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3 years ago

I need 12/-30 simplified

1 answer:

6 0

Both the numerator and denominator are divisible by 6. You need to find the greatest common factor, or GCF, which in this case is 6. So divide both the top and the bottom by 6 and you get 2/-5, and that is your final answer in simplified form.

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The points A(1, 4), B(5,1) lie on a circle. The line segment AB is a chord. Find the equation of a diameter of the circle.

tangare [24]

Check the picture below.

well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.

bearing in mind that <u>perpendicular lines have negative reciprocal</u> slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.

$\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}$

so, it passes through the midpoint of AB,

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)$

so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}$

4 0

3 years ago

A store sold a total of 21,650 balls. It sold 11,795 baseballs It sold 4,150 fewer basketballs than baseballs. The rest of the b

oksian1 [2.3K]

Answer:

The store sold 2,210 footballs.

Step-by-step explanation:

7 0

3 years ago

He speeds (in MPH) of automobiles traveling in a city are given below:

professor190 [17]

Answer:

Mean speed = 41.3 mph

Step-by-step explanation:

Given that,

The speeds of an automobiles are given below:

20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58

We need to find the mean speed of the cars.

Mean = sum of observations/ no. of observation

$M=\dfrac{20+35+42+52+65+49+24+37+23+41+50+58}{12}\\\\M=41.3$

So, the mean speed of the cars is equal to 41.3 mph.

7 0

3 years ago

An outdoor amphitheater has 100 seats in the front row and each subsequent row has 6 more seats than the previous row. how many

fiasKO [112]

If each row have 6 more seats than the previous, then there is a common difference of 6 seats. This, in turn, becomes an arithmetic progression, with a₁ being 100 and d being 6. Now, we want to know the total number of seats when n = 23, so we need to use the sum of an arithmetic progression form:

$S_n = \frac{n}{2}(2a_1 + (n - 1)d)$
$S_{23} = \frac{23}{2}(2(100) + 22 \cdot 6)$
$S_{23} = \frac{23}{2}(200 + 132)$
$S_{23} = 3818$

Hence, there are 3818 seats in the first 23 rows.

5 0

3 years ago

1. What is the mass of an object if it takes a net force of 25 N to accelerate it at a rate of 0.88 m/s2?

IrinaVladis [17]

Answer:

28.4 kg

Step-by-step explanation:

F = ma

F is 25 N and a is 0.88 m/s^2

25 = 0.88m

Divide both sides by 0.88

m = 28.4 kg

7 0

3 years ago