First we need to factor the left side. Since it is a perfect square (as is the process with completing the square, we know we can take half of the middle number along with x to be in the two parenthesis.
(x - 4)(x - 4) = 25
Now we simplify to show it as a square.
(x - 4)^2 = 25
Next we take the square root of both sides
x - 4 = +/- 5
Note that we have plus or minus 5. This is because either square would give us positive 25. Now we add 4 to both sides
x = 4 +/- 5
4 + 5 = 9
4 - 5 = -1
We can assume that the point the ladder creates with the ground and building is a triangle. You can use the Pythagorean theorem to solve this.
A^2 + B^2 = C^2
The ladder is C, and the building can act as A or B, so for the purpose of this explanation, I’ll make it A.
11^2 + B^2 = 14^2
Figure out the squares
121 + B^2 = 196
Subtract 121 from both sides
B^2 = 75
Square root B^2 and 75
B = 5 root3
Answer:
Step-by-step explanation:
The sum of the angles is ...
x° + (x +8)° + 2x° = 180°
4x +8 = 180 . . . . . . . . . . . collect terms, divide by °
x +2 = 45 . . . . . . . . . . divide by 4
x = 43 . . . . . . . . . . subtract 2
x +8 = 51
2x = 86
The angles are 43°, 51°, 86°.
Answer:
The weight of the water in the pool is approximately 60,000 lb·f
Step-by-step explanation:
The details of the swimming pool are;
The dimensions of the rectangular cross-section of the swimming pool = 10 feet × 20 feet
The depth of the pool = 5 feet
The density of the water in the pool = 60 pounds per cubic foot
From the question, we have;
The weight of the water in Pound force = W = The volume of water in the pool given in ft.³ × The density of water in the pool given in lb/ft.³ × Acceleration due to gravity, g
The volume of water in the pool = Cross-sectional area × Depth
∴ The volume of water in the pool = 10 ft. × 20 ft. × 5 ft. = 1,000 ft.³
Acceleration due to gravity, g ≈ 32.09 ft./s²
∴ W = 1,000 ft.³ × 60 lb/ft.³ × 32.09 ft./s² = 266,196.089 N
266,196.089 N ≈ 60,000 lb·f
The weight of the water in the pool ≈ 60,000 lb·f
Hey there!
Okay, so when you get a problem like this, all you need to do in insert the given value into the function and solve.
For example:
As you can see, they state that <em>(a) = 27, </em>so you insert 27 in for a in the function and it will look like this:
h(27) = 3(27) + 5
Now you solve on the right side of the equal sign:
3(27) = 81 (you multiply them)
81 + 5 = 86
When you plug the value of 27 in for a in this function, your output is equal to 86.
