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Oliga [24]
3 years ago
9

Why are equivalent equations important when solving a system using linear combination?

Mathematics
1 answer:
TiliK225 [7]3 years ago
7 0

Answer:

Linear equations are an important tool in science and many everyday applications. They allow scientist to describe relationships between two variables in the physical world, make predictions, calculate rates, and make conversions, among other things. Graphing linear equations helps make trends visible.

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Please help!!!!! <br> Which defines the piecewise function shown?
denis-greek [22]
<h2>Hello!</h2>

The answer is:

The second piecewise function,

f(x)=\left \{ {{-x-2,x

<h2>Why?</h2>

To answer the question, we need to find which piecewise function contains the graphs shown in the picture, we have that first line shown, is decreasing and exists from the negative numbers to 0,  and the line cuts the x-axis and the y-axis at "-2", for the second line shown,  we have that is decreasing but exists from 0 (including it) to the the positive numbers.

So, finding which piecewise satisfies the function shown, we have:

- First piecewise function:

f(x)=\left \{ {{-x-2,x

First line,

We have the first line,

-x-2

The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exists from all the numbers less than 0, to 0, and it cuts the x-axis at -2 and the y-axis at -2.

Second line,

\frac{x}{2}\geq 0

The variable has positive coefficient, meaning that the function (line) is increasing.

Hence, since the second line is not decreasing, the piecewise function is not the piecewise function shown in the picture.

- Second piecewise function,

f(x)=\left \{ {{-x-2,x

First line,

We have the first line,

-x-2

The variable has a negative coefficient (-1), meaning that the function (line) is decreasing, also we can see that the function does exist from all the numbers less than 0, to 0.

Second line,

-\frac{x}{2}\geq 0

The variable has a negative coefficient ((-\frac{1}{2}), meaning the the unction (line) is decreasing, also we can see that the function does exists from 0 (including it) to the positive numbers.

Hence, we have that the correct option is the second piecewise function,

f(x)=\left \{ {{-x-2,x

Note: I have attached a picture for better understanding.

Have a nice day!

3 0
3 years ago
Read 2 more answers
In order to make a specific shade of green paint, a painter mixes 1 1/2 quarts of blue paint, 2 cups of green paint, and 1/2 gal
ella [17]

Answer:

Step-by-step explanation:

In order to make a specific shade of green paint, a painter mixes 1 1/2 quarts of blue paint. Converting 1.5 quarts to cup,

1 quart = 4 cups

1.5 quarts = 1.5 × 4 = 6 cups

She also used 1/2 gallon of white paint. Converting 0.5 gallons to cup,

0.0625 gallons = 1 cup

0.5 gallons = 0.5/0.0625 = 8 cups

This means that the ratio of cups of blue paint to green paint to white paint is 6: 2 :8

Total ratio = 6 +2 + 8 = 16

To make 100 cups of this shade of green,

Cups of blue paint needed = 6/16 × 100 = 37.5 cups

Cups of green paint needed = 2/16 × 100 = 12.5 cups

Cups of white paint needed = 8/16 × 100 = 50 cups

7 0
2 years ago
Find point P that divides segments AB into a 2:3 ratio.
nasty-shy [4]
\bf ~~~~~~~~~~~~\textit{internal division of a line segment}&#10;\\\\\\&#10;A(-3,1)\qquad B(3,5)\qquad&#10;\qquad \stackrel{\textit{ratio from A to B}}{2:3}&#10;\\\\\\&#10;\cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-3,1)=2(3,5)\\\\&#10;-------------------------------\\\\&#10;P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)

\bf -------------------------------\\\\&#10;P=\left(\cfrac{(3\cdot -3)+(2\cdot 3)}{2+3}\quad ,\quad \cfrac{(3\cdot 1)+(2\cdot 5)}{2+3}\right)&#10;\\\\\\&#10;P=\left(\cfrac{-9+6}{5}~~,~~\cfrac{3+10}{5}  \right)\implies P=\left(-\frac{3}{5}~~,~~\frac{13}{5}  \right)
6 0
3 years ago
Tony collected 16.2 pounds of pecans from the trees on his farm. He will give the same weight of pecans to each of 12 friends. H
netineya [11]

Answer:

1.35 pounds each

Step-by-step explanation:

16.2 divided by 12 equals 1.35

6 0
2 years ago
In this circle, the area of sector COD is 50.24 square units.
Bezzdna [24]

Answer:

Radius = 8 units

Length of arc AB = 8.37758 units

Step-by-step explanation:

The sector COD is 1/4 the size of the circle.

the vertex angle is 90° and a circle has 360° at the center.

So the area of sector COD/area of Circle = 90/360 = 1/4

This means the area of the circle is 4 * 50.24 = 200.96 square units

Area of circle = πr² where r is the radius
πr² = 200.96

r² = 200.96/ π = 63.9676 ≅ 64
Therefore r = √64 = 8 units

The circumference of the circle is 2πr = 16π units

arc AB has a vertex angle of 30°.

30°/360° = 1/6

So the length of the arc is 1/6th the circumference of the circle =

(1/6) * 16π  = 2.67π  units or 8.37758 units

3 0
1 year ago
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