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3 years ago

The table represents a linear function. find the values of a,b, and c. Show your work.

Mathematics

1 answer:

viva [34]3 years ago

6 0

Answer:

The values of a , b , c are ⇒ a = 1 , b = 10 , c = 9

Step-by-step explanation:

* Lets describe the meaning of the linear function

- Linear function is represented by a line graphically

- The equation of the line is y = mx + c, where m is the slope

of the line and c is the y-intercept (the point of intersection

between the line and the y-axis is (0 , c))

- m = change of y/change of x

- We can find m from any two points on the line

* Lets use m to find a, b and c

- Use the points (3 , 8) and (5 , 9) to find m

∵ m = (y2 - y1)/(x2 - x1)

∴ m = (9 - 8)/(5 - 3) = 1/2

- Find a by using points (a , 7) and (3 , 8) ⇒ (or (5 , 9))

∵ m = (8 - 7)/(3 - a) = 1/2

∴ 1/(3 - a) = 1/2 ⇒ by using cross multiplication

∴ 3 - a = 2 ⇒ subtract 3 from both sides

∴ -a = -1 ⇒ × -1 both sides

∴ a = 1

- Find b by using points (5 , 9) and (7 , b) ⇒ (or (3 , 8))

∵ m = (b - 9)/(7 - 5) = (b - 9)/2

∴ (b - 9)/2 = 1/2 ⇒ by using cross multiplication

∴ 2(b - 9) = 2 ⇒ open the bracket

∴ 2b - 18 = 2 ⇒ add 18 to both sides

∴ 2b = 20 ⇒ ÷ 2

∴ b = 10

- Find b by using points (5 , 9) and (c , 11) ⇒ (or (3 , 8))

∵ m = (11 - 9)/(c - 5) = 2/(c - 5)

∴ 2/(c - 5) = 1/2 ⇒ by using cross multiplication

∴ c - 5 = 4 ⇒ add 5 to both sides

∴ c = 9

* The values of a , b , c are ⇒ a = 1 , b = 10 , c = 9

Read more on budgeted cost here:

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6 0

2 years ago

Determine the number of solutions: 6x-2=x+13

Finger [1]

Answer: B) one solution

Reason: if we solve for the sides of the equation by putting like terms together we get that x = 3

There is no solution when the numbers don’t equal each other, take for instance 1 = 2

It has infinite solutions when the numbers are equal to each other like
1 = 1

It has one solution when the x value is equal to something like x = 9

I also worked out the equation on paper, so you could get a more visual way of how I solved it.

Hope this helps

3 0

3 years ago

Floors, Inc. offers terms of 2/10, n/30 to credit customers. Tile Magic Corp. purchased 100 tile cutters with a list price of $2

expeople1 [14]

Answer:

Step-by-step explanation:

The term 2/10, n/30 is a credit term and means the following:

2 is the discount percentage being offered by the seller.

10 indicates the number of days (from the invoice date) within which the buyer should pay the invoice in order to receive the stated discount.

n/30 states that if the buyer does not pay the (full) invoice amount within the 10 days to qualify for the discount, then the net amount is due within 30 days after the sales invoice date.

Tile Magic Corp. purchased 100 tile cutters with a list price of $20 each on August 5, 2016.

Tile Magic Corp. paid the invoice on August 31, 2016. which is 26 days after the Invoice was issued.

Per the terms of agreement, the discount is only taken into consideration when the invoice is paid within 10 days of its issuance.

Therefore Tile Magic Corp. will receive no discount from Floors Inc.

6 0

3 years ago

01:59:13

BlackZzzverrR [31]

Correct Question:

Stan ran $4\frac{7}{10}$ miles, which was $1\frac{3}{10}$ fewer miles than Matt ran. Four students wrote and solved equations to find m, the number of miles that Matt ran. Which student wrote and solved the equation correctly?