Answer:
6.79 miles
Step-by-step explanation:
Consider triangle ABC where A marks the starting point and C indicates the end point.
|AB|=5.2 miles
|BC|=3.0 miles
∠ABC = 90 + 75 = 165°
We're given two side lengths and an angle that is not opposite to either side.
The approach to resolve this scenario is known as the Cosine Rule.
Each side opposite an angle is designated by the corresponding lowercase letter.
The Cosine Rule asserts that:
b² = a² + c² - 2acCosB
|AC|²=3² + 5.2² - (2 × 5.2 × Cos 165°)
|AC|²=9 + 27.04 + 10.05
|AC|²=46.09
|AC|=√46.09=6.79 miles
Thus, the straight-line distance from A to C measures 6.79 miles
Answer:
24 minutes
Step-by-step explanation:
Let y represent the rate of 120 envelopes per minute.
40/8 = 120/y
40y = 8 * 120
40y = 960
y = 960/40
= 24 minutes
Answer:
The correct response is: b)
Step-by-step explanation:
a4b=24, where a × 4 × b = 24 implies a × b = 6
The pairs of numbers with a product of 6 include: {1,6} and {2,3}
In base 10, a4b translates to 100a + 40 + b
Calculating gives us:
100×1+40+6=146
100×6+40+1=641
100×2+40+3=243
100×3+40+2=342
Summing these results yields: 146 + 641 + 243 + 342 = 1372
The correct answer is: b)
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:
To find the number of genuine solutions for a system of equations consisting of a linear equation and a quadratic equation
1) With two variables, say x and y, rearrange the linear equation to express y, then substitute this y in the quadratic equation
After that, simplify the resulting equation and determine the number of real roots utilizing the quadratic formula, 
for equations of the type 0 = a·x² - b·x + c.
When b² exceeds 4·a·c, two real solutions emerge; if b² equals 4·a·c, there will be a single solution.
Step-by-step explanation:
