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3 years ago

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

2 answers:

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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The sum of twice a number and<br> 9 is -25 how do i translate the expression

Marina86 [1]

Answer:

$x+9=-25$

(The solved portion if needed) $x=-34$

Step-by-step explanation:

Let us break down each portion of the phrase: The sum of twice a number and 9 is -25.

The first important part is "The sum". This means that the next two listed numbers (Or expressions) will be added together

Next is, "A number and 9". "A Number" is just an unknown variable. We can just name this x. "And 9" shows the other number that is being added.

At this point we have $x+9$

The next is, "is -25". Is means equals, so this part would be $=-25$

Now we can put these two parts together to get $x+9=-25$

*I'm not certain whether you need to solve it afterwards, so I'll do that here*

$x+9=-25\\\\x=-34$

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3 years ago

Determine whether the lines given in each box are parallel, perpendicular, or neither

Reika [66]

What lines? i dont see any

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3 years ago

The sum of 2 fractions is 5/6. Their difference is 1/2. Their least common denominator is 6. The denominator of one is twice the

valentinak56 [21]

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the first fraction is : $\frac{a}{b}$

Suppose the second fraction is : $\frac{c}{d}$

The sum of both fraction is given as : $\frac{5}{6}$

$\frac{a}{b}+\frac{c}{d}=\frac{5}{6}$ .......................equation (1)

The difference of both fraction is given as : $\frac{1}{2}$

$\frac{a}{b}-\frac{c}{d}=\frac{1}{2}$ .........................equation (2)

Adding equation (1) and equation (2)

$\frac{c}{d} \ will \ be \ cancelled$

$\frac{2a}{b}=\frac{5}{6}+\frac{1}{2}$

making common denominator

$\frac{2a}{b}=\frac{5}{6}+ \frac{3}{6}$

$\frac{2a}{b}=\frac{8}{6}$

Hence,

$\frac{a}{b}=\frac{2}{3}$

Plugging the value of $\frac{a}{b}$ in equation (1)

$\frac{2}{3}+\frac{c}{d}=\frac{5}{6}$

Subtracting $\frac{2}{3}$ in both sides

$\frac{c}{d}=\frac{5}{6}-\frac{2}{3}$

$\frac{c}{d}=\frac{1}{6}$

Hence both fractions are $\frac{2}{3} \ and \ \frac{1}{6}$ ...................Answer

Hope it will help :)

7 0

3 years ago

An item that was selling for 72.00 dollars is reduced to 60.00 dollars. find the percent decrease in price

Blababa [14]

The percentage decrease is 16.667%
72-60=12
12/72 =0.166
0.1666×100%
16.667%

6 0

4 years ago

Julio and his friends go to the movies on 3 different nights . The first night they purchase 4 bags of popcorn and 6 sodas at a

Alexus [3.1K]

Answer

The answer is that is would cost $ to buy 3 bags of popcorn and 4 sodas.

Step-by-step explanation:

To answer this question you will set up a system of equations to represent each scenario. Solve for one variable and substitute that in to the other equation to find the missing value. This example will have you solving for p, the price of popcorn or s for the price of soda.

The equation for the first night would look like where p is popcorn and s is soda:

4p + 6s = 32.70

The equation for the second night would look like where p is popcorn and s is soda:

2p + 4s = 19.30

so first you'd solve the first equation and it would look like this:

4p + 6s = 32.70

-4p -4p *minus 4p from both sides*

6s = -4p + 32.70

/6 /6 *divided by 6 on both sides*

s = 5.45 − 2/3p

Then put (-2/3p + 5.45) into the second equation for S. Then solve which will look like this:

2p + 4 (−2/3p + 5.45)

2p − 8/3p + 21.8 = 19.3

*To write 2p as a fraction with a common denominator, multiply by

3/3*

2p ⋅ 33 − 8/3p + 21.8 = 19.3

*simplify terms*

2p ⋅ 3 - 8/3p + 21.8 = 19.3

−2/3p + 21.8 = 19.3

- 21.8 - 21.8

-2/3p = -2.5

/(-2/3) /(-2/3)

p = 3.5

The price of popcorn is 3.50 and the soda is 5.45 − 2/3(3.5) *filling in 3.50 for P* which equals 3.11

So 3 bags of popcorn and 4 sodas will cost 22.94.

my answer my not be right but the process is. so try to go through it yourself.

4 0

3 years ago