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ryzh [129]
3 years ago
13

Write an equation of the line, in point-slope form, that passes through the two given points.

Mathematics
2 answers:
yuradex [85]3 years ago
8 0
Slope is -10/20=-1/2

y-7=(-1/2)(x+15). answer C
kiruha [24]3 years ago
5 0
\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~{{ -15}} &,&{{ 7}}~) 
%  (c,d)
&&(~{{ 5}} &,&{{ -3}}~)
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{-3-7}{5-(-15)}\implies \cfrac{-3-7}{5+15}

\bf \cfrac{-10}{20}\implies -\cfrac{1}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=-\cfrac{1}{2}[x-(-15)]
\\\\\\
y-7=-\cfrac{1}{2}(x+15)
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How many and what type of solutions does the equation have?
Natali [406]
Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0

As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81

Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2

So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2

A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.

3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.

So 2k^2 = 9 + 3k have two rational solutions (Option B).

Hope this Helps! :)
7 0
3 years ago
Read 2 more answers
In a recent year, 27.9% of all registered doctors were female. If there were 53,700 female registered doctors that year, what wa
Elis [28]

Answer:

The total number of registered doctors was 192,473.

Step-by-step explanation:

This question can be solved using a rule of three.

53700 is 27.9% = 0.279. The total number of registered doctors is x, which is 100% = 1. So

53700 doctors - 0.279

x doctors - 1

0.279x = 53700

x = \frac{53700}{0.279}

x = 192473.11

Rounding to the nearest whole number.

The total number of registered doctors was 192,473.

5 0
3 years ago
25 Points!! The graph represents the first three terms in an arithmetic sequence.
Drupady [299]

Answer:

Step-by-step explanation:

y-1=\frac{4-1}{2-1}(x-1)\\y-1=3(x-1)\\y=3x-3+1\\y=3x-2

b.

an=an-1+3

C.

when x=15

y=3×15-2=45-2=43

a15=43

4 0
3 years ago
Read 2 more answers
Question part points submissions used as a science project, you drop a watermelon off the top of the empire state building, 320
Nataly [62]
We are given a watermelon dropped at free fall from a building 320 meters above the sidewalk. Superman is headed down at 30 meters per second. We are asked to determine how fast is the watermelon going when it passes Superman. To solve for the final velocity of the watermelon, we will use one of the kinematic equations (free fall):

vf = vi + a*t

where vf is the final velocity
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            t is time

we also need to set-up another equation using the distance:

d = vf + vi / 2 * t

(1) 320 m = vf * t /2

(2) vf = 9.8 m/s^2 * t

From here, we have two equations and two unknown, thus we can solve the problem by substitution. 

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8 0
3 years ago
Ramon is interested in whether the global rise in temperature is also showing up locally in his town, Centerdale. He plans to lo
denis-greek [22]

Answer:

d. The random variable is the number of years in which the temperature increased from the previous year.

Step-by-step explanation:

The random variable is the amount of years that have higher average temperatures than its previous year.

As the sample is from 5 years, the random variable can take values from 0 (where none of the years increase their average temperature from its previous year) to 4 (where every year increases the average temperature).

8 0
3 years ago
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