All categories

3 years ago

4) Write an inequality for the graph below. If necessary, use <= for < or >= for .

Mathematics

1 answer:

navik [9.2K]3 years ago

6 0

9514 1404 393

Answer:

y < -1/4x -1

Step-by-step explanation:

The boundary line appears to go through the points (-4, 0) and (0, -1). This tells you it has a "rise" of -1 for a "run" of 4. The slope is ...

m = rise/run = -1/4

The y-intercept (b) is the point where the y-axis is crossed. The slope-intercept equation of the boundary line is ...

y = mx + b

y = -1/4x -1

The boundary line is dashed, so is not included in the solution set. The shading is below the line, so all y-values less than (but not equal to) the boundary line are in the solution set:

y < -1/4x -1

You might be interested in

What is the first step in solving this system of equations by elimination? 5a + 3b = –9 2a – 5b = –16

Elis [28]

<span>Multiply one of the equations so that both equations share a common complementary coefficient.
In order to solve using the elimination method, you need to have a matching coefficient that will cancel out a variable when you add the equations together. For the 2 equations given, you have a huge number of choices. I'll just mention a few of them.
You can multiply the 1st equation by -2/5 to allow cancelling the a term.
You can multiply the 1st equation by 5/3 to allow cancelling the b term.
You can multiply the 2nd equation by -2.5 to allow cancelling the a term. You can multiply the 2nd equation by 3/5 to allow cancelling the b term.
You can even multiply both equations.
For instance, multiply the 1st equation by 5 and the second by 3. And in fact, let's do that. 5a + 3b = â€“9 2a â€“ 5b = â€“16 5*(5a + 3b = -9) = 25a + 15b = -45
3*(2a - 5b = -16) = 6a - 15b = -48
Then add the equations 25a + 15b = -45
6a - 15b = -48
=
31a = -93
a = -3
And then plug in the discovered value of a into one of the original equations and solve for b.</span>

5 0

3 years ago

-4x < 16<br> How do I solve this inequality?

agasfer [191]

Answer:

x>-4

Step-by-step explanation:

Divide by negative 4 on both sides, and since its a negative, you have to flip the inequality sign, so it comes out to be x> -4

6 0

2 years ago

Let Y be a random variable with a density function given by

Neporo4naja [7]

From the given density function we find the distribution function,

$F_Y(y)=P(Y\le y)=\displaystyle\int_{-\infty}^y f_Y(t)\,\mathrm dt=\begin{cases}0&\text{for }y$

(a)

$F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)$

$\implies F_{U_1}(u_1)=\begin{cases}0&\text{for }u_1$

$\implies f_{U_1}(u_1)=\begin{cases}\frac{{u_1}^2}{18}&\text{for }-3\le u_1\le3\\0&\text{otherwise}\end{cases}$

(b)

$F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y$

$\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2$

$\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}$

(c)

$F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})$

$\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3$

$\implies f_{U_3}(u_3}=\begin{cases}\frac32\sqrt u&\text{for }0\le u\le1\\0&\text{otherwise}\end{cases}$

5 0

3 years ago

Write the ratio in simplest form: 2 pints to 2 gallons.

ryzh [129]

Answer:

2 pints: 0.25 gallons

16 pints: 2 gallons

Step-by-step explanation:

1 gallon = 0.125 pints

5 0

2 years ago

Mrs. Pollo was making pizza. She used 3/8 of a cup of olives to make 1 pizza. At this rate, what amount of olives would she use

-BARSIC- [3]

Answer is 3/16 cup
She used 3/8 cup of olives on one pizza
She is going to use 1/2 of 3/8 cup for 1/2 pizza
1/2 of 3/8 = x
Multiply (1/2)(3/8) =
3/16 cup of olives

4 0

2 years ago

Read 2 more answers