I believe he should add 2ft to the height of the tree as well
Definition of an exterior angle
At each vertex of a triangle, an exterior angle of the triangle may be formed by extending ONE SIDE of the triangle. See picture below.
Calculating the Angles
We can use equations to represent the measures of the angles described above. One equation might tell us the sum of the angles of the triangle. For example,
x + y + z = 180
Let s represent the length of any one side of the original square. The longer side of the resulting rectangle is s + 9 and the shorter side s - 2.
The area of this rectangle is (s+9)(s-2) = 60 in^2.
This is a quadratic equation and can be solved using various methods. Let's rewrite this equation in standard form: s^2 + 7s - 18 = 60, or:
s^2 + 7s - 78 = 0. This factors as follows: (s+13)(s-6)=0, so that s = -13 and s= 6. Discard s = -13, since the side length cannot be negative. Then s = 6, and the area of the original square was 36 in^2.
Answer:
The answers are below
Step-by-step explanation:
The greater sign is > and the less then symbol is <
Using the red arrows on the number line, you can tell which one is bigger or less. The dot is colored in so it has to have a line under it. So for the first one (top, left), The red arrow is pointing to the right side meaning x is bigger than 3. Therefore x ≥ 3.
In the next one (top, right) the arrow is pointing to the negative side so that one must be less than 3. The dot is also colored in meaning it is: x ≤ 3
In the next one (bottom, left) the arrow is pointing to the right, the dot not colored in, so it has no line. Therefore it is x > 3
Last one (bottom right) the arrow is pointing left, dot is white meaning that the answer is x < 3
If you're wondering what the open dots and closed dots mean:
An open dot is used to show that the ray's endpoint is not a component of the solution when the inequality is "strict" ( < or >).
A closed dot is used to denote that the endpoint is a component of the solution for the other types of inequalities (≥ and ≤ ).
Given:
40 people
box plot data:
minimum age : 20
Q1: 28
Median: 34
Q3: 42
maximum age: 48
Q1 represents 25% of the data set.
40 x 25% = 10
There are 10 people who are aged 28 and below.
1st quartile is equal to 25% of the data set, the median is equal to 50% of the data set, 3rd quartile is equal to 75% of the data set.
