Question: Which equation is equivalent to
Option A:
Option B:
Option C:
Option D:
Answer:
Option C:
Solution:
Given expression:
Convert 16 to the base 2 and 32 to the base 2.
Using exponential rule:
Using the rule,
8p = 5p + 15
3p = 15
p = 5
Substitute p = 5 in given expression, we get
<u>To find the equivalent expression to the given expression:</u>
Option A:
Using the rule,
⇒ 4p = 4p + 3
⇒ 0p = 3
No solution for p, so it is not equivalent to the given expression.
Option B:
Using the rule,
⇒ 4p = 4p + 12
⇒ 0p = 12
No solution for p, so it is not equivalent to the given expression.
Option C:
Using the rule,
⇒ 8p = 5p + 15
⇒ 3p = 15
⇒ p = 5
Substitute p = 5 in , we get
It is equivalent to the given expression.
Option D:
Using the rule,
⇒ 8p = 5p + 3
⇒ 3p = 3
⇒ p = 1
Substitute p = 1 in , we get
It is not equivalent to the given expression.
Hence Option C is the correct answer.
F(-3) = -4(-3)^2 + 15
f(-3) = -4(9) +15
f(-3) = -36 +15
f(-3) = -11
Answer:
Correct option is D. No, since the ratios of the corresponding sides are not proportional.
Step-by-step explanation:
Please refer to the attached figure
Let height of coach represents by AB = 6 feet
And shadow of coach represents by BC = 4 feet
Let height of goal post represents by DE = x feet
And Shadow of goal post represents by EF = 12 feet.
Since measurement of shadows are at same time. therefore ratio of height of coach and height of goal post must be same as ratio of shadow of coach and shadow of goal post.
⇒ 6/x = 4/12
⇒x = 72/4 = 18 feet
So goal post is not at regular height , since expected height is 20 feet while actual height is 18 feet . And if we consider value of x as 20 feet instead of 18 feet , ratio of corresponding sides will not match.
Hence correct answer is D. No, since the ratios of the corresponding sides are not proportional.
Answer: Number 4 Hankins car travels faster
Step-by-step explanation:
Because 600+20=620 and Andres bike travels slower because 300+12=312