All categories

3 years ago

1. Find the area of the composite figure to the nearest hundredth.

Mathematics

2 answers:

balandron [24]3 years ago

8 0

Answer:

1. 745.31 mm²
2. 426.96 km²

Step-by-step explanation:

We can separate the figure into 3 parts and sum the areas.

Semicircle with radius 12.5 mm:

A = 1/2(πr²) = 1/2(3.14*12.5²) = 245.31 mm²

Rectangle with sides 12.5 mm and its double size:

A = 12.5*(2*12.5) = 312.5 mm²

Triangle with height 12.5 mm and base 30 mm:

A = 1/2*(55 - 2*12.5)*12.5 = 187.5 mm²

Sum of the three:

245.31 + 312.5 + 187.5 = 745.31 mm²

The shaded region is the difference of the areas of the triangle and the circle

Triangle:

A = 1/2*27*40 = 540 km²

Circle:

A = πr² = πd²/4 = 3.14*12²/4 = 113.04 km²

Shaded region:

540 - 113.04 = 426.96 km²

Leto [7]3 years ago

6 0

Answer:

#1: 751.56 mm²

#2: 477 km²

Step-by-step explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

12.5 squared is 156.25.

1/2(3.14 * 156.25)

Multiply 3.14 by 156.25 to get 490.625.

1/2(490.625)

Divide 490.625 by 2 to get 245.3125.

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

Multiply 12.5 by 25 to get 312.5.

312.5 + 1/2(31 * 12.5)

Multiply 31 by 12.5 to get 387.5.

312.5 + 1/2(387.5)

Multiply 1/2 by 387.5 to get 193.75

312.5 + 193.75

Add 312.5 and 193.75 to get 506.25.

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

Multiply 40 by 27 to get 1080.

1/2(1080)

Multiply 1/2 by 1080.

590 km² for the triangle.

Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

590 - 113.04

476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².

You might be interested in

Empirical rule (statistics)Help please!!!

emmasim [6.3K]

The empirical rule you're referring to is the 68-95-99.7 rule, which asserts that for a normal (bell-shaped) distribution, approximately 68% of the distribution lies within 1 standard deviation of the mean; 95% lies within 2 standard deviations of the mean; and 99.7% lies within 3 standard deviations of the mean.

Let $X$ be the random variable denoting vehicle speeds along this highway. We want to find $P(61$ . To use the rule, we need to rephrase this probability in terms of the mean and standard deviation.

Notice that $61=70-9=70-3\cdot3$ , and $79=70+9=70+3\cdot3$ . In other words, 61 and 79 both lie exactly 3 standard deviations away from the mean, so $P(61$ .

8 0

3 years ago

16. [-12 Points]

Cerrena [4.2K]

Answer:

Answer: A. 5:4 Step-by-step explanation: Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 16. So the ratio is 20:16 which is simplified to = 20 and Remaining 5:4.

8 0

3 years ago

If 7 litres of petrol cost $14.70 ,calculate the cost of 15 litres of petrol Kindly answer

erastovalidia [21]

Answer:

The cost of 15 liters is $31.50

Step-by-step explanation:

1. Find the price for 1 liter of petrol.

Divide the cost by the number of liters:

$14.70 / 7 = $2.10 per liter.

2. Multiply the price for 1 liter by the new number of liters, 15.

$2.10 per liter x 15 liters = $31.50

3 0

3 years ago

What is the area of the figure shown?

musickatia [10]

Check the picture below.

now, we're making an assumption that, the two blue shaded region are equal in shape, and thus if that's so, that area above the 14 is 6 and below it is also 6, 14 + 6 + 6 = 26.

so hmm if we simply get the area of the trapezoid and subtract the area of the yellow triangle and the area of the cyan triangle, what's leftover is what we didn't subtract, namely the shaded region.

$\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=15\\ a=14\\ b=26 \end{cases}\implies A=\cfrac{15(14+26)}{2}\implies A=300 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\stackrel{trapezoid}{300}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(26)(9)}~~ - ~~\stackrel{cyan~triangle}{\cfrac{1}{2}(15)(6)}} \\\\\\ 300~~ - ~~117~~ - ~~45\implies 138\qquad \textit{blue shaded area}$

8 0

2 years ago

Suppose m = 2 + 6i, and | m + n | = 3√10, where n is a complex number.

Ksju [112]

Answer: a) √50

b) n = 1 + 7i

Step-by-step explanation:

first, the modulus of a complex number z = a + bi is

IzI = √(a^2 + b^2)

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

n = a + bi

Im + nI = 3√10

Im + n I = √(a^2 + b^2 + 2^2 + 6^2)= 3√10

= √(a^2 + b^2 + 40) = 3√10

a^2 + b^2 + 40 = 3^2*10 = 9*10 = 90

a^2 + b^2 = 90 - 40 = 50

√(a^2 + b^2 ) = InI = √50

The modulus of n must be equal to the square root of 50.

now we can find any values a and b such a^2 + b^2 = 50.

for example, a = 1 and b = 7

1^2 + 7^2 = 1 + 49 = 50

Then a possible value for n is:

n = 1 + 7i

6 0

3 years ago