Answer:
25% increase in height
Step-by-step explanation:
60 - 48 = 12 inches taller
12 ÷ 48 = .25 = 25% increase in height
<span>The area of the triangle with height 12 inches and the base of 5 inches is 30 square inches. The area (A) of a triangle with height, h, and base, b, is: A = h * b / 2. We know that h = 12 in and that b = 5 in. Therefore, the area of this triangle will be: A = 12 in * 5 in / 2 = 60 in^2 / 2 = 30 in^2. The area of the triangle is 30 square inches.</span>
Answer:
![\Huge \boxed{-15y-9}](https://tex.z-dn.net/?f=%5CHuge%20%5Cboxed%7B-15y-9%7D)
Step-by-step explanation:
To solve this problem, first you have to use the distributive property of
.
First, expand.
![\displaystyle -2(5y+6)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-2%285y%2B6%29)
![-2*5=-10](https://tex.z-dn.net/?f=-2%2A5%3D-10)
![\displaystyle -2*6=-12](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-2%2A6%3D-12)
![\displaystyle -10y-12](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-10y-12)
![\displaystyle -10y-12+3-5y](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-10y-12%2B3-5y)
Next, solve.
![\displaystyle -10-12+3-5=\boxed{-15y-9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20-10-12%2B3-5%3D%5Cboxed%7B-15y-9%7D)
In conclusion, the correct answer is -15y-9.
Answer:
They should add
gallons of the store-bought lemonade.
Step-by-step explanation:
Given that,
Two friends make 2 gallons of lemonade containing 30% lemon juice.
The amount of lemon juice in 2 gallons of lemonade is
= 30% of 2 gallons
![=\frac{30}{100}\times 2 \ gallons](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30%7D%7B100%7D%5Ctimes%202%20%5C%20gallons)
gallons
Let they added x gallons of store-bought lemonade that contains 20% lemon juice.
The amount of lemon juice in x gallons of lemonade is
= 20% of x gallons
![=\frac{20}{100}\times x \ gallons](https://tex.z-dn.net/?f=%3D%5Cfrac%7B20%7D%7B100%7D%5Ctimes%20x%20%5C%20gallons)
gallons
Now the total amount of lemon juice in the mixture is
gallons
gallons
Total amount of lemonade is = (2+x) gallons.
The percentage of lemon juice in the lemonade is
![=\frac{\textrm{The amount of lemon juice}}{\textrm{The amount of lemonade}}\times 100](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctextrm%7BThe%20amount%20of%20lemon%20juice%7D%7D%7B%5Ctextrm%7BThe%20amount%20of%20lemonade%7D%7D%5Ctimes%20100)
![=\frac{\frac{60+20x}{100}}{2+x}\times 100](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cfrac%7B60%2B20x%7D%7B100%7D%7D%7B2%2Bx%7D%5Ctimes%20100)
![=\frac{60+20x}{2+x}\%](https://tex.z-dn.net/?f=%3D%5Cfrac%7B60%2B20x%7D%7B2%2Bx%7D%5C%25)
According to the problem,
![\frac{60+20x}{2+x}=23](https://tex.z-dn.net/?f=%5Cfrac%7B60%2B20x%7D%7B2%2Bx%7D%3D23)
⇒ 60+20x= 23(2+x)
⇒60+20x= 46+23x
⇒23x-20x= 60-46
⇒3x=14
![\Rightarrow x=\frac{14}{3}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%5Cfrac%7B14%7D%7B3%7D)
gallon
They should add
gallons of the store-bought lemonade.
The mixed number for 41/12 would be 3 (whole number) 5/12