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vovangra [49]
3 years ago
15

The functions f(x) = (x + 1)2 − 2 and g(x) = −(x − 2)2 + 1 have been rewritten using the completing-the-square method. Apply you

r knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.
Mathematics
1 answer:
galina1969 [7]3 years ago
8 0

Answer:

f(x)=(x+1)^2-2 is the minimum and g(x)=-(x-2)^2+1 is the maximum

Step-by-step explanation:

Looking at the graph, (you should be able to graph this) the parabola for f(x)=(x+1)^2-2 is pointing downwards and stops at the vertex. This vertex is negative which is the lowest point possible which makes it the minimum. The parabola for -(x-2)^2+1 is pointing upwards and stops at the vertex which is the highest point possible which makes it the maximum.

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What is the probability that the roll of a six-sided die will be either even or odd? A) 1 6 B) 1 4 C) 1 2 D) 1
Step2247 [10]

Answer:

D) 1

Step-by-step explanation:

Every whole number (including the ones on a die) are either even or odd, nothing else. So it is guaranteed for the number to be even or odd.

6 0
2 years ago
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B = 4 and c = -5, evaluate b 2 - c 2
NISA [10]

Hey!

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Steps To Solve:

~Substitute

(4)2 - (-5)2

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8 - (-10)

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18

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Answer:

18

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Hope This Helped! Good Luck!

4 0
3 years ago
Read 2 more answers
Given klmn is a trapezoid, kl = mn, m<1 = m<2, lm/kn = 8/9, pklmn = 132. Find: the length of the legs
Ilia_Sergeevich [38]

Answer:

The length of legs lm, mn, and lk is 32 while that of kn is 36.

Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

This leads the two set of legs such as

\dfrac{lm}{kn}=\dfrac{8}{9}

Or this could be written as

lm=8x\\kn=9x

Now the remaining two sides are given as

lk=lm as this form an isosceles triangle so

lk=8x

Similarly

mn=lm\\

Or

mn=8x

Now the perimeter is given as

\text{perimeter}=lm+mn+kn+lk\\

Here perimeter is given as 132 so this gives:

\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4

So the four legs are of length as given below:

lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36

So the length of legs lm, mn, and lk is 32 while that of kn is 36.

6 0
2 years ago
A bag contains 6 blue, 10 green, and 8 red marbles. What
Evgesh-ka [11]

Answer:

1/4, 3/4

Step-by-step explanation:

First let's find how many marbles there are in total

6+10+8=24 marbles

Now we find the probability of drawing a blue marble

6/24=1/4 (There are 6 blue marbles)

The compliment is 3/4

4 0
2 years ago
3.5x^3-2.3x^2+1.4x+15.6-1.2x^3+4.5x^2-0.3x-3.2
Kamila [148]

Answer: 12.4 + 1.1x + 2.2x^2 + 2.3x^3

Step-by-step explanation:

add the like variables

8 0
2 years ago
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