Answer:
<em>(1, - 2) </em>
Step-by-step explanation:
2x - y = 4
3x + y = 1
A = ![\left[\begin{array}{cc}2&-1\\3&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-1%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D)
= 2(1) - 3( - 1) =2 + 3 = 5
= ![\left[\begin{array}{cc}4&-1\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-1%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D)
= 4(1) - 1(- 1) = 4 + 1 = 5
= ![\left[\begin{array}{cc}2&4\\3&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%264%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D)
= 2(1) - 4(3) = 2 - 12 = - 10
<em>x </em>= 
=<em> 1</em>
<em>y </em>= 
= <em>- 2</em>
<em>(1, - 2)</em>
Answer:
2
Step-by-step explanation:
4x+3=x+9
4x-x=9-3
3x=6
x=6/3
x=2
Answer:
He must survey 123 adults.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
The margin of error is:
Assume that a recent survey suggests that about 87% of adults have heard of the brand.
This means that 
90% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage?
This is n for which M = 0.05. So
Rounding up:
He must survey 123 adults.
Answer:
There may be 1 or 3 tricycles in the parking lot.
Step-by-step explanation:
Since at any point in time, there could be bicycles, tricycles, and cars in the school parking lot, and today, there are 53 wheels in total, if there are 15 bicycles, tricycles, and cars in total, to determine how many tricycles could be in the parking lot, the following calculation must be performed:
13 x 4 + 1 x 3 + 1 x 2 = 57
11 x 4 + 1 x 3 + 3 x 2 = 53
10 x 4 + 3 x 3 + 2 x 2 = 53
8 x 4 + 5 x 3 + 2 x 2 = 51
10 x 2 + 1 x 3 + 4 x 4 = 39
9 x 3 + 1 x 2 + 5 x 4 = 49
Therefore, there may be 1 or 3 tricycles in the parking lot.
3. Look at the picture.
We have the right angle triangle. We know the sum of measures of angles in triangle is equal 180°. Therefore:
4.
Look at the picture.
Use Pythagorean theorem:
5.
TRUE: 1; 2; 4
6.
We find a slope of the line OP:
We have:
Now, we must find the slope of the line perpendicular to the line OP.
We know:
therefore
So. We have the answer! :)
