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
Assoli18 [71]
3 years ago
8

If the triangles are congruent,

Mathematics
1 answer:
harkovskaia [24]3 years ago
5 0

Answer:

x = 3

Step-by-step explanation:

If the triangles are congruent then

4x + 1 = 13

4x = 12

x = 3

You might be interested in
Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
jok3333 [9.3K]

Answer:

\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}

And, the distance from P to (0, -2) will be:

\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}

So sum of the two distances must be 6. Therefore:

d_1+d_2=6

Now, by substitution:

(\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6

Simplify. We can subtract the second term from the left:

\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}

Square both sides:

(x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)

We can cancel the x² terms and continue squaring:

y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

-8y=36-12\sqrt{x^2+(y+2)^2}

We can divide both sides by -4:

2y=-9+3\sqrt{x^2+(y+2)^2}

Adding 9 to both sides yields:

2y+9=3\sqrt{x^2+(y+2)^2}

And, we will square both sides one final time.

4y^2+36y+81=9(x^2+(y^2+4y+4))

Distribute:

4y^2+36y+81=9x^2+9y^2+36y+36

The 36y will cancel. So:

4y^2+81=9x^2+9y^2+36

Subtracting 4y² and 36 from both sides yields:

9x^2+5y^2=45

And dividing both sides by 45 produces:

\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

5 0
3 years ago
Read 2 more answers
Find the cube of 0.5. A. 0.125 B. 0.25 C. 1.5 D. 1.25
Hatshy [7]
Cubed is a number that is multiplied by itself 3 times. So you will multiply .5 by itself once and get .25 then multiply it by .5 again and get .125. The answer is A.
3 0
2 years ago
Read 2 more answers
- If MML = (11x - 5), mJK = (4x + 26)° and mZMNL = (10x – 12),<br><br><br><br> find mZMNL.
GenaCL600 [577]

Answer:

m∠ MNL = 78º

Step-by-step explanation:

<u>Arcs meassures </u>

mML = (11x - 5)º

mJK = (4x + 26)°

<u>Angle meassure</u>

m∠MNL = (10 x – 12)º

______________________

angle measure = average of arcs

m∠MNL  = (mML+ mJK)/2

Replacing

(10x – 12)º =  ((11x - 5)º + (4x + 26)° )/ 2

10x -12 =  (15x + 21 )/2

10x - 7.5x = 10.5 + 12

2.5x = 22.5

x= 9

m∠MNL = (10 x – 12)º

             = 90 - 12

             = 78º

3 0
3 years ago
Two plants, plant A and B, are being grown in a science experiment. Plant A is 6 cm tall and growing at a rate of 4 cm/day. Plan
Irina18 [472]
By the second day of growth
6 0
3 years ago
375000000 divided by 1570000000
Zielflug [23.3K]

Answer: 0.238853503185

(I obviously used a calculator.)

If you rounded this answer, it would be 0.24. Hope this helps!

8 0
3 years ago
Read 2 more answers
Other questions:
  • Can anyone factor 8x^2 + 10x -25? Please Help!
    13·2 answers
  • Ethan burns 659 calories when he runs for 1 hour. Suppose he runs for 5 houtse in one week. How many calories does Ethan burn in
    9·2 answers
  • The McPhearson family went fishing. They caught 7 fish. The weights of the fish were 15, 16, 15, 13, 19, 20, and 21 pounds. What
    10·1 answer
  • Two consecutive numbers whose squares add up to 685
    13·1 answer
  • HELLPPPPPPPPPPPPPPPPPPP
    11·1 answer
  • The area of a poster board is x2+3x-10 square inches. Find the dimensions of the poster board if x=14
    8·1 answer
  • Two wheel gears are connected by a chain. The larger gear has a radius of 5 centimeters and the smaller gear has a radius of 3 c
    9·1 answer
  • (PLEASE HELP DUE NOW! I DON'T UNDERSTAND!)
    15·2 answers
  • Please help will give brainliest
    8·1 answer
  • !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!