In the diagram shown, M, N and P are collinear and QM=QN as shown. If mMQN = 48" andmNQP = 33. Justify why QNP must be isosceles.
Answers
An isosceles triangle is that the triangle must have two sides of equal length.
Triangle QNP is isosceles triangle because, QN = PN
In triangle QMN,
Since, QM = QN
So, ∠QMN = ∠QNM
By property of triangle:
∠MQN + ∠QNM + ∠QMN = 180
48 + 2 ∠QNM = 180
∠QNM = = 66 degree
So, ∠QMN = ∠QNM = 66 degree
from figure,
∠QNM + ∠QNP = 180
∠QNP = 180 - 66 = 114 degree.
In triangle QNP,
∠QNP + ∠PQN + ∠QPN = 180
∠QPN = 180 - 33 - 114 = 33 degree
Since, ∠QNP = ∠QPN = 33 degree
Therefore, triangle QNP is isosceles triangle.
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Answer/Step-by-step explanation:
Let's find the measure of the angles of ∆QNP.
∆QMN is am isosceles ∆, because it has two equal sides. Therefore, its base angles would be the same. Thus:
m<MNQ = ½(180 - 48) (one of the base angles of ∆QMN)
m<MNQ = ½(132) = 66°
Next, find m<QNP
m<QNP = 180° - m<MNQ (linear pair angles)
m<QNP = 180° - 66° (Substitution)
m<QNP = 114°
Next, find m<P
m<P = 180 - (m<QNP + m<PQN) (sum of ∆)
m<P = 180 - (114 + 33)
m<P = 180 - 147
m<P = 33°
Thus, in ∆QNP, there are two equal angles, namely, <P and <PQN.
An isosceles ∆ had two equal base angles. Therefore, ∆QNP must be an isosceles ∆.
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Answer:
The probability that the selected ball is not blue is .
The probability that the selected ball is green is .
Step-by-step explanation:
The question is:
There are 10 brown balls, 5 blue balls and 15 green balls in a basket. If one is drawn at random, what is the probability that it is not blue? What is the probability that it is green?
Solution:
The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.
The probability of the given event not taking place is known as the complement of that event.
Complement of the event E is,
1 – P (E)
The number of different color balls are as follows:
Brown = n (Br) = 10
Blue = n (Bu) = 5
Green = n (G) = 15
Total = N = 30
Compute the probability of selecting a blue ball as follows:
Compute the probability of not selecting a blue ball as follows:
Thus, the probability that the selected ball is not blue is .
Compute the probability of selecting a green ball as follows:
Thus, the probability that the selected ball is green is .
Answers
Answer:
d(x) = √[(x - 2)² + (3x - 1)²]
Step-by-step explanation:
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, the distance between point (2,0) and a point (x,y)
d = √[(x - 2)² + (y - 0)²]
d = √[(x - 2)² + (y)²]
But the point (x,y) is on the line y = 3x - 1
We can substitute for y in the distance between points equation.
d(x) = √[(x - 2)² + (3x - 1)²]
QED!
(2x^3– 5x – 7) by (x + 2) ?
Answers
Answer:
this is the remainder.
Final answer:
To find the remainder, use polynomial long division to divide (2x^3 - 5x - 7) by (x + 2).
Explanation:
To find the remainder when dividing (2x^3 - 5x - 7) by (x + 2), we can use polynomial long division. First, divide the first term of the numerator by the first term of the divisor to get the quotient. Multiply the divisor by the quotient and subtract it from the numerator. Repeat this process until you have subtracted all terms of the divisor from the numerator. The resulting polynomial after division will be the remainder. In this case, the remainder will be 17x - 31.
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B: 751.29
C: 1954.13
D: 1536.19
Solution:
use formula P[((1+(r/n)^(nt))-1)/(r/n)]
Solution 50[((1+(0.48/12)^(2 x 12))-1)/(0.48/12)]
= C $1954.13
Answers
It is given that you have invested $50 a month in an annuity that earns 48% APR compounded monthly. We can conclude that after 2 years you will have $1954.13 in your account.
How to solve future value?
To solve this we are going to use the formula for the future value of an ordinary annuity:
where
FV is the future value
P is the periodic payment
r is the interest rate in decimal form
n is the number of times the interest is compounded per year
t is the number of years
It is given that you have invested $50 a month in an annuity that earns 48% APR compounded monthly. we need to find how much money you have in this account after 2 years.
Since the interest is compounded monthly, it is compounded 12 times per year; therefore,
r = 48% = 0.48
n = 12
Let's put the values in our formula:
Thus, We can conclude that after 2 years you will have $1954.13 in your account.
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What is the product of (2x2 + 4x - 2) and (x+6) ?
A. 6x3 + 24x2 - 18x - 12
B. 6x3 + 12x2 - 6x -12
C. 6x3 + 24x2 +18% -12
D. 6x3 + 12x2 +24x - 12
Answers
Answer: B
Step-by-step explanation: