What is the value of x? Enter your answer in the box.

Graph the solution set of: 2x - 4 ≤ 8 and x + 5 ≥ 7

Alex17521 [72]

Answer:

x ≤ 6 and x ≥ 2

Step-by-step explanation:

For now, we will start with doing each problem at a time. Here is your equation:

2x - 4 ≤ 8

First, you want to get the variable by itself. So, you add 4 to both sides. It will look like this:

2x - 4 ≤ 8

+ 4 + 4

The four being added on the left side cancels out, and you add 4 to 8. Now, it should look like this:

2x ≤ 12

Next, you want the x by itself. So, you would divide both sides by 2.

2x ≤ 12

/2 /2

2 divided by 2 cancels out, and 12 divided by 2 equals 6. Now, you have a final answer of:

x ≤ 6

But, you now have to do the other one!

Here is what you start off with:

x + 5 ≥ 7

First, you want the variable side by itself. So, you subtract 5 from both sides.

x + 5 ≥ 7

- 5 -5

Now, you have this:

x ≥ 2

Because the variable is already by itself, you don't need to do any more division and this is you final answer. Now put both answers you got together which equals:

x ≤ 6 and x ≥ 2

8 0

3 years ago

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Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many h

Elden [556K]

Let

x-----> the number of hours that Candice spent doing her homework

y-----> the number of hours that Ronald spent doing his homework

we know that

$x=5\frac{1}{4}\ hours$

convert mixed number to an improper fraction

$5\frac{1}{4}\ hours=\frac{5*4+1}{4}= \frac{21}{4}\ hours$

so

$x=\frac{21}{4}\ hours$ -------> equation A

$y=\frac{1}{2}x$ ------> equation B

Substitute equation A in equation B

$y=\frac{1}{2}*\frac{21}{4}=\frac{21}{8}\ hours$

convert an improper fraction to a mixed number

$\frac{21}{8}\ hours=2.625=2+0.625=2+\frac{5}{8}=2\frac{5}{8}\ hours$

therefore

the answer is the option B

$2\frac{5}{8}\ hours$

5 0

3 years ago

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if serena invested the 2500 in the cd that she yields at 4% interest, what will the cdbe worthafte 2 years?

Naya [18.7K]

Your answer would be 2700

Using I=P*r*t

P= 2500

R= 4% (substitue to 0.04)

T= 2 Years

I= 2500* 0.04 * 2

I= 100* 2

I= 200

2500+200=

2700

6 0

3 years ago

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10 lbs ≈

sergejj [24]

Answer:

D. 4.5 kg

Step-by-step explanation:

7 0

3 years ago

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Test the series for convergence or divergence (using ratio test)

Triss [41]

Answer:

$\lim_{n \to \infty} U_n =0$

Given series is convergence by using Leibnitz's rule

Step-by-step explanation:

Step(i):-

Given series is an alternating series

∑ $(-1)^{n} \frac{n^{2} }{n^{3}+3 }$

Let $U_{n} = (-1)^{n} \frac{n^{2} }{n^{3}+3 }$

By using Leibnitz's rule

$U_{n} - U_{n-1} = \frac{n^{2} }{n^{3} +3} - \frac{(n-1)^{2} }{(n-1)^{3}+3 }$

$U_{n} - U_{n-1} = \frac{n^{2}(n-1)^{3} +3)-(n-1)^{2} (n^{3} +3) }{(n^{3} +3)(n-1)^{3} +3)}$

Uₙ-Uₙ₋₁ <0

Step(ii):-

$\lim_{n \to \infty} U_n = \lim_{n \to \infty}\frac{n^{2} }{n^{3}+3 }$

$= \lim_{n \to \infty}\frac{n^{2} }{n^{3}(1+\frac{3}{n^{3} } ) }$

= $= \lim_{n \to \infty}\frac{1 }{n(1+\frac{3}{n^{3} } ) }$

$=\frac{1}{infinite }$

=0

$\lim_{n \to \infty} U_n =0$

∴ Given series is converges

3 0

3 years ago