All categories

3 years ago

If m∠UNR = 180° find m∠RNS A. 27° B. 34° C. 59° D. 94°

Mathematics

1 answer:

LenaWriter [7]3 years ago

7 0

Answer:

Option A) m∠RNS=27°

Step-by-step explanation:

We know that $m$ ∠UNR = 180°. This tells us that the Sum of the enclosed angles should equal 180°, by trigonometry. So the enclosed angles are:

$m$ ∠RNS = $(3x+6)^{o}$

$m$ ∠SNT= $(13x+3)^{o}$

$m$ ∠TNU= $(10x-11)^{o}$

Now let us add all the angles and solve for the value of $x$ as follow:

$m_{RSN}+m_{SNT}+m_{TNU}=m_{UNR}\\\\(3x+6)+(13x+3)+(10x-11)=180\\\\3x+13x+10x+6+3-11=180\\\\26x-2=180\\\\26x=180+2\\\\26x=182\\\\$

$x=\frac{182}{26} \\\\x=7$

Now lets plug in the value into the expression for angle $m$ ∠RNS to find the angle as:

$RNS = (3x+6)^{o}\\\\RNS=(3(7)+6)^{o}\\\\RNS=(21+6)^{o}\\\\RNS=27^{o}$

Thus Option A. is the correct answer.

You might be interested in

Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has

Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0), Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0

3 years ago

Patrick earns $40 per hour. He earned an extra $1000 for working on a special project. His pay check for the month was 7420. How

Likurg_2 [28]

Patrick worked 160.5 hours because you have to subtract 1000 from 7420 then divide that by 40 for your answer. Also, Patrick has a sweet job.

3 0

3 years ago

Read 2 more answers

Is it translation,rotation,reflection or dilation?

UkoKoshka [18]

Just looking at it, I can tell it's not a rotation because it's not rotated, it's not a reflection because its not flipped and it's not a translation because it became smaller, didn't just move. That makes this a dilation!

8 0

3 years ago

Read 2 more answers

In your own words, explain how debit resequencing works.

mezya [45]

Answer:

Explained below.

Step-by-step explanation:

Debit resequencing is a practice whereby a bank will process the debit and credit to an account in such a way that it causes account balances to fall faster which in turn leads to a boost in potential overdraft fees.

This is how it works;

For example, if you send two cheques on a given date — one sent to your credit card company for $300 and the second one sent to your local electric company for $150, the credit card company and the local electric company will try to get their money from your account on the same date. Now, you've set up an automatic withdrawal to pay your rent which also hits your account with your rent being is $600.

Now, if on the date that those three amount of money above hits your account, you have a balance of say $175, the bank could clear the $150 charge first, thereby resulting in two overdraft fees.

However, Instead of that process above, many banks use a software that reorders the transactions. This software will first of all present the $600 charge, followed by the $300 charge and then finally the $150 charge. In this way, you will end up paying three overdraft fees rather than just two. Banks normally use this method in order to maximize profit rather than with the aim of pleasing their customers.

6 0

3 years ago

Help me smart people don't guess the answer!!!!!

Rus_ich [418]

Unit rate = 300/6= 50 mph
50 mph x 5 = 250 miles

4 0

4 years ago

Read 2 more answers