These triangles can be proven congruent by the

Mathematics

1 answer:

Marina86 [1]2 years ago

3 0

Answer:

Step-by-step explanation:

These triangles are congruent by the 3 sides of 1 triangle being congruent to 3 sides of the other. SSS

The fact that one has been rotated in terms of the other means nothing.

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Nine friends just graduated from college with business degrees and are ready to start their own businesses. The presentations be

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3 years ago

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Solve the equation `x^{4}+13x^{2}+36=0` for all values of `x`.

Zolol [24]

Answer: x4+13x2+36=0

Step-by-step explanation:

Let's solve your equation step-by-step.

x4+13x2+36=0

Step 1: Factor left side of equation.

(x2+4)(x2+9)=0

Step 2: Set factors equal to 0.

x2+4=0 or x2+9=0

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3 years ago

Third-degree, with zeros of -4, -2, and 1, and a y-intercept of -11.

Cloud [144]

$\begin{cases} x = -4\implies &x+4=0\\ x=-2\implies &x+2=0\\ x=1\implies &x-1=0 \end{cases}\qquad \implies (x+4)(x+2)(x-1)=\stackrel{y}{0}$

now, that's the equation or polynomial in factored form, hmmm we also know that it has a y-intercept of -11, namely, when x = 0 y = -11, well let's plug in a factor to it, that will reflect those values, namely say hmmm factor "a", so

$(x+4)(x+2)(x-1)=y\qquad \stackrel{\textit{adding "a" factor for vertical shift}}{a(x+4)(x+2)(x-1)}=y \\\\\\ \stackrel{\textit{we know that when x = 0, y = -11}}{a(0+4)(0+2)(0-1)=-11}\implies -8a=-11\implies a=\cfrac{-11}{-8}\implies a = \cfrac{11}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\mathbb{FOIL}}{\cfrac{11}{8}(x^2+6x+8)}(x-1)=y\implies \cfrac{11}{8}(x^3+6x^2+8x-x^2-6x-8)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{11}{8}(x^3+5x^2+2x-8)=y~\hfill$

4 0

2 years ago

I need help solving. The answer is (2,-6)

faust18 [17]

Since we are given x in terms of y, the most efficient way to solve it would be to substitute in the $\frac{1}{2}y+5$ for x in the second equation. So, we then have:

$2(\frac{y}{2}+5)+3y=-14 \implies \\
y+10+3y=-14 \implies \\
4y+10=-14 \implies\\
4y=-24 \implies \\
y=-6$

So, now that we have our y, we can find x. We can actually use either equation, top or bottom, to find x, but to be efficient we should use the top one since we have x in terms of y, so:

$x=\frac{-6}{2}+5 \implies \\
x=-3+5 \implies \\
x=2$