All categories

2 years ago

What is the area of this composite shape?

Mathematics

1 answer:

guajiro [1.7K]2 years ago

8 0

Step-by-step explanation:

parallelogram area is:h×base

10×14=140

we have two so

140×2=280

traingle is:h×base/2

18-10=8=h

8×14/2=56

56×3=168

168+280=448

You might be interested in

Mrs. Garcia is painting a portion of her wall as shown.

Alexandra [31]

Answer:

Step-by-step explanation:

3 0

2 years ago

A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

kkurt [141]

Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

Volume of box, V= $b^2h$

Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

$\implies 3b^2=18$

$b^2=6$

$b=\pm \sqrt{6}$

$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

7 0

2 years ago

Which inequality is true?

kipiarov [429]

3/4 is greater than 2/3 is the right one. Because 1/2 is more than 1/3. -1/4 is not less than -2/3, and -1 is not greater than 3/4s. I hope it helps

6 0

3 years ago

Kimberly's curtain company is making curtains for a local hotel. She wants each curtain to be 24 inches long. At the fabric stor

lesya692 [45]

Answer: She will need 142 ft of curtain.

Step-by-step explanation:

Hi, first we have to convert the length of the curtain from inches to foot.

Since 1 inch = 1/12ft

For 24 inches:

24 inches x 1/12 = 2 ft

Since the company wants to make 71 curtains, we have to multiply the length of each curtain (2ft) by 71.

2ft x 71 = 142ft

She will need 142 ft of curtain.

Feel free to ask for more if needed or if you did not understand something.

6 0

2 years ago

Read 2 more answers

A circle is centered at the point (5,-4) and passes through (-3,2). The equation of this circle is (x+___)²+(y+___)²=____.

JulsSmile [24]

The equation of a circle is:
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the location of the center and r is the radius. So we need to find h, k, and r. The center is given as (5,-4) so h = 5 and k = -4:
(x-5)^2 + (y-(-4))^2 = r^2
(x-5)^2 + (y+4)^2 = r^2
So we need to find r. Use the distance formula to find the distance between (5,-4) and (-3,2):
r = [(5-(-3))^2+((-4)-2)^2]^1/2
r = [8^2 + (-6)^2]^1/2
r = [64 + 36]^1/2
r = 100^1/2
r= 10
The final equation is:
(x-5)^2 + (y+4)^2 = 10^2

7 0

2 years ago