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2 years ago

Use long division to find the quotient. Write your answer as a decimal 99 divided by 12

Mathematics

1 answer:

ad-work [718]2 years ago

7 0

Answer:

Please refer to the image

Step-by-step explanation:

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The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

5 0

2 years ago

Find the probability of getting a head when you flip a coin, and then getting a vowel when you draw from a bag of letters with t

lesantik [10]

Answer:

UM I am not sure how you want this but a coin it is 50 50 or 1/2 and with the probability of getting a vowel is 5/26.

Step-by-step explanation:

Pls tell me if I am wrong I have no learned this yet if I am wrong I will edit it to be right.

6 0

3 years ago

Read 2 more answers

Please help me, I will be so thankful

worty [1.4K]

Answer:

Step-by-step explanation:

g(-4) = 4 , x < -2

g(-2) = (x - 1)² ; -2≤x< 1

= (-2-1)²

= (-3)²

g(-2) = 9

g(0) = (x -1)² ; -2 ≤ x < 1

= (0 -1)²

= (-1)²

= 1

8 0

2 years ago

Just the answer please

nordsb [41]

Answer:b is the right choice hopefully dont be mad if it is wrong

Step-by-step explanation:

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2 years ago

Select all the correct answers. Which sequence of transformations proves that shape I is similar to shape II? A. a reflection ac

Scilla [17]

The answer is b hope it helps

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2 years ago