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Graph the line with the slope -3/4 passing through the point (4,-1)

-Dominant- [34]

Answer:

Step-by-step explanation:

Plot the point (4, -1) in the 4th Quadrant.

The slope (-3/4) tells us what to do next:

With your pencil point initially on (4, -1), move it 4 units to the right, to (8, -1).

With your point initially on (8, -10, move it down 3 units, to (8, -4). Plot (darken) (8, -4).

Draw a line through (4, -1) AND (8, -4)

7 0

3 years ago

A devastating freeze in California’s Central Valley in January 2007 wiped out approximately 75% of the state’s citrus crop. It t

inna [77]

The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

The linear equation of the function is: $g(P) =22.9P +7$ , while its inverse is: $g^{-1}(c) = \frac{c - 7}{22.9}$ .
The domain is from 0% to 100%, while the range is from 7 to 29.9

Given that:

$c = g(P)$

Input and Output quantity

The input quantity is the percentage of frozen citrus crop, while the output quantity is the cost of box of oranges

Linear Function

The given parameters can be written as:

$(P_1,c_1) = (20\%, 11.58)$

$(P_2,c_2) = (80\%, 25.32)$

Calculate the slope (m)

$m = \frac{c_2 - c_1}{P_2 - P_1}$

So, we have:

$m = \frac{25.32 - 11.58}{80\% - 20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

The equation is then calculated using:

$c =m(P - p_1) + c_1$

So, we have:

$c =22.9(P - 20\%) + 11.58$

$c =22.9P - 4.58 + 11.58$

$c =22.9P +7$

So, the function is:

$g(P) =22.9P +7$

The domain and the range

The domain is the possible input value (i.e. possible values of P).

Because P is a percentage, its possible values are 0% to 100%.

Hence, the domain of the function is: $[0\%,100\%]$

The range is the possible output value (i.e. possible values of c).

When P = 0% and 100%

$c = 22.9 \times 0\% + 7 = 7$

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

The meaning of $g^{-1}(12)$

$g^{-1}(12)$ is an inverse equation, where 12 represents the cost of box of oranges.

So, $g^{-1}(12)$ represents the percentage of frozen citrus crop, when the cost is $12.

The inverse formula

We have:

$c =22.9P +7$

Make P the subject

$22.9P = c - 7$

Divide by 22.9

$P = \frac{c - 7}{22.9}$

So, the inverse function is:

$g^{-1}(c) = \frac{c - 7}{22.9}$

This is used to calculate the percentage of frozen citrus crop, when the cost is known.

$g^{-1}(c) = \frac{c - 7}{22.9}$

Substitute 12 for c

$g^{-1}(12) = \frac{12 - 7}{22.9}$

$g^{-1}(12) = \frac{5}{22.9}$

$g^{-1}(12) = 22\%$

Read more about linear equations at:

brainly.com/question/19770987

4 0

3 years ago

For a particular cable,the radius of the base of the inner layer is 2 millimeters (mm) and the radius of the base of the outer l

andrew11 [14]

Answer:

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

π is a constant whose value is 3.14

r represents the radius of the circle.

Considering the inner layer

radius = 2 millimeters

Area of base = 3.14 × 2² = 12.56 mm²

Considering the outer layer,

Radius = 6 mm

Area of base = 3.14 × 6² = 113.04 mm²

Percent of the area of the base of the outer layer that is the area of the base of the inner layer is

12.56/113.04 × 100 = 11.1%

4 0

4 years ago

The area of a rectangle is found by multiplying the base times the height. A rectangle with an area represented by 12x2 + 6x – 8

maria [59]

$\bf \textit{area of a rectangle}\\\\
A=bh~~
\begin{cases}
b=base\\
h=height\\
---------\\
A=12x^2+6x-8\\
h=4x
\end{cases}\implies 12x^2+6x-8=b(4x)
\\\\\\
\cfrac{12x^2+6x-8}{4x}=b\implies \cfrac{12x^2}{4x}+\cfrac{6x}{4x}-\cfrac{8}{4x}=b\implies 3x+\cfrac{3}{2}-\cfrac{2}{x}=b$

7 0

3 years ago

Read 2 more answers

(2g+9h-5)-(6g-4h+2) g=-2 h=5

xxTIMURxx [149]

(2(-2)+9(5)-5)-(6(-2)-4(5)+2)
(-4+45-5)-(-12-20+2)
(45-9)-(-32+2)
36+30
66

3 0

3 years ago

Read 2 more answers