The second one is the correct equation. The constant to the right should be the diameter squared, while the numbers inside the parentheses should be the opposite.

5 0

3 years ago

Read 2 more answers

8 + 3x=29 +2x <br> I need answer ASAP

borishaifa [10]

Answer:

x = 21

Step-by-step explanation:

8 + 3x = 29 + 2x

8 + 3x - 2x = 29

8 + x = 29

x = 29 - 8 = 21

x = 21

3 0

3 years ago

I need help with this!

7nadin3 [17]

Answers:

False
True
True
False
True
False

===============================================

Explanations:

If we can write a number as a ratio (or fraction) of two whole numbers, then that number is considered rational. The denominator can never be 0. In the case of 6/4, this is a rational number. Therefore, the statement "6/4 is irrational" is false.
This is a true statement. We cannot write sqrt(2) as a fraction of two integers. The proof of this is fairly lengthy, but one way is to use a proof by contradiction to show that sqrt(2) = a/b is impossible. Since we cannot make sqrt(2) into a ratio of two integers, we consider it irrational.
This is a true statement. Any terminating decimal is always rational. In this case, 1.3 = 13/10.
This is false. Any repeating decimal can be converted to a fraction through a bit of work. It turns out that 17.979797... = 1780/99 which makes the value to be rational.
Any integer is rational. We can write the integer over 1. So something like -16 is the same as -16/1, showing how it is rational. So that's why this statement is true.
This statement is false because we found true statements earlier.

4 0

3 years ago

11 and 13 ONLY

gulaghasi [49]

11. The sum S of the first n consecutive positive integers, 1, 2, 3, ... , n, is given by the formula S=0.5n(n+1). Find n when S=120 and check your answer by addition.

$120 = \frac 1 2 n (n+1)$

$240 = n^2 + n$

$n^2 + n -240 = 0$

We need two numbers whose sum is 1 and multiply to -240, so two numbers whose difference is 1 and multiply to 240, 15 and 16. We factor:

$(n+16)(n-15)= 0$

$n=-16 \textrm{ or } n=15$

We reject the negative root.

n=15

Check:

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15

=1+15 + 2+14 + 3+13 + 4+12 + 5+11 +6+10 + 7+9 + 8

= 7(16)+8

= 120 good

13. A boat travels downstream (with the current) for 36 miles and then makes the return trip upstream (against the current). The trip downstream took 3/4 of an hour less than the upstream trip. If the rate of the current is 4 mph, find the rate of the boat in still water and the time for each part of the trip.

Let v be the speed of the boat in still water.

The speed downstream is v+4 so the time to travel 36 miles downstream is 36/(v+4)

The speed upstream is v-4 so the time to travel 36 miles upstream is 36/(v-4)

Writing our equation,

3/4 = 36/(v-4) - 36/(v+4)

3 = 144 (1/(v-4) - 1/(v+4))

3(v-4)(v+4) = 144( (v+4) - (v-4) )

v^2 - 16 = 48(8)

v^2 = 48(8) + 16 = 400

v = 20 mph, the rate of the boat in still water

Time downstream is 36/(20+4)=36/24 = 3/2 = 1.5 hours

Time upstream is 36/(20-4)=36/16=9/4 = 2.25 hours

3/4 hour difference, good

5 0

3 years ago