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4 years ago

A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?

Mathematics

2 answers:

Xelga [282]4 years ago

8 0

Here, Total area of Trapezoid = Area of square in it + Area of Triangle

Area of square = a² = 5² = 25 Ft²

Area of Triangle = 1/2 × b × h = 1/2 × 5 × 3 = 7.5

So, Total area = 25 + 7.5 = 32.5 Ft²

In short, Your Answer would be Option A

Hope this helps!

Iteru [2.4K]4 years ago

6 0

Find the area of the square first.
5x5=25
Now find the area of the triangle.
5x3=15
Since its a triangle we divide 15/2
15/2=7.5

25+7.5= 32.5

Please mark brainliest 3 more to rankup

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The formula for glue says to add 60 mL of hardener to each container of resin. How much hardener should be added to 19 container

Inessa05 [86]

60 mL = 60/1000 L
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1 container of resin = 0.06L
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3 years ago

Solve this quadratic equation by completing the square x^2-8x+10=0

aev [14]

Answer:

x = 4 ± $\sqrt{6}$

Step-by-step explanation:

Given

x² - 8x + 10 = 0 ( subtract 10 from both sides )

x² - 8x = - 10

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = - 10 + 16

(x - 4)² = 6 ( take the square root of both sides )

x - 4 = ± $\sqrt{6}$ ( add 4 to both sides )

x = 4 ± $\sqrt{6}$ ← exact solutions

6 0

3 years ago

Find the value of x² - x+1 when x=√3 -1, in the form a+b√3 where a and b are integers

lidiya [134]

Answer:

$6-3\sqrt{3}$

If you compare this to $a+b\sqrt{3}$ , then $a=6$ and $b=-3$ .

Step-by-step explanation:

We are given $x=\sqrt{3}-1$ and we are asked to find the value of $x^2-x+1$ .

So we will need to find $x^2$ .

$x=\sqrt{3}-1$

Square both sides:

$x^2=(\sqrt{3}-1)^2$

Expand using identity: $(x-a)^2=x^2-2ax+a^2$ .

$x^2=(\sqrt{3})^2-2(\sqrt{3})(1)+1^2$

$x^2=3-2\sqrt{3}+1$

$x^2=4-2\sqrt{3}$

Let's go back to the full $x^2-x+1$ .

$x^2-x+1$

$(4-2\sqrt{3})-(\sqrt{3}-1)+1$

$4-2\sqrt{3}-\sqrt{3}+1+1$

$6-3\sqrt{3}$

If you compare this to $a+b\sqrt{3}$ , then $a=6$ and $b=-3$ .

5 0

4 years ago

4pi/3 find the exact trigonometric ratios for the angle whose radian measue is given

bulgar [2K]

Answer:

All trigonometric ratios.

Step-by-step explanation:

We have to find all the trigonometric ratios.

Given:

$\theta = \dfrac{4\pi}{3} = \pi + \dfrac{\pi}{3}$

Formula:

$\sin(\pi +x) = -\sin(x)\\\cos(\pi +x) = -\cos(x)$

$\sin(\pi + \dfrac{\pi}{3}) = -\sin(\dfrac{\pi}{3}) = -\dfrac{\sqrt{3}}{2}$

$\cos ((\pi + \dfrac{\pi}{3})) = -\cos(\dfrac{\pi}{3}) = -\dfrac{1}{2}$

Formula:

$\tan\theta =\dfrac{\sin\theta}{\cos\theta}\\\cot\theta = \dfrac{1}{\tan\theta}\\\sec\theta = \dfrac{1}{\cos\theta}\\\csc\theta = \dfrac{1}{\sin\theta}$

$\tan(\pi + \dfrac{\pi}{3})= \dfrac{\sin(\pi + \dfrac{\pi}{3})}{\cos(\pi + \dfrac{\pi}{3})}\\\\\tan(\pi + \dfrac{\pi}{3}) = \dfrac{\frac{-\sqrt{3}}{2}}{\frac{-1}{2}} = \sqrt{3}$

$\cot(\pi + \dfrac{\pi}{3}) = \dfrac{1}{\tan(\pi + \dfrac{\pi}{3})} = \dfrac{1}{\sqrt{3}}$

$\sec(\pi + \dfrac{\pi}{3}) = \dfrac{1}{\cos(\pi + \dfrac{\pi}{3})} = -2$

$\csc(\pi + \dfrac{\pi}{3}) = \dfrac{1}{\sin(\pi + \dfrac{\pi}{3})} = -\dfrac{2}{\sqrt{3}}$

8 0

3 years ago

Find the width of a photograph whose length is 8 inches and whose proportions are the same as a photograph that is 18 inches wid

lara [203]

6 inches because 24 is 3 times greater than 8, so you would do 18/3.

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3 years ago