To make some extra money over the summer, Kelsey and Olivia got jobs mowing the 5 acres of grass at the local park. Each week, the girls worked together to mow all the grass, splitting it equally. How many acres did each girl mow each week?

Answer:

Question 1) 72

Question 2) 40

Question 3) Both C and D.

Question 4) Both A and C.

Step-by-step explanation:

Question 1)

We are given that:

[tex]\displaystyle \int_1^5f(x)\, dx=8\text{ and we want to find} \int_1^5xf'(x)\, dx[/tex]

We will use integration by parts, given by:

[tex]\displaystyle \int_a^b u\, dv=uv-\int_a^b v\, du[/tex]

We will let:

[tex]u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \Rightarrow v=f(x)[/tex]

Therefore:

[tex]\displaystyle \int_1^5xf'(x)\, dx=xf(x)\Big|_1^5-\int_1^5f(x)\, dx[/tex]

Substitute:

[tex]\displaystyle \int_1^5xf'(x)\, dx=(5(f(5))-(1(f(1))-(8)[/tex]

Evaluate:

[tex]\displaystyle \int_1^5xf'(x)\, dx=75-(-5)-8=72[/tex]

Question 2)

Similarly, we will let:

[tex]\displaystyle u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \text{ so } v=f(x)[/tex]

Hence:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=xf(x)\Big|_0^3-\int_0^3f(x)\, dx[/tex]

Evaluate:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=(3f(3))-(0(f(0))-(2)[/tex]

Thus:

[tex]\displaystyle \int_0^3 xf'(x)\, dx=3(14)-2=40[/tex]

Question 3)

We are given:

[tex]\displaystyle g(x)=\int_4^xf(x)\, dx[/tex]

By the Fundamental Theorem of Calculus:

[tex]g'(x)=f(x)>0[/tex]

The derivative of g is always positive. So, the values of g are always increasing.

The tables that reflect this are C and D.

And there are, as I understand it, no way to determine their exact values. Both C and D are correct.

Question 4)

Similarly, we are given:

[tex]\displaystyle g(x)=\int_{-2}^xf(x)\, dx[/tex]

By the FTC:

[tex]g'(x)=f(x)<0[/tex]

So, g should be decreasing for all x.

The tables that reflect this are A and C.

So, both A and C are correct.

Answer:

14x²-41x+15

Step-by-step explanation:

Answer:

8x^3-6x^2-57x+55

Tell me if you would like an explanation If you need one :D

Answer:

-3x² -2y² -8xy +5y

34x² + 51xy - 8y + 6y²

7x² - 11xy +12y - 8y²

Step-by-step explanation:

Given:

A: 5x²+3xy +2y

B: 2y²-xy +4x²

С: 12xy+4x²-3y

Find:

1) А-В-С

2) 2A+3B+4C

3) 3A-4B--2C

Computation:

1) А-В-С

5x²+3xy +2y - [2y²-xy +4x²] - [12xy+4x²-3y]

5x²+3xy +2y -2y² +xy -4x² -12xy -4x²+3y

-3x² -2y² -8xy +5y

2) 2A+3B+4C

2[5x²+3xy +2y]+3[2y²-xy +4x²]+4[12xy+4x²-3y]

10x² + 6xy + 4y + 6y² - 3xy + 8x² + 48xy + 16x² - 12y

34x² + 51xy - 8y + 6y²

3) 3A-4B-2C

3[5x²+3xy +2y]-4[2y²-xy +4x²]-2[12xy+4x²-3y]

15x² + 9xy + 6y -8y² + 4xy - 16x² - 24xy - 8x² +6y

7x² - 11xy +12y - 8y²

Answer:

130

Step-by-step explanation:

Answer:

cevap 480 dirrrrrrrrrrr

Answer: 2.71 packs

Step-by-step explanation:

Answer:225cm

Step-by-step explanation:15x5x3

Answer:

The area is 225 ft. sq.

Step-by-step explanation:

Multiply 15cm, 5cm, and 3cm together!

Answer:

Step-by-step explanation:

the x is 30

60=2x

x=30

Answer:

d

Step-by-step explanation:

its d i think

Answer:

8.1

Step-by-step explanation:

We denote the number as x.

6 * x = 48.6

We can divide both sides by 6 to get,

x = 8.1

Answer:

8.1

Step-by-step explanation:

Let the unknown number be n.  Translating this statement into symbols, we get:

6n = 48.6

Solving for n by dividing both sides by 6, we get  n = 8.1

The number is 8.1

Step-by-step explanation:

[tex]y = - 4[/tex]

[tex]y = - 4[/tex]

Answer:

y=-4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-(-4))/(-6-4)=(-4+4)/-10=0/-10=0

slope is 0

y-y1=m(x-x1) where m=slope

y-(-4)=0(x-4)

y+4=0

y=0-4=-4

y=-4

Step-by-step explanation:

= 55 - 2x is the answer .

plz mark my answer as brainlist if you find it useful.

Answer:

Add 5 and 50

−2x + 55

Step-by-step explanation:

Answer:

t = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

1/4t - 6 = -4

Step 2: Solve for t

Answer:

t=8

Step-by-step explanation:

1/4 = 0.25

0.25t - 6 = -4

0.25t = -4 + 6

0.25t = 2

t = 2/0.25

t = 8

Answer:

99.7%

Step-by-step explanation:

Given that:

sample size (n) = 655

sample mean ([tex]\overline x[/tex]) = 43.29

Standard deviation [tex]\sigma[/tex] = 2.75

Let's assume we are to estimate the percentage between $33.72 and $51.54

Then;

The test statistics at 33.72 is :

[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]Z = \dfrac{33.72 -43.29}{2.75}[/tex]

[tex]Z = -3.48[/tex]

Z at 51.54

[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]Z = \dfrac{51.54 -43.29}{2.75}[/tex]

[tex]Z = 3.00[/tex]

Using the empirical standard rule, the percentage will be 99.7%

Answer:

Step-by-step explanation:

4 1/4x7/8

I think 119/32

The height of fence will be "[tex]\frac{41}{8}[/tex]".

According to the question,

Length of posts,

= [tex]4\frac{1}{4} \ feet[/tex]

Length of posts below ground level,

= [tex]\frac{7}{8} \ feet[/tex]

Now,

→ The height of the fence will be:

=  [tex]4\frac{1}{4} +\frac{7}{8}[/tex]

=  [tex]\frac{17}{4}+\frac{7}{8}[/tex]

=  [tex]\frac{34}{8}+\frac{7}{8}[/tex]

=  [tex]\frac{34+7}{8}[/tex]

=  [tex]\frac{41}{8}[/tex]

Thus the above is the right answer.

Learn more:

https://brainly.com/question/24395658

Answer:

c I think

Step-by-step explanation:

can you help me with this question In Lines 23 and 24 of his poem "Chicago", Sandburg uses which poetic device? A Simile - a comparison of two unlike things using "like" or "as" B. Metaphor - a comparison of two unlike objects C. Repetition

Answer: 20

Step-by-step explanation: I LOVE THIS I HATE THIS I CAN SEE THIS SO I JUST GEUSSED HOPE IT IS RIGHT BYE

Answer:

9/15=3/5

so 3/5 is equivalent fraction of the 9/15

Answer:

Note: If this is really sixth grade math, then im a cucumber. It's way easier than MY math, and I'm in 6th grade lol :P

Another Note: Please vote me "Brainliest", I put a lot of work into this :)

1. 40

2. 60

3. 1.35

4. 6

5. Do this yourself, it requires actually explaining and you have to use your own words. :)

6. Do this yourself, it requires actually explaining and you have to use your own words. :)

7. Do this yourself, it requires actually explaining and you have to use your own words. :)

8. 600 people

9. 4200 people

10. 149 people

11. Sahil came up with his answer so quickly because if 45 is 10% of x, then obviously 30% of x would be 45 times 3 and that is 135. Due to this, he quickly new that the number of people between the ages of 30 and 49 that voted is 135 people.

That's it, please heart my answer and vote me brainliest :)

Step-by-step explanation:

Do you really need this part? I didn't do it because it would take forever LOL

Answer:

what grade is this ?

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

3x+9=36

subtract 9 from both sides

3x=27

divide by 3 on both sides

x=9

The solution to the equation 3x + 9 = 36 is x = 9.

To solve the equation 3x + 9 = 36, we'll perform the necessary steps to isolate the variable x on one side of the equation.

Given equation:

3x + 9 = 36

First, we'll subtract 9 from both sides to eliminate the +9 term on the left side:

3x + 9 - 9 = 36 - 9

3x = 27

Next, to isolate the variable x, we divide both sides by 3:

(3x)/3 = 27/3

x = 9

Therefore, the solution to the equation 3x + 9 = 36 is x = 9.

In this equation, we start with an expression involving the variable x and a constant term. By performing algebraic operations, we manipulate the equation to have x on one side and the constant value on the other side. This isolates the variable and provides us with a specific value for x that satisfies the equation. In this case, the value of x is determined to be 9, which can be verified by substituting it back into the original equation to see if it holds true.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ6

Answer:

The answer is 1 and 4

Step-by-step explanation:

.25 x 4y = Y

36 divided by 4 = 9

Answer:

It b

Step-by-step explanation:

We know this because 1/2 is 0.5 while 2/3 is 0.67. With this we can say that 1/2 is least than 2/3

Hope this Helped

Answer:

15/28 are women

Step-by-step explanation:

2/7 + 1/4 + x = 100%

2/7+1/4= 15/28

9514 1404 393

Answer:

  13/28

Step-by-step explanation:

The fraction that are women is found by subtracting the given fractions from 1.

  1 - 2/7 - 1/4 = 28/28 -8/28 -7/28 = (28 -8 -7)/28 = 13/28

The fraction that are women is 13/28.

Answer:

area of real bedroom = 32 cm²

hope it helps..

Answer:

Bedroom: 32 cm living room: 81 cm

Step-by-step explanation:

Bedroom: 4 x 8 = 32

Living room : 9 x 9 = 81

( if combining bedroom and living room, it’s 113 cm)(81 + 32 = 113)

Hope this helps

Answer:

1.02

Step-by-step explanation:

Answer:

Step-by-step explanation:

Because 7(7)=(-7)(-7)=49 the square roots of 49 are 7 and -7

Answer:

The answer is below

Step-by-step explanation:

Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement.

(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)

.The polynomial simplifies to an expression that is a____

A.quadratic

B.liner

C.constany

A.trinomial

B.binomial

C.monomial

with a degree of____

A.1

B.2

C.0

Solution:

A polynomial is an expression involving operations of addition, subtraction, multiplication, exponents which consists of variables and their coefficient. A trinomial is a polynomial consisting of three terms, while a binomial consist of two terms and a monomial consist of one term.

The degree of a polynomial is the highest degree of any of the terms of the polynomial. If it has a degree of 0 it is a constant, a degree of 1 it is linear while for a degree of 2 it is quadratic.

(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)

= (-5x² - 2x + 4) + (8x² - x - 1) + (x² -5x + 2x - 10)

= (-5x² - 2x + 4) + (8x² - x - 1) + (x² - 3x - 10)

= (-5x² + 8x² + x² - 2x - x - 3x + 4 - 1 - 10)

= 4x² - 6x - 7

Therefore:

.The polynomial simplifies to an expression that is a quadratic trinomial of degree 2.

5 or more add 1

4 or less stays the same

Answer:

Step-by-step explanation:

(2-4x)+(2-4x)+(-2x+8)=12-10x

Answer:

3.24 feet

Step-by-step explanation:

A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 79 . Find the distance between the building and the ladder

We solve the above question using the Trigonometric function of Cosine

cos x = Adjacent/Hypotenuse

Adjacent = x feet

Hypotenuse = 17 ft

The angle = 79°

Hence,

cos 79 = x/17

Cross Multiply

x = cos 79 × 17

x = 3.2437529214.feet

Approximately = 3.24 feet

Therefore, the distance between the ladder and the building = 3.24 feet