MATHEMATICAL CONNECTIONS Use the given information to write and solve a system of linear equations to find the values of $x$x​ and y$y$y​ . The text reads triangle L M N is congruent to triangle P Q R, the measure of angle L equals 40 degrees, the measure of angle M equals 90 degrees, the measure of angle P equals left parenthesis 17 x minus y right parenthesis degrees, the measure of angle R equals left parenthesis 2 x plus 4 y right parenthesis degrees. The equations are is equal to 40$=\ 40$= 40​ and is equal to 50$=\ 50$= 50​ . Question 2 $x\ =$x =​ and $y\ =$y =​

Answers

Answer 1

The value of x and y is 2 and 11.5

The sum of the interior angle of a triangle is 180 degrees.

Since LMN and PQR are similar, hence:

m<L = m<P

m<M = m<Q

m<N = m<R

Given the following parameters

m< L = 40 degrees

m<M = 90 degrees

m<P = 17x - y

m<R = 2x + 4y

Get the measure of m<N

m<M + m<N + m<L = 180

90n+ m<N + 40 = 180

m<N = 180 - 130

m<N = 50degrees

Since m<P = m<L, hence;

17x - y = 40 ....... 1

Also m<R = m<N

2x + 4y = 50 .......... 2

Solve simultaneously

17x - y = 40 ....... 1  * 4

2x + 4y = 50 .......... 2 * 1

___________________________

68x - 4y = 160

2x + 4y = 50

Adding both equations

68x + 2x = 160 + 50

70x = 210

x = 2

Substitute x = 3 into the equation 2x + 4y = 50

2(2) + 4y = 50

4 + 4y = 50

4y = 50 - 4

4y = 46

y = 46/4

y =  11.5

Hence the value of x and y is 2 and 11.5

Learn more here: https://brainly.com/question/15165519


Related Questions

Question 7 50 points


Is there enough information to prove that the triangles are congruent?


If yes, provide the correct Triangle Congruence Postulate or Theorem and a congruence statement.


If no, justify your answer.

Answers

Answer:

1f 2×4 -3׳ 12k is divided by × - 3 the remainder is 21 find the value of k

3. A gym charges a fee of $15 per month plus an additional charge for every group class
attended. The total monthly gym cost T can be represented by this equation: T = 15+c*n,
where c is the additional charge for a group class, and n is the number of group classes
attended
Which equation can be used to find the number of group classes a customer attended if we
know c and T?
a. n = I - 15
N
b. n=1 – 150
c. n = (T - 15) - C.
(T-15)
d. n=
1

Answers

Answer:

Option D)  [tex]\huge\sf{n\:=\:\frac{(T\:-\:15)}{c}}[/tex]

Step-by-step explanation:

Given the equation, T = 15 + c × n, where:

T = represents the total monthly gym cost

c =  represents the additional charge for a group class, and

n = represents the number of group classes attended

Solution:

In order to determine which equation can be used to find the number of group classes a customer attended, if there are given values for c and T, we must isolate the variable, n  algebraically.

The first step is to subtract 15 from both sides:

T = 15 + c × n

T - 15 = 15 - 15 + c × n

T - 15 = c × n

Next, divide both sides by c to isolate n :

[tex]\huge\mathsf{\frac{({T\:-\:15})}{c}\:=\:\frac{{c\:\times\:n}}{c}}[/tex]

[tex]\huge\sf{n\:=\:\frac{(T\:-\:15)}{c}}[/tex]

Therefore, the correct answer is Option D) [tex]\huge\sf{n\:=\:\frac{(T\:-\:15)}{c}}[/tex].

how do you translate nine equals the quotient of a number and 54

Answers

Answer:

9 = [tex]\frac{n}{54}[/tex] or n ÷ 54

Step-by-step explanation:

nine equals the quotient of a number and 54

       /\

9 = the quotient of a number and 54

             /\

9 =       will be division of a number and 54

                                /\

                    9 = [tex]\frac{n}{54}[/tex] or n ÷ 54

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Today everything at a store is on sale the store offers a 20
% discount the regualr price of a t shirt is 18 what is the discount price

Answers

Answer:

$14.40 is the discount price.

Step-by-step explanation:

0.2 x 18 = 3.6

18 - 3.6 = 14.4

(2x+y)2-y2 if x=-3 y=4 and z=-5

Answers

Answer:
-12
Hope this helps!
So your equation it (2x+y)2-y2 so then you will substitute meaning your equation will now be 2(-3)+4*2-(4)2 and I assume it’s squared and there is a lot of things missing but I get -6+8-16 all together it would be 14 that’s what I get at least

2. A house costs $30,000. A buyer is given a 1/10 discount. How much money does the buyer save?

Answers

Answer:

3000

Step-by-step explanation:

Which of the following is true?

|−5| < 4
|−4| < |−5|
|−5| < |4|
|−4| < −5

Answers

Answer:

|-4| < |-5|

Step-by-step explanation:

because if modules is given sub sign will be deducate

(4, 7); y = 3x + 6 plz help me

Answers

y=3x+6.

y=3x-5

I did it with a parallel line

HURRY PLEASE! Do questions 4,5,6 on paper

Answers

This should be right , if any doubt please comment

solve pls brainliest

Answers

Answer:

Yes, This is a repeating decimal

No, This is a decimal that neither terminates or repeats

No, This is a decimal that neither terminates or repeats

Yes, This is a terminating decimal

PLEASE HELP ME!!! jacky starts biking to meet up with her friend. she knows that if she bikes at a speed of 10 mph, she will be 3 minutes late. jacky also know that if she bikes at a speed of 12 mph, she will be there 2 minutes before they agree to meet. how much time does she have left before the appointed time?

Answers

Answer:

27s

Step-by-step explanation:

d = distance to rendezvous point in miles

t = time of arrival at 10mph, i.e. 3 mins later than appointed time

10 mph = 10 miles per hour = ¹/₆ miles per min

12 mph = ¹/₅ miles per min

t = d/(¹/₆)

t = 6d

5 min = ¹/₁₂ hr

t - ¹/₁₂ = d/(¹/₅)

t = 5d + ¹/₁₂

Elimination of t:

6d = 5d + ¹/₁₂

d = ¹/₁₂ mi

t = 6(¹/₁₂)

t = ¹/₂ min

Time left to appointed time = ¹/₂ - ³/₆₀

= ¹⁰/₂₀ - ¹/₂₀

= ⁹/₂₀.min → 27 seconds

Answer:

27 min

Step-by-step explanation:

rsm

Please help ASAP !!!

THANKS!!

Answers

Answer:

rotation

Step-by-step explanation:

Answer:

Reflection

Step-by-step explanation:

I think its reflection because if you reflect them across the y axis then the x axis I believe they will be in those positions.

A delivery company's charge for an overnight package weighing in excess of one pound is given by the formula c= 2.53w + 15, 16
where w is the weight of package in pounds. Find the following.

Answers

What’s the question or equation? Is there a picture?

Identify the vertex of the parabola represented by the equation y=−2x2+8x−1.


(−4, −65)

(4, −1)

(2, 7)

(−2, −25)

Answers

Answer:

it is correct but -65 is not correct

Using the appropriate Algebraic identity evaluate the following:(4a - 5b)²​

Answers

Solution:

[tex](4a - 5b)^{2} \\ by \: \: \: using \: \: \: (x - y)^{2} = {x}^{2} - 2xy + {y}^{2} \\ = {(4a)}^{2} - 2(4a)(5b) + {(5b)}^{2} \\ = {16a}^{2} - 40ab + 25 {b}^{2} [/tex]

Answer:

[tex] {16a}^{2} - 40ab + {25b}^{2} [/tex]

Hope it helps.

Do comment if you have any query.

When there’s a power to the second outside of the parentheses, you multiply the entire equation by its self, so (4a - 5b)(4a-5b)=16a^2-40ab+25b^2

a number of students are standing in a circle. they are evenly spaced and the fith student is directly opposite the eleventh student. how many students are there all together

Answers

Answer:

There would be 12

Step-by-step explanation:

(27/8)^1/3×[243/32)^1/5÷(2/3)^2]
Simplify this question sir pleasehelpme​

Answers

Step-by-step explanation:

[tex] = {( \frac{27}{8} )}^{ \frac{1}{3} } \times ( \frac{243}{32} )^{ \frac{1}{5} } \div {( \frac{2}{3} )}^{2} [/tex]

[tex] = { ({ (\frac{3}{2} )}^{3}) }^{ \frac{1}{3} } \times {( {( \frac{3}{2}) }^{5} )}^{ \frac{1}{5} } \div {( \frac{2}{3} )}^{2} [/tex]

[tex] = {( \frac{3}{2} )}^{3 \times \frac{1}{3} } \times {( \frac{3}{2} )}^{5 \times \frac{1}{5} } \times {( \frac{3}{2} )}^{2} [/tex]

[tex] = \frac{3}{2} \times \frac{3}{2} \times {( \frac{3}{2} )}^{2} [/tex]

[tex] = {( \frac{3}{2} )}^{1 + 1 + 2} [/tex]

[tex] = {( \frac{3}{2} )}^{4} \: or \: \frac{81}{16} [/tex]

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\sf{\longmapsto{\bigg( \dfrac{27}{8} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{243}{32} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\[/tex]

We can write as :

27 = 3 × 3 × 3 = 3³

8 = 2 × 2 × 2 = 2³

243 = 3 × 3 × 3 × 3 × 3 = 3⁵

32 = 2 × 2 × 2 ×2 × 2 = 2⁵

[tex]\sf{\longmapsto{\bigg( \dfrac{3 \times 3 \times 3}{2 \times 2 \times 2} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 2} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg( \dfrac{{(3)}^{3}}{{(2)}^{3}} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{({3}^{5})}{{(2)}^{5}} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\[/tex]

Now, we can write as :

(3³/2³) = (3/2)³

(3⁵/2⁵) = (3/2)⁵

[tex]\sf{\longmapsto{\left\{\bigg(\frac{3}{2} \bigg)^{3} \right\}^{\frac{1}{3}} \times \Bigg[\left\{\bigg(\frac{3}{2} \bigg)^{5} \right\}^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\[/tex]

Now using law of exponent :

[tex]{\sf{({a}^{m})^{n} = {a}^{mn}}}[/tex]

[tex]\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{3 \times \frac{1}{3}} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{5 \times \frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\[/tex]

[tex] \sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{\frac{3}{3}} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{\frac{5}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times\Bigg[\bigg(\frac{3}{2} \bigg)^{1} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{1} \times \bigg(\dfrac{3}{2} \bigg)^{2}\Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{1} \times \bigg(\dfrac{3}{2} \times \dfrac{3}{2} \bigg)\Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2} \bigg)^{1} \times \bigg(\dfrac{3 \times 3}{2 \times 2}\bigg)\Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2} \bigg)^{1} \times \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\[/tex]

[tex] \sf{\longmapsto{\bigg( \frac{3}{2} \bigg)\times \Bigg[\bigg(\frac{3}{2} \bigg)\times \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \: \: \dfrac{3}{2} \times \dfrac{9}{4} \: \: \Bigg]}}\\[/tex]

[tex]\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \: \: \dfrac{3 \times 9}{2 \times 4} \: \: \Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\bigg(\dfrac{3}{2} \bigg)\times \Bigg[ \: \: \dfrac{27}{8} \: \: \Bigg]}} \\[/tex]

[tex]\sf{\longmapsto{\dfrac{3}{2} \times \dfrac{27}{8}}} \\[/tex]

[tex]\sf{\longmapsto{\dfrac{3 \times 27}{2 \times 8}}} \\[/tex]

[tex] \sf{\longmapsto{\dfrac{81}{16}}\: ≈ \:5.0625\:\red{Ans.}} \\[/tex]

The domain for f(x) is all real numbers ___ than or equal to 2

Answers

Step-by-step explanation:

f(x) = 2x² + 5√(x - 2)

Domain

√(x - 2) ≥ 0

x - 2 ≥ 0

x ≥ 2

x is greater than or equal to 2

Answer: Greater than

Step-by-step explanation:

You plan on joining a gym. The joining fee is $30 and you must pay $12 a month fee. If you have $100, how many months can you use the gym? Write and solve an inequality to represent the solution.

I need the process for this otherwise I won't get credit for it!!

Answers

Answer:

Inequality: 30+12x < 100

x ≈ 5 months

Step-by-step explanation:

To solve, first create the inequality. In this problem, 30 dollars is the flat fee for joining the gym and thus a constant. Additionally, 12 is the monthly payment and thus the coefficient for a variable because it changes with the number of months. Finally, 100 is the most that can be spent (the max), so it should be on the other side of the inequality and the sign should be less than or equal to 100.

This makes the inequality: 30+12x < 100

To find the number of months solve the inequality for x.

30+12x<10012x<70x<5.8

So, the inequality equals x<5.8. However, the question asks for the number of full months. And, no more than 100 dollars can be spent. So, while you would normally round up. In this case, you must round down to 5 months.

Answer all of the following questions. 3 Points a question. ALSO NO LINKS!

Is 2 a prime number?
Is 3 a prime number?
Is 11 a prime number?
Is 18 a prime number?
Is 20 a prime number?
Is 27 a prime number?

Answers

Answer:

no

yes

yes

no

no

yes

Step-by-step explanation:

a prime number cant be devided by any thing other than itself or one

Answer:

Step-by-step explanation:

Is 2 is 3 is 11 is 18 is 20 is 27

Express the tan G as a fraction in simplest terms.

Answers

Answer:

[tex]\frac{\sqrt{70} }{5}[/tex]

The dimensions of a rectangular prism are 3 cm, 15 cm, and k cm. Its volume is
90 cm. Find the value of k.

Answers

Answer:

k = 2 cm

Step-by-step explanation:

3 x 15 x k = 90 cm^3

45 x k = 90 cm^3

k = 90/45 = 2 cm

Please help this is my fifth time asking this question please answer it correctly with explanation

Answers

Step-by-step explanation:

There are two attachments to this post. The first attachment shows the numbered angles formed through the intersection of the transversal, t, into the parallel lines, m and n, which will be used to determine how each angle relates to other angles.

First attachment:

The corresponding angles in the first attachment are:

∠1 and  ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

Corresponding angles have the same measure.

The same-side exterior angles are the pair of angles that are outside the parallel lines, and on the same side of the transversal.  In the first attachment, the same-side exterior angles are:

∠1  and ∠8

∠2 and ∠7

These angles are supplements of each other, meaning that the sum of their measure equal 180°.

Second Attachment:

Given parallel lines, m and n that are cut by a transversal, t.

The angle that has a measure of  ∠(10x + 5)° is a supplement of ∠(5x + 25)°.  In order to solve for the value of x, we must establish the following equation:

m∠(10x + 5)° + m∠(5x + 25)° = 180°

10x° + 5° + 5x° + 25° = 180°

Combine like terms:

15x° + 30° = 180°

Subtract 30 from both sides:

15x° + 30° - 30° = 180° - 30°

15x° =  150°

Divide both sides by 15:

15x°/15 = 150°/15

x = 10°

Verify whether we have correct value for x by substituting its value into the established equation:

m∠(10x + 5)° + m∠(5x + 25)° = 180°

10(10)° + 5° + 5(10)° + 25° = 180°

100° + 5° + 50° + 25° = 180°

180° = 180° (True statement).

Therefore, we have the correct value for x = 10°.

m∠(10x + 5)°  = 105°

m∠(5x + 25)° = 75°

(20pts) I need to know who is incorect and why

Answers

Answer:

i thig it is hj

Step-by-step explanation:

jk

.4(x + 7)

.4 + 7x- 5x -6

Answers

Answer:6/5x=7/x+2 Two solutions were found : x =(10-√940)/12=(5-√ 235 )/6= -1.722 x =(10+√940)/12=(5+√ 235 )/6= 3.388 Rearrange: Rearrange the equation by subtracting what is to the right

Step-by-step explanation:

make a conjecture (prediction) about the table. what will happen if we continue the table, going down? ​

Answers

278 would be it I think but not sure

fill in the blank with the letter of the description that best matches the term for the verb porter, match the subject pronoun with the correct form of the verb. i'll mark Brainliest if the answers are correct.

A. portons
B. porte
C. portez
D. portes
E. portent
FILL IN THE BLANK

je ____
tu ____
nous ____
vous ____
ils ____

Answers

Step-by-step explanation:

je........porte

tu.......portes

nous.......portons

vous........portez

ils......portent

Can someone help me with this please​

Answers

Answer:

y=1/2x

Step-by-step explanation:

Answer:

10

9

8

7

6

5

4

3

2

1

0 1 2 3 4 5 6 7 8 9 10

Step-by-step explanation:

So the arrow is pointing at 10 and  5

Answer 10 5

Not 5

its 10 5

So the answer is 10 5

e
Week 6: Culmination Knowledge Check
CLEAR MY CHOICE
Question 8
You buy milk in 1-gallon containers. One portion of waffles requires 2 ounces of milk. How many portions can be made with one container? Select one
a 128
b. 16
c. 32
d. 64
CLEAR MY CHOICE
Question 9
You have 24 quarts of brown stock. You need 75 cups to make one serving of kidney beans. How many servings can you make? Select one

Answers

B.16 is the answer to your question

Answer this question for me ASAP

Answers

Answer:

Option A: (It's just that the y-intercept and slope are in different spots.)

Line in (y=mx+b) form is y = 2x + 4

Slooe is 2

y-intercept is 4

Step-by-step explanation:

Slope-intercept form is written as y=mx+b, where m is slope and b is y-intercept.

By looking at the graph, we can already tell that the y-intercept is positive 4, since the line crosses the y-axis at that point.

Now use rise/run to find slope. (Remember that rise is movement up or down, and run is movement left or right.) With this in mind, the slope is 4/2, and if we simplify it, it's 2/1 (or basically just 2). Because we go upwards 4 units and to the right 2 units.

Hope this helps :)

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