Answer:
height = 4.8 cm
area = 120 cm²
perimeter = 62 cm
Step-by-step explanation:
<u>**Please refer to the attached diagram when following the step-by-step**</u>
First, find m∠C (green angle on diagram) by using the cosine rule:
Therefore, the interior angle of the right triangle at point C (blue angle on diagram) is:
Now use the Sine Rule (for finding sides) to determine height (h):
So the height = 4.8 cm
Now we have determined the height, we can calculate the area by using the area of a parallelogram formula:
Area of a parallelogram = base x perpendicular height
⇒ area = 25 x 4.8 = 120 cm²
Parallelogram is a four-sided shape made up of two pairs of straight parallel lines that are equal in length.
Perimeter = sum of the sides
⇒ perimeter = 6 + 6 + 25 + 25 = 62 cm
Answer: 114°
Step-by-step explanation:
<h2>Concept: </h2>
Here, we need to know the idea of the "Exterior Angle theorem".
<u>The exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.
If you are still confused, then refer to the attachment below for a graphical explanation.
<h2>Solve:</h2>
Given
24 + (2x + 18) = 3x + 6
Put like terms together
24 + 18 + 2x = 3x + 6
Combine like terms
42 + 2x = 3x + 6
Subtract 6 on both sides
42 + 2x - 6 = 3x + 6 - 6
36 + 2x = 3x
Subtract 2x on both sides
36 + 2x - 2x = 3x - 2x
x = 36
Exterior angle = 3x + 6 = 3(36) + 6 = 114°
Hope this helps!! :)
Please let me know if you have any questions
Answer:
-3 < x ≤ 8
Step-by-step explanation:
First, write this statement with symbols:
2x - 5 > -3, but also:
2x - 5 ≤ 11
Adding 5 to both sides of the first inequality yields 2x > 2. pr x > 1.
Adding 5 to both sides of the second inequality results in 2x ≤ 16, or x ≤ 8.
Thus, -3 < x ≤ 8 is the shortest way in which to write the given information.
Answer:
Step-by-step explanation:
Vertex form is accomplished by completing the square on the quadratic. Do this by first setting the parabola equal to 0 then moving the constant over to the other side:
Now take half the linear term, square it, and add it to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9:
The reason we do this is to create a perfect square binomial on the left:
(obviously the 0 results from the addition of 9 and -9). Move the 0 back over to the other side and set the quadratic back equal to y:
This gives you a vertex of (-3, 0), which is a minimum value, since the parabola opens upwards.
