<span>Let A = a3b + 9a2b2 - 4ab5, and B = a3b - 3a2b2 + ab5. The difference can be expressed as A - B = a3b + 9a2b2 - 4ab5 - (a3b - 3a2b2 + ab5). When the negative sign is in front of the parentheses, all the internal signs change: this leads to: A - B = a3b + 9a2b2 - 4ab5 - a3b + 3a2b2 - ab5 = a3b - a3b + 9a2b2 + 3a2b2 - 4ab5 - ab5 = 12a2b2 - 5ab5. The first term’s degree is 2 + 2 = 4, while the second term’s degree is 1 + 5 = 6. Thus, the correct response is that the difference is a binomial of degree 6.</span>
Complete Question
Angela has constructed a wedge-shaped pillow for her TV watching needs. It contains 0.35 m³ of fluffy material. The pillow's base area measures 0.5m², and its height stands at 1m.
What is the length of the pillow?
Provide an exact answer (no rounding).
Answer:
1.4m
Step-by-step explanation:
A wedge can be defined as a Triangular prism. Thus,
The volume formula for a wedge (Triangular prism) is given by: 1/2 × B × H × L
b = 0.5m
h = 1 m
l =??
Volume of the wedge = 0.35 m³
0.35 = 1/2 × 0.5 × 1 × L
0.35 = 0.25 × L
Solving for L, we get: L = 0.35/0.25
L = 1.4m
The correct answer is A. According to the question's details, we're provided with key statistics on zucchini weights, which suggest that the average turns out to be typically 0.8 pounds, while the standard deviation is noted as 0.25 pounds. The probability of a randomly selected zucchini weighing between 0.55 pounds and 1.3 pounds can be mathematically expressed. Observing the provided normal distribution options, option A aligns with our specified weight range.
(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now we will express 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
This reduces to
1 ≡ -1082 * 1234 (mod 4321)
Thus, the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.
