We will use the tangent ratio since we have the adjacent side to the 65 degrees and we need to find the opposite side to the 65 degrees.
Tan α = opp/adj
Tan 65 = x/30
To solve, multiply both sides by 30.
30 Tan65 = x
x = 64 ft
Answer:
Oh uh
Step-by-step explanation:
Answer:
All real numbers
Step-by-step explanation:
we have
f(x) = 3x +9
The linear function has a range of all real numbers -------> (-∞, ∞)
f(x) can take any real value.
Please see attached image below, for more information
The translated function is given by:
g(x) = 3|x + 1| - 3.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the parent function is given by:
f(x) = |x + 1| - 1.
For a vertical stretch by a factor of 3, the function is multiplied by 3, hence the translated function is given by:
g(x) = 3f(x) = 3(|x + 1| - 1) = 3|x + 1| - 3.
More can be learned about translation concepts at brainly.com/question/4521517
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So, to begin, we can set the scenario into an equation to solve for the amount of magnets that Sarah had...
Joseph had 28 magnets, plus an unknown amount, <em>x</em> :
28 + x
Sarah had 157, plus the same unknown amount.
157 + x
Also, Sarah had <u>four</u> times the amount of Joseph at the end:
4(28 + x)
As a full equation:

Now, all we have to do is solve for <em>x</em>, the unknown amount:

Use the Distributive Property on <em>4(28 + x)</em>:

Subtract <em>x</em> on both sides:


Subtract <em>112</em> on both sides:


Divide by <em>3</em> on both sides:

<em>15</em> is the unknown amount added to each pile of magnets!
Hope I could help you out!
Have a good one, and God bless!