What is five million four thousand three hundred in standard form

. A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $24,700

lozanna [386]

Answer:

1) P(x) =14400x+10300 2)y=-4x+19 3) $y=\frac{-2x}{3} -14$ 4) x=-11

(Please check the pictures for better understanding)

Step-by-step explanation:

1) Firstly, let's organize the data. Let the dependent variable x be the years, and the Range P(x) the Profit. So arranging these linear functions y=ax+b and plugging the coordinates for each point (1, 24700) and (4, 67900). Goes:

24,700=x+b

67,900=4x +b

1.1)Solving for b, this Linear System of Equation by the Addition Method goes:

$24,700=x+b*(-4)\\67,900=4x+b\\----------\\-98,800=-4x-4b\\67,900=4x+b\\ -----------\\-30900=-3b\\\frac{3b}{3} =\frac{30900}{3}\\ b=10300$

1.2) Now, let's find the slope based on those two points (1, 24700) and (4, 67900) and using the formula to find the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{67900-24700}{4-1}\\ m=\frac{43200}{3}\\ m=14400$

So now we can write this Linear Equation for the Profit:

P(x) =14400x+10300

2) An equation of the line perpendicular to 4y=x-8 has a slope equal to $m_{2}$ =- $\frac{-1}{m_{1}}$ the line. In this case, an equation perpendicular to 4y=x-8 .

Rearranging the given equation of the line 4y=x-8 goes:

$y=\frac{x}{4} -\frac{8}{4} \\ y=\frac{x}{4}-2$

2.1) The slope of this new line is equivalent to m=-4 since -4 is opposite inverse value for the slope of its perpendicular line (1/4).

If the line passes through the point (6,-5), then this point already belongs to this line.

Then, we can write.

-5=-4(6)+b

-5=-24+b

-5+24=-24+24+b

b=19

Now we can write the function:

y=-4x+19

3) Firstly, let's rearrange the equation. Into a General Equation of the Line y=ax+b

2x+3y=5

-2x+2x+3y=5-2x

3y=5-2x

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

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

3.2) Let's find out b, the linear coefficient by plugging the coordinates of the point (-3,-8).

Also, Parallel lines have the same value for the slope such as $m_{1}=m_{2}$

-8=-3(-2/3)+b

-8=2+b

-8-2=2-2+b

b=-10

Then the equation of this parallel line is:

$y=\frac{-2x}{3} -10$

4) Now on this last question, we have to find an equation of the line through the point (-11,-4) perpendicular to another line y=15

Suppose the slope of the first line is $m_{1}$ and the value of the slope of its perpendicular is $m_{2}=\frac{-1}{m_{1}}$

y=15 is a horizontal line with slope equals zero, we can rewrite it as y=0x+15.

Then the slope is zero for horizontal lines.

A perpendicular line to a horizontal line is a vertical one.

In addition to this, a vertical line passes through only one point in the x-axis. Then, there is no horizontal variation. This leads the formula of a slope to an undefinition for Real Set.

$m=\frac{y_{2}-y_{1}}{0}$

The only perpendicular line which passes through the point (-11,-4) to y=15 is the line x=-11.

7 0

3 years ago

The school band is scheduled to march in the annual parade, but the band’s starting point is changed the day before the parade.

sattari [20]

D. 40

follow the pattern

1 band director calls 3 members. = 4

Each member calls 3 more members 3(3) = 9

Then each of those 9 call 3 more members 9(3) = 27

Add them up

4+9+27 = 40

3 0

4 years ago

At a dog park , there are 10 black dogs, 5 brown dog, 2 white dog, and 12 multi color dogs

Sophie [7]

What question are you trying to ask?

5 0

3 years ago

Read 2 more answers

What are prime and composite numbers

alexgriva [62]

Answer:

A prime number is a number ( greater than 1) and it cannot be found/formed by multiplying two smaller numbers.

A composite number is a positive number/integer that can be found/formed by multiplying two smaller numbers/integers.

Hope this helps! Have a great day/night! :)

8 0

3 years ago

Tell me if I'm right, 10 points on the line

Llana [10]

<h3>Answer: Choice F) 1</h3>

=============================================

Explanation:

x^2+8x+7 factors to (x+1)(x+7)

x^2+4x-21 factors to (x-3)(x+7)

Therefore, the numerator (x^2+8x+7)(x-3) updates to (x+1)(x+7)(x-3)

The denominator (x^2+4x-21)(x+1) updates to (x-3)(x+7)(x+1)

We have three pairs of terms that will cancel between the numerator and denominator. The (x+1) terms pair up and cancel out, so do the (x+7) terms and also the (x-3) terms as well. Everything cancels out. The only thing left is 1 because x/x = 1 where x is nonzero. We can have a more complicated expression replace x to get the same basic idea. This is what I mean by "canceling".

5 0

4 years ago

Read 2 more answers