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MrRa [10]
3 years ago
8

The width of a rectangle is the length minus 3 units. The area of the rectangle is 40 units. What is the width, in units, of the

rectangle?
Mathematics
1 answer:
marusya05 [52]3 years ago
5 0

Width of the rectangle is 5 units

<u>Explanation:</u>

Let length (l) = l units

Given,

width (b) = l-3 units

Area of rectangle = 40 units

We know,

Area of rectangle = l X b

40= l(l-3)\\40=l^{2} - 3l\\l^{2} - 3l -40=0\\l=8units

If l = 8 units then, b = 8-3 units

b = 5 units

Therefore, width of the rectangle is 5 units.

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An algebra book weighs 6 oz less
Mashcka [7]

Answer:

Algebra book weighs 24 oz

Grammar book weighs 15 oz

Step-by-step explanation:

algebra = x and grammar = y

x = 2y-6

5x = 8y

5(2y-6) = 8y

10y - 30 = 8y

2y - 30 = 0

2y = 30

y = 15

x = 2(15)-6

x = 30-6

x = 24

8 0
2 years ago
Simplify the expression cos x cot x+ sin x please select the best answer from the choices provided a.0, b.csc x, c. Tan x, d sec
expeople1 [14]

Answer:

cot x = \frac{cos x}{sin x}

cos x \frac{cos x}{sin x} + sin x

\frac{cos^2 x}{sin x} +sin x

sin^2 x + cos^2 x =1

Solving for cos^2 x we got cos^2 x =1 -sin^2 x and replacing this we got:

\frac{1-sin^2 x}{sin x} +sin x

\frac{1}{sin x} -\frac{sin^2 x}{sin x} +sin x

csc x -sin x + sin x = csc x

And then the best option for this case would be:

b.csc x

Step-by-step explanation:

For this case we have the following expression given:

cos x cot x + sin x

We know from math properties that the definition for cot is cot x = \frac{cos x}{sin x}

If we use this definition we got:

cos x \frac{cos x}{sin x} + sin x

\frac{cos^2 x}{sin x} +sin x

Now we can use the following identity:

sin^2 x + cos^2 x =1

Solving for cos^2 x we got cos^2 x =1 -sin^2 x and replacing this we got:

\frac{1-sin^2 x}{sin x} +sin x

\frac{1}{sin x} -\frac{sin^2 x}{sin x} +sin x

csc x -sin x + sin x = csc x

And then the best option for this case would be:

b.csc x

4 0
3 years ago
A circular disc has a circumference of 16pi meters. if we multiply the radius of the circular disc is by 10, what is the circumf
Flauer [41]

The circumference of the new disc 160Π that is 10 time of old circumference.

Step-by-step explanation:

Given,

Circumference of circular disc = 16Π (pi = Π)

Let, the radius of the circle be 'r'

Formula

The circumference of a circle with r radius = 2 Π r

According to the problem,

2 Π r = 16Π

or, 2r = 16 ( by eliminating the value of Π from both the side)

or, r = 8

Now, we multiply the radius by 10

so, the new radius is 8 X 10 = 80

Now the circumference = 2 Π X 80

= 160Π

Hence, the new circumference also will be 10 times of the older one.

6 0
3 years ago
Please answer this in two minutes
NeTakaya

Answer:

15

Step-by-step explanation:

Use the Pythagorean Thereom:

r^{2} = 9^{2}+12^{2}

r^{2} = 81+144

r^{2} = 225

r= 15

Please mark me as Brainliest!

8 0
3 years ago
The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? 18+12.125π units² 36
andreyandreev [35.5K]

Answer:

18+12.125π units²

Step-by-step explanation:

The diameter of the semicircle can be found by the use Pythagoras theorem.

Δx²+Δy²=d²

Δx=3--1=4

Δy=3--6=9

d²=4²+9²

d=√(16+81)

Area=πr²/2

=π×(√(16+81)/2)²÷2

=[π×(97)/4]/2

=97π/8

=18+12.125π units²

97π/8 is equivalent to 18+12.125π units²

3 0
3 years ago
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