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3 years ago

Find the area of the trapezoid below.

Mathematics

1 answer:

Pani-rosa [81]3 years ago

7 0

Answer: 54 cm²

Step-by-step explanation: In this problem, we're asked to find the area of the trapezoid shown. A trapezoid is a quadrilateral with one pair of parallel sides.

The formula for the area of a trapezoid is shown below.

$Area =\frac{1}{2} (^{b} 1 + ^{b}2)h$

The <em>b's</em> represent the bases which are the parallel sides and <em>h</em> is the height.

So in the trapezoid shown, the bases are 6 cm and 12 cm and the height is 6 cm. Plugging this information into the formula, we have $\frac{1}{2} (6 cm +12cm)(6 cm)$ .

Next, the order of operations tell us that we must simplify inside the parentheses first. 6 cm + 12 cm is 18 cm and we have $\frac{1}{2}(18 cm)(6 cm)$ .

$\frac{1}{2} (18 cm)$ is 9 cm and we have 9 cm · 6 cm of 54 cm²

So the area of the trapezoid shown is 54 cm².

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I NEED HELP FOR THIS QUESTION PLSSS

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Solve the triangle A = 2 B = 9 C =8

VARVARA [1.3K]

Answer:

$\begin{gathered} A=\text{ 12}\degree \\ B=\text{ 114}\degree \\ C=54\degree \end{gathered}$

Step-by-step explanation:

To calculate the angles of the given triangle, we can use the law of cosines:

$\begin{gathered} \cos (C)=\frac{a^2+b^2-c^2}{2ab} \\ \cos (A)=\frac{b^2+c^2-a^2}{2bc} \\ \cos (B)=\frac{c^2+a^2-b^2}{2ca} \end{gathered}$

Then, given the sides a=2, b=9, and c=8.

$\begin{gathered} \cos (A)=\frac{9^2+8^2-2^2}{2\cdot9\cdot8} \\ \cos (A)=\frac{141}{144} \\ A=\cos ^{-1}(\frac{141}{144}) \\ A=11.7 \\ \text{ Rounding to the nearest degree:} \\ A=12º \end{gathered}$

For B:

$\begin{gathered} \cos (B)=\frac{8^2+2^2-9^2}{2\cdot8\cdot2} \\ \cos (B)=\frac{13}{32} \\ B=\cos ^{-1}(\frac{13}{32}) \\ B=113.9\degree \\ \text{Rounding:} \\ B=114\degree \end{gathered}$ $\begin{gathered} \cos (C)=\frac{2^2+9^2-8^2}{2\cdot2\cdot9} \\ \cos (C)=\frac{21}{36} \\ C=\cos ^{-1}(\frac{21}{36}) \\ C=54.3 \\ \text{Rounding:} \\ C=\text{ 54}\degree \end{gathered}$

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1 year ago

Identify the domain of the exponential function shown in the following graph: WARNING ITS NOT D

mamaluj [8]

Answer is B.
The x-values of this function are all real numbers greater than or equal to zero.

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3 years ago

Let v⃗ 1=⎡⎣⎢033⎤⎦⎥,v⃗ 2=⎡⎣⎢1−10⎤⎦⎥,v⃗ 3=⎡⎣⎢30−3⎤⎦⎥ be eigenvectors of the matrix A which correspond to the eigenvalues λ1=−1, λ2

kaheart [24]

Answer:

- x as a linear combination :

x = -1 v1+ 0 v2+ 1 v3.

- Transpose Ax = (12, -6, -6)

Step-by-step explanation:

Given v1 = (0 3 3),v2 = (1 −1 0), v3 = (3 0 −3) be eigenvectors of the matrix A which correspond to the eigenvalues λ1 = −1, λ2 = 0, and λ3 = 1, respectively, and let x = (−2 −4 0). Express x as a linear combination of v1, v2, and v3, and find Ax .

To write x as a linear combination of v1, v2, and v3

x = -1 v1+ 0 v2+ 1 v3.

To find Ax

Write A = (0 ......3 ......3 )

...................(1 ......-1 ......0)

...................(3 ......0......-3)

Since transpose x = (-2, 4, 0)

Ax =......... (0 ......3......3 )(-2)

...................(1 ......-1 ......0)(4)

...................(3 ......0......-3)(0)

= (0×-2 + 3×4 + 3×0)

...(1×-2 + -1×4 + 0×0)

.. (3×-2 + 0×4 + -3×0)

As = (12)

....(-6)

Transpose Ax = (12, -6, -6)

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3 years ago

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nikklg [1K]

Answer:

GK=JK

Step-by-step explanation:

SSS congruency is side-side-side congruency. We are given that GH=JH and KH=KH, which are both sides.

For SSS, we need 3 pairs of congruent sides. We already have 2 pairs.

The options are:

<G=<J

<H=<H

GK=JK

the first two options, <G=<J and <H=<H are talking about congruent angles. We don't need to know about congruent angles for SSS

GK=JK is talking about a pair of congurent sides. Then, we would have 3 pairs of congruent sides, satisfying the criteria needed for SSS. Therefore, we must know that GK=JK.

Hope this helps!

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