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2 years ago

(Zoom in) I’m just typing cause it needs to b 20 characters long.

Mathematics

1 answer:

Romashka [77]2 years ago

8 0

Answer:

Step-by-step explanation:

ABC is congruent to GEF. The transformation made was reflecting over the origin.

<h2>I'm always happy to help :)</h2>

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Choose the correct simplification of (3xy6)2(y3)3.

tigry1 [53]

The answer is 18xy^9, hope it helps.

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3 years ago

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

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2 years ago

Describe what math step you would do to solve this equation ?

Vanyuwa [196]

Answer:

Multiply each side by 14.7

Step-by-step explanation:

cos 50 = m / 14.7

Multiply each side by 14.7

14.7 cos 50 = m /14.7 *14.7

14.7cos 50 = m

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3 years ago

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In ΔABC , angle C is a right angle.

guajiro [1.7K]

Answer: Choice A. sin(A) = cos(B)

============================================================

Explanation:

The rule is that sin(A) = cos(B) if and only if A+B = 90.

Note how

sin(A) = opposite/hypotenuse = BC/AB
cos(B) = adjacent/hypotenuse = BC/AB

Since both result in the same fraction BC/AB, this helps us see why sin(A) = cos(B). Similarly, we can find that cos(A) = sin(B).

In the diagram below, the angles A and B are complementary, meaning they add to 90 degrees. So this trick only applies to right triangles.

The side lengths can be anything you want, as long as you're dealing with a right triangle.

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2 years ago

If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 3 and passes through point (2, 5).

Ugo [173]

Part A: The equation of the ship's path is $y=3x-1$

Part B: The two ships sails perpendicular to each other.

Explanation:

Part A: It is given that $m=3$ and point (2, 5)

Substituting these in the slope intercept form, we have,

$y-y_{1}=m\left(x-x_{1}\right)$

$\begin{aligned}y-5 &=3(x-2) \\y-5 &=3 x-6 \\y &=3 x-1\end{aligned}$

Thus, the equation of the ship's path in slope intercept form is $y=3x-1$

Part B: The equation of the second ship is $x+3 y-6=0$

Let us bring the equation in the form of slope intercept form.

$\begin{aligned}3 y &=-x+6 \\y &=-\frac{1}{3} x+2\end{aligned}$

Thus, from the above equation the slope is $m=-\frac{1}{3}$

To determine the two ships sailing perpendicular to each other, we have

$m_{1} \times m_{2}=-1$

where $m_{1}=3$ and $m_{2}=-\frac{1}{3}$

$\begin{aligned}3 \times-\frac{1}{3} &=-1 \\-1 &=-1\end{aligned}$

Since, both sides of the equation are equal, these two ships sails perpendicular to each other.

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2 years ago