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.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-15})\qquad (\stackrel{x_2}{14}~,~\stackrel{y_2}{r}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{r}-\stackrel{y1}{(-15)}}}{\underset{run} {\underset{x_2}{14}-\underset{x_1}{2}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{4}}\implies \cfrac{r+15}{12}~~ = ~~\cfrac{3}{4}\implies r+15 = \cfrac{12\cdot 3}{4} \\\\\\ r+15=9\implies \boxed{r=-6}[/tex]

Answer:

x≤5p

Step-by-step explanation:

40/8=5 Kaitlin can buy UP TO 5 pounds of candy at $8/pound. So she will buy less than or equal to 5 pounds

The true proportion of air traffic controllers in Canada with resting heart rates over 100 bpm is; 0.2717 or 27.17%

We are given;

Sample size; n = 173

Number of people who had  a resting heart rate over 100 bpm = 47

Now, formula for true proportion is;

p' = x/n

where;

x represents the number of successes

n represents the sample size.

p′ is the sample proportion which is the point estimate for the true population proportion.

Thus;

p' = 47/173

p' = 0.2717

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Answer:

AB : XY = 2 : 3

Step-by-step explanation:

We know that :

So, if the areas ΔABC and ΔXYZ are in the ratio 4 : 9, then :

Answer:

60th percentile = 23.5

Step-by-step explanation:

Put numbers in order from lowest to highest:

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

Formula:

60th percentile = 60% x Total number of elements

We have 20 scores,

60th percentile = 60% x 20

                          = 0.60 x 20

                          = 12

the 60th percentile is the 12th number on the list

14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29

The 60th percentile is between 23 and 24

23 + 24 / 2 = 23.5

Answer:

10y^2 + 39y + 35

Step-by-step explanation:

Simplify using FOIL

Answer: The final price is less than the original

Step-by-step explanation:

    Let us break this down a bit.

The original price is $500

-> At the beginning, the price was marked up by 20%

-> At the end, the price at the beginning of the season is marked down by 20%

    We are solving for: "How does the final price compare with the original price of $500​"

        First, we will find the price at the beginning.

-> Please note a percent divided by 100 becomes a decimal

20% / 100 = 0.2

$500 * 0.2 = $100

$500 + $100 = $600

     Now, we will find the price at the end.

$600 * 0.2 = $120

$600 - $120 = $480

     The final price is less than the original price of $500.

Answer:

Step-by-step explanation:

price marked up by 20%= 500+ [tex]\frac{20}{100}[/tex]×500

                                        =$600

price marked down by 20%= 600- [tex]\frac{20}{100}[/tex]×600

                                             =$480

the final price is less than the original price

Answer:

10.2956

Step-by-step explanation:

formula:

d = √((x2-x1)2 + (y2-y1)2)

(x1, y2) and (x2, y2)

 (-5,2) and (4,-3).

Find the difference between coordinates:

(x2-x1) = (4 - -5) = 9

(y2-y1) = (-3 - 2) = -5

Square the results and sum them up:

(9)2 + (-5)2 = 81 + 25 = 106

Now Find the square root and that's your result:

Exact solution: √106 = √106

Approximate solution: 10.2956

Answer:

  see attached

Step-by-step explanation:

We prefer to solve these by rewriting the equations to the form f(x) = 0, then having a graphing calculator show us the x-intercepts of f(x). This is illustrated in the second attachment.

__

The applicable rules of logarithms are ...

We can apply these rules to the given expressions to solve for x algebraically.

__

Taking antilogs, we have ...

  (x -1)(5x) = 10^2 = 100

  x(x -1) = 20 . . . . . . . . . . . divide by 5

  x² -x -20 = 0 . . . . subtract 20, put in standard form

  (x -5)(x +4) = 0 . . . . factor

  x = 5  or  x = -4 . . . . . . the latter is an extraneous solution

  x = 5 only

__

Taking antilogs, we have ...

  x +5 = (x +1)(x -1)

  x² -x -6 = 0 . . . . . . . subtract (x+5), write in standard form

  (x -3)(x +2) = 0 . . . . factor

  x = 3  or  x = -2 . . . . . . the latter is an extraneous solution

  x = 3 only

__

Taking natural logarithms, we have ...

  x² = 4x +5

  x² -4x -5 = 0 . . . . . write in standard form

  (x -5)(x +1) = 0 . . . . factor

  x = 5  or  x = -1 . . . . values that make the factors zero

__

Taking antilogs, we have ...

  5x² +2 = x +8

  5x² -x -6 = 0 . . . . . write in standard form

  (5x -6)(x +1) = 0 . . . . factor

  x = 6/5  or  x = -1 . . . . values that make the factors zero

_____

Additional comment

A solution is extraneous when it does not satisfy the original equation. Here, solutions are extraneous because they make the argument of the log function be negative in the original equation. The log function is not defined for negative arguments. (Actually, it gives complex values for negative arguments.)

We could have gone to the trouble to determine the applicable domain of each of the log equations. It is easier to (a) use a graphing calculator, or (b) test the solutions found.

Answer:

Option A, rational numbers

Step-by-step explanation:

Step 1:  Determine which option is correct

Option B and D are automatically ruled out because only one of them is a whole number and the other one is a decimal.  Option C doesn't work also because natural numbers are all the whole numbers that are greater than 1.  The only option that makes sense is option A which includes whole numbers and decimals.

Answer:  Option A, rational numbers

By applying the law of cosine, the smallest angle which the swimmers must turn between the buoys is 41.4°.

In order to determine the smallest angle which the swimmers must turn between the buoys, we would apply the law of cosine.

Given the following data:

Form the law of cosine, we have:

[tex]CosC =\frac{a^2 + b^2 - c^2}{2ab} \\\\CosC =\frac{500^2 + 600^2 - 400^2}{2 \times 500 \times 600}\\\\CosC =\frac{450000}{600000}\\\\C = cos^{-1} 0.75\\\\[/tex]

C = 41.4°.

For angle B, we have:

[tex]CosB =\frac{a^2 + c^2 - b^2}{2ac} \\\\CosB =\frac{500^2 + 400^2 - 600^2}{2 \times 500 \times 400}\\\\CosB =\frac{1}{8}\\\\B = cos^{-1} 0.125\\\\[/tex]

B = 82.8°.

For angle A, we have:

[tex]CosA =\frac{b^2 + c^2 - a^2}{2bc} \\\\CosA =\frac{600^2 + 400^2 - 500^2}{2 \times 600 \times 400}\\\\CosA =\frac{9}{16}\\\\A = cos^{-1} 0.5625\\\\[/tex]

A = 55.8°.

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Area of hexagon

Now

area of upper 6 triangles

Total area

Answer:

770 m²

Step-by-step explanation:

The surface area of a regular pyramid comprises the area of the base (regular polygon) and the area of each of the slanted sides (triangles).

Apothem:  The line segment from the center of the regular polygon to the midpoint of one of its sides.

Area of the base

The base of the prism is a regular polygon with 6 sides (hexagon).

[tex]\textsf{Area of a regular polygon}=\sf \dfrac{1}{2}nsa[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Base area}& =\sf \dfrac{1}{2}\cdot 6 \cdot 12 \cdot 6\sqrt{3}\\ & = \sf 216\sqrt{3}\:m^2\end{aligned}[/tex]

Area of one side

The sides of the regular pyramid are congruent triangles.

[tex]\textsf{Area of a triangle} = \sf \dfrac{1}{2} \times base \times height[/tex]

Given:

Substitute the given values into the formula:

[tex]\implies \textsf{Area of a triangle} = \sf \dfrac{1}{2} \times 12 \times 11=66\:m^2[/tex]

Total Surface Area

[tex]\begin{aligned}\implies \textsf{Total Surface Area} & = \sf base \: area + 6 \times side \: area\\& = \sf 216\sqrt{3}+6 \cdot 66\\& = \sf 216\sqrt{3}+396\\& = \sf 770\:m^2\:(nearest\:whole\:number)\end{aligned}[/tex]

Answer:

∠ FLW = 112°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ FLW is an exterior angle of the triangle , then

∠ FLW = x + 32 , that is

2x - 48 = x + 32 ( subtract x from both sides )

x - 48 = 32 ( add 32 to both sides )

x = 80

Then

∠ FLW = 2x - 48 = 2(80) - 48 = 160 - 48 = 112°

The required steps are explained below to convert the quadratic function into a perfect square.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the quadratic function be y = ax² + bx + c.

The first step is to take common the coefficient of x². We have

[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x \right) + c[/tex]

Add and subtract the half of the square the coefficient of x,

[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x + \dfrac{b^2}{4a^2} \right) - a \times \dfrac{b^2}{4a^2} + c[/tex]

Then we have

[tex]\rm y = a \left (x + \dfrac{b}{a} \right)^2 - \dfrac{b^2}{4a} + c[/tex]

These are the required step to get the perfect square of the quadratic function.

More about the parabola link is given below.

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The approximate amount of water that remains in the tub after the 6 spherical balls are placed in the tub are 3479.12 in³.

The first step is to determine the volume of the cylinder.

Volume of the tub = πr²h

Where:

3.14 x 9² x 20 = 5086.8 in³

The second step is to determine the volume of the 6 balls.

Volume of a sphere= 4/3πr³

r = diameter / 2 = 8/2 = 4 inches

6 x (3.14 x 4/3 x 4³) = 1607.68 in³

Volume that remains in the tub = 5086.8 in³  -  1607.68 in³ = 3479.12 in³

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Answer:

30 again if I’m wrong then it’s 40

Step-by-step explanation:

most of the pizzas that are sold are in the 30’s or below

Answer:

5/9

Step-by-step explanation:

Solution

The gradient of the line ment when two segment given (X1, Y1) and (X2, Y1) is points

m =

[tex] \frac{y2 - y1}{x2 - x1 } [/tex]

Here two points given, (-5,-2) and (4,3)

gradient (m):

[tex] \frac{3 - ( - 2)}{4 - ( - 5)} [/tex]

The height of the rectangular prism is 3.1

[tex]6.9x=21.39[/tex]

[tex]21.39[/tex] ÷ [tex]6.9=3.1[/tex]

Sure hope this helps

Answer:

The correct answer is b)

Step-by-step explanation:

The values of the numbers m and n that makes the given expression true are 3 and 12 respectively

From the question, we are to determine the values of the numbers m and n that will make the given expression true

The given expression is

(2x + m)² = 4x² + nx + 9

Opening the bracket on the left hand side,

(2x + m)²

(2x + m)(2x + m)

4x² + 2mx + 2mx + m²

4x² + 4mx + m²

∴ 4x² + 4mx + m² = 4x² + nx + 9

By comparing,

4mx = nx;

Then, 4m = n

and

m² = 9

∴ m = ±√9

m = ±3

Since we are given that both m and n are positive numbers,

∴ m = 3

Substitute the value of m into the equation, 4m = n

4×3 = n

∴ n = 12

Hence, the values of the numbers m and n that makes the given expression true are 3 and 12 respectively

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Answer:

111.75 degrees

Step-by-step explanation:

EDF = cos^-1((b²+c²-a²)/2bc)

EDF = cos^-1((10.4²+19.6²-13.2²)/2(10.4)(19.6))

EDF = 111.75 degrees

Answer:

This was a nice way to spend my time :) how'd I do?

Step-by-step explanation:

Total: 6

1. +8

After stop 1, total is 14 people

2. +4, -2

After stop 2, total is 16 people

3. +15, -4

After stop 3, the total is 27 people

4. -8

Total # of people on the bus: 19

(A little voice in the back of my mind is telling me that I overthought this entire problem, and that the answer is just 6)

I will help u so fast, first

you help me

can u answer this

some fanicial and environmental damages that have been made by cars.

please help me

this is exam

teacher giving us 10 minutes to discuss about and I am in washroom of school writing this

Answer:

6

Step-by-step explanation:

Since this is a cube, and the lengths that are given are 1 mm, then you just add all the sides of a cube. There are 6 sides in a cube, 1+1+1+1+1+1=6

Answer:

A= 10

Step-by-step explanation:

[10 + 2/360˚(10)]

Answer:

well x-(-18) x+18 but the if part is x<-18 will stay the same

Step-by-step explanation:

Answer:

12 ft - 2 ft = 10 ft

The rope is 10 feet long.

10 · cos 30° = 10 · √3 / 2 = 8.66 ft

x = 12 - 8.66 = 3.34 ft

Answer:

A ) 3.34 feet