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3 years ago

What is the range of the function f(x) = |x − 1| − 2?

1 answer:

8 0

You obtain the graph of function $f(x)=|x-1|-2$ translating the graph of function $g(x)=|x|$ 1 unit left and 2 units down.

The range of the graph $g(x)=|x|$ is $[0,\infty]$ . When you make the needed translations you can see that the range of the function $f(x)$ is $[-2,\infty]$ .

Answer: $[-2,\infty]$ .

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A homeowner is installing a swimming pool in his backyard. he want its length to be 4 feet longer than its width. then he wants

marishachu [46]

1. You have that:

- The homeowner want the length of the swimming pool to be 4 feet longer than its width.
- He wants to surround it with a concrete walkway 3 feet wide.
- He can only afford 300 square feet of concrete for the walkway.

2. Therefore, the tota area is:

At=L2xW2

L2 is the lenght of the walkway (L2=L1+3+3⇒L2=(W1+4+6)⇒L2=W1+10).
W2 is the width of the walkway (W1+3+3⇒W2=W1+6)

3. The area of the walkway is:

A2=At-A1

A2=300 ft²

4. Therefore, you have that the width of the swimming pool is:

A2=(W1+10)(W1+6)-(W1+4)(W1)
300=(W1²+6W1+10W1+60)-(W1²+4W1)
W1²+16W1+60-W1²-4W1-300=0
12W1-240=0
W1=240/12
W1=20 ft

5. And the length is:

L1=W1+4
L1=20+4
L1=24 ft

8 0

3 years ago

Question

tatiyna

Answer:

Wes

Step-by-step explanation:

This represents a positive correlation, meaning that when x increases, so does y. Because of x, y increases meaning that Wes is correct

3 0

2 years ago

Round 69581.491337 to the nearest thousand.

Anika [276]

Answer:

7000

Step-by-step explanation:

lets start with 695

9 is the thousand

you check the number next to 9

less then 4 let it rest

more than 5 let it soar

something like that lol

anyways since 5 is next to the 9 we round up from 9 to the next number which is 10

so that changes the whole number to 7000

hope this makes sense!

3 0

3 years ago

What is the degree measure of b? A)) 29° B) 32° C) 61° D) 64°

Lemur [1.5K]

Answer:

B 32

Step-by-step explanation:

The exterior angle is the sum of the measure of the measure of the opposite interior angles.

151 = 119+b

Subtract 119 from each side.

151-119 = 119-199+b

32 = b

5 0

3 years ago

Read 2 more answers

How many complex zeros does the polynomial function have? f(x)=−3x^6−2x^4+5x+6

REY [17]

one way would be to factor

I can't factor it so we will have to use Descartes' Rule of Signs which is helpful for finding how many real roots you have

it goes like this:

for a polynomial with real coefients, consider $f(x)=-3x^6-2x^4+5x+6$ .

after arranging the terms in decending order in terms of degree, count how many times the signs of the coeffients change direction and minus 2 from that number until you get to 1 or 0. that will be the number of even roots the function can have

We have (-, -, +, +). the signs changed 1 times, so it has 1 real positive root

to get the negative roots, we evaluate f(-x) and see how many times the root changes

$f(-x)=-3x^6-2x^4-5x+6$

signs are (-, -, -, +). there was 1 change in sign

so the function has 1 real negative root

a total of 2 real roots

a function of degree $n$ can have at most, $n$ roots

our function is degree 6 so it has 6 roots

if 2 are real, then the others must be complex

6-2=4 so there are 4 complex roots

you can also show that there are only 2 real roots by using a graphing utility to see that there are only 2 real roots

7 0

3 years ago