9514 1404 393
Answer:
30 in
Step-by-step explanation:
The enclosing rectangle is 4 by 10, so has a perimeter of ...
P = 2(L+W) = 2(10+4) = 28
The notch adds 2 inches to the perimeter, so the total of all side lengths is ...
28 +2 = 30 . . . inches
<h2>Answer:
y = - ¹/₂ x OR y - 1 = - ¹/₂ (x + 2) </h2>
<h3>Step-by-step explanation: </h3>
For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:
The question gives us two points, (-2, 1) and (-8, 4), from which we can find the slope and later the equation of the line.
<u>Finding the Slope </u>
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= (4 - 1) ÷ (-8 - (-2))
= - ¹/₂
<u>Finding the Equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 1 = - ¹/₂ (x - (-2))
∴ y - 1 = - ¹/₂ (x + 2)
we could also transform this into the slope-intercept form ( y = mx + c)
since y - 1 = - ¹/₂ (x + 2)
⇒ y = - ¹/₂ x
<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>
<h3>
Answer: Choice C</h3>
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Work Shown:
Reference angle = P
Opposite side = QR = 8.5
Adjacent side = QP = 16
tan(angle) = opposite/adjacent
tan(P) = QR/QP
tan(P) = 8.5/16
tan(P) = 0.53125
tan(P) = 0.53