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3 years ago

Andy completes the square for the function y = x^2 + 6x -8 Which of the following functions reveals the vertex of the parabola?

Mathematics

2 answers:

quester [9]3 years ago

8 0

Answer:

y = (x + 6)^2 - 17

Step-by-step explanation:

LiRa [457]3 years ago

4 0

Answer:

B. y = (x + 3)^2 - 17

Step-by-step explanation:

When Andy completes the square, he adds and subtracts the square of half the x-coefficient. That is, he adds and subtracts (6/2)² = 9:

... y = x² +6x +9 -8 -9

... y = (x² +6x +9) -17

... y = (x +3)² -17 . . . . . . . . matches selection B

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If abj=28, abc "congruent to" dbj, find jbc.

Rom4ik [11]

DBJ + ABJ = 90 DBJ = ABC DBC + ABC = 90 JBC + DBC + ABJ = 90 And last but not least: ABJ = 28

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4 years ago

A pump moves 42 gallons in seven minutes. Find the unite rate

avanturin [10]

Answer:

6 Gallons per min

Step-by-step explanation

Unit rate is a fraction that has a one in the denominator

so you have 42/7 = n/1 so to make 7 a 1 , we divide by 7 . We do the same thing on top 42 divided by 7 is 6.

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4 years ago

In the same shop(as in question 8) , under the same conditions of discount, find the marked price of the articles whose selling

guapka [62]

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3 years ago

If sin theta = (4)/(7), theta in quadrant II, find the exact value of (a) cos theta (b) sin (theta + (pi) / (6) ) (c) cos (the

EleoNora [17]

Answer:

a) $\cos(\theta) = \frac{\sqrt[]{33}}{7}$

b) $\sin(\theta + \frac{\pi}{6})\frac{-3\sqrt[]{11}+4}{14}$

c) $\cos(\theta-\pi)=\frac{\sqrt[]{33}}{7}$

d) $\tan(\theta + \frac{\pi}{4}) = \frac{\frac{-4}{\sqrt[]{33}}+1}{1+\frac{4}{\sqrt[]{33}}}$

Step-by-step explanation:

We will use the following trigonometric identities

$\sin(\alpha+\beta) = \sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)$

$\cos(\alpha+\beta) = \cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)$ $\tan(\alpha+\beta) = \frac{\tan(\alpha)+\tan(\beta)}{1-\tan(\alpha)\tan(\beta)}$ .

Recall that given a right triangle, the sin(theta) is defined by opposite side/hypotenuse. Since we know that the angle is in quadrant 2, we know that x should be a negative number. We will use pythagoras theorem to find out the value of x. We have that

$x^2+4^2 = 7 ^2$

which implies that $x=-\sqrt[]{49-16} = -\sqrt[]{33}$ . Recall that cos(theta) is defined by adjacent side/hypotenuse. So, we know that the hypotenuse is 7, then

$\cos(\theta) = \frac{-\sqrt[]{33}}{7}$

b)Recall that $\sin(\frac{\pi}{6}) =\frac{1}{2} , \cos(\frac{\pi}{6}) = \frac{\sqrt[]{3}}{2}$ , then using the identity from above, we have that

$\sin(\theta + \frac{\pi}{6}) = \sin(\theta)\cos(\frac{\pi}{6})+\cos(\alpha)\sin(\frac{\pi}{6}) = \frac{4}{7}\frac{1}{2}-\frac{\sqrt[]{33}}{7}\frac{\sqrt[]{3}}{2} = \frac{-3\sqrt[]{11}+4}{14}$

c) Recall that $\sin(\pi)=0, \cos(\pi)=-1$ . Then,

$\cos(\theta-\pi)=\cos(\theta)\cos(\pi)+\sin(\theta)\sin(\pi) = \frac{-\sqrt[]{33}}{7}\cdot(-1) + 0 = \frac{\sqrt[]{33}}{7}$

d) Recall that $\tan(\frac{\pi}{4}) = 1$ and $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}=\frac{-4}{\sqrt[]{33}}$ . Then

$\tan(\theta+\frac{\pi}{4}) = \frac{\tan(\theta)+\tan(\frac{\pi}{4})}{1-\tan(\theta)\tan(\frac{\pi}{4})} = \frac{\frac{-4}{\sqrt[]{33}}+1}{1+\frac{4}{\sqrt[]{33}}}$

5 0

3 years ago

Can someone help me with this? I literally cant think today. ;-; Thanks if you answer it correctly. ಥ‿ಥ

AleksandrR [38]

Answer:

The slope is 300

Step-by-step explanation:

Rise over run we see two points how many times do we rise and run to get there?

(Slope= rise/run)

So you rise 300 times (Since half of 600 is 300) then you run 1 time which is 300/1 which is 300

4 0

3 years ago