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strojnjashka [21]
3 years ago
13

Line CD passes through points C(3, -5) And D(6, 0). What is the equation of line CD in standard form?

Mathematics
2 answers:
Fynjy0 [20]3 years ago
8 0
Y = mx + b
m = (0 - -5)/(6 - 3) = 5/3
y = 5/3x + b
0 = 5/3(6) + b
b = -10
(y = 5/3x - 10)3
3y = 5x - 30
3y - 5x = -30
5x - 3y = 30
Free_Kalibri [48]3 years ago
7 0

Answer:

5x - 3y = 30

Step-by-step explanation:

First we find the slope of the line using the formula

m=\frac{y_2-y_1}{x_2-x_1}

Using our points, we have

m = (-5-0)/(3-6) = -5/(-3) = 5/3

Next we write the equation using point-slope form.  Using the slope of 5/3 and the second point, we have

y-0 = 5/3(x-6)

y = 5/3(x-6)

Using the distributive property, we have

y = 5/3(x)-5/3(6)

y = 5/3(x)-5/3(6/1)

y = 5/3(x)-30/3

y = 5/3x - 10

We cannot have fractions in standard form.  To deal with this, we will multiply all 3 terms by 3:

3y = 5/3x(3) - 10(3)

3y = 5x - 30

We want x and y on the same side; subtract 5x from each side:

3y-5x = 5x-30-5x

-5x+3y = -30

We want x to be positive; multiply all 3 terms by -1:

5x-3y = 30

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51/25 and 27/4

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Which mathematical statement represents “17 more than a number is 26”?
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17 + x = 26

17 +n = 26

n + 17 = 26


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Please help! ive been stuck on this for so long and i just keep getting frustrated can someone help walkme through this?
bagirrra123 [75]

For firework launched from height 100ft with initial velocity 150ft/sec, equation made is correct

(a) equation will be h(t) = -16t^2+150t+100

(b) Now we have to see when it will land. At land or ground level height h will be equal to 0. So simply plug 0 in h place in equation made in part (a)

0 = -16t^2 + 150t + 100

Now we have to solve this quadratic. We will use quadratic formula method to solve this equation.

t = \frac{-b \pm  \sqrt{b^2-4ac}}{2a}

a = -16, b = 150, c = 100.

Plugging these values in quadratic formula we get

t = \frac{-150 \pm  \sqrt{150^2-4(-16)(100)}}{2(-16)}

t = \frac{-150 \pm  \sqrt{22500+6400}}{-32}

t = \frac{-150 \pm  \sqrt{28900}}{-32}

t = \frac{-150+170}{-32}  = \frac{20}{-32} = -0.625

time cannot be negative so we will drop this answer

then t = \frac{-150-170}{-32}  = \frac{-320}{-32} = 10

So 10 seconds is the answer for this

(c) To make table simply plug various value for t like t =0, 2, 4, 6, 8 till 10. Plug values in equation mad in part (a) and find h value for each t as shown

For t =0 seconds, h = -16(0)^2+150(0)+100 = 100 feet

For t =2 seconds, h = -16(2)^2+150(2)+100 =336 feet

For t =4 seconds, h = -16(4)^2+150(4)+100 = 444 feet

For t =6 seconds, h = -16(6)^2+150(6)+100 = 424 feet

For t =8 seconds,h = -16(8)^2+150(8)+100 = 276 feet

For t =10 seconds, h = -16(10)^2+150(10)+100 = 0 feet

(d) Axis of symmetry is given by formula

x = \frac{-b}{2a}

t = \frac{-150}{2(-16)} =\frac{-150}{-32} = 4.6875

t = 4.6875 is axis of symmetry line

(e) x-coordinate of vertex is again given by formula

x = \frac{-b}{2a}

so t = 4.6875

then to find y coordinate we will plug this value of t as 4.6875 in equation made in part (a)

For t =4.6875, h = -16(4.6875)^2+150(4.6875)+100 = 451.563

so vertex is at (4.6875, 451.563)

(f) As the firework is launched so in starting time is t=0, we cannot have time before t=0 (negative values) practically. Also we cannnot have firework going down into the ground so we cannot have h value negative physically.

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