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astra-53 [7]
2 years ago
14

F(x) = x2 - 8x - 20 What is the axis of symmetry, vertex, and y intercept

Mathematics
1 answer:
igor_vitrenko [27]2 years ago
5 0

1. vertex is -4 because:

x^2-8x-20,

a=1, b=-8 , c=-20

use vertex form! -b/2a = -8/2(1) = -8/2 = -4.

2. axis of symmatry is the x which is also -4. The same steps go for the second one.

3. y intercept, I think the answer is -20. Im not sure for this one.

IF YOU LIKE THIS ANSWER PLEASE GIVE ME BRAINLIEST.

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Write your answer as a whole number and remainder.530/34
arsen [322]
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3 years ago
To reduce 16 ounces of a 25% solution of antiseptic to a 10% solution, how much distilled water should a nurse add?
yan [13]

Answer:

24 ounces

Step-by-step explanation:

Here's a more intuitive approach to use here.

You know that your initial solution has a percent concentration, presumably volume by volume, of  

25

%

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1

part solute and  

3

parts solvent.

The target solution must have a concentration of  

10

%

, which means that any volume of this solution will contain  

1

part of solute and  

9

parts solvent.

Your starting solution has a volume of  

16

ounces, or  

4

parts, each with a volume of  

4

ounces.

In order to get to a solution that has a total of  

10

parts, you must add  

6

parts of solvent to the initial solution. Since we know that

1 part  

=

4 ounces

it follows that you must add

6

parts

⋅

4 ounces

1

part solvent

=

24 ounces

of distilled water, which is your solvent, to the initial solution.

The target solution will contain  

1

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parts distilled water for a total of  

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7 0
3 years ago
Which set of shapes could be used to form a net for a square tvyranni?
Bumek [7]
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8 0
3 years ago
Please help me with the below question.
Snezhnost [94]

6a. By the convolution theorem,

L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}

6b. Similarly,

L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}

7. Take the Laplace transform of both sides, noting that the integral is the convolution of e^t and f(t).

\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau

\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)

where g(t) = e^t. Then G(s) = \frac1{s-1}, and

F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}

We have the partial fraction decomposition,

\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)

Then we can easily compute the inverse transform to solve for f(t) :

F(s) = -\dfrac1s + \dfrac4{s+3}

\implies \boxed{f(t) = -1 + 4e^{-3t}}

6 0
1 year ago
7ft,25ft, 4ft<br> Volume of a pyramid
Tju [1.3M]

Answer:

700 cubic ft

Step-by-step explanation:

25*4=100

7*100=700

4 0
2 years ago
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