While she was training for a marathon Lucy ran a total of 120 kilometers. How many meters did she run

Lyrx [107]

Part A.

We could take, for example:

$\begin{cases}x\geq-3\\y\geq3\end{cases}$

For x ≥ -3 we have vertical line (x-intercept = -3) and shaded region on the right side of the line.
For y ≥ 3 we have horizontal line (y-intercept = 3) and shaded region above that line.

Part B.

Simply, substitute x and y coordinates of D and E <span>to the system of inequalities from part A, and check if its is true, what we get.
</span>
$D=(-2,4)\\\\\begin{cases}x\geq-3\\y\geq3\end{cases}\quad\implies\quad\begin{cases}-2\geq-3\qquad\text{True}\\4\geq3\qquad\text{True}\end{cases}$

so point D is a solution,

$E=(2,4)\\\\\begin{cases}x\geq-3\\y\geq3\end{cases}\quad\implies\quad\begin{cases}2\geq-3\qquad\text{True}\\4\geq3\qquad\text{True}\end{cases}$

and point E is also a solution to <span>our system of inequalities.
</span>
Part C.

There are two ways we could do that. First is the same as in part B. We substitute x and y coordinates of each school and check if inequality is true or false:

$A=(-5,5)\\\\y\ \textless \ 3x-3\quad\implies\quad5\ \textless \ 3\cdot(-5)-3\quad\implies\quad5\ \textless \ -18\quad\text{False}\\\\\\
B=(-4,-2)\\\\y\ \textless \ 3x-3\quad\implies\quad-2\ \textless \ 3\cdot(-4)-3\quad\implies\quad-2\ \textless \ -15\quad\text{False}\\\\\\
C=(2,1)\\\\y\ \textless \ 3x-3\quad\implies\quad1\ \textless \ 3\cdot2-3\quad\implies\quad1\ \textless \ 3\quad\text{True}\\\\\\
D=(-2,4)\\\\y\ \textless \ 3x-3\quad\implies\quad4\ \textless \ 3\cdot(-2)-3\quad\implies\quad4\ \textless \ -9\quad\text{False}\\\\\\
E=(2,4)\\\\y\ \textless \ 3x-3\quad\implies\quad4\ \textless \ 3\cdot2-3\quad\implies\quad4\ \textless \ 3\quad\text{False}\\\\\\$

$F=(3,-4)\\\\y\ \textless \ 3x-3\quad\implies\quad-4\ \textless \ 3\cdot3-3\quad\implies\quad-4\ \textless \ 6\quad\text{True}\\\\\\$

So Timothy can attend schools C and F.

We can also draw a graph of that inequality (pic 2).

8 0

3 years ago

Read 2 more answers

Pls pls help i need help

Gala2k [10]

Answer:

3 m/s/s

Step-by-step explanation:

F = ma

28 = 4m

m = 7

m is constant throughout

21 = 7a

a = 3

3 m/s/s

3 0

3 years ago

A number is chosen at random from the first 100 positive integers. Find the probability that the number is a multiple of 7.

Iteru [2.4K]

100÷7=14...
Probability is 14/100=7/50

8 0

3 years ago

Read 2 more answers

What is the LCM of two numbers that have no common factors greater than 1? give an example.

joja [24]

Answer:

Their product.

Step-by-step explanation:

Question:

What is the LCM of two numbers that have no common factors greater than 1? give an example.

Answer:

Heya, I heard you need help! Well, let me explain for ya! c:

The answer is their product. The LCM is the smallest number that is a multiple of two numbers. If two numbers have no common factors greater than 1, then their LCM would be their product.

Here, let me provide an example, love:

Take the numbers 4 and 9. As they do not have a common factor greater than 1, you would multiply them as if they were factors. Therefore, the LCM would be the product, 36.

Hope that helped! If you have anymore questions, just comment down and I will try my best to help you! Au revoir!

~ Sienna

4 0

3 years ago

Read 2 more answers

I already posted this photo once asking for answers, but I only said "Thank you, have a nice day." with the photo, and apparentl

kirill115 [55]

Answer:

12 outcomes

Step-by-step explanation:

To get a red on the counter, it's a 50% chance. To get a number greater than 3 on a spinner with numbers labeled 1 to 6, it's another 50% chance. To get the chance of both happening, you'll have to multiply both percents together. 50% x 50% = 25%

2/5 = 0.4 = 40%

40% of 80 is 32

25% of 80 is 20

32 - 20 is 12

5 0

3 years ago