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NeX [460]
2 years ago
6

Put each line into slope-intercept form:

Mathematics
1 answer:
Shtirlitz [24]2 years ago
6 0

Step-by-step explanation:

Slope-intercept form: y = mx + c

y = x + 3 is already in this form.

3x + 3y = -9,

3y = -3x - 9

y = -x - 3.

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Evaluate the definite integral using the graph of f(x)<br> (Image included)
Tanya [424]

a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

\displaystyle \int_0^3 f(x) \, dx = \frac12 \times 3 \times 5 = \boxed{\frac{15}2}

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

\displaystyle \int_3^5 f(x) \, dx = \int_3^4 f(x) \, dx + \int_4^5 f(x) \, dx = \int_3^4 f(x) \, dx - \int_3^4 f(x) \, dx = \boxed{0}

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

\displaystyle \int_5^9 f(x) \, dx = -4\times5 = -20

Then by linearity, we have

\displaystyle \int_0^9 f(x) \, dx = \left\{\int_0^3 + \int_3^5 + \int_5^9\right\} f(x) \, dx = \frac{15}2 + 0 - 20 = \boxed{-\frac{25}2}

8 0
2 years ago
Lia has 7 blue pencils and 28 red pencils. Maria has 14 blue pencils and 42 red pencils, and Tia has 10 blue pencils and 30 red
Sergeeva-Olga [200]
Maria and Tia have the same ratio
6 0
3 years ago
Read 2 more answers
The volume of a boys' basketball is 434 cubic inches. Dan would like to get a ball
Nataly_w [17]

Answer:

The correct answer is A. 9.4 inches.

Step-by-step explanation:

Given that the volume of a boys' basketball is 434 cubic inches, and Dan would like to get a ball with half the volume for his son, to determine what is the diameter of the ball that Dan will buy for his son, the following calculation has to be done, knowing that the volume of a sphere is four thirds multiplied by pi multiplied by the radius cubed:

4/3 x 3.14 x X ^ 3 = 434

4.186 x X ^ 3 = 434

X ^ 3 = 434 / 4.186

X = 3√ 103.662

X = 4.7

In turn, since the radius of a sphere is equal to half its diameter, the diameter of the basketball is 9.4 inches (4.7 x 2).

4 0
3 years ago
25= 5(3X-4)^1/3<br> PLEASE HELP AND SHOW WORK!<br> THANKS SM
Effectus [21]

Answer:

x=43

Step-by-step explanation:

Given equation:

25=5(3x-4)^{\frac13}

Divide both sides by 5:

\implies 5=(3x-4)^{\frac13}

Cube both sides:

\implies 5^3=((3x-4)^{\frac13})^3

\implies 125=(3x-4)^{\frac33}

\implies 125=(3x-4)^1

\implies 125=3x-4

Add 4 to both sides:

\implies 129=3x

Divide both sides by 3:

\implies x=43

8 0
2 years ago
Read 2 more answers
I need to know the answers for these, anyone help please
storchak [24]

Answer:

1- G

2- C

3- G

4- A

Step-by-step explanation:

choose has brainlist

3 0
3 years ago
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