Answer:
The equation of the line is ![y = -\frac{1}{3}x - 8](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B3%7Dx%20-%208)
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
In which m is the slope and b is the y-intercept.
Slope of - 1/3
This means that ![m = -\frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B3%7D)
So
![y = -\frac{1}{3}x + b](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B3%7Dx%20%2B%20b)
Through the point (-6, -6)
This means that when
. So
![y = -\frac{1}{3}x + b](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B3%7Dx%20%2B%20b)
![-6 = -\frac{1}{3}(-6) + b](https://tex.z-dn.net/?f=-6%20%3D%20-%5Cfrac%7B1%7D%7B3%7D%28-6%29%20%2B%20b)
![b + 2 = -6](https://tex.z-dn.net/?f=b%20%2B%202%20%3D%20-6)
![b = -8](https://tex.z-dn.net/?f=b%20%3D%20-8)
The equation of the line is ![y = -\frac{1}{3}x - 8](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B3%7Dx%20-%208)
Answer/Step-by-step explanation:
a. First, find the value of a.
Sum of the interior angles of a triangle = 180° (triangle sum theorem)
Therefore:
3a + 2a + a = 180°
Add like terms
6a = 180°
6a/6 = 180/6
a = 30
Thus:
a = 30°
2a = 2(30) = 60°
3a = 3(30) = 90°
b. The triangle is an isosceles triangle because it has two sides that are indicated to be equal. This also implies that the angels opposite each of the equal sides are also congruent to each other.
Therefore, sum of the isosceles triangle would be:
2(2x) + 5x = 180°
4x + 5x = 180
9x = 180
9x/9 = 180/9
x = 20
Thus:
2x = 2(20) = 40
5x = 5(20) = 100
Answer:
The answer should be A.
.
Step-by-step explanation:
Start with the second inequality, which is more straightforward than the first. Add
to both sides of this equation to separate
from the numbers:
. The direction of the inequality sign shall stay the same.
.
On the other hand, simplifying the first inequality takes a bit more work. Start by dividing both sides by
. However, keep in mind that dividing or multiplying both sides of an inequality with a negative number will invert the direction of the inequality sign. For example, the left-hand side of an inequality might have been greater than the right-hand side. When both sides are multiplied with a number less than zero, the new left-hand side would become smaller than the new right-hand side.
Because
is a negative number, dividing both sides of the first inequality inequality by
will turn the "greater-than" sign into a "less-than" sign.
The inequality used to be:
.
After dividing both sides by the negative number
, it becomes:
.
.
.
The question connected the two original inequalities with "or". Therefore, the conditions will be satisfied as long as either of at least one of the two inequalities is true. Note, that
is true whenever
is true. Therefore, any real number that is smaller than
will meet the requirements- not just those that are smaller than
.
The corresponding interval will be
.
I would agree with Mark6633 and go with 3
Step-by-step explanation:
I assume AB is supposed to be a straight line. yes ?
in that case please remember that all angles on top of a line (and then again below a line) must sum up to 180 degrees (this is what it takes to flip a "stick" on that line from left to right).
so, COD covers already 90 degrees of these 180.
that means AOD + BOC = 180 - 90 = 90 degrees.
now we know that the 2 angles are in the ratio of 1:5.
that means that BOC is 5 times as large as AOD.
and we can be more direct :
since the 2 angles are in the ratio 1:5 we are actually splitting the remaining 90 degrees into 6 parts (5+1).
and BOC gets then 5 of these 6 parts, and AOD gets the remaining 1 part.
so,
90/6 = 15
therefore, one of these parts is 15 degrees.
so, we know AOD = 15 degrees.
BOC = 5×15 = 75 degrees
or simply 90 - 15 = 75 degrees