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3 years ago

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The graph of the parabola defined by the equation y=-(x+1)^2+1 is shifted 1 unit to the right, then shifted 5 units down, then r

otated 180 degrees about its vertex. The resulting parabola has zeros at x=a and x=b, where b > a. What is b-a?

2 answers:

Vlad [161]3 years ago

8 0

Answer:

Step-by-step explanation:

45

erica [24]3 years ago

4 0

Answer:

4

Step-by-step explanation:

y = -(x + 1)² + 1

Shift 1 unit to the right:

y = -(x + 1 − 1)² + 1

y = -x² + 1

Shift 5 units down:

y = -x² + 1 − 5

y = -x² − 4

Rotate 180° about the vertex:

y = -(-x²) − 4

y = x² − 4

Find the zeros:

0 = x² − 4

x² = 4

x = -2 or 2

Therefore, a = -2 and b = 2, so b−a = 4.

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The price of a computer component is decreasing at a rate of 15% per year. State whether this decrease is linear or exponential

Margaret [11]

Answer:

Since the price is given by an exponential function, the decline in price is exponential.

The component will cost $36.8475 in three years.

Step-by-step explanation:

The equation for the price of a component has the following format:

$P(t) = P(0)(1-r)^{t}$

In which P(t) is the price after t years, P(0) is the initial price, and r is the rate that the price decreases.

Since the price is given by an exponential function, the decline in price is exponential.

The price of a computer component is decreasing at a rate of 15% per year.

This means that $r = 0.15$

Component costs $60 today

So P(0) = 60. Then

$P(t) = P(0)(1-r)^{t}$

$P(t) = 60(1-0.15)^{t}$

$P(t) = 60(0.85)^{t}$

What will it cost in three years?

This is P(3).

$P(t) = 60(0.85)^{t}$

$P(3) = 60(0.85)^{3} = 36.8475$

The component will cost $36.8475 in three years.

6 0

3 years ago

1/2,1/3,1/8 find the sum

Zarrin [17]

Answer:

23/24

Step-by-step explanation:

To find the sum you must ad.

Fractions can only be added and subtracted when the denominators (the bottom numbers) are the same.

24 is the smallest number that 2, 3 and 8 go into.

1/2 = 12/24, 1/3 = 8/24, 1/8 = 3/24

$\frac{12}{24} + \frac{8}{24} + \frac{3}{24} = \frac{23}{24}$

23/24

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3 years ago

Which angle is a horizontal translation of the first angle?

grin007 [14]

Step-by-step explanation:

B becuase it keeps the same orientation and have the same distance from each point and they both produce rigid motion.

A is a reflection.

C is a dilation.

D is a rotation.

3 0

3 years ago

If tn = 4n+1, find t1, t2, t3, and tn+1. Express tn+1−tn in its simplest form.

Doss [256]

Answer:

$t_1=5$

$t_2=9$

$t_3=13$

$t_{n+1}-t_n=4$

Step-by-step explanation:

We have that:

$t_n=4n+1$

When we substitute n=1, we get:

$t_1=4*1+1=5$

When we substitute n=2 we get:

$t_2=4*2+1=9$

When we substitute n=3, we get:

$t_3=4*3+1=13$

When we substitute n=n+1, we get:

$t_{n+1}=4*(n+1)+1=4n+5$

Now

$t_{n+1}-t_n=4n+5-(4n+1)$

We expand and simplify to obtain:

$t_{n+1}-t_n=4n+5-4n-1$

$t_{n+1}-t_n=4$

3 0

3 years ago

PLEASE HURRY<br><br> 9x^2 + 64 = 0<br><br> I NEED THE WORK SHOWN IN ORDER TO GET CREDIT

seropon [69]

Answer:

x = ± $\frac{8}{3}$ i

Step-by-step explanation:

subtract 64 from both sides

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x² = - $\frac{64}{9}$ ( take the square root of both sides )

x = ± $\sqrt{-64/9}$ = ± $\frac{8}{3}$ i

6 0

3 years ago

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