Answer:
9) 6.3 units
11) n=6√2 and m=12,
10) m=6√3, n=6
12) 330.6 ft
Step-by-step explanation:
1) The Pythagoras Theorem says that, the square of the hypotenuse is the sum of the squares of the two shorter legs.
Let the missing side, which is the hypotenuse be x.
Then
The missing side is 6.3 units to the nearest tenth.
2) This is an isosceles right triangle.
This implies that, the two legs are equal.
The hypotenuse can be found using Pythagoras Theorem.
3) The side lengths of 30°-60°-90° are in the ratio, 2x,x√3,x
From the diagram, the hypotenuse is 12, therefore the other two legs are
and
4) The height of the monument is 115 feet, the hypotenuse is 350.
By Pythagoras Theorem,
Plug 8 for y
8 = 2x + 4
Subtract 4
4 = 2x
Divide by 2
x = 2
Plug 16 for y
16 = 2x + 4
Subtract by 4
12 = 2x
Divide by 2
x = 6
Substitute 20 for y
20 = 2x + 4
16 = 2x
x = 8
Substitute 22 for y
22 = 2x + 4
18 = 2x
9 = x
So the values are 2, 6, 8, 9
Let her monthly salary be x
1/8x = $65
x = $65 × 8 = $520
Her weekly pay is $520 ÷ 4 = $130
From the given ordered pair representing Jacinda's progress, her speed is equal to 10 miles per hour. Letting x be the time it takes for Jacinda to catch up with Raj, the total distance Raj would travel is
1.5 + 4.5x
and Jacinda's total distance is 10x. Mathematically,
1.5 + 4.5x = 10x
The value of x from the equation is 0.27 hours. Therefore, Jacinda needs to run 2.7 miles to catch up with Raj.
To simplify the problem it would be: -18xy+18y^2
