The answer is the mean.
"For a data set, the arithmetic mean, also called the mathematical expectation or average, is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values."- Wikipedia
AnsweTo see if multiple ratios are proportional, you could write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportional ratios.r:
Step-by-step explanation:
Since complementary angles add to 90°, (4x - 1) and (5x + 19), also add to 90°.
Thus, lets form an equation:
90 = 5x + 19 + 4x - 1
72 = 9x
x = 9
Thus, the measure of angle B is 64°.
OK, so for this equation, your goal is to get the d, and ONLY the d, on one side of the equation. So, to start out, you need to multiply the entire equation, meaning both sides, by 8 because we are trying to get rid of those pesky fractions.
8(1/8(3d-2)=1/4(d+5))
The equation then turns into this because the 8 and 4 cancelled out with the 8.
1(3d-2)=2(d+5)
Now, we need to distribute the left over numbers into the parenthesis.
3d-2=2d+10
And finally, we need to get the d's on one side, and the numbers on the other, so we subtract 2d from both sides and add the 2 to both sides. They then cancel out to make
d=12
Hope it helps! :)
Answer:
This linear system has one solution.
Step-by-step explanation:
First equation: y = x + 2
Second equation: 6x - 4y = -10
Let's change the second equation in slope-intercept form y = mx + b.
<u>Slope-intercept form</u>
y = mx + b
m ... slope
b ... y-intercept
![6x - 4y = -10](https://tex.z-dn.net/?f=6x%20-%204y%20%3D%20-10)
![6x + 10 = 4y](https://tex.z-dn.net/?f=6x%20%2B%2010%20%3D%204y)
![\frac{6}{4}x + \frac{10}{4} = y](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B4%7Dx%20%2B%20%5Cfrac%7B10%7D%7B4%7D%20%3D%20y)
![\frac{3}{2}x + \frac{5}{2} = y](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7Dx%20%2B%20%5Cfrac%7B5%7D%7B2%7D%20%3D%20y)
If two lines have the <em>same slope </em>but <em>different y-intercept</em>, they are parallel - <u>system has no solutions</u>.
If two lines have the <em>same slope</em> and the <em>same y-intercept</em>, they are the same line and are intersecting in infinite many points - <u>system has infinite many solutions</u>.
If two lines have <em>different slopes</em> then they intersect in one point - <u>system has one solution</u>.
We see that lines have different slopes. First line has slope 1 and the other line has slope
. So the system has one solution.
You can also check this by solving the system.
Substitute y in second equation with y from first.
6x - 4y = -10
6x - 4(x + 2) = -10
Solve for x.
6x - 4x - 8 = -10
2x = -2
x = -1
y = x + 2
y = -1 + 2
y = 1
The lines intersect in point (-1, 1). <-- one solution