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3 years ago

Classify each pair of labeled angles as complementary, supplementary, or neither.

Mathematics

1 answer:

Blizzard [7]3 years ago

5 0

Answer:

The angles 53 and 127 are supplementary.

The angles 56 and 34 are complementary.

The angles 67 and 67 are neither.

Step-by-step explanation:

Supplementary angles are two angles that add up to 180 degrees.

Complementary angles are two angles that add up to 90 degrees.

Add the angles found in each choice to get 180, 90, and 134.

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The angle turns through 1/6 of the circle. What is the measure of the

s344n2d4d5 [400]

Answer:

Step-by-step explanation:

A circle is 360 degrees. If we rotate through 1/6 of the circle

360 *1/6 = 60

We rotate through 60 degrees

7 0

4 years ago

A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

olga55 [171]

We know that:

$(x-a)^2+(y-b)^2=r^2$

is an equation of a circle.

When we substitute x and y (from the pairs we have), we'll get a system of equations:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}$

and all we have to do is solve it for a, b and r.

There will be:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\
\begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\
\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\
$

From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

7 0

3 years ago

What is the precision of your measurement of line AB

vodomira [7]

Find the difference (subtract) between the accepted value and the experimental value, then divide by the accepted value. To determine if a value is precise find the average of your data, then subtract each measurement from it.

4 0

4 years ago

Members of a high school club sold hamburgers at a baseball game to raise money. They sold 278 hamburgers. If the buns come in p

Mariulka [41]

The answer, at least what I got, is 17.375 . They'd have to open an eighteenth package because the extra .375 is not in the original package, so I would go with B .

5 0

4 years ago

Read 2 more answers

How does the graph of the function g(x) = 5x + 1 differ from the graph of f(x) = 5*?

elena-14-01-66 [18.8K]

Answer:

C. It is translated up 1 unit.

Step-by-step explanation:

Translations of a function f(x)

To translate a function f(x) a units to the right, we have f(x-a)

To translate a function f(x) a units to the left, we have f(x+a)

To translate a function f(x) a units up, we have f(x) + a

To translate a function f(x) a units down, we have f(x) - a

In this question:

g(x) = 5x + 1

f(x) = 5x

This means that the function g(x) is 1 added to the function f(x), that is, it is translated up 1 units, and the correct answer is given by option c.

7 0

3 years ago