangle

b) since GEO is an isosceles triangle  then :

m∠SEG = m∠GOM = measure of the arc GM (mGM)  (result 1)

On the other hand :

m∠SEG = m∠SEG = (1/2)×(mAS - mGM)  (it’s a formula)   (result 2)

Now ,we equate  (result 1) and  (result 2) :

m∠SEG = mGM  

m∠SEG = (1/2)×(mAS - mGM)

Then

mGM = (1/2)×(mAS - mGM)

c) mGM = (1/2)×(mAS - mGM)

⇔ 2mGM = mAS - mGM

⇔ 3mGM = mAS

⇔ 3m∠SEA = m∠SOA

Remember:

mGM = m∠GOM = m∠SEA

Answer:

It's Store C

Hope this helps :)

Step-by-step explanation:

Got it right on USA TEST PREP :)

              - - - - - - - - - - - - - - - - - - - - - - - - - -- -

[tex]\diamond\large\textsf{\textbf{\underline{Question:-}}}[/tex]

          ✥ 19 more than the number c is 4.

[tex]\diamond[/tex] [tex]\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

◆ First, the word "more" indicates that we add.

Here we have 19 more than c, so we add c plus 19, which looks as follows:-

 ✳︎ [tex]\sf{19+c}[/tex]

This expression is equal to 4:-

✳︎[tex]\sf{19+c=4}[/tex]

If you also need to find c, subtract 19 on both sides:-

So we conclude that the value of c is -15.

         - -- - - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

19 + c = 4

Step-by-step explanation:

Given:

We know that:

Therefore, we can make the following replacements:

When we replace the bolded text in the statement, we get;

⇒ 19 more than the number c is 4

⇒ 19 more than the number c is 4                       ["19" ⇒ "19"]

⇒ 19 + than the number c is 4                            ["more" ⇒ "+"]

⇒ 19 + c is 4                                             ["than the number c" ⇒ "c"]

⇒ 19 + c = 4                                                            ["is" ⇒ "="]

⇒ 19 + c = 4                                                            ["4" ⇒ "4"]

Thus, the expression/equation that represents the statement is [tex]\small\text{19 + c = 4.}[/tex]

The volume of the cone that has a radius of 8 in. and a height of 10.5 in. is: 703.7 in.³

Volume = 1/3πr²h

Given the parameters:

Volume of the cone = 1/3πr²h = 1/3π(8²)(10.5)

Volume of the cone = 1/3π(64)(10.5)

Volume of the cone = 703.7 in.³

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Answer:

224Pi inches cubed

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Formula :

Finding a₅ :

Finding a₆ :

Answer:

the more successful school is A

with a percentage pass rate of 74 % (to the nearest whole number)

Step-by-step explanation:

The percentage pass rate of school A :

(284÷386)×100 = 73.575129533679 %

The percentage pass rate of school B :

(154÷220)×100 = 70 %

73.575129533679 > 70

Then ,the more successful school is A

with a percentage pass rate of 74 % (to the nearest whole number)

Answer:

Step-by-step explanation:

you have a rotation angle of 360 °, take out the known values ​​(360 ° -90 ° -144 ° = 126), 144 ° is part of a flat angle of 180 °, from 180 ° remove 144 and you have 36 °, they are opposite angles therefore the same. therefore 360 ​​- 144 - 90 - 36 - 36 = 54.

54 is 3x, so x = 18 ° (54 : 3 = 18)