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2 years ago

What is the area of the composite figure?

Mathematics

1 answer:

lana [24]2 years ago

8 0

Hello! :)

$\large\boxed{A = 32.5cm^{2}}$

We can use the following area to solve for the area of the trapezoid pictured:

$A = \frac{1}{2}(b_{1} + b_{2})h$

Where:

h = height

b1 = bottom base

b2 = top base

Plug in the given values:

$A = \frac{1}{2}(9 + 4)(5)$

Simplify:

$A = \frac{1}{2}(65)\\\\A = 32.5 cm^{2}$

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Assume that A ABC= A POR. Which of the following congruence statements are correct? Check all that apply. A. AB = OR B. BE PO C.

yulyashka [42]

For congruence of triangles.

If;

$\Delta ABC\cong\Delta PQR$

Then the corresponding sides and angles will be equal.

$\begin{gathered} AB=PQ \\ BC=QR \\ AC=PR \\ \measuredangle A=\measuredangle P \\ \measuredangle B=\measuredangle Q \\ \measuredangle C=\measuredangle R \end{gathered}$

Only the above congruence statements are true.

Any options that has any of the above congruence statement is true.

3 0

9 months ago

Find the length of an arc of 40° in a circle with an 8 inch radius.

lora16 [44]

The length of an arc is the fraction of its circumference based on the given intercepted angle. This is given by the equation,
L (arc) = (Angle / 360) x 2πr
Substituting the known values,
L (arc) = (40 / 360) x 2π(8 inch) = 16π/9 inch
Thus, the length of the arc is approximately equal to 5.585 inches.

7 0

3 years ago

Read 2 more answers

Find the length of side x in the simplest radical form with a rational denominator.

krok68 [10]

Answer:

$\sqrt{2}$

Step-by-step explanation:

We can use either angle, but I'm going to use the one on the bottom. So, in order to find x, we need to use tangent. One side we know is the adjacent, and the side we don't know is the opposite, therefore we need tangent. Here's the equation:

$tan(45)=\frac{x}{\sqrt{2}}$

Obviously, we can't have a root in our denominator, so we need to get rid of it somehow. Here's how:

We multiply the denominator of the fraction by $\sqrt{2}$ . $\sqrt{2}$ multiplied by itself is simply 2. Try it! We also want to multiply the numerator by $\sqrt{2}$ , but there isn't really a number we can use with that, so we'll just add it to the side. The equation you have now is:

$tan(45)=\frac{x\sqrt{2} }{2}$

Let's try to work this out now. Since the denominator is 2, we have to multiply both sides by it to find x.

$\frac{x\sqrt{2} }{2*2} =x\sqrt{2}$

$tan(45)*2=2$

We can plug 2 in for the x in the numerator now:

$\frac{2\sqrt{2} }{2}$

2 and 2 cancel out, so you get 1 in both the numerator and denominator. That's how we get our answer of $x=\sqrt{2}$

Also, because this is a 45-45-90 triangle, you don't really have to do all that work. If it's a 45-45-90 triangle, both legs should be the same length. :)

7 0

3 years ago

I think of a number. If I divide the sum of 6 and the number by 3,the result is 4 more than one quarter of the number. Find the

Alex17521 [72]

Answer:

Step-by-step explanation:

Let the number be x.

Sum of the number and 6: $6+x$