Using the formula r = d/t, where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 212.5 miles in 2.5 hours?

a- 71 mph
b- 106 mph
c- 150 mph
d- 85 mph ?

What is the simplified form of the following expression?

-(8d - 3w)

a. 8d + 3w
b. 8d - 3w
c. -8d + 3w ?
d. -8d - 3w

What is the simplified form of the following expression?

12(6^2 / (5^2 - 4^2) + 7))

a. 12.6
b. 195
c. 33.8
d. 132 ?

What is the simplified form of the following expression?

(-28st)/(-4s)

a. -7t
b. 7t ?
c. -7s
d. 7s

all ok , but.......

12(6^2 / (5^2 - 4^2) + 7))

the number of right-sided brackets must match the number of left-sided brackets. You have 2 going right, 3 going left.

Even Wolfram didn't like it , and fixed it for you
http://www.wolframalpha.com/input/?i=12%286%5E2+%2F+%285%5E2+-+4%5E2%29+%2B+7%29%29+

Thank you, the extra bracket was a typo. So, is my answer correct on that one?

Why did the math book go on a diet?

Because it had too many expressions to simplify!

Now, let's get to your questions.

For the first question, we can use the formula r = d/t. Given that d = 212.5 miles and t = 2.5 hours, we can divide 212.5 by 2.5 to get the rate, which is 85 mph. So the answer is d - 85 mph.

For the second question, the expression -(8d - 3w) can be simplified by distributing the negative sign to both terms inside the parentheses. This gives us -8d + 3w. So the answer is c - -8d + 3w.

For the third question, we need to simplify the expression 12(6^2 / (5^2 - 4^2) + 7). First, let's solve the exponentiation inside the parentheses: 6^2 is 36, 5^2 is 25, and 4^2 is 16. Simplifying further, we have 12(36 / (25 - 16) + 7). Inside the parentheses, 25 - 16 is 9, so we have 12(36/9 + 7). Now, we can divide 36 by 9 to get 4, giving us 12(4 + 7). Finally, we can add 4 and 7 to get 11, so the answer is d - 132.

For the fourth question, we can simplify the expression (-28st)/(-4s) by canceling out the common factor of -4s in the numerator and denominator. This leaves us with -28t/1, which can be further simplified to -28t. So the answer is a - -7t.

I hope that clears things up and puts a smile on your face!

To find the answer to the first question, we can use the formula r = d/t, where d is the distance, r is the rate, and t is the time.

Given:
d = 212.5 miles
t = 2.5 hours

Plugging in the values into the formula:
r = 212.5 miles / 2.5 hours

Simplifying:
r = 85 miles per hour

Therefore, the correct answer is (d) 85 mph.

Moving on to the second question, we need to simplify the expression -(8d - 3w).

Distributing the negative sign:
-(8d) + (-3w)

Simplifying:
-8d - 3w

Therefore, the correct answer is (d) -8d - 3w.

For the third question, we need to simplify the expression 12(6^2 / (5^2 - 4^2) + 7).

Calculating the values within the parentheses:
12(6^2 / (25 - 16) + 7)
12(36 / (9) + 7)
12(36 / 9 + 7)
12(4 + 7)
12(11)

Multiplying:
132

Therefore, the correct answer is (d) 132.

Lastly, for the final question, we need to simplify the expression (-28st)/(-4s).

Canceling out the negative sign:
(28st) / (4s)

Simplifying:
7t

Therefore, the correct answer is (b) 7t.

To find the rate at which you must travel to cover a certain distance in a certain time using the formula r = d/t, you simply divide the distance by the time.

For the first question:
Given: d = 212.5 miles, t = 2.5 hours

Using the formula, we have:
r = d / t
r = 212.5 / 2.5
r = 85 mph

So, the correct answer is d. 85 mph.

For the second question, to simplify the expression -(8d - 3w), we distribute the negative sign to both terms inside the parentheses:

-(8d - 3w) = -8d + 3w

Therefore, the simplified form is a. -8d + 3w.

For the third question, we need to follow the order of operations (PEMDAS/BODMAS) to simplify the expression:

12(6^2 / (5^2 - 4^2) + 7)
First, calculate the values in the parentheses:
5^2 = 25 and 4^2 = 16
Now, simplify the expression further:
12(6^2 / (25 - 16) + 7)
12(6^2 / 9 + 7)
12(36 / 9 + 7)
12(4 + 7)
12(11)
132

So, the simplified form is d. 132.

For the fourth question, we can simplify the expression (-28st)/(-4s) by canceling out the common factors:

(-28st)/(-4s) = (28st)/(4s)
Now, we can simplify further by canceling out the common factor of 4:
(28st)/(4s) = 7t

So, the simplified form is b. 7t.