X + x +8 = 32
2x + 8 = 32
2x = 24
x = 12
So gerardo has won 12 and jenny has won 20
Answer:
Only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
Step-by-step explanation:
We will solve to find out Which expression has a positive quotient.
We know the division rule:
and ![\frac{-a}{b}=\frac{-a}{b}](https://tex.z-dn.net/?f=%5Cfrac%7B-a%7D%7Bb%7D%3D%5Cfrac%7B-a%7D%7Bb%7D)
We will use these rules
1) Negative three-fourths divided by Negative two-thirds
![=\frac{-\frac{3}{4} }{-\frac{2}{3} }\\=-\frac{3}{4}\times -\frac{3}{2}\\=\frac{9}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-%5Cfrac%7B3%7D%7B4%7D%20%7D%7B-%5Cfrac%7B2%7D%7B3%7D%20%7D%5C%5C%3D-%5Cfrac%7B3%7D%7B4%7D%5Ctimes%20-%5Cfrac%7B3%7D%7B2%7D%5C%5C%3D%5Cfrac%7B9%7D%7B8%7D)
The quotient is positive.
2) Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth
![\frac{-\frac{1}{8} }{3\frac{1}{5} }\\=\frac{-\frac{1}{8} }{\frac{16}{5} }\\=-\frac{1}{18} \times \frac{5}{16}\\=-\frac{5}{288}](https://tex.z-dn.net/?f=%5Cfrac%7B-%5Cfrac%7B1%7D%7B8%7D%20%7D%7B3%5Cfrac%7B1%7D%7B5%7D%20%7D%5C%5C%3D%5Cfrac%7B-%5Cfrac%7B1%7D%7B8%7D%20%7D%7B%5Cfrac%7B16%7D%7B5%7D%20%7D%5C%5C%3D-%5Cfrac%7B1%7D%7B18%7D%20%5Ctimes%20%5Cfrac%7B5%7D%7B16%7D%5C%5C%3D-%5Cfrac%7B5%7D%7B288%7D)
The quotient is negative.
3) 2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth
![\frac{2\frac{2}{7} }{-\frac{1}{5} }\\= \frac{\frac{16}{7} }{-\frac{1}{5} }\\=\frac{16}{7} \times -5\\=-\frac{80}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Cfrac%7B2%7D%7B7%7D%20%7D%7B-%5Cfrac%7B1%7D%7B5%7D%20%7D%5C%5C%3D%20%5Cfrac%7B%5Cfrac%7B16%7D%7B7%7D%20%7D%7B-%5Cfrac%7B1%7D%7B5%7D%20%7D%5C%5C%3D%5Cfrac%7B16%7D%7B7%7D%20%5Ctimes%20-5%5C%5C%3D-%5Cfrac%7B80%7D%7B7%7D)
The quotient is negative.
4) Negative 6 divided by Five-thirds
![\frac{-6}{\frac{5}{3} }\\=-6 \times \frac{3}{5}\\=-\frac{18}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%7D%7B%5Cfrac%7B5%7D%7B3%7D%20%7D%5C%5C%3D-6%20%5Ctimes%20%5Cfrac%7B3%7D%7B5%7D%5C%5C%3D-%5Cfrac%7B18%7D%7B5%7D)
The quotient is negative.
So, only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
Answer:
![x(x-3)(x+2)](https://tex.z-dn.net/?f=x%28x-3%29%28x%2B2%29)
Step-by-step explanation:
1. Find the GCF (Greatest Common Factor)
![GCF=x](https://tex.z-dn.net/?f=GCF%3Dx)
2. Factor out the GCF and simplify.
![x(x^{2} -x-6)](https://tex.z-dn.net/?f=x%28x%5E%7B2%7D%20-x-6%29)
3. Factor ![x^{2} -x-6.](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-x-6.)
Which two numbers add up to -1 and multiply to -6?
<u>-3 and 2</u>
Rewrite the expression using the numbers above.
![(x-3)(x+2)](https://tex.z-dn.net/?f=%28x-3%29%28x%2B2%29)
4. Done!
![x(x-3)(x+2)](https://tex.z-dn.net/?f=x%28x-3%29%28x%2B2%29)
12. On addition, you can just combine like terms.
2v^3+(-v^3)=v^3
-v+v cancels each other out
8+(-3)=5
So you have v^3+5
14 On subtraction, you have to remember to distribute the negative sign so after you do that you have:
4h^3+3h+1+5h^3-6h+2
Then you can combine like terms
4h^3+5h^3=9h^3
3h-6h=-3h
1+2=3
So you end up with:
9h^3-3h+3
Hope that helps and feel free to ask any questions.
She can buy maximum of
packages while staying within her budget.
Minimum spending limit
$
.
Maximum spending limit
$
.
Cost of one package of beads
$
.
Number of packages of beads bought
.
Cost of one package of charms
$
.
Let the number of packages of beads bought be
.
![4.956 \times 5 + x \times 6.55 \geq 50](https://tex.z-dn.net/?f=4.956%20%5Ctimes%205%20%2B%20x%20%5Ctimes%206.55%20%5Cgeq%2050)
![24.78+6.55x\geq 50](https://tex.z-dn.net/?f=24.78%2B6.55x%5Cgeq%2050)
![6.55x\geq 25.22](https://tex.z-dn.net/?f=6.55x%5Cgeq%2025.22)
![x\geq 3.85](https://tex.z-dn.net/?f=x%5Cgeq%203.85)
![4.956 \times 5 + x \times 6.55 \leq 60](https://tex.z-dn.net/?f=4.956%20%5Ctimes%205%20%2B%20x%20%5Ctimes%206.55%20%5Cleq%2060)
![24.78+6.55x\leq 60](https://tex.z-dn.net/?f=24.78%2B6.55x%5Cleq%2060)
![6.55x\leq 35.22](https://tex.z-dn.net/?f=6.55x%5Cleq%2035.22)
![x\leq 5.38](https://tex.z-dn.net/?f=x%5Cleq%205.38)
So, she can buy maximum of
packages while staying within her budget.
Learn more about solving inequalities here:
brainly.com/question/12189350?referrer=searchResults