In a class, 7 students walk to school, two fifths ride and 32% are dropped off by their parents.

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

If quadrilateral ABCD is a parallelogram, what are the correct values for x and y? x = 30, y = 3 x = 30, y = 2 x = 70, y = 2 x =

jeka57 [31]

Answer:

-70 is the correct answer

Step-by-step explanation:

To add fractions, find the LCD and then combine

4 0

3 years ago

Read 2 more answers

Help me answer pls :) what is the value of y when x=43

Leona [35]

Answer:

87

Step-by-step explanation:

f(x) = 2x+1

6 0

3 years ago

Let s(t) = 36 − t. find the equation of the tangent line to s(t) when t = 0.

tatiyna

When t = 0 the point on the graph is (0,36). Your equation is just a line and always has the same tangent line so your equation is the same s = 36 - t.

5 0

3 years ago

Find the area of a circle with a radius of 2.

ruslelena [56]

Answer:

A =12.56 units^2

Step-by-step explanation:

The area of a circle is found by

A = pi r^2

We know the radius is 2

A = pi (2)^2

A = 4pi

Using 3.14 as pi

A = 4(3.14)

A =12.56 units^2

5 0

3 years ago

Read 2 more answers