Answer:
(x+2)^2 = 7
Step-by-step explanation:
is this what you're looking for??
1.x^12
2.4^7
ok so basically when it’s multiplication u just have to add the exponents and when its : u have to subtract them
Considering that the points are part of the same linear function, the missing x-value is given by:
a. 1.1.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
Given two points, the slope is given by <u>change in y divided by change in x</u>. In this problem, we are given points (6, 10.2) and (1.5, 3.45), hence the slope is:
m = (10.2 - 3.45)/(6 - 1.5) = 1.5.
Hence:
y = 1.5x + b.
When x = 6, y = 10.2, hence we use it to find b as follows:
10.2 = 1.5(6) + b
9 + b = 10.2
b = 1.2.
Hence the function is:
y = 1.5x + 1.2.
The value of x when y = 2.85 is given by:
y = 1.5x + 1.2.
2.85 = 1.5x + 1.2.
1.5x = 1.65.
x = 1.65/1.5
x = 1.1.
Hence option A is correct.
More can be learned about linear functions at brainly.com/question/24808124
#SPJ1
Answer:
62°
Step-by-step explanation:
it basically falls under the formula of SOH CAH TOA
Answer:
![(\frac{48}{61} , -\frac{40}{61} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B48%7D%7B61%7D%20%2C%20-%5Cfrac%7B40%7D%7B61%7D%20%29)
Step-by-step explanation:
The closest point to the given line must be on a line perpendicular to it.
So we start by finding the slope of the given line and then evaluating what the slope of the perpendicular line to it must be.
First write the given line in slope_y-intercept form:
SO solve for y in
:
![y=\frac{6x-8}{5} = \frac{6}{5} x -\frac{8}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B6x-8%7D%7B5%7D%20%3D%20%5Cfrac%7B6%7D%7B5%7D%20x%20-%5Cfrac%7B8%7D%7B5%7D)
Since the slope is 6/5, the slope of a perpendicular line to the given one must be the "opposite of the reciprocal": -5/6
So the line that we are looking for must have the form:
![y=-\frac{5}{6} x + b](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B6%7D%20x%20%2B%20b)
Since we want it to go through the origin of coordinates (0,0) because we are finding the point closer to the origin, the y-intercept b must be zero:
![y=-\frac{5}{6} x](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B6%7D%20x)
Now, to find the point of intersection of both lines (the given one and the perpendicular one through the origin) we equal both expressions:
![\frac{6}{5}x -\frac{8}{5} = -\frac{5}{6} x](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B5%7Dx%20-%5Cfrac%7B8%7D%7B5%7D%20%20%3D%20-%5Cfrac%7B5%7D%7B6%7D%20x)
and solve this equation for "x": ![x(\frac{6}{5} +\frac{5}{6} ) = \frac{8}{5}](https://tex.z-dn.net/?f=x%28%5Cfrac%7B6%7D%7B5%7D%20%2B%5Cfrac%7B5%7D%7B6%7D%20%29%20%3D%20%5Cfrac%7B8%7D%7B5%7D)
Therefore ![x=\frac{48}{61}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B48%7D%7B61%7D)
Now to find the y-value of the point on the line, we replace this x in either line equation:
![y=-\frac{5}{6} (\frac{48}{61})=-\frac{40}{61}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B6%7D%20%28%5Cfrac%7B48%7D%7B61%7D%29%3D-%5Cfrac%7B40%7D%7B61%7D)
Then the closest point is: ![(\frac{48}{61} , -\frac{40}{61} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B48%7D%7B61%7D%20%2C%20-%5Cfrac%7B40%7D%7B61%7D%20%29)