1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
igor_vitrenko [27]
2 years ago
13

For which value(s) of x are the triangles congruent?​

Mathematics
1 answer:
Varvara68 [4.7K]2 years ago
8 0

Step-by-step explanation:

The solutions are 2 and 5

Because it's asking what would make the triangles congruent, you would set up the equation like this because the angles (angle 3 and angle 4) need to be equal:

x^2 = 7x - 10

Next, you add 10 to both sides. This is so that you can move it to the other side, addition is the inverse of subtraction.

x^2 + 10 = 7x

Now subtract 7x from both sides. Subtraction is the inverse of addition. You do this to get it on the other side so you can factor it. You can move the 10 and 7x to the other side in any order or at the same time, I just did it like this.

x^2 - 7x + 10 = 0

Now, factor. I don't really know how to explain factoring, you just get a feel for it with a lot of practice.

(x - 2)(x - 5) = 0

You can use FOIL to check this if you want to. x(x) is x^2, -2(-5) is 10), -2x - -5x is -7x. Now, find what you need to do to make what's in each of the groups of parentheses equal to 0.

x - 2 = 0

x = 2

One of the solutions is 2, because you add 2 to x to get 0.

x - 5 = 0

x = 5

The other solution is 5, because you add 5 to x to get 0. Lastly, check your solutions by plugging them in to the original equation.

2^2 = 7(2) - 10

4 = 14 - 10

So 2 is definitely a solution.

5^2 = 7(5) - 10

25 = 35 - 10

5 is also a solution.

Hope that helps :]

You might be interested in
This is confusing<br> (2x+y)^2−(x−2y)^2
Iteru [2.4K]

Answer:

{(2x + y)}^{2}  -  {(x - 2y)}^{2}

<  {(x + y)}^{2}  =  {x}^{2}  + 2xy +  {y}^{2}  >

<  {(x - y)}^{2}  =  {x}^{2}  - 2xy +  {y}^{2}  >

{(2x)}^{2}  + 2(2x)(y) +  {(y)}^{2}  -  {(x)}^{2}  - 2(x)(2y) +  {(2y)}^{2}

{4x}^{2}  + 4xy +  {y}^{2}  -  {x}^{2}  - 4xy +  {4y}^{2}

{4x}^{2}   -  {x}^{2}  +  {4y}^{2}  +  {y}^{2}

= {3x}^{2}  +  {5y}^{2}

5 0
3 years ago
Read 2 more answers
Q 14. Two friends Tina and Reeta simplified two different expressions during the revision
frez [133]
I really don’t know the answer I’m sorry
7 0
3 years ago
Upon hitting a bat, a baseball has a change in momentum of 16.5 kg-ms. What is the average
olya-2409 [2.1K]

Answer:

The average force applied to the baseball is 8.25kN

Step-by-step explanation:

This problem bothers on the impulse of a force

We know that the change in momentum is expressed as

Ft= mv-mu

Given

Ft=16.5 kg-ms

Time t of impact =0.00200s

The force applied can be solved for

By making F subject of formula

F= (mv-mu)/t

F=16.5/0.002

F= 8250N

F= 8.25kN

4 0
3 years ago
Please Help!<br><br> Car X travels 174 miles in 3 hours.
DiKsa [7]

Answer:

The graph =

<h3>y = 58x</h3>

Step-by-step explanation:

(a)

distance covered (y) = 174 miles

time taken (x) = 3 hours

Therefore the points = (3, 174) and (0, 0) = stationary position

Find the gradient (m)

m = 174-0 / 3-0

m = 58

Therefore the equation =

<h3>y = 58x</h3>

(distance = 58 × time)

For the distance = 174 and time = 3 hours, the equation to find either distance or time = y = 58x

(b) the graph is constant, because the time and distance are also contant when the speed used is the same.

____________________

#IndonesianPride - kexcvi

5 0
2 years ago
In 2 yrs time ella will be twice the age she was 5 yrs ago. how old is she now?
chubhunter [2.5K]
8 because 2 times 5 is ten
7 0
3 years ago
Other questions:
  • A shop has a sale that offers 20% off all prices.
    10·1 answer
  • At midnight, the temperature was 30 degrees F. By 6:00 a.m., it had dropped 5 degrees and by noon, it had increased by 11 degree
    15·1 answer
  • Someone Help please!
    15·1 answer
  • 14(5-1/5×25)+2÷4×1 How Do I Evaluate This Expression ?
    10·1 answer
  • Francine uses \dfrac23
    12·1 answer
  • Identify the exponential function for the given graph.
    6·1 answer
  • Help please! This is timed!
    13·1 answer
  • According to a survey of 100 people regarding their movie attendance in the last year, 40 had seen a science fiction movie, 55 h
    12·1 answer
  • Find the median and mean of the data set below:<br> 48,32,5, 13, 11, 22, 2
    9·2 answers
  • Find the missing term.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!