MATHEMATICS MIDDLE SCHOOL

A central angle of a circle measures 1.2 radians, and the length of the related intercepted arc measures 6 cm. What is the diameter of the circle?

Answers

Answer 1

Answer:

Answer:

The diameter of the circle is 10 cm.

Step-by-step explanation:

A central angle of a circle measures 1.2 radians, and

The length of the related intercepted arc measures 6 cm.

The arc length formula is given by:

$s\:=\:r\theta$

where

$r$ is the radius of the circle

$\theta$ is the central angle in radians

First lets find r,

$\:(s)/(\theta \:)\:=\:r$

$(6)/(1.2\:)\:=\:r$ ∵ s = 6 cm and $\theta$ = 1.2 radians

$\:r\:=\:5\:cm$

Diameter 'd' is 2r.

$d\:=\:2r$

$d\:=\:2\left(5\right)$

$d = 10$ cm

Therefore, the diameter of the circle is 10 cm.

Answer 2

Answer:

Answer:

Its 10 cm

Step-by-step explanation:

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Please help!!!!!!!!!!!!

Answers

Answer:

yes they are inverserve of each other

Step-by-step explanation:

f(x) = y just for say

y=3x+9

switch the x and y value and solve for y

x=3y+9

x-9=3y

(x-9)/3 = y

inverserve of f(x) is g(X)

and now g(x) = y

y= (x-9)/3

switch x and y and solve for y

x=(y-9)/3

3x= y-9

3x+ 9 = y

inverserve of g(x) is f(X)

Carleen Bailey works at a boutique eight hours a day, earning $9.48 an hour. She is asked to work two additional hours at time and a half to help prepare for an incoming shipment. How much will she earn for these two hours of overtime?

Answers

Answer:

The correct answer is $23.70.

Step-by-step explanation:

9.48 times 2.5 is 23.7

Final answer:

Carleen Bailey would earn $28.44 for the two hours of overtime she worked. She earns 1.5 times her normal hourly wage for overtime hours.

Explanation:

Carleen Bailey earns $9.48 for each regular hour she works. When she works overtime, she earns 1.5 times her normal rate for each additional hour. That means her overtime rate is $9.48 * 1.5 = $14.22 per hour. Therefore, if she works 2 hours of overtime, she will earn $14.22 * 2 = $28.44 in total for the overtime hours.

Learn more about overtime pay here:

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PLSSSS HELP ITS DUE TODAY!!!!!

Answers

Answer:

Both Jules' and Lauren's equations are correct because they have slopes that are the negative reciprocal of the slope of the given line, making them perpendicular to the given line.

Step-by-step explanation:

Let's reevaluate the equations based on the corrected given line equation:

$\sf y - 2 = (1)/(5)(x - 3)$

The given line equation is in point-slope form: $\sf \boxed{\sf y - y_1 = m(x - x_1)}$ , where m is the slope.

Given line equation: $\sf y - 2 = (1)/(5)(x - 3)$

While comparing, we get

$\textsf{The\underline{ slope (m) }of the given line is }(1)/(5)$

For a line to be perpendicular to the given line, its slope must be the negative reciprocal of the slope of the given line.

The negative reciprocal of $\sf (1)/(5)$ is $\sf -5.$

Now let's check the slopes of the equations provided by Jules and Lauren:

1. Jules' equation: $\sf y = -5x + 1$

The slope of Jules' equation is -5, which matches the negative reciprocal of the slope of the given line.

2. Lauren's equation: $\sf y = -5x + 7$

The slope of Lauren's equation is also -5, which again matches the negative reciprocal of the slope of the given line.

Both Jules' and Lauren's equations have a slope of -5, which is the negative reciprocal of the slope of the given line $(1)/(5)$ .

Therefore, both equations are correct and satisfy the condition of being perpendicular to the given line $\sf y - 2 = (1)/(5)(x - 3)$

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

$y-2=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}(x-3)\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\n \cline{1-1} \n y-y_1=m(x-x_1) \n\n \cline{1-1} \end{array} \n\n[-0.35em] ~\dotfill$

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{1}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{1} \implies -5}}$

so ANY line that is perpendicular to that equation above, will have a slope of -5, so any of these are all perpendicular to it

$\begin{array}{llll} \stackrel{ Jules }{y=-5x+1} \n\n\n \stackrel{ Lauren }{y=-5x+7} \n\n\n y=-5x+999999999 \n\n\n y=-5x-93789 \end{array}\hspace{5em} \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\n \cline{1-1} \n y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \n\n \cline{1-1} \end{array}$

-4x -30 < -6
X > -6
X > 9
X < 9
X < -6

Answers

Answer:X <9

Step-by-step explanation:

What is 10 to the third power times ten

Answers

10 to the 3rd power will be 1,000

It is ten-thousand (10,000) because you do this: 10*10*10*10 the first three tens being the exponents and the fourth one being the last ten.

Does anyone know how to do this

Answers

Answer:

m+n=140

Step-by-step explanation:

While it may seem you need to find the measure of m and n, you don't. Looking at the angle with measure of 40 degrees you can see inside the triangle that the top angle is congruent to the angle of 40 degrees. Now that you know that the top of the angle is 40 degrees then knowing a triangle is 180 degrees total you can infer that m+n=140 because adding 140 to 40 is also 180.

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