All categories

3 years ago

Which of the following represents 3x-5y+10=0 written in slope-intercept form?

Mathematics

1 answer:

taurus [48]3 years ago

5 0

For this case we have that by definition, the equation of a line in the slope-intercept form is given by:

$y = mx + b$

Where:

m: Is the slope

b: Is the cut-off point with the y axis

We have the following equation:

$3x-5y + 10 = 0$

We manipulate algebraically:

We subtract 10 from both sides of the equation:

$3x-5y = -10$

We subtract 3x from both sides of the equation:

$-5y = -3x-10$

We multiply by -1 on both sides of the equation:

$5y = 3x + 10$

We divide between 5 on both sides of the equation:

$y = \frac {3} {5} x + \frac {10} {5}\\y = \frac {3} {5} x + 2$

Thus, the equation in the slope-intercept form is $y = \frac {3} {5} x + 2$

Answer:

$y = \frac {3} {5} x + 2$

You might be interested in

4(1-x)+2x=-3(x+1 solve for x

ipn [44]

Answer:

Step-by-step explanation:

6 0

3 years ago

Anyone help me please?

solmaris [256]

For the first one false false and the second on is true true

4 0

2 years ago

Read 2 more answers

If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?

lys-0071 [83]

Answer:

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

$3x^2-(3k-2)x-(k-6) \text{ with }k=2$ :

$3x^2-(3\cdot 2-2)x-(2-6)$

$3x^2-4x+4$

I'm going to solve $3x^2-4x+4=0$ for x using the quadratic formula:

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

$\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}$

$\frac{4\pm \sqrt{16-16(3)}}{6}$

$\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}$

$\frac{4\pm 4\sqrt{-2}}{6}$

$\frac{2\pm 2\sqrt{-2}}{3}$

$\frac{2\pm 2i\sqrt{2}}{3}$

Let's see if uv=u+v holds.

$uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}$

Keep in mind you are multiplying conjugates:

$uv=\frac{1}{9}(4-4i^2(2))$

$uv=\frac{1}{9}(4+4(2))$

$uv=\frac{12}{9}=\frac{4}{3}$

Let's see what u+v is now:

$u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}$

$u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}$

We have confirmed uv=u+v for k=2.

4 0

3 years ago

Hampsphire hill is 87/9 meters tall. Write its height as a mixed number.

Umnica [9.8K]

I think it is 9 6/9 but im not quite sure .

4 0

3 years ago

Read 2 more answers

Please help explanation if possible

Eva8 [605]

Answer:

612 adults

361 students

Step-by-step explanation:

To solve this question, set two equations:

Let x be number of adults and y be number of students.

As there are in total 937 people, the equation would be the sum of both adults and children:

$x+y=937$

$x=937-y$ ...... ( 1 )

As the total sale amount is $1109, the equation would be to add up the ticket fee:

$2x+0.75y=1,109$ ...... ( 2 )

Put ( 1 ) into ( 2 ):

$2(937-y)+0.75y=1,109$

$1874-2y+0.75y=1,109$

$-1.25y=-765$

$y=763/1.25$

$y=612$

Put y into ( 1 ):

$x=973-612$

$x=361$

Therefore there are 612 adults and 361 students.

5 0

3 years ago