All categories

2 years ago

Does the graph shown below represent y as a linear function of x?

Mathematics

1 answer:

marshall27 [118]2 years ago

5 0

Answer: No, it is not a linear function

Explanation:

We can see that it's a function because it passes the vertical line test, but it's not linear. To be linear, it needs to be one single straight line only (instead of composed of multiple pieces of different straight lines). This graph is considered a piecewise function.

So if your teacher asked "is this a function?" then the answer would be "yes". However, the "linear" portion is what makes the final answer "no".

You might be interested in

Factorise by grouping: x² - 5x + 2x - 10

IrinaK [193]

Answer:

(x + 2)(x - 5)

Step-by-step explanation:

Here are the steps:

$x^2-5x+2x-10\\(x^2-5x)+(2x-10)\\x(x-5) + 2(x-5)\\(x + 2)(x-5)$

4 0

2 years ago

Matthew is packing 120 pencils and 108 notebooks

Rasek [7]

9514 1404 393

Answer:

12 boxes
10 pencils, 9 notebooks

Step-by-step explanation:

a) The number of boxes will be the greatest common divisor (GCD) of the numbers 120 and 108. That number is 12.

120 = 12×10

108 = 12×9 . . . . 12 is the greatest common divisor

Matthew can make 12 boxes with equal numbers of the items.

b) 120 pencils divided by 12 will be 10 pencils per box.

108 notebooks divided by 12 will be 9 notebooks per box.

_____

<em>Additional comment</em>

It helps to be familiar with multiplication tables up to about 12×12.

The GCD can always be found using Euclid's algorithm. Look at the remainder when the larger number is divided by the smaller. If it is not zero, then replace the larger number with the remainder and repeat. If the remainder is zero, the divisor is the GCD.

Here, we have ...

120/108 = 1 r 12.

108/12 = 9 r 0 ⇒ 12 is the GCD

7 0

2 years ago

Ryan drove 715 miles in 13 hours At the same rate, how long would it take him to drive 385 miles?

musickatia [10]

Answer:

7 hours

Step-by-step explanation:

715 / 13 = 55 miles per hour

385 / 55 = 7 hours

Best of Luck!

5 0

2 years ago

Read 2 more answers

Each line represents a proportional relationship. Write an equation for each line. Show your work.

tiny-mole [99]

Answer:

The equation of line a is y = x

The equation of line b is y = $\frac{2}{3}$ x

Step-by-step explanation:

The equation of the proportional is y = m x, where

m is the slope of the line (constant of proportionality)

The rule of the slope of a line is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the line

∵ Line a passes through points (0, 0) and (3, 3)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = $\frac{3-0}{3-0}=\frac{3}{3}$

∴ m = 1

→ Substitute in the form of the equation above

∴ y = (1)x

∴ y = x

∴ The equation of line a is y = x

∵ Line b passes through points (0, 0) and (3, 2)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 2

→ Substitute them in the rule of the slope above

∵ m = $\frac{2-0}{3-0}=\frac{2}{3}$

∴ m = $\frac{2}{3}$

→ Substitute in the form of the equation above

∴ y = ( $\frac{2}{3}$ ) x

∴ y = $\frac{2}{3}$ x

∴ The equation of line b is y = $\frac{2}{3}$ x

7 0

2 years ago

Stacy is driving at a speed of 48 miles per hour. How many feet is she travelling per minute?

Nonamiya [84]

48(miles/hour)*(1 mi/5280 ft)(1 hour/60 min)
-----
= (48*1*1)/(1*5280*60)(ft/min)

3 0

2 years ago