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3 years ago

What are the vertex and x-intercepts of the graph of the function below?

Mathematics

1 answer:

geniusboy [140]3 years ago

5 0

y= x^2 - 6x-7

Vertex = -b /2a

b= -6

a= 1

-(-6)/2(1)= 3

x= 3

Use the substitution method to find y

y= (3)^2-6(3)-7

(3)(3)-18-7

9-25

y= -16

Vertex is (3, 16)

Find x- intercept (y= 0)

y= x^2 - 6x-7

(x-7)(x+1)

x-7= 0

Move -7 to the other side. Sign changes from -7 to 7

x-7+7= 0+7

x= 7

x+1= 0

Move +1 to the other side. Sign changes from +1 to -1

x+1-1= 0-1

x= -1

Answer :B. Vertex: (3, -16); Intercepts: x=-1,7

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Boston, Massachusetts had a population of 617,594 people during January 1 2010, and 675,647 people on January 1 2020.

tigry1 [53]

Answer:

See below

Step-by-step explanation:

Exponential function is:

y = abˣ

If we consider the time difference in years as x and the initial population as a, then we get:

675647 = 617594*b¹⁰

Find the value of b:

b¹⁰ = 675647/617594
b¹⁰ = 1.09399864636
b = 1.09399864636^(1/10)
b = 1.009 (rounded)

The equation we got is:

y = 617594*1.009ˣ

Here we have y- population after x years since 2010, x - the number of years since 2010 and 1.009 is the population growth rate.

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1 year ago

Tim needs 23 3/4 m of wood trim to remodel a room. Wood trim is sold in lengths of 1 1/4 m. What equation can be used to find th

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3 years ago

Please help!!! 20 points

V125BC [204]

Answer:

A) x = (-8log(6)-2log(17))/(-2log(17)+log(6))

Step-by-step explanation:

Taking the logarithm of the equation, you have ...

(x+8)log(6) = (2x-2)log(17)

Subtracting the right side from the equation gives ...

x(log(6) -2log(17)) +8log(6)+2log(17) = 0

Subtracting the constant and dividing by the coefficient of x gives ...

x = -(8log(6) +2log(17))/(log(6) -2log(17)) . . . . . matches selection A

___

You don't need to work out the whole solution to determine the correct answer choice. Once you take the initial log, you find that the x-coefficient includes a multiplier of 2log(17). This term only appears in the denominator of choice A. (The value of x will be found after dividing by the x-coefficient, so you know this must show up in the denominator of the answer.)

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3 years ago

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the

kodGreya [7K]

Answer:

p=0.7103 (4-game series)
p=0.6480 (2-game series)

Step-by-step explanation:

Let X be the random variable equal the the first 4 straight wins. An overall win for the stronger team implies a negative binomial function with the parameters n=4, p=0.6:

$P(X=4)={{i-1}\choose {4-1}}0.6^40.4^{i-4},\ i=4,5,6,7$

#We find probabilities for the different values of i:

$P(X=4)={3\choose 3}0.6^4=0.1296\\\\P(X=5)={4\choose 3}0.6^40.4^1=0.2074\\\\P(X=6)={5\choose 3}0.6^40.4^2=0.2074\\\\P(X=4)={6\choose 3}0.6^40.4^3=0.1659$

Hence, probability of the stronger team winning overall is:

$=P(X=4)+P(X=5)+P(X=6)+P(X=7)\\\\=0.7103$

#Define Y as the random variable for winning 2/3 games.:

$P(Y=2)={1\choose 1}0.6^2=0.3600\\\\P(Y=3)={2\choose3}0.6^20.4=0.2880\\\\P(win)=0.2880+0.3600=0.6480$

Hence, probability of the stronger team winning in 2 out 3 game series is 0.6480

The stronger team has a higher chance of winning in a 4-game series(0.7103>0.6480)

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2 years ago

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