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skelet666 [1.2K]
3 years ago
10

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

Mathematics
2 answers:
LekaFEV [45]3 years ago
5 0
For f(x) to be g(x), the equation f(x) would shift left one
swat323 years ago
4 0

Answer:

graph of g(x) will be translated 1 unit to the left

Step-by-step explanation:

g(x) = x^2 + 2x +1

LEts write the given g(x) in vertex form

WE apply completing the square method

WE take coefficient of x and then divide it by 2 and then square it

2 by 2= 1

1^2=1

add and subtract 1

g(x) = x^2 + 2x +1

g(x) =(x^2 + 2x +1)-1+1

now we factor  x^2+2x+1= (x+1)(x+1)

g(x) =(x+1)(x+1)-1+1

g(x) =(x+1)^2

Now we compare with the graph of f(x)= x^2

In g(x), 1 is added with x

So graph of g(x) will be translated 1 unit to the left

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1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the a
Rudik [331]

Answer:

Part A) \$42,888.48  

Part B) A=\$22,304

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12  

substitute in the formula above  

A=8,500(1+\frac{0.0812}{12})^{12*20}  

A=8,500(1.0068)^{240}  

A=\$42,888.48  

Part B) What if the deposit were compounded monthly with simple interest?  

we know that

The simple interest formula is equal to

A=P(1+rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=20\ years\\ P=\$8,500\\r=0.0812

substitute in the formula above

A=8,500(1+0.0812*20)

A=\$22,304

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

A(t)=8,500(1.0068)^{12t} ------> equation A

A(t)=8,500(1+0.0812t)  -----> equation B

using a graphing tool  

see the attached figure  

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.

5 0
3 years ago
A hot air balloon went from an elevation of 6,678 feet to an elevation of 3,438 feet in 48 minutes. What was its rate of descent
gregori [183]

Answer:

The rate  of descent is -67.5\frac{feet}{minute}

Step-by-step explanation:

we know that

The formula to calculate the rate or slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

Let

x------> the time in minutes

y----> the elevation in feet

we have

A(0,6,678)\ B(48,3,438)

Substitute the values

m=\frac{3,438-6,678}{48-0}

m=\frac{-3,240}{48}

m=-67.5\frac{feet}{minute}

4 0
3 years ago
Given QT = SR, QV = SU, and the diagram, prove that triangles QUT and SVR are congruent. Write a paragraph proof.
QveST [7]

Answer:

Triangles QUT and SVR are congruent because the defining two sides and an included angle of triangles QUT and SVR are equal

Step-by-step explanation:

Here we have QT = SR and

QV = SU

Therefore,

QT = √(UT² + QU²)........(1)

RS = √(VS² + RV²)..........(2)

Since QS = QU + SU = QV + VS ∴ QU = VS

Therefore, since SR = QT and QU = VS, then from (1) and (2), we have UT = RV

Hence since we know all sides of the triangles QUT and SVR are equal and we know that the angle in between two congruent sides of the the triangles QUT and SVR that is the angle in between sides QU and UT for triangle QUT and the angle in between the sides RV and VS in triangle SVR are both equal to 90°, therefore triangles QUT and SVR are congruent.

5 0
3 years ago
The temperature was 8°C then the temperature feel 9°C what was the temperature after it fell?
Vladimir79 [104]

Answer:

-1°C

Step-by-step explanation:

8°C - 9°C = -1°C

Hope it helps

4 0
3 years ago
Paris is 4,000 miles away from Columbus, Ohio. It takes an airplane 8 hours to fly there. What is the speed of the airplane
eimsori [14]

Answer:

500

Step-by-step explanation:

if you take 4,000 miles and divide it by 8 hours, it will give you 500, so that how we figure the speed.

The final answer is 500.

5 0
2 years ago
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