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SashulF [63]
3 years ago
15

The longer leg of a right triangle is 3 inches more than the length of the shorter leg tripled. the hypotenuse is 3 inches less

than four times the length of the shorter leg. find the length of the hypotenuse
Mathematics
1 answer:
lukranit [14]3 years ago
4 0
We have this equation.
A²+B²=C²
We have bits of information that'll help us simplify the equation so there's only one variable.
The longer leg, A, is 3 inches more than the length of the shorter leg, B, tripled.
A=3B+3
Let's plug that in.
(3b+3)²+B²=C²
The hypotenuse, C, is 3 inches less than four times the length of the shorter leg. C=4B-3
Let's plug that in.
(3b+3)²+B²=(4B-3)²
Let's solve.
9B²+18B+9+B²=16B²-24B+9
10B²+18B+9=16b²-24b+9
Let's subtract 9 from both sides.
10b²+18b=16b²-24b
Let's subtract 10b² from both sides.
18b=6b²-24b
Let's add 24b from both sides.
42b=6b²
Let's divide each side by 6.
7b=b²
With this, you can tell that b is 7 since it times 7 equal itself squared.
The shorter leg is 7 inches.
Now, let's look back at the bits of information.
The longer leg of a right triangle is 3 inches more than the length of the shorter side tripled.
3(7)+3=24
So, the longer side is 24. We can either use the other information or plug it into the equation. We can do both. 
The hypotenuse is 3 less than four times the shorter leg.
4(7)-3=25
7²+24²=
49+576=625
√625=25
So, the length of the hypotenuse is 25 inches.
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Determine whether the lines are parallel, intersect, or coincide. x-5y=0, y+1=1/5(x+5)
MAXImum [283]

<u>Answer-</u>

<em>The lines are two </em><em>coinciding lines</em><em> or the </em><em>same lines</em><em>.</em>

<u>Solution-</u>

The given line equations are

the first one,

\Rightarrow x-5y=0  

the second one,

\Rightarrow y+1=\dfrac{1}{5}(x+5)\\\\\Rightarrow 5y+5=x+5\\\\\Rightarrow 5y=x\\\\\Rightarrow x-5y=0

As we know two line equations A_1x+B_1y+C_1=0 and A_2x+B_2y+C_2=0 will be,

  1. Parallel if, \dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}
  2. Coincide if, \dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}
  3. Intersect if, \dfrac{A_1}{A_2}\neq \dfrac{B_1}{B_2}

As here,

\Rightarrow \dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}

\Rightarrow \dfrac{1}{1}=\dfrac{-5}{-5}

(C₁ and C₂ aren't considered as they are 0)

Therefore, the lines are two coinciding lines or the same lines.

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What is the first step in writing f(x) = 3x2 + 6x – 8 in vertex form?
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The first step in writing f(x) = 3x² + 6x - 8 in vertex form is

E. Factor out 3 from the first two terms.

f(x) = 3x² + 6x - 8
f(x) = 3(x² + 2x) - 8
f(x) + 8 = 3(x² + 2x + __)
f(x) + 8 + 1 = 3(x² + 2x + 1)
f(x) + 9 = 3(x+1)²
f(x) = 3(x+1)² - 9

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HELP NEEDED ASAP!!! PLEEEEASE HELP!!!
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Answer:

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Step-by-step explanation:

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I'm not the best at explaining but you can search google to get the better Idea.

(btw this is for the fist question)

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