Plissss helP meee!!!!!
Question 10 of 10
Which is the graph of the parent function f(x) = |x|?
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a. The value of the definite integral [tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]

b.  The value of the definite integral [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]

To answer the question, we need to know what definite integrals are.

These are integrals which are evaluated between two values of the variable.

[tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]

Given that [tex]\int\limits^{10.5}_0 {f(x)} \, dx = 9, \int\limits^{3.5}_0 {f(x)} \, dx = 7 and \int\limits^{10.5}_7 {f(x)} \, dx = 3[/tex]

We require  [tex]\int\limits^7_{3.5} {f(x)} \, dx[/tex]

So,  [tex]\int\limits^{10.5}_0 {f(x)} \, dx = \int\limits^{3.5}_0 {f(x)} \, dx + \int\limits^7_{3.5} {f(x)} \, dx + \int\limits^{10.5}_7 {f(x)} \,dx[/tex]

So,  [tex]\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx[/tex]

Substituting the values of the variables into the equation, we have

So,  [tex]\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx[/tex]

 [tex]\int\limits^7_{3.5} {f(x)} \, dx = 9 - 7 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = 2 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]

So, [tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]

[tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]

[tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = \int\limits^7_{3.5} 5{f(x)}\, dx - \int\limits^7_{3.5} 3\, dx\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = 5\int\limits^7_{3.5} {f(x)}\, dx - 3(7.5 - 3)\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= 5 X (-1 ) - 3 X 4.5 \\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= -5 - 13.5\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]

So,  [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]

Learn more about definite integrals here:

https://brainly.com/question/17074932

Answer:

3 3

6 3

Step-by-step explanation:

for reflecting over line y=x, you just change the places of y and x.

(6,3) becomes (3,6).

Answer: Please check the image below.

Answer:

The surface area of the tent is 21.4 m²

Step-by-step explanation:

To find the surface area of a prism you must calculate:

1. The perimeter of the base

2. The area of the base

3. The height of the prism

We have a triangular prism:

Its base is an equilateral triangle of side length 2 m and height 1.7 m

The height of the prism is 3 m

∵ The surface are of the prism is:

  S.A = perimeter of the base × height + 2 × area of the base

∵ The perimeter of the equilateral triangle = 3 × length of a side

∵ The length of the side = 2 m

∴ The perimeter of the base = 3 × 2 = 6 m

∵ The area of the triangle =  × base × height

∵ The length of the base of the triangle = 2 m

∵ The height of the triangle = 1.7 m

∴ The area of the base =  × 2 × 1.7 = 1.7 m²

∵ S.A = perimeter of the base × height + 2 × area of the base

∵ The perimeter of the base = 6 m

∵ The area of the base = 1.7 m²

∵ The height of the prism = 3 m

∴ S.A = 6 × 3 + 2 × 1.7

∴ S.A = 18 + 3.4

∴ S.A = 21.4 m²

The surface area of the tent is 21.4 m²

Started with $70

Coffee at $8.74/lb

Ended with $35.04

Susan bought 4 pounds of coffee.

:)

Answer:

The equation of the line is y = 4.

Step-by-step explanation:

It looks like they are asking for the equation of the bold line.

Answer:

E. Point E

Step-by-step explanation:

First, you would move along the x-axis horizontally for 4½ units. Then, you move along the y-axis vertically for 5 units and land on point E.

I hope this helps.

Answer:

0.875 is just 7/8, so 133.875 is 133 7/8 or (133*8+7)/8 = 1071/8

Answer:

3/10

Step-by-step explanation:

3 of the vertical bars are highlighted out of the 10 total bars. 3/10 is equivalent to 0.3.

#1

ac=6(-2)=-12

#2

#3

ac=-24

Answer:

(a)  [tex](2x-3)(x+2)[/tex]

(b)  [tex](5a-1)(2a+1)[/tex]

(c)  [tex](2c-3)(c+4)[/tex]

Step-by-step explanation:

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]

Part (a)

Given expression:  [tex]2x^2+x-6[/tex]

[tex]\implies ac=2 \cdot -6=-12[/tex]

Factors of -12 that sum to 1:  4 and -3

[tex]\implies 2x^2+4x-3x-6[/tex]

Factor first two terms and last two terms separately:

[tex]\implies 2x(x+2)-3(x+2)[/tex]

Factor out common term [tex](x+2)[/tex]:

[tex]\implies (2x-3)(x+2)[/tex]

Part (b)

Given expression: [tex]10a^2+3a-1[/tex]

[tex]\implies ac=10 \cdot -1=-10[/tex]

Factors of -10 that sum to 3:  5 and -2

[tex]\implies 10a^2+5a-2a-1[/tex]

Factor first two terms and last two terms separately:

[tex]\implies 5a(2a+1)-1(2a+1)[/tex]

Factor out common term [tex](2a+1)[/tex]:

[tex]\implies (5a-1)(2a+1)[/tex]

Part (c)

Given expression: [tex]2c^2+5c-12[/tex]

[tex]\implies ac=2 \cdot -12=-24[/tex]

Factors of -24 that sum to 5: 8 and -3

[tex]\implies 2c^2+8c-3c-12[/tex]

Factor first two terms and last two terms separately:

[tex]\implies 2c(c+4)-3(c+4)[/tex]

Factor out common term [tex](c+4)[/tex]:

[tex]\implies (2c-3)(c+4)[/tex]

Answer:

Let x = son's age

Let 38-x = Mr. Bellini's age (since the sum of their ages must be equal to 38)

Set up the equation using the second statement:

(38 - x) - 4 = 5(x - 4)

Solving,

34 - x = 5x - 20

34 + 20 = 6x

54 = 6x

x = 9 years old (son's age)

38-x = 29 years old (Bellini's age)

Answer:

x = 1, y = -2

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

Answer:Option A is correct. (light blue color in the triangle choices)

Answer:

76 chess sets

Step-by-step explanation:
Since they bought 16 cases and each contains 18 sets, let's multiply them

16 x 18 = 288
There were already 16 sets before that so lets add those as well

288 + 16 = 304
Now since there are 4 teachers we divide this among them

304/4 = 76

76 is the answer.

Answer: B

Step-by-step explanation:B because -3 + 5 is 2 and the line goes from -3 to 2

yes

Step-by-step explanation:

After the point the first number of the first number is 0 while the second one is 1

Answer:

[tex]\frac{a-3}{(a-2)(a-6)}[/tex]

Step-by-step explanation:

[tex]a^{2}-3a[/tex] has the common multiple of a. If you factor it out, you get [tex]a(a-3)[/tex].

[tex]a^3-8a^2+12a[/tex] also has a common multiple of a. Once factored, you get [tex]a(a^2-8a+12)[/tex]. This equation can be further factored to get [tex](a-2)(a-6)[/tex].

Put these two expressions over one another and you get  [tex]\frac{a-3}{(a-2)(a-6)}[/tex].

Answer:

9 and 11

Step-by-step explanation:

let two numbers be X and X+2

so

x+X+2=20

solve for X

x=9

x=20

Answer:

11 + 9 = 20

Step-by-step explanation:

Consecutive odd nymbers are odd numbers that follow each other.

think which two consecutive odd number when added will give 20.

odd numbers = 1 3 5 7 9 11 13 15 17 19

9 follows 11 and when added will equal 20

Answer:

t = 40

Step-by-step explanation:

The sum of the two angles is 70

70 = t+30

70-30 =t+30-30

40 =t

Answer:

40

Step-by-step explanation:

t = 70 - 30

t = 40

hope it helps

Answer:79 degrees i believe

Step-by-step explanation:

Answer:

79 degrees.

Step-by-step explanation:

There is many ways you can take this problem.  The easiest is alternate exterior.  Since the 79 degree angle and angle B is outside and on opposite sides, they are the same value.

Answer: 1

Step-by-step explanation:

9 - 3 ÷ 1/3 + 1 = 9 - 3 × 3/1 + 1

= 9 - 9 + 1 = 10 - 9 = 1.

' . , ' ' . , "-" & "+" . ' , ' .

. ^-^

Answer:

10[tex]\sqrt{2\\} \\[/tex] or 14.14 appromiximately

Step-by-step explanation:

Area of square = 100

So length on side = 10 because all sides of square equal.

Length of Diagonal = Side x [tex]\sqrt{2}[/tex]

So the length of diagonal is 14.14 approximately

Answer:

Orange juice is $6.50 per gallon and Peach juice is $12.00 per gallon

Step-by-step explanation:

Step 1:  Determine the price of the Orange juice

$3.25 per 0.5 gallon

($3.25 * 2) per (0.5 * 2) gallon

($6.50) per (1) gallon

Step 2:  Determine the price of the Peach juice

$4.50 per 1.5 quarts

$4.50 per 0.375 gallon

($4.50 * 2.667) per (0.375 * 2.667) gallon

($12.00) per (1) gallon

Answer: Orange juice is $6.50 per gallon and Peach juice is $12.00 per gallon

Answer:

Part 1) 150

Part 2) 6

Step-by-step explanation:

Part 1) All you have to do is multiply 30 by 5, since 30 is only 20% of the number and you have to get to 100%

30×5 = 150

Part 2) There are multiple ways of doing this, but the way I did it is 30 divided by 100 so you have the number of each percentage. Then you multiply that number by 20 since you are trying to get 20%

30÷100 = 0.3

0.3×20 = 6

Please give brainliest if I helped!

Answer:

1

Step-by-step explanation:

Any number divided by itself is always 1

[tex] \frac{1}{4} \times \pi \times ({radius})^{2} = \\ [/tex]

[tex] \frac{1}{4} \times \pi \times {12}^{2} = \\ [/tex]

[tex] \frac{1}{4} \times \pi \times 144 = \\ [/tex]

[tex] \frac{144}{4} \pi = \\ [/tex]

[tex]36\pi[/tex]

Answer:

The employers pay their employees based on hourly rates, commission and salary.

Step-by-step explanation:

The employees get their pay based on hourly rates that can range from a minimum hourly rate of say $12 per hour to any maximum figure like $40 per hour.

The final salary is based on the numbers of hours worked multiplied by the hourly rate.

Secondly, the pays are also commission based. That is your base salary plus the commission.

The salary is typical in management positions. These are not hourly based but a lump sum pay.

So, the correct answers are : commission, hourly pay and salary.