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3 years ago

Can someone help me please

Mathematics

1 answer:

vlada-n [284]3 years ago

8 0

Answer:

y=(x+4)^2 is shifted four units to the left.

Step-by-step explanation:

When you think of this transformation you have to know that the parabola isn't changed and only the units do in this situation.

You might be interested in

1. Let f(x) = x + 3 and g(x) = 3x + 5. Find f(g(4)) - g(f(4)) 2. Let f(x) = 5x^2 - 5. What is f(f(x))? 3. Let f(g(x)) = 3x + 3 a

ludmilkaskok [199]

Answer:

1. f(g(4)) - g(f(4)) = -6

2. f(f(x)) = 125x^4 - 250x^2 + 120

3. a + b = 0

4. g(4) = -9

Step-by-step explanation:

First we need to find f(4) and g(4):

f(4) = 4 + 3 = 7

g(4) = 3*4 + 5 = 17

Then, we find g(f(4)) = g(7):

g(7) = 3*7 + 5 = 26

And we find f(g(4)) = f(17):

f(17) = 17 + 3 = 20

so f(g(4)) - g(f(4)) = 20 - 26 = -6

To find f(f(x)), we use the value of f(x) for every x in f(x):

f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5

f(f(x)) = 125x^4 - 250x^2 + 120

To find f(g(x)), we use the value of g(x) for every x in f(x):

f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3

ax + (b+6) = 3x + 3 -> a = 3 and b = -3

a + b = 3 - 3 = 0

If we assume g(x) = ax + b, we have:

g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x

2a = -4 -> a = -2

-3a + b = 5

6 + b = 5 -> b = -1

g(x) = -2x - 1

g(4) = -2*4 - 1 = -9

7 0

3 years ago

Say if the Earth rotates 1.25 degrees in 5 mintues. But a classmate wants to find out how many degrees the Earth can rotate in 2

givi [52]

Her error was dividing them by 2 she would place 1.25 over 5 then divide by 5 to get the unit rate per minute then multiply the quotient by 2 to get the rate of degrees moved for 2 minutes which is .5 or .50 degrees every two minutes.

4 0

3 years ago

What is the distance between the points (21 , 13) and (3 , 13) in the coordinate plane?

Oxana [17]

Answer:

$\displaystyle d = 18$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Identify

Point (21, 13)

Point (3, 13)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(3-21)^2+(13-13)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{(-18)^2+(0)^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{324+0}$
[√Radical] Add: $\displaystyle d = \sqrt{324}$
[√Radical] Evaluate: $\displaystyle d = 18$