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creativ13 [48]
3 years ago
15

3 + x = 4 is the same as 4 = 3 + x. This is an example of which algebraic property? a.

Mathematics
1 answer:
algol [13]3 years ago
5 0
D. Symmetric Property. If you flip it the = sign will be on the end
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Buying something in order to increase social status is known as _____ consumption.
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1) conspicuous consumption
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Paul can walk 15 steps in 5 minutes. How long does it take Paul to walk 75 steps at the same speed? I got 25 minutes am i right?
lina2011 [118]

The best way to solve this one is with a proportion:

     (15 steps) / (5 minutes) = (75 steps) / ('x' minutes)

Cross-multiply the proportion:    15 x = 5 x 75

Divide each side by 15  :                 x = 5 x 5 = <em>25 minutes</em>.

You are correct, and Paul walks very slowly.


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3 years ago
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Solve the following equation by completing the square. 3x^2-3x-5=13
mr Goodwill [35]

we'll start off by grouping some

\bf 3x^2-3x-5=13\implies (3x^2-3x)-5=13\implies 3(x^2-x)-5=13 \\\\\\ 3(x^2-x)=18\implies (x^2-x)=\cfrac{18}{3}\implies (x^2-x)=6\implies (x^2-x+~?^2)=6

so we have a missing guy at the end in order to get the a perfect square trinomial from that group, hmmm, what is it anyway?

well, let's recall that a perfect square trinomial is

\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2

so we know that the middle term in the trinomial, is really 2 times the other two without the exponent, well, in our case, the middle term is just "x", well is really -x, but we'll add the minus later, we only use the positive coefficient and variable, so we'll use "x" to find the last term.

\bf \stackrel{\textit{middle term}}{2(x)(?)}=\stackrel{\textit{middle term}}{x}\implies ?=\cfrac{x}{2x}\implies ?=\cfrac{1}{2}

so, there's our fellow, however, let's recall that all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add (1/2)², we also have to subtract (1/2)²

\bf \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2-\left[ \cfrac{1}{2} \right]^2 \right)=6\implies \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2 \right)-\left[ \cfrac{1}{2} \right]^2=6 \\\\\\ \left(x-\cfrac{1}{2} \right)^2=6+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{25}{4}\implies x-\cfrac{1}{2}=\sqrt{\cfrac{25}{4}} \\\\\\ x-\cfrac{1}{2}=\cfrac{\sqrt{25}}{\sqrt{4}}\implies x-\cfrac{1}{2}=\cfrac{5}{2}\implies x=\cfrac{5}{2}+\cfrac{1}{2}\implies x=\cfrac{6}{2}\implies \boxed{x=3}

6 0
3 years ago
Simplify the following surd expressions
olasank [31]

Answer:

<h2>see the answers ⤵️</h2>

Step-by-step explanation:

<h3>to understand the solving steps you need to know about</h3>
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<h3>adding or subtracting with redical experience is nothing but algebraic addition or subtraction</h3><h3>let's solve:</h3>

a)7 \sqrt{3}  - 2 \sqrt{3}  +  \sqrt{3}  - 3\sqrt{3}  \\ 8 \sqrt{3}  - 5 \sqrt{3}  \\ 3 \sqrt{3}

b)5 \sqrt{7}   + 4 \sqrt{7}   - 8  \sqrt{7}  \\ 9 \sqrt{7}  - 8 \sqrt{7}  \\  \sqrt{7}

6 0
3 years ago
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Please help me!!! I will mark.
miv72 [106K]

Answer:

the answer is the first one!

because if x=-3 we know that |x|=|-3|=3

7 0
2 years ago
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