Answer:
![=\frac{8a+6}{\left(a-3\right)\left(a+3\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B8a%2B6%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D)
the third option is your answer
Step-by-step explanation:
![\frac{5}{a-3}+\frac{3}{a+3}\\\mathrm{Least\:Common\:Multiplier\:of\:}a-3,\:a+3:\quad \left(a-3\right)\left(a+3\right)\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\=\frac{5\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}+\frac{3\left(a-3\right)}{\left(a+3\right)\left(a-3\right)}\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{5\left(a+3\right)+3\left(a-3\right)}{\left(a-3\right)\left(a+3\right)}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7Ba-3%7D%2B%5Cfrac%7B3%7D%7Ba%2B3%7D%5C%5C%5Cmathrm%7BLeast%5C%3ACommon%5C%3AMultiplier%5C%3Aof%5C%3A%7Da-3%2C%5C%3Aa%2B3%3A%5Cquad%20%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%5C%5C%5Cmathrm%7BAdjust%5C%3AFractions%5C%3Abased%5C%3Aon%5C%3Athe%5C%3ALCM%7D%5C%5C%3D%5Cfrac%7B5%5Cleft%28a%2B3%5Cright%29%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D%2B%5Cfrac%7B3%5Cleft%28a-3%5Cright%29%7D%7B%5Cleft%28a%2B3%5Cright%29%5Cleft%28a-3%5Cright%29%7D%5C%5C%5Cmathrm%7BSince%5C%3Athe%5C%3Adenominators%5C%3Aare%5C%3Aequal%2C%5C%3Acombine%5C%3Athe%5C%3Afractions%7D%3A%5Cquad%20%5Cfrac%7Ba%7D%7Bc%7D%5Cpm%20%5Cfrac%7Bb%7D%7Bc%7D%3D%5Cfrac%7Ba%5Cpm%20%5C%3Ab%7D%7Bc%7D%5C%5C%3D%5Cfrac%7B5%5Cleft%28a%2B3%5Cright%29%2B3%5Cleft%28a-3%5Cright%29%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D)
![\mathrm{Expand}\:5\left(a+3\right)+3\left(a-3\right):\quad 8a+6\\=\frac{8a+6}{\left(a-3\right)\left(a+3\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BExpand%7D%5C%3A5%5Cleft%28a%2B3%5Cright%29%2B3%5Cleft%28a-3%5Cright%29%3A%5Cquad%208a%2B6%5C%5C%3D%5Cfrac%7B8a%2B6%7D%7B%5Cleft%28a-3%5Cright%29%5Cleft%28a%2B3%5Cright%29%7D)
Answer:
Selling price of hockey game set is $145.32 , markup price is $210.54 and profit is $96 .
Step-by-step explanation:
Let us assume that the selling price of hockey game set be x .
As given
Pyotr Tchaikovsky Sporting Goods operates on a 45% overhead based on the selling price, which results in an overhead of $65.34 on the newest version of an air hockey game set.
45% is written in the decimal form .
![= \frac{45}{100}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B45%7D%7B100%7D)
= 0.45
Thus the equation becomes
0.45 × x = 65.34
0.45x = 65.34
![x = \frac{65.34}{0.45}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B65.34%7D%7B0.45%7D)
x = 145.2
Therefore the selling price of the hockey game set is $145.2 .
Thus
Markup price = Selling price + Overhead Price
= $145.2 + $65.34
= $ 210.54
As given
If the air hockey game set costs Pyotr Tchaikovsky Sports $49.32 .
i.e Cost price of the hockey game set = $ 49.32
Profit = Selling price - Cost price
= 145.32 - 49.32
= $ 96
Therefore selling price of hockey game set is $145.32 , markup price is $210.54 and profit is $96 .
Answer:
the units were only misalignes by a few cm
To solve this, we should make an equation. The equation has to be in terms of L, which is Leon since Kim has $17 more than him.
The equation:
(L+17) + L = 111
The parenthesis represent how much Kim has. We can take the parenthesis out to actually solve the equation.
L + 17 + L = 111
Let's add like terms, which is L.
2L + 17 = 111
Subtract 17 on both sides.
2L= 94
Divide.
L= 47
We know Leon has 47, now we have to solve Kim by just adding 17 since she has 17 more than Leon.
47+17= 64
So Kim has 64. Let's check by adding and making sure their two values are equal up to 111.
64+47=111
Leon has $47 and Kim has $64.
Answer:
3.2
Step-by-step explanation:
Given Height = constant * width
So constant = Height / width
Now we use the point on the graph and find out constant
Lets take (0.5,1.6)
Here width =0.5 and height = 1.6
![constant = \frac{height}{width} =\frac{1.6}{0.5} = 3.2](https://tex.z-dn.net/?f=constant%20%3D%20%5Cfrac%7Bheight%7D%7Bwidth%7D%20%3D%5Cfrac%7B1.6%7D%7B0.5%7D%20%3D%203.2)
Lets check with one more point (1,3.2)
Here width =1 and height = 3.2
![constant = \frac{height}{width} =\frac{3.2}{1} = 3.2](https://tex.z-dn.net/?f=constant%20%3D%20%5Cfrac%7Bheight%7D%7Bwidth%7D%20%3D%5Cfrac%7B3.2%7D%7B1%7D%20%3D%203.2)