We try to represent each number inside the square root as a product of a square and another number.
a) 7√32 - 5√2 + √8
√32 = √(16 *2) = √16 * √2 = 4* √2 = 4√2
√8 = √(4 *2) = √4 * √2 = 2* √2 = 2√2
7√32 - 5√2 + √8 = 7*(4√2) - 5√2 + 2√2 =
= 28√2 - 5√2 + 2√2 Factorize out √2
= (28 - 5 + 2)√2
= 25√2
b) 2√150 - 4√54 + 6√24
√150 = √(25 * 6) = √25 * √6 = 5*√6 = 5√6
√54 = √(9 * 6) = √9 * √6 = 3*√6 = 3√6
√24 = √(4 * 6) = √4 * √6 = 2*√6 = 2√6
2√150 - 4√54 + 6√24 = 2*(5√6) - 4*(3√6) + 6*(2√6)
= 2*5√6 - 4*3√6 + 6*2√6
= 10√6 - 12√6 + 12√6 Factorize √6
= (10 - 12 + 12)√6
= 10√6
We would apply the formula for determining simple interest which is expressed as
I = PRT/100
I is the interest
P is the principal or initial amount
R = interest rate
T = time in years
From the information given,
P = 1200
r = 18
Since there are 12 months in a year,
T = 9/12 = 0.75
Thus,
I = (1200 x 18 x 0.75)/100
Interest = $162
Step 1. Subtract 3/4 from both sides
x = 1/2 - 3/4
Step 2. Simplify 1/2 - 3/4 to -1/4
x = -1/4
Answer:
m∠7 = 64°
Step-by-step explanation:
∠7 and ∠8 are supplementary meaning they add up to 180°.
m∠7 + m∠8 = 180°
m∠7 + 116° = 180°
m∠7 = 64°
Answer: D
Step-by-step explanation:
You have -5 1/2 to find the complete opposite all you have to do is take away the negative sign and find the number on the number line.
Good luck !
