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sashaice [31]
3 years ago
9

1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 24. How old is each

Mathematics
1 answer:
Andre45 [30]3 years ago
5 0

Answer:

a) Let Kim's age be k, then Kim's sister's age is k/2

k+\frac{k}{2}=24

b) k+\frac{k}{2}=24

1\frac{1}{2}k=24

k=16

\frac{k}{2}=8

Kim's age is 16 while her sister's age is 8.

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Find angle D if angle B = 50
Mariana [72]
<h3>Answer:  80 degrees</h3>

============================================================

Explanation:

I'm assuming that segments AD and CD are tangents to the circle.

We'll need to add a point E at the center of the circle. Inscribed angle ABC subtends the minor arc AC, and this minor arc has the central angle AEC.

By the inscribed angle theorem, inscribed angle ABC = 50 doubles to 2*50 = 100 which is the measure of arc AC and also central angle AEC.

----------------------------

Focus on quadrilateral DAEC. In other words, ignore point B and any segments connected to this point.

Since AD and CD are tangents, this makes the radii EA and EC to be perpendicular to the tangent segments. So angles A and C are 90 degrees each for quadrilateral DAEC.

We just found angle AEC = 100 at the conclusion of the last section. So this is angle E of quadrilateral DAEC.

---------------------------

Here's what we have so far for quadrilateral DAEC

  • angle A = 90
  • angle E = 100
  • angle C = 90
  • angle D = unknown

Now we'll use the idea that all four angles of any quadrilateral always add to 360 degrees

A+E+C+D = 360

90+100+90+D = 360

D+280 = 360

D = 360-280

D = 80

Or a shortcut you can take is to realize that angles E and D are supplementary

E+D = 180

100+D = 180

D = 180-100

D = 80

This only works if AD and CD are tangents.

Side note: you can use the hypotenuse leg (HL) theorem to prove that triangle EAD is congruent to triangle ECD; consequently it means that AD = CD.

5 0
3 years ago
Find the x value 4x-28 9x
andriy [413]

Answer: -5.6

Step-by-step explanation:

Simplifying

(4x + -28) = 9x

Reorder the terms:

(-28 + 4x) = 9x

Remove parenthesis around (-28 + 4x)

-28 + 4x = 9x

Solving

-28 + 4x = 9x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9x' to each side of the equation.

-28 + 4x + -9x = 9x + -9x

Combine like terms: 4x + -9x = -5x

-28 + -5x = 9x + -9x

Combine like terms: 9x + -9x = 0

-28 + -5x = 0

Add '28' to each side of the equation.

-28 + 28 + -5x = 0 + 28

Combine like terms: -28 + 28 = 0

0 + -5x = 0 + 28

-5x = 0 + 28

Combine like terms: 0 + 28 = 28

-5x = 28

Divide each side by '-5'.

x = -5.6

Simplifying

x = -5.6

5 0
3 years ago
Write down the 3rd term in the sequence given by: T(n) = n2 + 4 pls explain how to do It plsss
crimeas [40]

Answer:

T(3) = 13

Step-by-step explanation:

If we are trying to find the 3rd term of this <em>specific </em>sequence, then we simply plug in 3 as n.

T(3) = (3)² + 4

T(3) = 9 + 4

T(3) = 13

However, this isn't proper notation for an arithmetic or geometric sequence.

8 0
3 years ago
Read 2 more answers
Find the soultion(s) to the system of equations. Select all that apply
neonofarm [45]

Answer:

(0,-3)

(3,0)

Step-by-step explanation:

The solutions to the system of equations are where the two graphs cross

The first is at x=0 and y=-3

The second is at x=3 and y=0

3 0
3 years ago
A gaming console that is $300 plus 8% tax. What is the final cost of the console? (Round to nearest cent)
Novay_Z [31]

Answer:

It should be 324.

Step-by-step explanation:

7 0
3 years ago
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