What is the quotient of (2x3 – 29x + 13) ÷ (x + 4)?

Write the equation of the line that passes through the points

sesenic [268]

Answer:

$y+5=2(x-3)$ or $y+9=2(x-1)$

Step-by-step explanation:

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the ordered pairs

(3,-5) and (1,-9)

substitute the values

$m=\frac{-9+5}{1-3}$

$m=\frac{-4}{-2}$

$m=2$

step 2

Find the equation in point slope form

$y-y1=m(x-x1)$

Analyze two cases

First case

we have

$m=2$

$point\ (3,-5)$

substitute

$y+5=2(x-3)$

Second case

we have

$m=2$

$point\ (1,-9)$

substitute

$y+9=2(x-1)$

Note: The equation of the line in point slope form varies according to the point you choose, in contrast to the slope-intercept form

6 0

3 years ago

85432.67 Scientific notation

Elina [12.6K]

Answer:

8.543267 × $10^{4}$

I hope this helps!

8 0

3 years ago

*please help word problem* Adam and Barb had a used book sale over the weekend. Adam sold 4 hardcover books and ten paperbacks a

vekshin1

Let us assume charge for a hardcover book = $ h

And charge for a paperback = $ p.

Adam sold 4 hardcover books and 10 paperbacks and earned $64.

So, we can setup an equation by using above statement.

4h + 10p = 64 -------------equation(1)

Barb sold 5 hardcover books and 7 paperbacks and made $58.

So, we can setup another equation by using above statement.

5h + 7p = 58 -------------equation(2)

Let us solve equation(1) and eqation (2) by elimination method.

Multiplying first equation by -5 and second equation by 4 and adding, we get

-20h -50p = -320

20h +28p = 232

___________________

-22p = -88

Dividing both sides by -22, we get

-22p/-22 = -88/-22

p=4.

Plugging p=4 in first equation.

4h + 10(4) = 64

4h +40 =64

Subtracting 40 from both sides, we get

4h = 24.

Dividing both sides by 4, we get

4h/4 = 24/4

h=6.

Therefore, they charge $6 for a hardcover and $4 for a paperback.

3 0

3 years ago

Mrs Vargas is 4 years less than 4times her daughter anas age. Mrs Vargas son Leo is 3years more than two times Ana's age.If Ana

shusha [124]

Answer: 2a - 7

Step-by-step explanation:

Ana: a

Mrs Vargas: 4a - 4

Leo: 2a + 3

Mrs Vargas - Leo

= (4a - 4) - (2a + 3)

= 4a - 4 -2a - 3

= 2a - 7

5 0

3 years ago

Linda can bicycle 48 miles in the same time as it takes her to walk 12 miles. She can ride 9 mph faster than she can walk. How f

Marrrta [24]

Answer:

$\frac{48}{r+9}=\frac{12}{r}$

Step-by-step explanation:

Let r represent Linda's walking rate.

We have been given that Linda can ride 9 mph faster than she can walk, so Linda's bike riding rate would be $t+9$ miles per hour.

$\text{Time}=\frac{\text{Distance}}{\text{Rate}}$

We have been given that Linda can bicycle 48 miles in the same time as it takes her to walk 12 miles.

$\text{Time while riding}=\frac{48}{r+9}$

$\text{Time taken while walking}=\frac{12}{r}$

Since both times are equal, so we will get:

$\frac{48}{r+9}=\frac{12}{r}$

Therefore, the equation $\frac{48}{r+9}=\frac{12}{r}$ can be used to solve the rates for given problem.

Cross multiply:

$48r=12r+108$

$48r-12r=12r-12r+108$

$36r=108$

$\frac{36r}{36}=\frac{108}{36}$

$r=3$

Therefore, Linda's walking at a rate of 3 miles per hour.

Linda's bike riding rate would be $t+9\Rightarrow 3+9=12$ miles per hour.

Therefore, Linda's riding the bike at a rate of 12 miles per hour.

7 0

3 years ago