Solve the system of equations; x - 2y = 2 and 3x - 5y = 9 by writing and solving a matrix equation. Show all your work.

Answers

Answer 1

Answer: y= $(28)/(11)$
x= $(3)/(11)$

Working;
Start by forming a matrix as shown below;
$\left[\begin{array}{ccc}1&-2\n3&5\end{array}\right] ( \left[\begin{array}{ccc}x\ny\end{array}\right])= ( \left[\begin{array}{ccc}2\n9\end{array}\right])$

Step II
Finding the inverse of the matrix as shown below;
Determinant;
(1*5)-(3*(-2)=11
Inverse;
$(1)/(11) \left[\begin{array}{ccc}5&2\n-3&1\end{array}\right] \left[\begin{array}{ccc}1&-2\n3&5\end{array}\right] \left[\begin{array}{ccc}x\ny\end{array}\right]= (1)/(11) \left[\begin{array}{ccc}5&2\n-3&1\end{array}\right] \left[\begin{array}{ccc}2\n9\end{array}\right]$

Evaluating further;
$(1)/(11) \left[\begin{array}{ccc}11&0\n0&11\end{array}\right] \left[\begin{array}{ccc}x\ny\end{array}\right] = (1)/(11) \left[\begin{array}{ccc}28\n3\end{array}\right]$

x= $(28)/(11) and y = (3)/(11)$

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Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}.What is A ∩ B?

{50, 55, 60, 65, 70, 75, 70, 85, 90, 95}
{55, 65, 75, 85, 95}
{all odd numbers between 1 and 99}
{numbers between 1 and 150 that are evenly divisible by 5}

Answers

Answer: {55, 65, 75, 85, 95}

Step-by-step explanation:

Given: A = {odd numbers between 0 and 100}

B= {numbers between 50 and 150 that are evenly divisible by 5}

Thus, A={1,2,3,4,5,6,7,8,.......99}

and B={55,60,65,70,75,80,85,90,95......145}

The notation A ∩ B means A intersection B which is the set of elements that are common in set A and in set B.

Now, $A\bigcap B=\left \{ 55,65,75,85,95 \right \}$

The elements of set A ∩ B are {55, 65, 75, 85, 95}

The sets are given as:

A = {odd numbers between 0 and 100}

B= {numbers between 50 and 150 that are evenly divisible by 5}

The above means that:

A = {1,2,3,4,5,6,7,8,.......99}

B = {55,60,65,70,75,80,85,90,95......145}

To calculate set A ∩ B, we list the common elements in both sets, without repetition.

So, we have:

A ∩ B = {55, 65, 75, 85, 95}

Hence, the elements of set A ∩ B are {55, 65, 75, 85, 95}

Answers

that is height
h=16t^2+16t+480
when h=0 is when it hits the water

0=16t^2+16t+480
undistribbute 16 for ease
0=16(t^2+t+30)
16*0=0 so assume
t^2+t+30=0
factor
(t+6)(t-5)=0
set to zero

t+6=0
minus 6
t=-6
false, since you cannot have negative time

t-5=0
add 5
t=5

at t=5 she hits the water

5 seconds

What is the sin of 60°?

Answers

SOHCAHTOA
Therefore Sine of 60 = opposite side over hypotenuse
so 9 square roots of 3 over y

I believe the answer is -17.9
Sorry if that is not correct.

In ∆ABC, AC = 15 centimeters, m B = 68°, and m C = 24°. What is BC to two decimal places?6.58 centimeters
9.88 centimeters
13.57 centimeters
16.17 centimeters
19.25 centimeters

Answers

I dont know which math you are in but you can use the law of sins. (A/sin(a))=(B/sin(b)) where the capital letters are the sides (in this case you would put AC or whatever side length it is) and the lower case letters are the measures on the angles.
that may have been confusing but look up the laws of sines and cosine because you'll need to learn them and it's very helpful.
15/sin68 = x/sin88 x is the side BC and to get angle A, do 180-68-24
so x= sin88 (15/sin68)
so the answer to this question would be 16.17 cm

Answer:

16.17 cm would be the answer

Samantha buys one vase and x roses. The vase costs $15 and each rose costs $2.What function equation represents the amount of money Samantha spends?

f(x)=15x−2

f(x)=2x−15

f(x)=2x+15

f(x)=15x+2

Answers

I believe the correct answer from the choices listed above is the third option. The equation that would represent the amount of money Samantha spends would be f(x)=2x+15 where 15 represents the value of the vase which is a fix amount and 2x is the value of the roses.

Hope this answers the question. Have a nice day.

Answer:

f(x)=2x+15

Step-by-step explanation:

Im so confused, how do i get the variance with just the standard deviation

Answers

Answer:

To figure out the variance, divide the sum, 82.5, by N-1, which is the sample size (in this case 10) minus 1. The result is a variance of 82.5/9 = 9.17. Standard deviation is the square root of the variance so that the standard deviation would be about 3.03.

hope this helps!

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