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Katena32 [7]
1 year ago
15

Given the equation y=2x+3, write a second equation that would create an independent consistent linear system

Mathematics
1 answer:
STALIN [3.7K]1 year ago
3 0

Two equations will be called independent if their graphs touch only on one point (they have one solution for the x-value and one solution for the y-value), and two equations will be dependent if they touch at every point (there is an infinite number of solutions).

This definition of independent and dependent equations is shown in the following diagram. Consider that there are two lines, one red line and one blue line:

They are independent if they touch only on one point and dependent if they touch at every point (they are the same line).

In our case, we are asked to write an equation in order to create an independent consistent linear system.

Note: Consistent means that the system has a solution.

First, we graph the given equation:

y=2x+3

There are many different equations that will form an independent consistent linear system with this equation.

We are going to choose the following line equation:

y=-x+1

Because when we graph this equation next to the previous line:

We can see that they touch at one point, thus there is a solution and the system is independent --> we have created an independent consistent linear system.

Answer:

y=-x+1

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Sally Reynolds sells real estate along the coastal area of Northern California. Below are her total annual commissions between 2
tatiyna

Answer:

Mean = $229.32

Median = $231.15

Mode = $268.4

Step-by-step explanation:

Mean = the average.

The average is the sum of variables divided by the number of variables.

x = each variable

N = number of variables = 11

Average = (Σx)/N = (236.09 + 204.43 + 253.82 + 268.4 + 231.15 + 205.7 + 262.18 + 162.77 + 268.4 + 224.45 + 205.17)/11

Mean = 2522.56/11 = $229.32

b) Median is the value that falls at the middle of the data set if all the variables are arranged in ascending or descending order.

So, to find the Median, we first arrange the variables in ascending order.

162.77

204.43

205.17

205.70

224.45

231.15

236.09

253.82

262.18

268.4

268.4

Since there are 11 variables, the Median is the number that falls at the middle of the distribution, that is, at the sixth position.

Median = $231.15

c) Mode is the number that appears the most in a distribution.

In this distribution, only 268.4 appears more than once.

Hence, the more is $268.4

8 0
3 years ago
Please Answer!!!!
ExtremeBDS [4]

First mug holds the most

<em><u>Solution:</u></em>

Given that,

You are choosing between two mugs

<em><u>The volume of cylinder is given as:</u></em>

V = \pi r^2h

Where,

r is the radius and h is the height

<em><u>One has a base that is 5.5 inches in diameter and a height of 3 inches</u></em>

radius = \frac{diameter}{2}

Therefore,

r = \frac{5.5}{2}\\\\r = 2.75

Also, h = 3 inches

<em><u>Thus volume of cylinder is given as:</u></em>

V = \pi \times 2.75^2 \times 3\\\\V = 3.14 \times 22.6875\\\\V = 71.23875 \approx 71.24

Thus first mug holds 71.24 cubic inches

<em><u>The other has a base of 4.5 inches in diameter and a height of 4 inches</u></em>

Radius = \frac{4.5}{2}\\\\r = 2.25

h = 4 inches

Therefore,

V = 3.14 \times 2.25^2 \times 4\\\\V = 3.14 \times 20.25\\\\V = 63.585

Thus the second mug holds 63.585 cubic inches

On comparing, volume of both mugs,

Volume of first mug > volume of second mug

First mug holds the most

8 0
4 years ago
How do you solve this (5/6)(5/6)
Vikentia [17]

Answer:

25/36

Step-by-step explanation:

Use the top top, bottom bottom method.

5*5 = 25

6*6 = 36

6 0
3 years ago
Read 2 more answers
Can someone please help!?
bogdanovich [222]

Answer:

II

Step-by-step explanation

hope that helped

7 0
3 years ago
The rule (x, 3/4y) is applied to a polygon. Is the image similar to the original polygon? Explain.
Mnenie [13.5K]
Yes.  The new polygon is 3/4 the size of the old one.
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4 years ago
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