Luke cut down a tree that was 26.4 feet tall. Then he cut the tree into 6 equal pieces to take it away.

Which of the following is an even function g(x) = (x – 1)2 + 1g(x) = 2x2 + 1g(x) = 4x + 2g(x) = 2x

GuDViN [60]

An even function can be reflected about the y axis and map onto itself
example: y=x^2

an odd function can be reflected about the origin and map onto itself
example: y=x^3

a simple test is the following

if f(x) is even then f(-x)=f(x)
if f(x) is odd then f(-x)=-f(x)

so

even function
subsitute -x for each and see if we get the same function
remember to fully expand these

g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original one

g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
not same because the original has -2x
not even

g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
same, it's even

g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
not the same, not even

g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
not same, not even

g(x)=2x²+1 is the even function

8 0

3 years ago

Read 2 more answers

What value of x <br> in the solution set of 2(3x – 1) ≥ 4x – 6?

Brrunno [24]

First, you must distribute 2(3x-1).
To do that, you will multiply 2•3x, and 2•-1 because you are taking the number outside of the parentheses and multiplying (distributing) it to all the numbers inside

After distributing, the left side of your inequality will be 6x-2

Now you have
$6x - 2 \geqslant 4x - 6$

To find the value of x, you must subtract an x value from both sides of the equation, as well as a constant from each side.

so you have
$6x - 2 \geqslant 4x - 6 \\ - 6x \geqslant + 6$
And that will make the equation
$- 4 \geqslant - 2x$
Now, divide the variable side, ***BUT, because you are dividing by a negative number in an inequality, the inequality will switch sides.

Then, the value of x is greater than or equal to 2

5 0

3 years ago

Read 2 more answers

What is the justification for each step in the solution of the equation?<br><br> 4(4x+6)−7=77−4x

zepelin [54]

Answer:

20x + 17 = 77 --> Addition Property of Equality:

You are adding (Addition Property) 4x to both sides of the equal sign (Equality).

20x = 60 --> Subtraction Property of Equality:

You subtracted (Subtraction Property) 17 from both sides of the equal sign (Equality).

x = 3 --> Division Property of Equality:

You divided (Division Property) 20 from both sides of the equal sign (Equality) to completely isolate the variable x.

~

6 0

3 years ago

A hypothesis test was used to see if less than 5% of all Americans would still drive to work if gas prices went above $10.00 a g

Kruka [31]

Answer:

The correct option is;

False

Step-by-step explanation:

Here, we note that the proportion of the test statistic which is used in the test is 5% and the P-value for the test is 0.03

The hypothesis test is meant to check if people will still drive to work when the gas prices are above $10.00 and the suggestion was that we can conclude that when the fuel price is above $5.00 everyone would still drive to work without a P-value for the test, hence we can not come to the stated conclusion.

8 0

3 years ago

Find the value of x and y

hram777 [196]

Answer:

x = 12
y = 20

Step-by-step explanation:

There is nothing in this diagram to suggest any particular values for x and y.

__

If we assume the figure is intended to be a kite, symmetrical about its horizontal diagonal, then each segment is congruent to the one above it.

x = 12

y = 20

4 0

2 years ago