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SSSSS [86.1K]
3 years ago
14

Suppose a triangle has sides 3, 4, and 5. Which of the following must be true?A. The triangle in question is a right triangle.B.

The triangle in question is not a right triangle.C. The triangle in question may or may not be a right triangle.
Mathematics
2 answers:
uranmaximum [27]3 years ago
5 0
You can prove the angle is a right angle by converse of pyth. Theorem
julsineya [31]3 years ago
3 0
A. It is a right triangle.
A^2 + B^2 = C^2
3^2 + 4^2 = C^2
9 + 16 = C^2
25 = C^2
Square Root
5 = C
Confirmed Right Triangle.
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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
As part of a company incentive, each sales person that sells over \$40{,}000$40,000dollar sign, 40, comma, 000 in merchandise th
worty [1.4K]

Answer:

$58,600

Step-by-step explanation:

Data provided in the question:

Commission on Sales upto and including $40,000 = 5%

Commission on Sales above $40,000 = 10%

Total commission = $3,860

Now,

For sales of $40,000

maximum commission = 5% of $40,000

= $2,000

Since the commission received is greater than $2,000

Therefore,

The value of s is greater than $40,000

Thus

Amount qualifying for 10% commission = s - $40,000

therefore,

Total commission = $2,000 + 10% of (s - $40,000)

or

$3,860 =  $2,000 + 0.10 × (s - $40,000)

or

$1,860 = 0.10 × (s - $40,000)

or

s - $40,000 = $18,600

or

s = $18,600 + $40,000

or

s = $58,600

4 0
3 years ago
Read 2 more answers
If 2X +1= 27,032 is true then 2x+3= ?
maxonik [38]
2x+1=27032
2x=27031
x=13515.5

2x+3
=2(13515.5)+3
=27034
6 0
3 years ago
What is the sum of all even numbers between 1 and 1000
weeeeeb [17]
There are 500 even numbers from 1 to 1000 starting with 2 and ending with 998. The sequence of even numbers is an arithmetic sequence with a common difference of 2. Using the equation for the arithmetic series,

                                       S = (a1 + an)(n/2)
and substituting, 
                                     
                                        S = (2 + 998)(500/2)
we get, 

                                        S = 250,000

Therefore, the sum of all even numbers between 1 and 1000 is 250,000.

4 0
3 years ago
To investigate whether or not sexism was present in the workplace, 48 male bank supervisors were each given a personnel file and
Volgvan
There is a clear bias. It is important however to not look at how many women got promoted with respect to men but which proportion of each subset got promoted. In the man files, 21/24 got promoted; this is a very high percentage, equal to 87.5%. Nonetheless, regarding women, 14/24 got promoted, 58,3%, barely over half of them. Hence, we conclude that there is a significant bias that favors male workers.
6 0
3 years ago
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