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andreev551 [17]
3 years ago
7

Factor each trinomial completely. 4x^2 - 25b^2 and x^2 - 81

Mathematics
1 answer:
GenaCL600 [577]3 years ago
8 0

Step-by-step explanation:

4x2 - 25b2

We can solve it by the squares so

(2x - 5b) (2x + 5b)

2) x2 - 81

The same case is here so

(x - 9) (x + 9)

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Large truck has 150 gallons of gasoline that is 2/3 full. How many gallons of gas will it take to fill the tank to it's capacity
Reika [66]
2/3 of the entire tank = 150 gallons

2/3x = 150
x = 150 / (2/3)
x = 150 * 3/2
x = 450/2
x = 225 <== the entire tank can hold 225 gallons
4 0
4 years ago
How do you do this problem? Please explain.
horrorfan [7]

Answer:  8.632

<u>Step-by-step explanation:</u>

First, you need to find the length of AE. Since ΔAEC is a right triangle, we can use:

sin\ C=\dfrac{AE}{AC}\\\\\\sin\ 50 = \dfrac{AE}{5}\\\\\\5\ sin\ 50=AE\\\\3.83=AE

Next, Use Heron's formula to find the Area of ΔADE.

  • AE = 3.83
  • ED = 6
  • AD = 9

Heron's formula is:

A=\sqrt{s(s-a)(s-b)(s-c)}\quad \text{where}\ s = \dfrac{a+b+c}{2}\\\\s=\dfrac{AE+ED+AD}{2}=\dfrac{3.83+6+9}{2}=\dfrac{18.83}{2}=9.415\\\\A=\sqrt{9.415(9.415-3.83)(9.415-6)(9.415-9)}\\\\.\quad=\sqrt{9.415(5.585)(3.415)(0.415)}\\\\.\quad=\sqrt{74.519}\\\\.\quad=8.632

5 0
3 years ago
The formula s=0.04n+2500 gives an employees monthly salary s, in dollars, after selling n dollars in merchandise at an appliance
topjm [15]
A) Find the inverse of the function
s=0.04n+2500
s-2500=0.04n+2500-2500
s-2500=0.04n
s/0.04-2500/0.04=0.04n/0.04
25s-62,500=n
n=25s-62,500
Answer: The inverse of the function is n=25s-62,500

Is <span>the inverse a function?
Yes, the inverse is a function, a linear function.

</span>b) Use the inverse to find the same amount of merchandise sold if the employees salary was $2820 last month.
s=2,820→n=25(2,820)-62,500
n=70,500-62,500
n=8,000
Answer: The amount of merchandise sold was $8,000
4 0
3 years ago
4. Lupe knows that there are 4 quarts in a gallon. She wants to convert 6 quarts to gallons, but cannot decide if she should mul
tangare [24]

Answer:

Step-by-step explanation:

4 quarts=1 gallon

1 quart=1/4 gallon

6 quarts 1/4×6=6/4 gallons=3/2 gallons =1  1/2 gallons

or we can say 4 quarts=1 gallon

2 quarts=1/2 gallon

(4+2=6)quarts=(1+1/2)=1 1/2 gallon.

3 0
3 years ago
Convert the exponential to a logarithmic form: 10 ^ 4 = 10000
Cerrena [4.2K]

Answer:

10^4 =  10 × 10 × 10 × 10
       =  10000

7 0
2 years ago
Read 2 more answers
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