5.9 converted into a decimal

Write the three forms of the line parallel to the line represented by the equation, 8x+3y=11 such that it passes through the poi

Misha Larkins [42]

Answer:

8x + 3y = 57
y = -8/3x + 19
y + 5 = -8/3(x - 9)

Step-by-step explanation:

Given function

8x+3y=11

Line parallel to the given has the same slope and passes through the point

(9, -5)

Determining the equation

8x + 3y = c
8*9 + 3*(-5) = c
c=72 - 15
c = 57

So the function is in standard form

8x + 3y = 57

Converting to slope-intercept form

y = mx + b
3y = -8x + 57
y = -8/3x + 573
y = -8/3x + 19

Point-slope form, using the given point

y - y1 = m(x - x1)
y - (-5) = -8/3(x - 9)
y + 5 = -8/3(x - 9)

6 0

3 years ago

A marching band is performing in a rectangular arrangement, with a width of $w$ people. The length consists of seven less people

Norma-Jean [14]

Answer:

There are 120 people in the marching band.

Step-by-step explanation:

Let no. of people in the band be x.

In the first rectangular arrangement,

Width of rectangle ( $w_{1}$ ) = w people.

Length of rectangle ( $l_{1}$ ) = (w-7) people

Therefore,

no. of people in the band(x) = Area of the rectangle = Product of width and Length

x = width $\times$ length

x = $w\times (w-7)$ (equation 1);

In the second rectangular arrangement,

Width of rectangle ( $w_{2}$ ) = (w-3) people.

Length of rectangle ( $l_{2}$ ) = (w-5) people

Therefore,

no. of people in the band(x) = Area of the rectangle = Product of width and Length

x = width $\times$ length

x = $(w-3)\times(w-5)$ (equation 2);

Therefore, from equation 1 and equation 2 , we get,

$w\times(w-7)=(w-3)\times(w-5)$

$w^{2}-7w=w^{2} - 8w + 15$

Therefore,

w = 15 (equation 3)

From equation 1 and equation 3, we get

x = $15\times(15-7)$

x = 120.

Therefore,

no. of people in the marching band = 120 people

8 0

3 years ago

Calculate the input when the output is n

ozzi

Answer:

You didn't post an image.

Step-by-step explanation:

6 0

3 years ago

Joe would like to paint a rectangular shaped wall. The measures of dimensions of the wall are 8 inches by 4 inches. Every 1 inch

Sergio [31]

Answer:

$90

Step-by-step explanation:

8 + 4 = 12

12 x 3 (3 feet for each inch) = 36

36 x 2.50 (cost per square foot) = $90

3 0

3 years ago

Read 2 more answers

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago