Solve for x. Leave your answer in simplest radical form.

Hokiris ladder has two legs that are each 8 feet long. When the ladder is opened safely and locked for use, the legs are 4 feet

guajiro [1.7K]

To solve this problem you must apply the proccedure shown below:

1- The ladder forms an isosceles triangle, because it has two equal sides.

2- Let's call the angle $\alpha$ . To calculate it , you can divide the triangle into two equal right triangles and the angle $\alpha$ will be divided into two equal parts too. Therefore, you can calculate the half of the angle and then multiply it by two, as following:

$Sin^{-1}(\alpha 1)=opposite/hypotenuse$

$Sin^{-1}(\alpha1)=8/2\\ \alpha1=14.47 degrees$

$\alpha =2\alpha 1\\ 2=2(14.47degrees)\\ \alpha =28.95degrees$

The answer is: $28.95degrees$

6 0

3 years ago

Write an expression for each sentence

Nitella [24]

Answer:

x^2+y
3(n-7)
37x-9.85

Step-by-step explanation:

1. If x represents a number, then x^2 represents its square. If y represents a second number, then the sum of that square and the second number is ...

x^2 + y

__

2. The difference of a number (n) and 7 is (n-7). Three times that difference is ...

3(n - 7)

__

3. If x represents a number, then the product of 37 and a number is 37x. 9.85 less than that is ...

37x - 9.85

7 0

2 years ago

Factorise x squared + 4x + 3

olganol [36]

<h3>Answer: (x+1)(x+3)</h3>

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Explanation:

Let's assume it factors into (x+a)(x+b)

The goal is to find the two numbers a and b.

FOIL out (x+a)(x+b) to get x^2+(a+b)x+ab

Note how a+b is the middle term and ab is the last term.

In the original expression, 4 is the middle term and 3 is the last term.

So we need to find two numbers that

add to 4
multiply to 3

There are two ways to multiply to 3 and they are

1 times 3 = 3
-1 times -3 = -3

But only the first way has the factors add to 4. So that means a = 1 and b = 3.

Therefore (x+a)(x+b) = (x+1)(x+3)

And x^2+4x+3 = (x+1)(x+3)

8 0

2 years ago

What is the number nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8?.

Tems11 [23]

10080 is the number nearest to 10000 that is divisible by 3, 4, 5, 6, 7, and 8.

Divisibility is being able to divide a number evenly and result to a whole number. Divisibility rules are set of rules to test if one number is divisible by another without doing much computation.

#1: divisibility by 2

A number is divisible by 2 if its last digit is even.

# 2: divisibility by 3:

A number is divisible by 3 if the sum of its digits is divisible by 3.

# 3: divisibility by 4

A number is divisible by 4 if the number represented by its last two digits is divisible by 4.

#4: divisibility by 5

A number is divisible by 5 if its last digit is 0 or 5.

# 5: divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

# 6: divisibility by 7

Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7.

#7: divisibility by 8

A number is divisible by 8 if the number represented by its last three digits is divisible by 8.

#8: divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

# 9: divisibility by 10

A number is divisible by 10 if its last digit or the digit in the ones place is 0.

To get the number nearest to 10000 that is divisible by 3, 4, 5, 6, 7, and 8, consider first the numbers that are divisible by 5(numbers ending in 5 or 0) and narrow it down to numbers ending in 0 since numbers ending in 5 is not divisible by 2, thus making it indivisible by 6.

The process goes on by narrowing the list by checking its divisibility by 3, 4, 7 and 8.

To know more about divisibility rules, visit brainly.com/question/9462805.

#SPJ4

7 0

1 year ago

How can complex fractions be used to solve involving ratios

Alex777 [14]

Bring them to the same denominator and solve for x

8 0

2 years ago