Both of these problems will be solved in a similar way, but with different numbers. First, we set up an equation with the values given. Then, we solve. Lastly, we plug into the original expressions to solve for the angles.
[23] ABD = 42°, DBC = 35°
(4x - 2) + (3x + 2) = 77°
4x+ 3x + 2 - 2 = 77°
4x+ 3x= 77°
7x= 77°
x= 11°
-
ABD = (4x - 2) = (4(11°) - 2) = 44° - 2 = 42°
DBC = (3x + 2) = (3(11°) + 2) = 33° + 2 = 35°
[24] ABD = 62°, DBC = 78°
(4x - 8) + (4x + 8) = 140°
4x + 4x + 8 - 8 = 140°
4x + 4x = 140°
8x = 140°
8x = 140°
x = 17.5°
-
ABD = (4x - 8) = (4(17.5°) - 8) = 70° - 8° = 62°
DBC =(4x + 8) = (4(17.5°) + 8) = 70° + 8° = 78°
The prallelogram whose adjacent sides are equal and one vertex angle is 90 degrees is a square.
The value of angle 1 is 90 degrees as the diagonal of the square intersect at 90 degrees.
The value of y is 23.
The diagonal of the square bisect the vertex angle hence the angle of 3x is 45 degrees.
Thus, the value of x is 15 degrees.
The value of 12z is 45 degrees.
Thus, the required value of z is 3.75 degrees.
The smallest 3 common multiples of 2 and 3 are 6, 12, and 18 .
The smallest 3 common multiples of 3 and 6 are also 6, 12, and 18 .
The inequalities are matched with their correct graph respectively as follows:
- D ⇒ {(x, y): y > x²}.
- G ⇒ {(x, y): y ≥ x²+ 3
- C ⇒ {(x, y): y ≤ 3x² + 2}
- A ⇒ {(x, y): y ≥ 2x² - 5x + 1}
- J ⇒ x²- 3x ≥ 0
- H ⇒ x² - 3x + 2 ≤ 0
- B ⇒ {(x, y): y ≤ 1 - x²}
- B ⇒ {(x, y): y ≥ -1}
<h3>What is a graph?</h3>
A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
<h3>What is an inequality?</h3>
An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
- Less than (<).
- Greater than (>).
- Less than or equal to (≤).
- Greater than or equal to (≥).
In Geometry, if the leading coefficient of a quadratic equation is greater than (>) zero, the parabolic curve would open upward while the parabolic curve would open downward when the leading coefficient of a quadratic equation is less than (<) zero.
Read more on graph of inequalities here: brainly.com/question/24372553
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Complete Question:
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2}
9. {(x, y): y ≥ -1}
Answer:
Step-by-step explanation:
the answer is 14
