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3 years ago

What is the area of this figure? ___ units^2

Mathematics

1 answer:

MrRissso [65]3 years ago

7 0

Answer:

Total Area = 42

Step-by-step explanation:

|x| means the positive value of x. So |-5| = 5

Top Triangle

H: The height is the maximum y value from 4 to 2 or (4 - 2) which is 2. The x value for both points is the same (-1) and so the distance is unaffected by the x value.

B: The base line is the x value from -5 to 2. That is a little trickier. You can say it is |-5| + 2 = 7

Area: The formula for the area is 1/2 B * H

Area = 1/2 7*2 = 7 units^2

Rectangle

L = B: The Length of the rectangle = the base of the triangle (7 units.

W: The y value from 2 to |-2| or 2 + 2 = 4

Area: the formula for the area is A = L*W

Area = L*W

Area = 7 *4 = 28 units^2

Bottom Triangle

B: The base of this triangle = B of the top triangle. The numbers are exactly the same.

H: |-4| - | - 2 |

H: 4 - 2

H: 2

Area: The area = 1/2 * 2 * 7 = 7 square units.

Total Area

Total Area = 7 + 28 + 7 = 42

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Pls help out need answers quick

maw [93]

Answer: answer is 8 because -5 + 1 = -4 then + 10 = 4

8 0

3 years ago

What is the derivative of x times squaareo rot of x+ 6?

Dafna1 [17]

Hey there, hope I can help!

$\mathrm{Apply\:the\:Product\:Rule}: \left(f\cdot g\right)^'=f^'\cdot g+f\cdot g^'$
$f=x,\:g=\sqrt{x+6} \ \textgreater \ \frac{d}{dx}\left(x\right)\sqrt{x+6}+\frac{d}{dx}\left(\sqrt{x+6}\right)x \ \textgreater \ \frac{d}{dx}\left(x\right) \ \textgreater \ 1$

$\frac{d}{dx}\left(\sqrt{x+6}\right) \ \textgreater \ \mathrm{Apply\:the\:chain\:rule}: \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx} \ \textgreater \ =\sqrt{u},\:\:u=x+6$
$\frac{d}{du}\left(\sqrt{u}\right)\frac{d}{dx}\left(x+6\right)$

$\frac{d}{du}\left(\sqrt{u}\right) \ \textgreater \ \mathrm{Apply\:radical\:rule}: \sqrt{a}=a^{\frac{1}{2}} \ \textgreater \ \frac{d}{du}\left(u^{\frac{1}{2}}\right)$
$\mathrm{Apply\:the\:Power\:Rule}: \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1} \ \textgreater \ \frac{1}{2}u^{\frac{1}{2}-1} \ \textgreater \ Simplify \ \textgreater \ \frac{1}{2\sqrt{u}}$

$\frac{d}{dx}\left(x+6\right) \ \textgreater \ \mathrm{Apply\:the\:Sum/Difference\:Rule}: \left(f\pm g\right)^'=f^'\pm g^'$
$\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(6\right)$

$\frac{d}{dx}\left(x\right) \ \textgreater \ 1$
$\frac{d}{dx}\left(6\right) \ \textgreater \ 0$

$\frac{1}{2\sqrt{u}}\cdot \:1 \ \textgreater \ \mathrm{Substitute\:back}\:u=x+6 \ \textgreater \ \frac{1}{2\sqrt{x+6}}\cdot \:1 \ \textgreater \ Simplify \ \textgreater \ \frac{1}{2\sqrt{x+6}}$

$1\cdot \sqrt{x+6}+\frac{1}{2\sqrt{x+6}}x \ \textgreater \ Simplify$

$1\cdot \sqrt{x+6} \ \textgreater \ \sqrt{x+6}$
$\frac{1}{2\sqrt{x+6}}x \ \textgreater \ \frac{x}{2\sqrt{x+6}}$
$\sqrt{x+6}+\frac{x}{2\sqrt{x+6}}$

$\mathrm{Convert\:element\:to\:fraction}: \sqrt{x+6}=\frac{\sqrt{x+6}}{1} \ \textgreater \ \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}}{1}$

Find the LCD
$2\sqrt{x+6} \ \textgreater \ \mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \ \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}\cdot \:2\sqrt{x+6}}{2\sqrt{x+6}}$

$Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions$
$\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{x+2\sqrt{x+6}\sqrt{x+6}}{2\sqrt{x+6}}$

$x+2\sqrt{x+6}\sqrt{x+6} \ \textgreater \ \mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c}$
$\sqrt{x+6}\sqrt{x+6}=\:\left(x+6\right)^{\frac{1}{2}+\frac{1}{2}}=\:\left(x+6\right)^1=\:x+6 \ \textgreater \ x+2\left(x+6\right)$
$\frac{x+2\left(x+6\right)}{2\sqrt{x+6}}$

$x+2\left(x+6\right) \ \textgreater \ 2\left(x+6\right) \ \textgreater \ 2\cdot \:x+2\cdot \:6 \ \textgreater \ 2x+12 \ \textgreater \ x+2x+12$
$3x+12$

Therefore the derivative of the given equation is
$\frac{3x+12}{2\sqrt{x+6}}$

Hope this helps!

8 0

3 years ago

vagabundo [1.1K]

Answer:

Step-by-step explanation:

We will use the tangent function since we know the opposite and adjacent sides.

Tangent = opposite/adjacent

Tan(e) = 16/10

Tan(e) = 1.6

Use the inverse tangent function to find the angle.

Arctan (1.6) = 57.9946168

Rounding this we get: 58°

4 0

3 years ago

Read 2 more answers

Estimate. 4,754 dived by 1.9 =

irinina [24]

Answer:

2502.1

Step-by-step explanation:

4754/1.9

= 2,502.1

Hence the andwer is 2502.1

8 0

3 years ago

Solve the system by graphing. 3x+8y=16 3x+8y=-64

Gnesinka [82]

-3x-y=10

4x-4y=8

or

y = -3x - 10

P(0,-10) and P(-2, -4) on this line: Plot and connect with the Line.

y = x - 2

P(0, -2) and (2,0) on this line: Plot and connect with the Line.

P(-2,-4) is the ordered pair that is the solution for this system of EQs

On may CHECK by substituting x= -2 and y = -4 into the EQs of these Lines

Hope this helps!!!

7 0

3 years ago