Answer:
PQ = 34.4
Step-by-step explanation:
First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74
Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)
This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.
We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that
NO/QR = MN/PQ
Thus,
11/27 = 14/PQ
multiply both sides by PQ to remove a denominator
PQ * 11/27 = 14
multiply both sides by 27 to remove the other denominator
PQ * 11 = 14 * 27
divide both sides by 11 to isolate the PQ
PQ = 14 * 27 /11
PQ = 34.4
Answer:
a. No
b. Yes
c. No
Step-by-step explanation:
a. For BC and B'C to both be parallel to the y-axis when BC is parallel to the y-axis the figure must be rotated by a multiple of 180 degrees.
b. When you rotate a figure none of the angles in the figure change.
c. For D and D' to have the same coordinates the figure must be rotated by 360.
Answer:
a = 5.07
Step-by-step explanation:
Here, we want to get the value of the side marked a
What we have is a right triangle
so, to find the value of a, we are to use the correct trigonometric ratio
The angle given faces a, which makes a the opposite
the side measure faces the right angle and that makes it the hypotenuse
The trigonometric ratio that connects the two is the sine
The sine is the ratio of the opposite to the hypotenuse
mathematically;
sine 25 = a/12
a = 12 * sine 25
a = 5.07
Answer:
m is the slope
Step-by-step explanation:
Answer:
x = 1/2
Step-by-step explanation:
First, let's put the statement into words:
6 * x^2 + 5x = 4
Now, we can see which values work in this equation.
-4/3 doesn't work
1/2 works!
-3/4 doesn't work
2 doesn't work.
