All categories

3 years ago

Simplify the following expression. 1/3 ( 21m + 27)

Mathematics

2 answers:

Marina86 [1]3 years ago

6 0

You would use distributive property to distribute the 1/3. That would equal 7m+9

zalisa [80]3 years ago

4 0

The correct answer is 7m+9

You might be interested in

What is the length of segment TU?

matrenka [14]

QR=RS+QS

UT cuts QR and QS in half equally.

that means that UT is equal to half of RS

4 0

3 years ago

the 11th term in a geometric sequence is 48 and the common ratio is 4. the 12th term is 192 and the 10th term is what?

Soloha48 [4]

Given:

The 11th term in a geometric sequence is 48.

The 12th term in the sequence is 192.

The common ratio is 4.

We need to determine the 10th term of the sequence.

General term:

The general term of the geometric sequence is given by

$a_n=a(r)^{n-1}$

where a is the first term and r is the common ratio.

The 11th term is given is

$a_{11}=a(4)^{11-1}$

$48=a(4)^{10}$ ------- (1)

The 12th term is given by

$192=a(4)^{11}$ ------- (2)

Value of a:

The value of a can be determined by solving any one of the two equations.

Hence, let us solve the equation (1) to determine the value of a.

Thus, we have;

$48=a(1048576)$

Dividing both sides by 1048576, we get;

$\frac{3}{65536}=a$

Thus, the value of a is $\frac{3}{65536}$

Value of the 10th term:

The 10th term of the sequence can be determined by substituting the values a and the common ratio r in the general term $a_n=a(r)^{n-1}$ , we get;

$a_{10}=\frac{3}{65536}(4)^{10-1}$

$a_{10}=\frac{3}{65536}(4)^{9}$

$a_{10}=\frac{3}{65536}(262144)$

$a_{10}=\frac{786432}{65536}$

$a_{10}=12$

Thus, the 10th term of the sequence is 12.

8 0

3 years ago

I’ve been stuck on this for 3 hours and got 4 different answers...

mestny [16]

Answer:

$14x-8$

Step-by-step explanation:

The sides for the square are equal to 2x-5 because that is the square root of the area. The length of the rectangle is 3x+6 and the width is 3x-6 because that is what you get when you factor the equation.

Now, you have add them up.

$4(2x-5)+2(3x-6)+2(3x+6)\\$

To take out the line in the middle of the shape we will subtract $2(3x-6)$ because we are assuming that this equation is equal to the shorter side. This makes the equation

$4(2x-5)+2(3x-6)\\14x-8$

If you are looking for a numerical answer, I can't say I know how to get it.

Hope this helps! <3

6 0

3 years ago

Please help me thank you

Anna11 [10]

Answer:

$\large\boxed{-\dfrac{8}{\sqrt{63}}}$

Step-by-step explanation:

$\csc\theta=\dfrac{1}{\sin\theta}\\\\\cos\theta=-\dfrac{1}{8}\qquad\text{use}\ \sin^2\theta+\cos^2\theta=1\\\\\sin^2\theta+\left(-\dfrac{1}{8}\right)^2=1\\\\\sin^2\theta+\dfrac{1}{64}=1\qquad\text{subtract}\ \dfrac{1}{64}\ \text{from both sides}\\\\\sin^2\theta=\dfrac{64}{64}-\dfrac{1}{64}\\\\\sin^2\theta=\dfrac{63}{64}\to\sin\theta=\pm\sqrt{\dfrac{63}{64}}\\\\180^o$

$\csc\theta=\dfrac{1}{-\frac{\sqrt{63}}{8}}=-\dfrac{8}{\sqrt{63}}$

5 0

3 years ago

..........................

QveST [7]

Answer:

x = 0.954

Step-by-step explanation:

We apply pythagorean to find x

(4-x)² = 1.2² + 2.8²

(4-x)² = 9.28

✓(4-x)² = ✓(9.28)²

4 - x = 3.046

- x = 3.046 - 4

- x = -0.954

x = 0.954

(Please heart and rate if you find it helpful, it's a motivation for me to help more people)

7 0

3 years ago