MATHEMATICS HIGH SCHOOL

Simplify, 5(2x + 3y) - 4(3x - 5y)

Answers

Answer 1

Answer:

5(2x + 3y) - 4(3x - 5y)

5(2x) + 5(3y) - 4(3x) + 4(5y)

(10x + 15y) + (-12x + 20y)

(10x - 12x) + (15y + 20y)

-2x + 35y

Answer 2

Answer:

Answer:

$-2x+35y$

Step-by-step explanation:

$5\left(2x+3y\right)-4\left(3x-5y\right)$

Expand:-

$\hookrightarrow 10x+15y-4\left(3x-5y\right)$

$\hookrightarrow 10x+15y-12x+20y$

Combine $10x$ and $-12x$ = $-2x$

$\hookrightarrow -2x+15y+20y$

Combine $15y$ and $20y$ = $35y$

$\hookrightarrow -2x+35y$

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Shivani is making greeting cards, which she will sell by the box at an arts fair. She paid $20 for a booth at the fair, and the materials for each box of cards cost $5. She will sell the cards for $7 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How many cards will that take?

Answers

Answer:

10 cards

Step-by-step explanation:

So to do this problem, you can make an equation where x is the number of cards sold, which would be:

7x - 20 - 5x = 0

This is because she makes $7 for every card she sells (so 7x), she paid $20 for the booth (so -20), it costs her $5 to make every card (so -5x), and you want to see how many cards it will take for her to cover everything she spent (so it would equal 0).

Then, solving:

$7x-20-5x=0$

combine like terms

$2x-20=0$

add 20 to both sides

$2x = 20$

divide both sides by 2

$x = 10$

This means the answer is 10 cards

What is the additive inverse of 4x

Answers

the additive inverse of 4x is -4x because if you add them together, you get zero. 4x+-4x=0.

Answer:

The additive inverse of 4x is -4x

What is

3x-2y=9
y=2x-7

Answers

Okay, these get easy with practice so don't post all of these online. First, substitute y in 3x-2y=9 for what it says y equals (2x-7). You now have: 3x-2(2x-7)=9. Breakdown:
3x-2(2x-7)=9
3x-4x+14=9
-1x=-5
x=5
next solve for y
y=2x-7
y=2(5)-7
y=10-7
y=3
And now we have x=5, and y=3.

Since you know that "y" is equivalent to "2x - 7" you can substitute that into the first equation

3x - 2y = 9
3x - [2(2x-7)]= 9
3x - (4x - 14) = 9
3x - 4x + 14 = 9
-x + 14 = 9
-x = -5
x = 5

y = 2x - 7
y = 2(5) - 7
y = 10 - 7
y = 3

F(-14) if f(x) = 2x - 3

Answers

Answer:

The correct answer is -31.

Step-by-step explanation:

f(-14) means that x=-14. You have to replace x with -14. Then, you multiply -14 by 2. That is -28. Next you subtract 3 from -28. That gives you -31.

How do you factor 2n^2+3n-9

Answers

Find the factors that multiply to give 2n^2 and -9 but add to give 3n.
2n and n give 2n^2
-3 and 3 give -9
2n*3=6n ... (1)
n*(-3)=-3n ... (2)
(1)+(2)=3n
Group the factors that do not have an effect/interaction to each other from the above.
That is, 2n and -3, and n and 3

2n^2+3n-9=(2n-3)(n+3)

A car factory produces 100 cars in a day. If c is the total number of cars produced in d days, which equation represents the number of cars as a function of the number of days?