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liubo4ka [24]
3 years ago
11

If f(x) = 2x + 7 and g(x) = 3x - 6, then what is (f + g)(x)?

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
8 0

9514 1404 393

Answer:

  (f+g)(x) = 5x +1

Step-by-step explanation:

Substitute the given expressions and simplify.

  (f+g)(x) = f(x) +g(x)

  (f+g)(x) = (2x +7) +(3x -6) = (2x +3x) +(7 -6)

  (f+g)(x) = 5x +1

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F ind the volume under the paraboloid z=9(x2+y2) above the triangle on xy-plane enclosed by the lines x=0, y=2, y=x
olga nikolaevna [1]

Answer:

The answer is 48 units³

Step-by-step explanation:

If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,

V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {z} \, dx dy\\V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {9(x^{2}+y^{2})} \, dx dy

Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,

V=9\int\limits^2_0 {4y^{3}/3} \, dy

After performing the elementary y integral we obtain the desired volume as below,

V= 48 units^{3}

4 0
3 years ago
96=-8k solve <br> Show work
larisa86 [58]

Answer:

k = -12

Step-by-step explanation:

<u>Step 1:  Divide both sides by -8</u>

<u />96 / -8 = -8k / -8

-12 = k

Answer: k = -12

3 0
3 years ago
Read 2 more answers
The perimeter of a rectangular flower garden is 66m and its area is 272m^2. Find the length of the garden.
ExtremeBDS [4]
So we have lengths a and b and are given:

2a+2b = 66 => a+b = 33 => a= 33-b
a*b = 272

plug in one into the other:

(33-b)b = 272 => -b^2 +33b - 272 = 0

Can be factored as (b-16)(b-17) = 0, if you don't "see" this immediately, use the well known abc formula to find b.

So a=16 and b=17 or vice versa.


6 0
2 years ago
A screening test for a disease shows a positive result in 91% of all cases when the disease is actually present and in 7% of all
Jobisdone [24]

Answer:

0.0713 = 7.13% probability that the result is positive.

Step-by-step explanation:

Probability of a positive test:

91% of 1/650(has the disease).

7% of 1 - 1/650 = 649/650(does not have the disease). So

p = 0.91\frac{1}{650} + 0.07\frac{649}{650} = \frac{0.91 + 0.07*649}{650} = 0.0713

0.0713 = 7.13% probability that the result is positive.

4 0
2 years ago
At a football game Jasmine bought a soft pretzel for $2.25 in a bottle of water for $1.50 she paid with a $5 bill how much thing
andrew11 [14]

Answer:

$1.25.

Step-by-step explanation:    

We have been given that at a football game Jasmine bought a soft pretzel for $2.25 in a bottle of water for $1.50 she paid with a $5 bill.

First of all let us find how much Jasmine spent on soft pretzel and water bottle by adding the cost of both items.

\text{Total amount spent on both items}=2.25+1.50

\text{Total amount spent on both items}=3.75

To find the amount that Jasmine will get as a change we will subtract the amount spent on both items from 5.

\text{Amount of change that Jasmine will get}=5-3.75

\text{Amount of change that Jasmine will get}=1.25

Therefore, Jasmine will get $1.25 back as change.

3 0
3 years ago
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