Answer:
x = 21, m∠A = 23°, the measure of angle in the right = 67°
Step-by-step explanation:
The angles of a triangle sum up to 180°.
Right angles equals to 90°.
Thus, (2x - 19)° + (3x + 4)° + 90° = 180°
=> 5x + 75 = 180
=> 5x = 105
=> x = 21
m∠A=> 2(21) -19 = 23°
the measure of angle in the right=> 3(21) + 4 = 67°
Answer:
24.5 unit²
Step-by-step explanation:
Area of ∆
= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |
= ½ | -7 - 42 |
= ½ | - 49 |
= ½ (49)
= 24.5 unit²
<u>Method 2:</u>
Let the vertices are A, B and C. Using distance formula:
AB = √(-1-6)² + (3-3)² = 7
BC = √(-6-1)² + (-4-3)² = 7√2
AC = √(-1-(-1))² + (4-(-3))² = 7
Semi-perimeter = (7+7+7√2)/2
= (14+7√2)/2
Using herons formula:
Area = √s(s - a)(s - b)(s - c)
here,
s = semi-perimeter = (14 + 7√2)/2
s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2
s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2
s - c = (14+7√2)/2 - 7 = (7 + √2)/2
Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²
Answer:
22
Step-by-step explanation:
Long but I got a lot done so i'm proud of myself. How was your day?
Answer:
238
Step-by-step explanation:
28÷4=7
7x6=42
7x3=21
7x4=28
7x7=49
7x3=21
7x3=21
7x4=28
(28x3)+(21x3)+49+42
84+(21x3)+49+42
84+63+49+42
147+49+42
147+91
238
Answer:
<em>(c) a straight line with positive slope.</em>
Step-by-step explanation:
<u>Functions</u>
We are required to find a function that relates the height of the water in a cup to the volume of water in the cup.
The cup has a shape of a cone open upwards. The volume of a cone of height h and radius r is
This function relates the height with the volume, to find the required function, let's solve for h
Rearranging
Being all the values positive, the height and the volume are linearly related with positive slope
Answer: (c) a straight line with positive slope.
