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horrorfan [7]
2 years ago
9

Plz solve this inequality

Mathematics
1 answer:
nasty-shy [4]2 years ago
8 0

Answer:

\{r | r \ge -3 \}

Step-by-step explanation:

7 - 9r - (r + 12) \le 25

Remember that to deal with the negative sign to the left of the parentheses, you must think of it as a -1 multiplying the parentheses, and you distribute the -1 by multiply each term inside the parentheses by -1. That changes all the signs inside the parentheses.

7 - 9r - r - 12 \le 25

Combine like terms on the left side.

-10r - 5 \le 25

Add 5 to both sides.

-10r \le 30

We now divide both sides by -10. Remember that when you divide both sides fo an inequality by a negative number, the inequality sign changes direction.

r \ge -3

Answer: \{r | r \ge -3 \}

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Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xyz , (3, 3, 9
Anna [14]

The derivative of f(x,y,z) in the direction of a vector \mathbf u is

\nabla_{\mathbf u}f=\nabla f\cdot\dfrac{\mathbf u}{\|\mathbf u\|}

With f(x,y,z)=xyz, we get

\nabla f=(yz,xz,xy)

and \mathbf u=(-1,-2,2),

\|\mathbf u\|=\sqrt{(-1)^2+(-2)^2+2^2}=3

Then

\nabla_{(-1,-2,2)}f(3,3,9)=(27,27,9)\cdot\dfrac{(-1,-2,2)}3=-21

8 0
3 years ago
How is using partial products to find the product of two 2-digit factors similar to how you have used partial products in the pa
klasskru [66]
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4 0
3 years ago
Read 2 more answers
Una piscina rectangular de 15 metros de largo por 9 metros de ancho està rodeada por un
stira [4]

Answer: 2 meters.

Step-by-step explanation:

Let w = width of the cement path.

Dimensions of pool : Length = 15 meters , width = 9 meters

Area of pool = length x width = 15 x 9 = 135 square meters

Along width cement path, the length of region = 2w+15

width = 2w+9

Area of road with pool =  (2w+15) (2w+9)

= 4w^2+30w+18w+135\\\\=4w^2+48w+135

Area of road = (Area of road with pool ) -(area of pool)

\Rightarrow\ 112 =4w^2+48w+135- 135\\\\\Rightarrow\ 112= 4w^2+48w\\\\\Rightarrow\ 4 w^2+48w-112=0\\\\\Rightarrow\ w^2+12w-28=0\ \ \ [\text{Divide both sides by 4}]\\\\\Rightarrow\ w^2+14w-2w-28=0\\\\\Rightarrow\ w(w+14)-2(w+14)=0\\\\\Rightarrow\ (w+14)(w-2)=0\\\\\Rightarrow\  w=-14\ or \ w=2

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Hence, the width of the road = 2 meters.

8 0
3 years ago
Show all work:
DerKrebs [107]

Answer:

m=-3

Step-by-step explanation:

m - 7 = -10

Ok so,

in order to get m by itself you just need to do the opposite of -7 which is +7 so you have to add 7 to both sides. On the left, both of the 7's cancel out and on the right -10 + 7 = -3. So, now it should look like this.

m=-3

To check you just need to plug in -3 into the question

Hope this helps! Have a good day

4 0
2 years ago
Tina babysat eight times. She earned $15, $20, $10, $12, $20, $16, $80, and $18. What is the average amount of money she made?
AleksAgata [21]
The mean is 23.875. That would be roughly $24 each time

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2 years ago
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