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2 years ago

10

A teacher asks four students to determine the area of a circle with a circumference of 50.24 feet. The table shows the students’

responses.
Which student determines the area of the circle correctly? (Use 3.14 as an approximation of pi.)

1 answer:

ololo11 [35]2 years ago

7 0

Student 3 is correct !!'

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Solve 9^x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.

Sauron [17]

Answer:

If you meant $9^x+4=11$ , then the answer is approximately 0.866.

If you meant $9^{x+4}=11$ , then the answer is approximately -2.909 which looks like what you meant based on the choices.

Step-by-step explanation:

$9^x+4=11$

First step is to get the exponential part by itself. The part that has the variable exponent which is the $9^x$ term.

To do this we need to subtract 4 on both sides:

$9^x=11-4$

Simplify:

$9^x=7$

The equivalent logarithmic form is:

$\log_9(7)=x$

I always say to myself the logarithm is the exponent that is how I know what to put opposite the side containing the log.

Anyways if you don't have options for computing $\log_b(a)$ in your calculator you need to use the change of base formula.

$\frac{\log(7)}{\log(9)}=x$

So $x \approx 0.8856$

I don't see this as a choice so maybe you actually meant the following equation:

$9^{x+4}=11$

Let's see if this is the correct interpretation.

So the exponential part is already isolated.

So we just need to put in the equivalent logarithmic form:

$\log_9(11)=x+4$

Now we subtract 4 on both sides:

$\log_9(11)-4=x$

Again if you don't have the option for computing $\log_b(a)$ in your calculator, you will have to use the change of base formula:

$\frac{\log(11)}{\log(9)}-4=x$

$x \approx -2.909$

6 0

3 years ago

5/6-1/3= (reduced form please)

Masteriza [31]

The correct answer is 0.5 as a decimal as a fraction it is 5/10 = 1/2 so it is what ever one u need 1/2 or 5/10 or 0.5. Hope this helps! ;D

7 0

2 years ago

Read 2 more answers

What is the ones digit of a number if its cube ends in 7

Ostrovityanka [42]

Well, I have never seen a question posed this way, but let's check it out by trial and error.

1^3 = 3

2^3 = 8

3^3 = 27 Hey! There's one. And the ones digit ends in 3.

Let's try another number that ends in 3 and see if it works as well.

13^3 = 2197 Wow. It works again. I never noticed this before, so you taught me something new.

I will test one more.

33^3 = 35937 Bingo. I think we have a winner.

3 0

2 years ago

The volume of a cylinder of radius 3r and height 6r is given by TT(3r)2(6r). Simplify the expression.

OLga [1]

Answer: $\pi 36r^{2}$

Step-by-step explanation:

ALRIGHT ARE YOU READY FOR EPIC MATH TIME?

because i know i am. so lets get this bread.

WATCH: we have $\pi (3r)2(6r)$

interesting... that first character is called pi. maybe i should have said, "lets get this pi".

so now lets do some algebra. i am going to work from right to left. lets multiply 6r by 2. that gives us 12r. now we have... $\pi (3r)(12r)$

WE ARE MAKING EPIC PROGRESS, AREN'T WE?

lets multiply 12r by 3r. then we have....

$\pi 36r^{2}$

notice how i multiplied 12 by 3 and also r by r (which gives 36 and $r^{2}$ respectively)

so your simplified expression is: $\pi 36r^{2}$

6 0

2 years ago

Sheila was given $30.00 for her birthday and spent $18.79 on a CD. How much was her change?

Elis [28]

Answer:

<em>$11.21</em>

Step-by-step explanation:

$30.00 - $18.79 = $11.21

4 0

3 years ago

Read 2 more answers