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3 years ago

Please explain how you got your answer .

Mathematics

1 answer:

posledela3 years ago

7 0

Alright for you to solve this you basically need to break down the components of each term
So 6 can't be rationalized anymore but 18 can be
sqrt(18) is basically sqrt(2) times sqrt(9)
sqrt(9) is 3. So its 3sqrt(2)

The answer is sqrt(6) / 3 sqrt(2) but we can simplify that to sqrt3/3

You might be interested in

A brace for a shelf has the shape of a right triangle. Its hypotenuse is 10 inches long and the two legs are equal in length. Ho

vagabundo [1.1K]

This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine:
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
This can be rewritten:
10sqrt2/sqrt(2•2)
=10sqrt2/sqrt4
=10sqrt2/2
=5sqrt2 Hope this helps!!

3 0

3 years ago

Show work please.<br><br> solve system of equations using matrices.

nadya68 [22]

Answer:

(t, t -1, t)

Step-by-step explanation:

You have three unknowns but only 2 equations, so you can't really SOLVE this...you can get a solution with a variable still in it (I forget what this is called. I think it refers to infinite many solutions). Here's how it works:

Set up your matrix:

$\left[\begin{array}{ccc}1&-2&1\\2&-1&-1\\\end{array}\right] \left[\begin{array}{ccc}2\\1\\\end{array}\right]$

You want to change the number in position 21 (the 2 in the scond row) to a 0 so you have y and z left. Do this by multiplying the top row by -2 then adding it to the second row to get that 2 to become a 0. Multiplying in a -2 to the top row gives you:

$\left[\begin{array}{ccc}-2&4&-2\\2&-1&-1\\\end{array}\right]\left[\begin{array}{ccc}-4\\1\\\end{array}\right]$

Then add, keeping the first row the same and changing the second to reflect the addition:

$\left[\begin{array}{ccc}-2&4&-2\\0&3&-3\\\end{array}\right] \left[\begin{array}{ccc}-4\\-3\\\end{array}\right]$

The second equation is this now:

3y - 3z = -3. Solving for y gives you y = z - 1. Let's let z = t (some random real number that will make the system true. Any number will work. I'll show you at the end. Just bear with me...)

lf z = t, and if y = z - 1, then y = t - 1. So far we have that y = t - 1 and z = t. Now we solve for x:

From the first equation in the original system,

x - 2y + z = 2. Subbing in t - 1 for y and t for z:

x - 2(t - 1) + t = 2. Simplify to get

x - 2t + 2 + t = 2 and x - t = 0, and x = t. So the solution set is (t, t - 1, t). Picking a random value for t of, let's say 2, sub that in and make sure it works. If:

x - 2y + z = 2, then t - 2(t - 1) + t = 2 becomes t - 2t + 2 + t = 2, and with t = 2, 2 - 2(2) + 2 + 2 = 2. Check it: 2 - 4 + 4 = 2 and 2 = 2. You could pick any value for t and it will work.

6 0

3 years ago

HELPPP PLEASEEEEEEEEE

liubo4ka [24]

Y=4x+7

So 4 is the rate of change because if you solve for y, x is the rate of change

4 0

3 years ago

Read 2 more answers

Mika is a local farmer who is interested in how often residents in her town go to a farmer's market each month. She surveys 124

TEA [102]

Answer:

The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.

Step-by-step explanation:

Margin of error

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation and n is the size of the sample.

Standard deviation of 1.3

This means that $\sigma = 1.3$

She surveys 124 families

This means that $n = 124$

Margin of error and meaning:

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 2.58\frac{1.3}{\sqrt{124}}$

$M = 0.3012$

The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.

6 0

2 years ago

Question in the middle please

oksian1 [2.3K]

So it wants you to write two equations, one for the number of fruit and another for the money spent. gather your important information first:

20 fruits for $11.50
apples cost $0.50
bananas cost $0.75

let's do the cost equation first. it's $0.50 per apple, so 0.50a, and $0.75 per banana, so 0.75b. the total cost is $11.50. put all of this information together:

0.50a + 0.75b = 11.50 ... so, the cost of apples bought plus the cost of bananas bought equals 11.50

note what your variables stand for. a represents the number of apples, b represents the number of bananas. to write an equation for how many fruits bought, you simply have to add these two and set them equal to 20 (the total number of fruits bought).

a + b = 20
and your other equation
0.50a + 0.75b = 11.50

these are your two equations. to solve the system of equations, you first want to get one variable alone; the first equation will be easier.

a + b = 20
a = 20 - b

now take this equation and plug it into the second equation.
0.50(20 - b) + 0.75b = 11.50 ... you'll notice that you only have one variable left: b. solve for it. the first step is to distribute 0.50 to the parentheses
10 - 0.50b + 0.75b = 11.50 ... combine like terms
10 + 0.25b = 11.50 ... subtract 10
0.25b = 1.5 ... divide by 0.25
b = 6

6 bananas were purchased. plug this back into an equation to find out how many apples were purchased.

a + 6 = 20 ... subtract 6
a = 14

14 apples and 6 bananas were bought.

3 0

3 years ago