What is 375 times 54 Answer in 1 min

Please help me! Find the number x such that f(x) =1

STatiana [176]

Answer:

D

Step-by-step explanation:

We have the piecewise function:

$f(x) = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

And we want to find x such that f(x)=1.

So, let's substitute 1 for f(x):

$1 = \left\{ \begin{array}{ll} -\frac{1}{2}x-1 & \quad x \leq -2 \\ x & \quad x > -2 \end{array} \right.$

This has two equations. So, we can separate them into two separate cases. Namely:

$1=-\frac{1}{2}x-1\text{ or } 1=x$

Let's solve for x in each case.

Case I:

We have:

$1=-\frac{1}{2}x-1$

Add 1 to both sides:

$2=-\frac{1}{2}x$

Let's cancel out the fraction by multiplying both sides by -2. So:

$2(-2)=(-2)\frac{-1}{2}x$

The right side cancels:

$-4=x\\$

Flip:

$x=-4$

So, x is -4.

Case II:

We have:

$1=x$

Flip:

$x=1$

This is the solution for our second case.

So, we have:

$x_1=-4\text{ or } x_2=1$

Now, can check to see if we have to to remove solution(s) that don't work.

Note that x=-4 is the solution to our first equation.

The first equation is defined only if x is less than -2.

-4 is less than -2. So, x=-4 is indeed a solution.

x=1 is the solution to our second equation.

The second equation is defined only if x is greater than or equal to -2.

1 is greater than or equal to -2. So, x=1 is also a solution.

Therefore, our two solutions are:

$x_1=-4\text{ or } x_2=1$

Out of our answer choices, we can pick D.

And we're done!

7 0

3 years ago

You can walk 3 miles per hour, jog 5 miles per hour, or run 10 miles per hour. You go a full hour before changing pace. At the e

Studentka2010 [4]

Answer:

b. How many ways arc there to go 12 miles?

≡ p(12) = 25

c. How many ways arc there to go 20 miles?

≡ p(20) = 131

d. How many ways arc there to go 22 miles?

≡p(22) 199

Step-by-step explanation:

a) supposed you walked for the first hour. Then you would have travelled 3 miles. if you jogged you would have covered 5miles and if you run you would have covered 10miles. now you have to decide how to run the rest miles from the n miles.

Thus, the number of ways one can cover n miles will be given by the recurrence relation

p(n) = p( n-3) + p( n-5) + p( n - 10)

now to solve the rest of the question, let us make a table which provides the number of ways for n = 1 to 22.

check the attachment for the table

b. How many ways arc there to go 12 miles?

≡ p(12) = 25

c. How many ways arc there to go 20 miles?

≡ p(20) = 131

d. How many ways arc there to go 22 miles?

≡p(22) 199

8 0

2 years ago

What is the solution to the system of equations? O (-4,1) O (-2, 1) O (1.4) O (1,-2)

Tcecarenko [31]

Answer:

$(1,-2)$

Step-by-step explanation:

Given

The attached graph

Required

Determine the solution

The solution here is the intersection points of the two lines. From the attachment, both lines meet

$x = 1$

$y = -2$

Hence, the solution is: $(1,-2)$

3 0

3 years ago

How can i estimate a number from a bar graph??

olga55 [171]

You should first find out what lines are what,
Like for example, If you had 5 - 10 - 15 as the Y Lines and the bar was between 5 and 10 then your best bet would be to estimate what the middle of 5 and 10 is which would be 7 or 8.

8 0

3 years ago

Answer ASAP!.......... I need help on 34 more questions.

lianna [129]

19

Step-by-step explanation:

Because when you and you need don't forget that when you

4 0

2 years ago