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Naddik [55]
2 years ago
15

24)The table represents some points on the graph of a linear function. Which function represents the same relationship?

Mathematics
1 answer:
Andru [333]2 years ago
8 0

Answer:

A) D) g(x) = 2x - 8

2) B) y = 3/4x - 1 and y = -4/3x + 9

Step-by-step explanation:

1)

In the table, we have the points

(5, 2)

(7, 6)

(9, 10)

(10, 12)

This seems to be a linear relationship, so let's try that:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1)

If we use the first two points, we get the slope:

a = (6 - 2)/(7 - 5) = 4/2 = 2

if we use the first and last point, we get the slope:

a = (12 - 2)/(10 - 5) = 10/5 = 2

Then we can conclude that this is a linear relationship with a slope equal to 2.

y = 2*x + b

To find the value of b, we can just replace any of the points of the data table in the equation, for example, i will use the point (5, 2).

this means that x = 5, and  y = 2.

2 = 2*5 + b

2 = 10 + b

2 - 10 = b

-8 = b

Then the equation is:

y = 2*x - 8

the correct option is: D) g(x) = 2x - 8

2) Here we have two lines, notice that we can with just looking at the image, know the y-intercept of each line.

The one with a positive slope (grows to the right) has a y-intercept = - 1.

The one with a negative slope (grows to the left) has a y-intercept =  9.

The two options that match this condition are:

B) y = 3/4x - 1 and y = -4/3x + 9

C) y = 3/4x - 1 and y = -3/4x + 9

Where the only difference is the slope of the black line.

so et's check which slope matches that line.

In the graph we can see that it passes through the points:

(0, 9) and the point (6, 1)

Then the slope is:

a = (1 - 9)/(6 - 0) = -8/6 = -4/3

Then the correct option is where the negative slope is -4/3, that one is

B) y = 3/4x - 1 and y = -4/3x + 9

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Answer:

1184

Step-by-step explanation:

Given :

No. of parts made by machine A in 10 minutes = 7

No. of parts made by machine A in 10*6 minutes (1 hour) = 7 * 6 = 42 parts

No. of parts made by machine A in 12 hours as

                                               required in problem = 42 * 12 =  504

______________________________________________________

No. of parts made by machine B in 15 minutes = 17

No. of parts made by machine A in 15*4 =60 minutes (1 hour) = 17 * 4= 68 parts

No. of parts made by machine B in 10 hours as

                                               required in problem = 68 * 10 =  680

______________________________________________________

There fore total no. of parts made by

machine A and machine B  on Monday = 680 + 504 = 1184 (Answer)

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Step-by-step explanation:

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What linear equation is represented by the table? 1
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Answer:

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8 0
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vovikov84 [41]
To solve this problem, we need to first find the dimensions of the side of the blue and purple squares.

We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.

The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.

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What is the solution to -2(8×-4)&lt;2x+5
Monica [59]
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