Use the number line to find the coordinate of the midpoint of ¯¯¯¯¯ J P .

Alex73 [517]

There are two ways to do this but the way I prefer is to make one of the equations in terms of one variable and then 'plug this in' to the second equation. I will demonstrate

Look at equation 1, $-2x+y=10$ this can quite easily be manipulated to show $y=10+2x$ .

Then because there is a y in the second equation (and both equations are simultaneous) we can 'plug in' our new equation where y is in the second one $4x-y=-14 \Rightarrow 4x-(10+2x)=-14$ which can then be solved for x since there is only one variable $4x-10-2x=-14 \Rightarrow 2x=-4 \Rightarrow x=-2$ and then with our x solution we can work out our y solution by using the equation we manipulated $y=10+2x = 10+(2 \times -2) = 10-4=6$ .

So the solution to these equations is x=-2 when y=6

8 0

3 years ago

A unicorn daycare center requires there to be 2 supervisors for every 18 unicorns.

kykrilka [37]

Answer: The number of supervisors are 9 times the number of unicorns.

Step-by-step explanation:

Let the number of supervisors be 'n'.

Let the number of unicorns be 'u'.

According to question, a unicorn daycare center requires there to be 2 supervisors for every 18 unicorns.

So, Mathematically, it is expressed as

$\dfrac{n}{u}=\dfrac{2}{18}\\\\\dfrac{n}{u}=\dfrac{1}{9}\\\\9n=u$

so, we established the relationship between the number of supervisors and number of unicorns.

Hence, the number of unicorns are 9 times the number of supervisors.

5 0

3 years ago

Read 2 more answers

If you have thirty -five (35) members in an organization that meets nine (9) times a year, how often will a member have to host

Olegator [25]

Answer:

the host will continue the way they are prepared.

3 0

3 years ago

A winter coat was originally $65 and is now marked up by 2% . What is the price after the markup?

ratelena [41]

It would be 66.3 because 2% Coverts to .02 then you multiply that to 65 and get 1.3 and then you add that to 65

5 0

3 years ago

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the sma

RSB [31]

Answer:

A.

Step-by-step explanation:

NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

$y=2(x+3)$

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

$y=3x+5$

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

$y=2(x+3)\\y=2x+6\\-2x+y=6$

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

$-2x+y=6\\2x-y=-6$

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

$y=3x+5\\-3x+y=5\\3x-y=-5$

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.

7 0

3 years ago