Which expression is equivalent to xy^2/9?

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

3 years ago

Read 2 more answers

10x-(-1-14x)=-12(x-4)

irina1246 [14]

PEMDAS use that it's gonna help you

6 0

3 years ago

All of these pleaseeeeeeeeee

kenny6666 [7]

Solving Two- Step Equations:
First you have to add or subtract the number without the variable, x, then divide with the variable with x in it.

1.) -2 - 2=26
Answer: x= -14
Try some on your own, if you still need help comment back!

5 0

3 years ago

Find Mean, Median, mode and range. Round to the nearest tenth.

stiv31 [10]

Answer:

Mean = 26.24

Median = 27

Mode = 32

Range = 38

Step-by-step explanation:

Plotting the original data from leaf plot

$9,11,12,12,14,17,25,25,27,32,32,32,33,35,41,42,47$

Finding Mean:

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$\mu=\frac{446}{17}$

= 26.24

Therefore, the range = 26.24.

Finding Median:

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

So, the median is 27 .

Finding Mode:

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

We see that the mode is 32.

Finding Range:

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

The lowest value is 9.

The highest value is 47.

The range = 47 - 9 = 38

4 0

2 years ago

Marie is purchasing a $108,000 home with a 30 year ortgage at 5.25%. What is her monthly principal and interest payment

schepotkina [342]

Answer:

Monthly interest rate is r=0,004375

Monthly principal c=590,625

Step-by-step explanation:

Monthly interest payment rate :

$r=\frac{5.25}{12}:100=0,0004375$

Now, we need to find monthly principal payment : $c=\frac{rP}{1-(1+r)^{-N}}$

Use this rule : $N=30*12=360$

P=108000

r=0,004375

$c=\frac{0.004375*108000}{1-(1+0.004375)^{-360}} =\frac{472.5}{0.8}=590,625$

5 0

3 years ago

Read 2 more answers