You only have to apply the theorem of Pythagoras here. Remember the square on the hypotenuse (the longest side) is equal to the sum of the squares on the other two sides :
1. AB is the hypotenuse, so, according to the theorem we can write :
AB² = AC² + CB²
c² = 5² + 4²
c²= 25 + 16
c² = 41
applying the square root of 41 we get :
c ≈ 6.40 rounded to the hundred
The next cases are exactly the same thing so there is no need for explanation :
2.
AB is the hypotenuse here because it is the biggest side clearl :
AB² = AC² + CB²
25² = 15² + b²
Thus
b² = 25² - 15²
we just subtracted 15² on each side of the equation
b² = 625 - 225
b² = 400
applying the square root of 400 we get
b = √400 = 20
So AC = 20
3. The longest side is clearly AB = 60
So
AB² = AC² + CB²
60² = 40² + a²
subtracting 40² on each side of the equation we get :
a² = 60² - 40²
I let you finish this using your calculator and doing exactly like the previous cases
4.
AB is the hypotenuse,
AB² = AC² + CB²
23² = b² + 14²
Subtracting 14² from each side of the equation we get
b² = 23² - 14²
5.
AB is the biggest side :
AB² = AC² + CB²
29² = 23² + a²
We subtract 23² on each sides of the equation :
a² = 29² - 23²
You can finish with your calculator
6.
AB² = AC² + BC²
78² = b² + 30²
subtraction...
b² = 78² - 30²
Good luck :)
F(-5)=6(5*5)+4(-5)-11
f(-5)=6(25)+-20+-11
f(-5)=150+20-11
f(-5)=130-11=119
What is it that we need to find?
24 + 0.44x = 19 + 1.69x
Subtract 19 from both sides
5 + 0.44x = 1.69x
Subtract 0.44x from both sides
5 = 1.25x
Divide by 1.25 on both sides
4 = x
Answer:
Option A. x = 8
Step-by-step explanation:
Please see attached photo.
From the attached photo,
we shall determine the value of y. This can be obtained by using pythagoras theory as illustrated below:
(√80)² = 8² + y²
80 = 64 + y²
Collect like terms
80 – 64 = y²
16 = y²
Take the square root of both side
y = √16
y = 4
Finally, we shall determine the value of x. This can be obtained as follow:
From the attached photo,
x = 2y
but:
y = 4
Therefore,
x = 2y
x = 2 × 4
x = 8
