Mathematics Middle School

A ladder is leaning against a wall. The top of the ladder is 999 feet (\text{ft})(ft)left parenthesis, f, t, right parenthesis above the ground. If the bottom of the ladder is moved 3\,\text{ft}3ft3, space, f, t farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?

Answers

Answer 1
The ladder is 166335 feet long. For this problem, we have a right triangle. The hypotenuse is the length of the ladder. The short leg is 999 feet long and the long leg is the length of the hypotenuse - 3. So let's make an equation to express this knowledge. 999^2 + (h-3)^2 = h^2 Expand expression 999^2 + h^2 - 6h + 9 = h^2 Subtract h^2 from both sides 999^2 -6h + 9 = 0 Add 6h to both sides 999^2 + 9 = 6h Do the squaring and adding. 998010 = 6h Divide both sides by 6 166335 = h So the ladder is 166335 feet long.

Related Questions

Is the value of the 1 in 1,440,000 10 times as great as the value of the 4 in the hundred thousands place?

Answers

If you multiply 400,000 by 10 you get 4,000,000. This means that, yes, the value of the 1 is 10 times the 4 in the hundred thousands place. 
Hope I helped :)
Final answer:

The value of the 1 in the number 1,440,000, which is in the million's place, is 2.5 times greater than the value of the 4 which is in the hundred thousand's place.

Explanation:

The value of the 1 in the number 1,440,000 is in the millions place, thus it represents 1,000,000. The 4 on the other hand, is in the hundred thousands place, and thus represents 400,000. The value of the 1 is therefore not just ten times the value of the 4, but in fact, it is 2.5 times greater.

Here is the process: value of 1 = 1,000,000, value of 4 = 400,000, so 1,000,000 / 400,000 = 2.5. Therefore, the value of 1 is 2.5 times the value of 4.

Learn more about Place Value here:

https://brainly.com/question/35447631

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How to solve a=9y+3yx

Answers

Therefore, the equation [tex]y = \frac{a}{9 + 3x}[/tex] represents y as a function of a and x, showing how changes in a and x affect the value of y.

The given equation a = 9y + 3yx is a literal equation, meaning it relates multiple variables (in this case, a and y) with constants. Our goal is to isolate y, which means we want y to be expressed solely in terms of a and x, without any other variables.

To do this, we first factor out the common factor y from the right side of the equation, leaving us with a = y(9 + 3x). This step simplifies the equation and makes it easier to isolate y.

Then, to solve for y, we divide both sides of the equation by (9 + 3x), effectively undoing the multiplication by (9 + 3x) on the right side. This leaves us with [tex]y = \frac{a}{9 + 3x}[/tex].

In this final expression, y is in terms of a and x, indicating that the value of y depends on the values of a and x. As a and x vary, the value of y changes accordingly, following the relationship described by the equation.

Complete Question:

Solve the literal equation for y.

a = 9y + 3yx

y =

how to simplify this

Answers

Factor it out.
Both exponent cancel out each other which equals 1.

3/4 x+5− 1/2 x=3 Solve For X Need Answer Fast Please!!!!!!!

Answers

3/4x + 5 - 1/2 x=3 = -8

I believe this is the right answer :)

Answer:

8 1/5

Step-by-step explanation:

True or false 6,859^1/3 can be written as square root 3 19^3

Answers

[tex]6859^{ \frac{1}{3}} [/tex]

Using the index law [tex]a^{ \frac{m}{n}} = (\sqrt[n]{a} )^m[/tex]

[tex] \sqrt[3]{6859}=19 [/tex], so we can also write this as
[tex]( \sqrt[3]{19^3} )[/tex]

Answer: TRUE

What is 239901 rounded to the nearest ten thousand

Answers

The answer is 240,000

One package of fruit drink contains 6 drinks. Which of the following list the ordered pairs (packages, number of drinks) for 1, 2, 3, and 4 packages of fruit drinks?

Answers

I think this is 

(1,6), (2,12), (3,18), (4,24)

1 package has 6 drinks so that = (1,6)

 then multiply 6 by the number of packages for total number of drinks

 so you end up with (1,6) (2,12) (3,18) (4,24)

Ms.Phipps made 12 dolls for gifts this year. She made 4 1/2 times that number last year. Find the total number of dolls she made this year and last year.

Answers

54 dolls were created this year and last year


12 x 4.5 = 54 

54 last year
12 this year

Susan currently has an account balance of $1,336.60. Her initial deposit on the account was $820 and it earned 4.5% simple interest. How long has Susan held the account?

Answers

Here we need the time, so
t = I/pr = (1336.6-820)/(820)(.045) = 14 years


Find last​ year's salary​ if, after a
2% pay​ raise, this​ year's salary is
$38,760.

Answers

Your answer would be $37,984.8

Compare the integers indicated on the graph below.

A. -6 > -12

B. -12 > -6

C. -4 > -8

D. -8 > -4






5)

Answers

The correct answer is A. -6 > -12


Hope that helped! :)

If I increase an amount by 7% what is the multiplier

Answers

The answer is:  " 1.07 " .
_______________________________________
Explanation:
_______________________________________
100 % + 7 % = 107 % ;
_______________________________________
107 % = 107/100 = 107 ÷ 100 =   1.07  .
_______________________________________
1.07 hope this helps

one type of insect is 0.0052 meter long.what is this length in scientific notation

Answers

Because scientific notation has to be in between 1 and 10, you would need this to be 5.2. Count the spaces and since its getting smaller your exponent is negative. 

Your answer should be 5.2*10^(-3)

−30+(−40)+(−70 equivalent expression

Answers

−30−40−70

=−70−70

=−140


Simplify. 4−8÷2+3

Please help me with this problem.

Answers

PEMDAS says the first thing you need to do is division:

4 - 4 + 3

Then, do subtraction and addition from left to right:

0 + 3
3

Hope this helped!

What is the value of the underlined digit? 5,678.321. The underlined digit is 1.

Answers

0.001

Hope this helps!
.001     the decimal is important because in the number the 1 is after the decimal, itrepresents the fact that its not a whole number. The two zeros are there to replace the two numbers that come before the 1 and after the decimal. they replace 32

In albany it is -4°f in chicago it is -14°f‚ in minneapolis it is -11°f‚ and in toronto it is -13°f. in which city is the coldest?

Answers

Chicago because on the number line, the numbers to the left get smaller, and the numbers to the right get bigger. Negatives on the number line are going right, and getting smaller, even though it seems the numbers are getting bigger.
EX: -14,-13, -12,-11,-10...

the largest negative number would be the coldest, so -14 would be the coldest.

 Chicago is the coldest city

Decimals between 5.1 to 5.2

Answers

There are an infinite number of decimals between 5.1 and 5.2, 5.11,5.11111111111111.
It very simple. There are multiple choices. 1.12, 1.13 ,1.14, 1.15, 1.16, 1.17 ,1.18, 1.19, 

I need the answer to this question ASAP please help.

Answers

(3/5)^3 = (3^3)/(5^3) = 27/125
3^3 = 3x3x3 = 27
5^3 = 5x5x5 = 625
27/625 is the answer and it can’t be simplified

math questions down below

Answers

#1 the correct answer is 6/7
#2 the correct answer is -9

explain the simplified form of 3abc/abc when abc doesn't equal zero?

Answers

Dividing abc, which is a*b*c, we get 3*a/a*b/b*c/c=3

explain in your own words what the mean of a negative exponent means?

Answers

A negative exponent is the opposite of a regular exponent so for example, 5 to the power of -3 is 1/125 

If each square in the grid has a side lengt of 8mm,what is the-width and height of the rectangle

Answers

one of them is 4 and one is 2

What is the value of 11−3m , when m = 2? (Please do it step by step because I dont know how to do this ;[ )

5

6

10

12

Answers

Substitute the variable for the value given.

11 - 3m becomes 11 - 3(2)

Now do the order of operations.

11 - 3(2) =
11 - 6 =
5

So, the answer is 5.

Please help not sure on this

Answers

If I am correct, it would be dropped at -3, side adding to negative numbers make them increase to positive numbers.

(2*1)+(6*1/1000) write in standard form

Answers



2+1006

=1008

1000+8=1008

Hope this helps

1. Four more than five times a number is less than 54. Evaluate this problem situation for values of the number.

2. Two times the sum of a number and four increased by three is at most six less than the number. Evaluate this problem of situation for values of the number.

Answers

1. 4 + 5x < 54
- subtract 4 to the right side
- divide by 5
- answer: x <10 

2. 2(x + 4) + 3 = 6 - x
- distribute 2 to x and 4
- add 8 and 3
- add -x to the left side
- subtract 11 to right side
- 2x= -5 
answer: x= -5/2
The answer is  -5/2
thanks (:


7.The mass of a grain of sand is approximately 2.8×10^−11 grams

Select from the drop-down menu to correctly complete the statement.
The mass of a grain of sand is approximately 2.8×10^−8

Answer Choices:
A. Milligram
B.Gram
C.Killogram

Answers

i just took the test.. the answer is A. Have a nice day!

Answer:

a

Step-by-step explanation:

Solve the equation ax+b=c for x

Answers

ax+b=c
ax=c-b
x=(c-b)/a
The solve of this equation will be X=(C-b)/A

Which is the better buy 3 pounds for 8.31 or 5 pounds for 12.95

Answers

answer:

5 pounds for 12.95

explanation:

to solve, find the unit rate. the cheaper unit rate is the best and cheapest choice.

8.31/3 = 2.77
12.95/5 = 2.59

5 pounds for 12.95 is the cheaper choice because it has a smaller unit rate.

Hope this helps! :D
It'd be better to buy the 5 pounds for 12.95.

If you divide the price by the amount, it results as 2.59 as opposed to 3 pounds for 8.31 which is 2.77 per pound, making it clear now that the 5 lb for 12.95 is the better deal
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