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3 years ago

What is this the relationship between the legs and the hypotenuse of a 45 - 45 - 90 triangle?

Mathematics

2 answers:

Studentka2010 [4]3 years ago

6 0

The length of the hypotenuse is (the length of each leg) times (the square root of 2).

Elena L [17]3 years ago

6 0

Answer:

Step-by-step explanation:

The length of the hypotenuse and the legs of a 45 45 90 triangle are no different from any right triangle. It's simply:

a^2+b^2=c^2 where a and b are the legs and c is the hypotenuse.

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NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z

Roman55 [17]

Answer:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

Step-by-step explanation:

Given system of equations:

$\begin{cases}y=x^2-9\\y=4x-4\end{cases}$

To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:

$\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}$

Factor the quadratic:

$\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}$

Apply the <u>zero-product property</u> and solve for x:

$\implies x+1=0 \implies x=-1$

$\implies x-5=0 \implies x=5$

Substitute the found values of x into the <u>second equation</u> and solve for y:

$\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}$

$\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}$

Therefore, the solutions are:

$(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}$

$(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}$

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1 year ago

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nexus9112 [7]

Answer:

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Step-by-step explanation:

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3 years ago

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qaws [65]

Answer:

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Step-by-step explanation:

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3 years ago

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What is the slope of the line 7, 0 and -5, 0

lutik1710 [3]

Answer:

Slope = (Y2 -Y1) ÷ (X2 -X1)

Slope = (0 -0) / (-5, -7)

Slope = 0 / -12 = 0

The slope of the line is zero. It is perfectly horizontal.

Step-by-step explanation:

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