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3 years ago

What is the measure of angle 3, in degrees, in the figure shown?

Mathematics

2 answers:

yanalaym [24]3 years ago

8 0

Answer:

38 degrees.

Step-by-step explanation:

There are 180 degrees in a triangle, so

m<1 = 180 - (43 + 74)

= 180 - 117

= 63 degrees.

m < 2 = m < 1 ( opposite angles) so

m < 2 = 63 degrees.

Finally, m < 3 = 180 - (63 + 79)

== 180 - 142

= 38 degrees.

Svetllana [295]3 years ago

7 0

Answer:

38 degrees

Step-by-step explanation:

assuming angles 1 and 2 are the same, you can get 1 by adding 74 and 43 to get 117 and 180-117 is 63. then do 63+79 to get 142. 142+38=180

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Is the point (3, -2) a solution to the following system of equations? How do you know?

iris [78.8K]

Answer:

YES

Step-by-step explanation:

Any straight line can be represented by an equation of the form

Y = mX + b

where m is the slope and b is the Y intercept, so these two equations are lines. The only solution is where the two lines cross, so must satisfy both equations. Plugging in 3 for X and -2 for Y we get

Y = -3X + 7

-2 = -3(3) + 7

-2 = -9 + 7

-2 = -2 True

AND,

Y = 2X - 8

-2 = 2(3) - 8

-2 = 6 - 8

-2 = -2 True

So since both are true, yes (3, -2) is the solution.

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3 years ago

A water hose had filled up 1⁄3 of a pool after 1⁄2 of an hour. At this rate, how many hours would it take to fill the pool?

Vlad1618 [11]

$\huge{ \rm{Question:}}$

A water hose had filled up 1⁄3 of a pool after 1⁄2 of an hour. At this rate, how many hours would it take to fill the pool?

$\huge{ \rm{Answer:}}$

It takes 1.5 hours or 1 hour and 30 min. to fill the pool.

Step-by-step explanation:

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2 years ago

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The volume of an oblique pyramid with a square base is V units3 and the height is h units. Which expression represents the area

givi [52]

Answer:

Area of the base of the pyramid = V/h

Step-by-step explanation:

Mathematically, we know that the volume of the pyramid can be calculated by multiplying the area of the base by the height of the pyramid

Now using the variables in the question;

V = area of base * height of pyramid

Area of base = V/height of pyramid

Area of base = V/h

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3 years ago

Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.

sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

$\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ =I.

First, we have to identify the matrix I. As it was said, the matrix is the identiy matrix, which means

I = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

So, $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ · X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Isolating the X, we have

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]$ - $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Resolving:

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]$

X· $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ = $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X= $\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ ⁻¹· $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

$\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]$ · $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a= $\frac{2}{11}$ ; b= $\frac{7}{33}$ ; c= $\frac{-1}{11}$ and d= $\frac{-3}{11}$ . Substituting:

X= $\left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11} \end{array}\right]$ · $\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]$

Multiplying the matrices, we have

X= $\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11} \end{array}\right]$

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3 years ago

Which is greater, 2 miles or 1,000 yards? How much greater? Explain. Of 2 miles and 1,000 yards, _____ is greater. Since 2 miles

skelet666 [1.2K]

Answer:

yards

Step-by-step explanation:

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3 years ago

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