Response:
b + d = 180°, a = d, and a = c
Detailed explanation:
In the diagram, we observe that the only condition for the lines to be parallel is that the angles correspond with their counterparts, for instance, a must equal d. The equation a = c indicates that all angles must be equal for lines m and n to remain parallel. Finally, the equation b + d = 180° confirms that this holds true only if lines m and n are parallel.
B refers to the base of the triangle,
and a signifies the length of the two identical sides.
The measurement labeled as 'a' is larger than 'b' since those equal sides are longer than the base. Given "one of the longer sides measures 6.3 cm," we assign a = 6.3.
Substitute 6.3 for each 'a' in the equation and solve for b:
2a + b = 15.7
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 15.7 - 12.6 (applying subtraction property of equality)
b = 3.1
Answer:
160/1001, 175/1001
Step-by-step explanation:
i) We calculate:
₈C₁ methods to select 1 new camera from a selection of 8
₆C₃ methods to select 3 refurbished cameras from a selection of 8
₁₄C₄ methods to select 4 cameras from the total of 14 cameras
The probability formula is:
P = ₈C₁ ₆C₃ / ₁₄C₄
P = 8×20 / 1001
P = 160 / 1001
P ≈ 0.160
ii) For at most one new camera, it means we want either one new camera or none at all. We've calculated the probability of selecting one new camera already. The probability of not selecting any new camera is equivalent to selecting 4 refurbished cameras:
P = ₆C₄ / ₁₄C₄
P = 15 / 1001
Therefore, the combined probability is:
P = 160/1001 + 15/1001
P = 175/1001
P ≈ 0.175
Answer:
- 8
Step-by-step explanation:
Given the expression
(3x² - 5)(4 + 4x²)
Each term from the second factor is multiplied by every term in the first factor, meaning
3x²(4 + 4x²) - 5(4 + 4x²) ← distribute both parentheses
= 12x² + 12
- 20 - 20x² ← combine like terms
= 12 - 8x² - 20
The coefficient for the x² term is - 8
