Answer:
One inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale.
Step-by-step explanation:
9514 1404 393
Answer:
AD= 8
DC= 15
Angle a= 112°
Angle b= 68°
Angle c= 112°
Step-by-step explanation:
We have to assume the figure is a parallelogram.
Opposite sides of a parallelogram are congruent, so ...
BC = AD = 8
AB = DC = 15
Opposite angles are congruent, and adjacent angles are supplementary.
180° - ∠D = Angle a = Angle c = 112°
∠D = Angle b = 68°
<em>Question:</em>
The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?
—————
<em>Solution:</em>
Call those two angles x and y, where x is the larger one.
If they are complementary, then their sum equals 90°:
x + y = 90° (i)
Also, the ratio between x and y is 3 : 2, so
x 3
—— = ——
y 2
Product of the extremes = product of the means:
2x = 3y
2x – 3y = 0 (ii)
Now, just solve this system of equations:
x + y = 90° (i)
2x – 3y = 0 (ii)
Solve it with elimination. Since you want to know the value of the larger angle, which is x, then eliminate the variable y by doing the following:
Multiply the equation (i) by 3,
3x + 3y = 270° (iii)
2x – 3y = 0 (ii)
then add both equations, so you cancel out the variable y:
3x + 2x + 3y – 3y = 270° + 0
3x + 2x = 270°
5x = 270°
270°
x = ———
5
x = 54° <——— this is the measure of the larger angle.
I hope this helps. =)
Tags: <span><em>system of linear equations elimination method solve complementary angles algebra geometry</em>
</span>
We have
x² + 24x = 17 (1)
Note that
(x + 12)² = x² + 24x + 144
By adding 144 to the left side of equation (1), it becomes a perfect square.
Therefore
x² + 24x = (x+12)² - 144 (2)
Substitute (2) into (1).
(x + 12)² - 144 = 17
(x + 12)² = 17 +144
(x + 12)² = 161
Answer:
We added 144 to the left side of equation (1) in order to make it a perfect square.
