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lyudmila [28]
3 years ago
10

How do I find the area of the isosceles triangle?

Mathematics
1 answer:
Paul [167]3 years ago
5 0
Use the Pythagorean Theorem to find 'h'.

\sf a^2+b^2=c^2

For right triangles, where 'a' and 'b' are the two legs and 'c' is the hypotenuse.

Divide the base by 2 to find the base length of one of the right triangles. 32/2 = 16. Now apply the Pythagorean Theorem:

\sf 16^2+b^2=20^2

Simplify:

\sf 256+b^2=400

Subtract 256 to both sides:

\sf b^2=144

Take the square root of both sides:

\sf b = 12

So the height is 12cm. Apply the formula for the area of a triangle:

\sf A=\frac{1}{2}bh

\sf A=\frac{1}{2}(32)(12)

\sf A=192cm^2
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Christopher earns $5. 80 an hour and time-and-a-half for all hours over 40 hours. How much did he earn the week he worked 44. 5
Monica [59]

Answer: $271.15

Step-by-step explanation:

$5.80 × 40 = 232

Time and a half = $8.70  

Overtime is 4.5 hours

$8.70 × 4.5 = 39.15

$232 + 39.15 = 271.15

6 0
2 years ago
Can someone explain how you do this and not only give me a answer?
german
You plug in 2 for the w and do 17 minus 2 and then you divide that by 3 so ur answer is going to be 17-2 which is 15 and then divide 15 by 3 and you get 5
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90 points!!
Svetllana [295]

Answer:

1) 2w + 2(3w) \leq 112

2) 850w > 300w + 7500

3) The greatest age that Sue could be is 7.

4) The smaller of the two integers is 92.

5) Don needs to earn at least 244 points in the fourth game.

Step-by-step explanation:

1) An rectangle has 2 dimensions: width(w) and length(l)

The perimeter P is:

P = 2w + 2l

The problem states that the length of a rectangle is three times its width. So l = 3w and:

P = 2w + 2(3w)

The perimeter of the rectangle is at most 112 cm. It means that the perimeter can be 112, so the equal sign enters the inequality. So

2w + 2(3w) \leq 112

2)

The problem states that he earns $850 per week in sales. His earnings is modeled by the following equation:

E = 850*w, in which w is the number of weeks.

The problem also states that he spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. So his expenses can be modeled by the following equation

C = 300*w + 7500, in which w is also the number of weeks.

He will make a profit when his earnings are bigger than his expenses, so: When they are equal, there is no profit, so the equal sign does not enter the inequality.

E > C

850w > 300w + 7500

3)

I am going to call Jenny's age x and Sue's age y.

The problem states that Jenny is eight years older than twice her cousin Sue’s age. So

x = 8 + 2y.

The sum of their ages is less than 32, so:

x + y < 32

8 + 2y + y < 32

3y < 24

y < \frac{24}{3}

y < 8

Sue's age has to be less than 8, so the greatest age that Sue could be is 7.

4)

The sum of two consecutive integers is at least 185.

There are two integers with sum of 185, so:

x + y = 185

They are consecutive so:

x = y + 1

Replacing in the sum equation:

y + 1 + y = 185

2y = 184

y = \frac{184}{2}

y = 92

The smaller of the two integers is 92.

5)

The average is the sum of all the scores divided by the number of games. So:

225 = \frac{192 + 214 + 250 + x}{4}

656 + x = 900

x = 900 - 656

x = 244

Don needs to earn at least 244 points in the fourth game.

8 0
3 years ago
the sales tax for an item was $30.10 and it cost $430 before tax. find the sale tax rate. write your answer as a percentage.
timurjin [86]
To find a percentage of a number, multiply by the decimal form of that percentage(20%=0.20). So, take the cost, $430, and multiply by common state sales tax (7% for me)---430 x 0.07 = 30.10  The sale tax rate is 7%.
4 0
3 years ago
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