The lines are parallel.
In order to figure this out, let's start off by simplifying both equations as much as we can:
2y = 16 + 4x
Divide by 2
y = 2x + 8
Remember that the slope of that equation is '2' since 'm' in the equation y = mx + b represents slope.
Simplify the next equation:
6y - 30 = 12 x
6y = 12x + 30
Divide by 6:
y = 2x + 5
As you can tell, this line also has a slope of 2.
Parallel lines is defined as two lines that have the same slope. Knowing this, we can infer that these two lines are parallel.
-T.B.
9514 1404 393
Answer:
96 yards
Step-by-step explanation:
The diagonal through the park cuts the rectangle into two right triangles. The Pythagorean theorem tells you the relationship between the sides of a right triangle and its hypotenuse: the sum of the squares of the sides is equal to the square of the hypotenuse.
The diagonal is the hypotenuse, so we have ...
100² = 28² + w²
w = √(10000 -784) = 96
The width of the park is 96 yards.
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<em>Additional comment</em>
The integer side lengths of a right triangle form what is called a "Pythagorean triple." One of the most often seen of these is (3, 4, 5). Other commonly seen Pythagorean triples are (5, 12, 13), (7, 24, 25), (8, 15, 17).
You may notice that the numbers here are those of the (7, 24, 25) Pythagorean triple, multiplied by 4. If you recognize the given lengths as having the ratio 28:100 = 7:25, you have the clue you need to determine the answer simply from your knowledge of Pythagorean triples.
Answer:
12
Step-by-step explanation:
d=rx2
9514 1404 393
Answer:
- sin(θ) = 4/5
- cos(θ) = 3/5
- tan(θ) = 4/3
Step-by-step explanation:
The mnemonic SOH CAH TOA was created to help you remember the relevant trig relationships. It is intended to remind you ...
Sin = Opposite/Hypotenuse
sin(θ) = 4/5
Cos = Adjacent/Hypotenuse
cos(θ) = 3/5
Tan = Opposite/Adjacent
tan(θ) = 4/3
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In a right triangle, the opposite side (PQ) is the one that is not part of the angle (∠R = θ). The adjacent side (QR) is the shorter side that makes up the acute angle. The longest side (PR) is the hypotenuse.
Answer:
- D. x-intercept is -4; y-intercept is 8
Step-by-step explanation:
<u>Given line:</u>
<u>Find x- intercept, when y = 0:</u>
<u>Find y- intercept, when x = 0:</u>
Correct choice is D
