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Alekssandra [29.7K]
2 years ago
7

Please help asap!the problem is in the picture

Mathematics
1 answer:
ladessa [460]2 years ago
8 0

Given:

AB=6\ BC=r,\ CD=r,\ AD=12.

To find:

The value of r.

Solution:

We have,

AB=6\ BC=r,\ CD=r,\ AD=12.

We know that the radius is perpendicular to the tangent at the point of tangency

AD is the tangent and CD is the radius. So, CD is perpendicular to AD at point D, i.e., m\angle D=90^\circ.

Using Pythagoras theorem, we get

AC^2=AD^2+CD^2

(6+r)^2=12^2+r^2

36+12r+r^2=144+r^2

12r=144+r^2-36-r^2

On further simplification, we get

12r=108

r=\dfrac{108}{12}

r=9

Therefore, the value of r is 9.

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Mr. Young is offered an investment opportunity. Kyra says she will invest his money at a 6% simple interest rate over the next 7
gregori [183]

Answer:

$126

Step-by-step explanation:

Given that:

Investment is done as per Simple interest.

Principal = $3000

Time for which the investment is to done = 7 years

Rate of interest = 6%

To find:

Interest earned when the investment matures?

Solution:

Formula for Simple Interest :

Simple\ Interest = \dfrac{PRT}{100}

Where P is the principal amount

R is the Rate of Interest

T is the time for which the investment is made

Putting the given values:

Simple\ Interest = \dfrac{3000\times 6\times 7}{100}\\\Rightarrow Simple\ Interest = \dfrac{12600}{100}\\Simple\ Interest = \$126

Therefore, the answer is:

Interest earned is <em>$126</em>.

8 0
3 years ago
What is the combined weight of all the kittens? Weight of kittens: 1/4 pound: 3 kittens. 3/8 pound: 2 kittens. 1/2 pound: 4 kitt
Naya [18.7K]

Answer:

6 pounds

Step-by-step explanation:

1/4 times 3 = 3/4

3/8 times 2: 6/8 = 3/4

1/2 times 4: 4/2 = 2

5/8 times 4: 20/8 = 2 1/2

3/4 + 3/4 = 6/4 = 1 1/2

2 + 2 1/2 + 1 1/2 = 6 pounds

5 0
3 years ago
Tom earns ​$16 a week mowing lawns. He spends 1 4 of his earnings on lunch and 1 2 of his earnings on music. He saves the rest.
labwork [276]
Tom is in debt, By -26 dollars.
4 0
3 years ago
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A cars value starts at $32,000. After 1 year, it is worth $27,200. What is the decay factor?
notka56 [123]

Answer:

15% × 7 = 1.05

32,000 - 1.05 = 31,998.95

31,998.95 ‐‐‐‐‐> 31,999

$31,999

(If you don't need to simplify, the answer would be $31,998.95, but I did it just incase you do)

Step-by-step explanation:

7 0
3 years ago
The standard golf ball has a mass of 45g. How many golf balls are there in a bag weighing 1.8kg?
Butoxors [25]
This is a working backwards question.
Since the golf ball was 45g, and the bag was 1.8kg,we need to make them the same units.
45g= 0.45kg
1.8kg= 1.8kg

Now that the units are the same, we put it in a calculator.


1.8÷0.45= 4

Therefore, there are 4 golf balls in the bags.
We can check this by doing 4×0.45= 1.8

Hope this helped!

4 0
3 years ago
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