You are going to mix a gallon bucket of window cleaner. The
You are going to mix a gallon bucket of window cleaner. The instructions
direct you to mix 1 part cleaner to 3 parts water. How much cleaning
solution will you need to use?*

Answers

Answer 1

Answer: x-amount of cleaning soulution
1Gal=x+3x
1Gal=4x
x=1/4 Gal

The amount of solution needed will be 0.25 Gal.
Hope it helped!

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Solve for x: ( sqrt 7) ^ 6x = 49 ^ (x-6)

Answers

$(√(7))^(6x)=49^(x-6) \n(7^(1)/(2))^(6x)=(7^2)^(x-6) \n7^{(1)/(2) * 6x}=7^(2(x-6)) \n7^(3x)=7^(2x-12) \n3x=2x-12 \n3x-2x=-12 \nx=-12$

The solution of x for the equation (√7)ˣ = 49ˣ⁻⁶ is,

⇒ x = 8

We have to given that,

An expression to simplify,

⇒ (√7)ˣ = 49ˣ⁻⁶

Now, We can simplify the expression for x as,

⇒ (√7)ˣ = 49ˣ⁻⁶

Since, 49 = 7² = (√7)⁴

Hence,

⇒ (√7)ˣ = (√7)⁴)ˣ⁻⁶

Apply the multiply rule in exponent,

⇒ (√7)ˣ = (√7)⁴ˣ⁻²⁴

By comparing,

⇒ x = 4x - 24

Solve for x,

⇒ x - 4x = - 24

⇒ - 3x = - 24

⇒ 3x = 24

⇒ x = 24 / 3

⇒ x = 8

Therefore, The solution of x for the equation (√7)ˣ = 49ˣ⁻⁶ is,

⇒ x = 8

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The volume of a pyramid with a square base is given by the expression 1 / 3 s2 ( 2 is the exponent ) h, where s is the length of a side of the base and h is the heigth. Find the volume of a pyramid with a square base of side length 24 feet and a heigth of 30 feet. Please I need help on this..

Answers

$V=(1)/(3)\cdot24^2\cdot30\nV=10\cdot576\nV=5760 \text { ft}^2$

Write an equation of a line parellel to -6x-2y=12 through (3,1)

Answers

Hello,

-6x-2y=12==>y=-3x-6 slope=-3

y-1=-3(x-3)==>y=-3x+10

What is the least common mulitple of 12,48,and 96

Answers

Answer:

Step-by-step explanation:

LCM of 12,48 and 96 is 96

Answer:

Step-by-step explanation:

12/2= 6

48/2= 14

96/2=48

At a concert 2/5 of the people were men, there were 3 times as many women as children. If there were 45 more men than children, how many people were there at the concert.

Answers

Final answer:

In solving the question, we establish two equations based on the condition provided, including the ratios among men, women, and children. Solving the equation, we find out that there were 270 people at the concert.

Explanation:

This question relates to the mathematical concept of ratio and proportion as well as fraction.

According to the question, 2/5 of the attendees at the concert were men and men outnumbered children by 45. First, let's make the number of children, x. So, the number of men will be x + 45. Because 2/5 of the total attendees were men, set up the equation: 2/5 * Total = x + 45.

There were 3 times as many women as children, thus the number of women will be 3x. So, the total number of people in the concert is the sum of the men, women, and children, which is (x + 45) + 3x + x. Simplifying this, we get 5x + 45 = Total. Therefore, if we substitute (x + 45) for 2/5 of the total in our original equation, we have 2/5 * (5x + 45) = x + 45. Solving this equation, we get x = 45.

So, if we substitute x=45 into our total equation, we get Total = 5(45) + 45 = 270. Therefore, there were 270 people at the concert.

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This involves creating some equations.

First, these are what the letters I used stand for:

c = children

w = women

m = men

x = total population

Then, we must make an equation for each statement.

2/5x = m (2/5 of the people are men)

3c = w (there are 3 times as many women than children)

45+c = m (there are 45 more men than children)

Now, let's start plugging in our numbers:

x = all the men, women, and children

2/5(m+w+c) = m

2/5 (45+c +3c + c) = m [Now simplify]

2/5 (45 + 5x) = m [Now Distribute]

2/5(45) + (2/5)(5x) = m

2c + 18 = m [Above we stated that there were the same amount as men as c +45]

2c + 18 = 45 +c [Now set equal to c]

2c (-c) +18 = 45 +c (-c)

c+18 (-18) = 45 (-18)

c = 27

Now that we know that there was 27 children, we can plug 27 in for c in the other equations.

MEN = 27 + 45

WOMEN = 3(27)

CHILDREN = 27

Now add those three answers to find your total!

Find the product mentally. [(x + 1)(x - 1)]2

Answers

[(x+1)(x-1)]2 = (x*x + -x + x + -1)2 = (x^2 - 1)2. This should be the simplest form.

Final answer:

The product of the given equation [(x + 1)(x - 1)]2 can be mentally calculated by recognizing it as a difference of squares expression followed by applying the square of a binomial formula, giving us x^4 - 2x^2 + 1 as the final answer.

Explanation:

To find the product of the given equation mentally, we need to understand some basic algebraic laws. (x + 1)(x - 1) is a difference of squares, which simplifies to x2 - 1. We then square this expression, as indicated by the '2' outside the parentheses, which gives us (x2 - 1)2.

Finally, applying the square of a binomial formula (a - b)2 = a2 - 2ab+ b2 on our expression, we get x4 - 2x2 + 1 as the final product. Now this final product is the simplest form of your given equation.