Area of a rectangle = length x height
Area = 135
Height = X
Lenght = x +6
135 = x * x+6
Simplify:
135 = x^2 +6x
Subtract 135 from both sides:
x^2 + 6x - 135 = 0
Solve:
2 numbers when added need to equal 6 and when multiplied equal -135
x = 9 and x = -15
The height can't be a negative number so the height is 9
Length = 9 +6 = 15
Height = 9cm, Length = 15 cm
Answer:
m = -1
Step-by-step explanation:
First write the line in slope intercept form y = mx+b where m is the slope and b is the y intercept
x-y = 6
subtract x from each side
-y = -x+6
Multiply each side by -1
y = x-6
The slope is 1
Perpendicular lines have slopes that multiply to -1
m * 1 = -1
m = -1
The slope of the perpendicular line is -1
Answer:
Step-by-step explanation:
Putting values
6(12) - 8.45(4)
= 38.2
Answer:
Earth
Step-by-step explanation:
You don't need scientific notation.
The areas of similar figures are proportional to the square of their linear scale factor. If Mars is 1/2 the diameter of Earth, its total surface area is (1/2)² = 1/4 that of Earth.
That is, the land area of Mars is 25% of the total area of Earth.
The land area of Earth is 1-70% = 30% of the total area of Earth. 30% is more than 25%.
Earth has more land area than Mars.
Answer:
There are two choices for angle Y: 
for 
, 
for 
.
Step-by-step explanation:
There are mistakes in the statement, correct form is now described:
<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>
The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:
(1)
If we know that 
, 
and 
, then we have the following second order polynomial:
(2)
By the Quadratic Formula we have the following result:
There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:
1)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-15.193%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
2)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-8.424%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
There are two choices for angle Y: for , for .
