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andreev551 [17]
2 years ago
9

Can u please help me with these three questions?? Please

Mathematics
1 answer:
V125BC [204]2 years ago
4 0

Hello! What you're seeing in these images are two parallel lines cut by a transversal. There are many relationships between angles here.

----

Problem g: What you are seeing here is alternate interior angles - they are both on the inside of the lines, and are on opposite sides of the transversal. These angles are proven to always measure the same thing.

Therefore, 8x - 4 = 60. Use this equation, and solve.

8x - 4 = 60

8x = 64

x = 8

----

Problem h: Here, you are seeing corresponding angles. When you look at the two intersection points, these two angles are located "between the same sides". These angles are also proven to always measure the same.

Therefore, 6x = 5x + 10. Use this equation, and solve.

6x = 5x + 10

x = 10

----

Problem i: These are alternate exterior angels. These are located on opposite ends of the transversal, and are on the outside of the parallel lines. These angles also always measure the same.

Therefore, -1 + 14x = 12x + 17. Now solve.

-1 + 14x = 12x + 17

2x = 18

x = 9

----

Therefore, your three answers are x = 8, x = 10, and x = 9.

Hope this helps!

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You plan to accumulate 100,000 at the end of 42 years by making the follow-
Mariana [72]

Answer:

  Y = 479.17

Step-by-step explanation:

At the end of year 14, the balance from the deposits of X can be found using the annuity due formula:

  A = P(1+r/n)((1 +r/n)^(nt) -1)/(r/n)

where P is the periodic payment, n is the number of payments and compoundings per year, t is the number of years, and r is the annual interest rate.

  A = X(1.07)(1.07^14 -1)/0.07 ≈ 24.129022X

This accumulated amount continues to earn interest for the next 28 years, so will further be multiplied by 1.07^28. Then the final balance due to deposits of X will be ...

  Ax = (24.129022X)(1.07^28) = 160.429967X

__

The same annuity due formula can be used for the deposits of Y for the last 10 years of the interval:

  Ay = Y(1.07)(1.07^10 -1)/.07 = 14.783599Y

__

Now we can write the two equations in the two unknowns:

  Ax +Ay = 100,000

  X - Y = 100

From the latter, we have ...

  X = Y +100

So the first equation becomes ...

  160.429967(Y +100) +14.783599Y = 100000

  175.213566Y +16,043.00 = 100,000

  Y = (100,000 -16,043)/175.213566 ≈ 479.17

Y is 479.17

7 0
3 years ago
Simplify 2(5+3x) + (x+10)
xz_007 [3.2K]

Answer:

7x + 20

I hope I helped :D

Step-by-step explanation:

8 0
3 years ago
a certain number of two digit is three times the sum of its digit and if 45 added to it the digit will be reversed find the numb
bogdanovich [222]
· Author has 184 answers and 67.6K answer views
Let the number be (10 x + y)

Then, 10 x + y = 3 * (x + y) (given)

Or, 10 x + y = 3 x + 3 y

Or, 10 x - 3 x = 3 y - y

Or, 7x = 2 y

Or, x = 2 y / 7 ( Eq. 1)

Also, 10 x + y + 45 = 10 y + x ( given)

Or, 10 x - x = 10 y - y - 45

Or, 9 x = 9 y - 45 ( Eq. 2)

Substituting the value of x from (Eq. 1) in (Eq. 2), we have:

9 * 2 y / 7 = 9 y - 45

Or, (9 y ) - (18 y / 7) = 45

Or, 63 y - 18 y = 315

Or, 45 y = 315

Or, y = 7

From (Eq. 1),

x = 2 * 7 / 7 = 2

So, the number is 10 x + y = (10 * 2) + 7 = (20 + 7) = 27

Answer

Check:

Sum of the digits = 2 + 7 = 9

9 * 3 = 27 ✓

Adding 45 to the number 27, we get 72. So, the digits get reversed.
5 0
3 years ago
A cylindrical soup can has a diameter of 3.6 in. and is 6.4 in. tall. Find the volume of the can.
arsen [322]
<h2>⚘Your Answer:------</h2>

<h3><u>Given</u><u> </u><u>Information</u><u>:</u></h3>

  • <u>Diameter of can</u>:- 3.6 cm
  • <u>Height of</u><u> </u><u>can</u><u>:</u><u>-</u> 6.4 cm

<h3><u>To</u><u> </u><u>Find</u><u> </u><u>Out</u><u>:</u></h3>

  • <u>Volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>Can</u><u>.</u>

<h3><u>Solution</u><u>:</u></h3>

Radius = (Diameter/2)

ㅤㅤㅤㅤ3.6 cm/2

ㅤㅤㅤㅤ1.8 cm

<u>So</u><u>,</u><u> </u><u>Radius</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>soup</u><u> </u><u>can</u><u> </u><u>is</u> 1.8 cm.

Volume øf cylinder = Volume øf can

Volume of cylinder = π r²h

(π = 22/7)

(r = radius = 1.8 cm)

(h = height = 6.4 cm

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 22/7×(1.8 cm)²× 6.4 cm

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 22/7× 3.24 cm² × 6.4 cm

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 22/7 × 20.736 cm³

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= (456.192/7) cm³

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 65.17 cm³

So, the Volume of the soup can is 65.17 cm³

ㅤㅤㅤㅤㅤㅤㅤㅤ⚘Thank You

7 0
2 years ago
Plz help!!!! Number 23
Minchanka [31]

Answer:

 (0 + m)/2, (0 + n)/2.

Step-by-step explanation:

The  x coordinate of the  midpoint must be halfway  between the x coordinates of  A and B, and the y coordinate must be  found in the same way.

So the midpoint is  (0 + m)/2, (0 + n)/2.

7 0
3 years ago
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