Is xy = 15 linear or non linear function

25% of the 96 coffee mugs at Oscar's Pancake House are dirty. How many dirty coffee mugs are there at the pancake house?

Anika [276]

Answer:

24 coffee mugs are dirty

Step-by-step explanation:

because 25% of 96 is 24

8 0

2 years ago

The line $y = 3$ intersects the graph of $y = 4x^2 + x - 1$ at the points $A$ and $B$. The distance between $A$ and $B$ can be w

raketka [301]

Answer:

61

Step-by-step explanation:

Let's find the points $A$ and $B$ .

We know that the $y$ -coordinates of both are $3$ .

So let's first solve:

$3=4x^2+x-1$

Subtract 3 on both sides:

$0=4x^2+x-1-3$

Simplify:

$0=4x^2+x-4$

I'm going to use the quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , to solve.

We must first compare to the quadratic equation, $ax^2+bx+c=0$ .

$a=4$

$b=1$

$c=-4$

$\frac{-1 \pm \sqrt{1^2-4(4)(-4)}}{2(4)}$

$\frac{-1 \pm \sqrt{1+64}}{8}$

$\frac{-1 \pm \sqrt{65}}{8}$

Since the distance between the points $A$ and $B$ is horizontal. We know this because they share the same $y-coordinate$ .This means we just need to find the positive difference between the $x$ -values we found for the points of $A$ and $B$ .

So that is, the distance between $A$ and $B$ is:

$\frac{-1+\sqrt{65}}{8}-\frac{-1-\sqrt{65}}{8}$

$\frac{-1+\sqrt{65}+1+\sqrt{65}}{8}$

$\frac{2\sqrt{65}}{8}$

$\frac{\sqrt{65}}{4}$

If we compare this to $\frac{\sqrt{m}}{n}$ , we should see that:

$m=65 \text{ and } n=4$ .

So $m-n=65-4=61$ .

5 0

2 years ago

Read 2 more answers

Carl collects coins compulsively, but he only likes quarters ($0.25) and dimes ($0.10). Carl currently has 125 coins for a total

Bogdan [553]

Answer:

Carl has 35 dimes and 90 quarters

Step-by-step explanation:

Let the number of quarters be q and the number of dimes be d

Total number of coins is 125;

Hence;

q + d = 125 •••••••••(i)

The total value of quarters present = q * 0.25 = 0.25q

The total value of dimes present = d * 0.1 = 0.1d

Adding both gives the total

0.25q + 0.1d =26 ••••••••(ii)

So we need to solve both equations simultaneously;

From i,

q = 125 - d

Substitute this into ii

0.25(125-d) + 0.1d = 26

31.25 -0.25d + 0.1d = 26

31.25 -26 = 0.25d -0.1d

5.25 = 0.15d

d = 5.25/0.15

d = 35

Recall; q = 125 - d = 125 -35 = 90

7 0

2 years ago

A line passes through the points (2,18) and (8,24). Write a linear function rule in terms of x and y for this line. The linear f

Alinara [238K]

Answer:

Step-by-step explanation:

hello : here is an solution

8 0

2 years ago

The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your an

xz_007 [3.2K]

9514 1404 393

Answer:

(a) 8 km

Step-by-step explanation:

Let m represent the distance (in kilometers) Michelle has walked. Then Janet walked a distance of (m-2). These distances are at right angles, so the distance between them can be found using the Pythagorean theorem.

m² +(m -2)² = 10²

m² +m² -4m +4 = 100

2m² -4m = 96 . . . . . . subtract 4, collect terms

m² -2m +1 = 49 . . . . . divide by 2 and add 1

(m -1)² = 7² . . . . . . .write as squares

m -1 = 7 . . . . . . positive square root

m = 8

Michelle walked 8 km.

5 0

2 years ago