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mestny [16]
3 years ago
8

In the diagram shown, M, N and P are collinear and QM=QN as shown. If mMQN = 48" and

Mathematics
1 answer:
fredd [130]3 years ago
6 0

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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You cannot divide by zero, because that is undefined, it approaches infinity, which is not a real value.  Some would say that division by zero is "not allowed" :P  

So in this case the divisor cannot equal zero.

x^2+4x+3=0  There are many methods to factor, I'll complete the square, just for conciseness (and it is good to know how the quadratic formula is derived)

Divide by the leading coefficient, which is just 1 in this case...

Move the constant to the other side, subtract 3 from both sides

x^2+4x=-3  Halve the linear coefficient, square it, then add that value to both sides...(4/2)^2=2^2=4

x^2+4x+4=1  Now the left side is a perfect square...

(x+2)^2=1  Take the square root of both sides

x+2=±√1  subtract 2 from both sides

x=-2±√1

x=-2±1

x=-3 and -1

So if the equation equals zero when x=-3 and -1, it's factors are:

(x+3)(x+1)

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6 0
4 years ago
Find the numbers 1-20 using only four 4's and any operation
Papessa [141]
0 = 44-44
1 = 44/44 or (4+4)/(4+4) or (4/4) / (4/4) or [(4! - 4)/ 4] - 4
2 = 4/4+4/4
3 = (4+4+4)/4
4 = 4*(4-4)+4
5 = (4*4+4)/4
6 = 4*.4+4.4
7 = 44/4-4
8 = 4+4.4-.4
9 = 4/4+4+4
10 = 44/4.4
11 = 4/.4+4/4
12 = (44+4)/4
13 = 4!-44/4
14 = 4*(4-.4)-.4
15 = 44/4+4
16 = .4*(44-4)
17 = 4/4+4*4
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5 0
4 years ago
You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a
Leno4ka [110]

Answer:

West Elm Savings and Loan

a) The amount of the down payment is:

= $34,000

b) The amount of the mortgage for which the Bradys are applying is:

= $170,000.

c) The amount of the principal of $136,000 ($170,000 - $34,000) and the interest portion of the monthly payment by the Brady's is:

= $730.32

d. The total amount of interest that will be paid over the life of the loan is:

= $126,915.20

e) Total monthly payment = $994.32

f) No, they will not qualify.

g) The monthly income that would be required to qualify for this size of mortgage payment is:

= $3,977.28

Step-by-step explanation:

a) Data and Calculations:

Market value of mortgage house = $170,000

Required down payment = 1/5 or 20%

a) The amount of the down payment = $34,000 ($170,000 * 20%)

b) The amount of the mortgage for which the Bradys are applying is = $170,000.

c) Interest on the loan = $5.37 for every $1,000

The amount of the principal of $136,000 ($170,000 - $34,000) and interest portion of the monthly payment by the Brady's = $730.32 ($5.37 * $136,000/$1,000)

d. The total amount of interest that will be paid over the life of the loan is:

= $126,915.20 ($262,915.20 - $136,000)

Sum of all periodic payments = $262,915.20 = ($730.32 * 12 * 30)

e) Annual Property tax =         $1,710

Annual Property insurance     1,458

Total additional annual pyts $3,168

Monthly additional costs = $264 ($3,168/12)

Total monthly payment = $994.32 ($730.32 + $264)

f) Bradys' combined monthly income = $3,750

Qualification threshold = $937.50 ($3,750/4)

No, they will not qualify.

g) The monthly income that would be required to qualify for this size of mortgage payment is:

= $3,977.28 ($994.32/0.25)

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation: temperatures e

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3 years ago
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