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kaheart [24]
2 years ago
11

What is the vertex of f(x)=x^2+6x+1 Write your answer as an ordered pair without spaces

Mathematics
1 answer:
netineya [11]2 years ago
5 0

Answer:

3

Step-by-step explanation:

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Please help with this math question picture is shown
maksim [4K]

Answer:

-20 gallons per minute

Step-by-step explanation:

3 0
3 years ago
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Which number line shows the solution set for |y-9| <12
RUDIKE [14]

Answer:

Option c

y\geq-3 or y \leq 21

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function f(x) = |x|  x> 0 for all real numbers.

Then the inequation:

|y-9| \leq 12 has two cases

(y-9)    if y \geq 9  (i)

-(y-9)    if y < 9 (ii)

We solve the case (i)

y \leq 9 + 12\\y\leq21

We solve the case (ii)

-y +9 \leq 12\\-y \leq 12-9\\y \geq -3

Then the solution is:

y\geq-3 or y \leq 21

8 0
3 years ago
How would the sum of cubes formula be used to factor x3y3 + 343? Explain the process. Do not write the factorization.
Svetllana [295]

Answer:

Given : Expression -x^3y^3+343

To find : How would the sum of cubes formula be used to factor given expression? Explain the process. Do not write the factorization.

Solution :

The formula of sum of cubes is,

a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)

First we convert the given expression in a^3+b^3

x^3y^3+343

Apply exponent rule : a^mb^m=(ab)^m

x^3y^3=(xy)^3

Rewrite 343=7^3

Therefore, x^3y^3+343  could be written as =\left(xy\right)^3+7^3

On comparison with the formula,

a=xy , b=7

\left(xy\right)^3+7^3=(xy+7)(xy^2-xy(7)+7^2)

\left(xy\right)^3+7^3=(xy+7)((xy)^2-7xy+49)            

5 0
3 years ago
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Help please and thank you
k0ka [10]

Answer:

2) C

3) D

4) D(5,-5)   E(2,-7)  F(4,-1)   G(8,-8)

Step-by-step explanation:

4 0
3 years ago
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Find the volume of the following solid. The solid between the cylinder ​f(x,y)equals=e Superscript negative xe−x and the region
PilotLPTM [1.2K]

It is hard to comprehend your question. As far as I understand:

f(x,y) = e^(-x)

Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.

That is all I understood. It would be easier to understand with a picture or some kind of visual aid.

Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.

\iint_{R}^{ } e^{-x}dA=\int_{-6}^{6} \int_{0}^{ln(6)} e^{-x}dx dy

Now evaluate,

\int_{0}^{ln(6)}e^{-x}dx

which evaluates to,  5/6 if I did the math correct. Correct me if I am wrong.

Now integrate this w.r.t. y:

\int_{-6}^{6}\frac{5}{6}dy = 10

So,

\iint_{R}^{ } e^{-x}dA=\int_{-6}^{6} \int_{0}^{ln(6)} e^{-x}dx dy = 10

7 0
3 years ago
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