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
Huh, this is presented pretty interesting to me.
To start with, if you actually had no idea what the answer to this question was, you wouldn't pick B or C because x has to be close to 91°. In this particular quadrilateral, it's especially important that we focus on the fact, "x - 15." This means that x has to be higher initially to be subracted to equal 91, or the opposite angle.
In order to subtract to 91, the answer would have to be 106, or D. This is a hunch, but I have a suspicion that angle B and D are going to be the same, being that their on opposite sides of the figure.
Hope this helps! If you have further questions, let me know.
What is -3 times x squared?-9x
Answer:
Solve by adding or subtracting like terms. (Ex. 2k + 4k = 6k; 9 + 7 = 16)
- 6k + 7k = 1k = k
(7 - 6 = 1)
12r - 8 - 12 = 12r - 20
(8 + 12 = 20 but sign is negative) 12r will stay the same because there are no terms with a letter r.
n - 10 + 9n - 3 = 9n + n - 10 - 3 = 10n - 10 - 3 = 10n - 13
(n = 1 so 9 + 1 = 10; 10 + 3 = 13 but negative sign)
- 4x - 10x = 14x
(10 + 4 = 14)
- r - 10r = 11r
(r = 1 so 10 + 1 = 11)
Answer:
The price of the admission is 15.
Step-by-step explanation:
From the information given, you can write the following equations:
a+3e=45 (1)
a+5e=65 (2), where:
a is the admission cost
e is the exhibition cost
First, you can solve for a in (1):
a=45-3e (3)
Second, you can replace (3) in (2):
45-3e+5e=65
45+2e=65
2e=65-45
2e=20
e=20/2
e=10
Finally, you can replace the value of e in (3):
a=45-3e
a=45-3(10)
a=45-30
a=15
According to this, the price of the admission is 15.
