Answer:
The cabin is located 567 yards away.
Step-by-step solution:
The bearing angle of 21.2° corresponds to the interior angle near the cabin in the triangle.
Apply the tangent function:
Opposite side length: 220 yards
Adjacent side length: x (distance to cabin)
tan(21.2°) = opposite / adjacent
tan(21.2°) = 220 yards / x
Multiply both sides by x:
x × tan(21.2°) = 220 yards
Isolate x:
x = 220 yards / tan(21.2°)
x = 220 / 0.388
x = 567 yards
Hence, the cabin is 567 yards away.
Answer:
The correct option is:
On the coordinate plane, there is a parabola that opens upwards, passing through the points (2, 10), having its vertex at (5, 1), and intersecting (8, 10).
Step-by-step explanation:
Initially, we must understand the translation rules
1) {f(x) + a} signifies f(x) moved up by (a) units
2) {f(x) – a} means f(x) moved down by (a) units
3) {f(x + a)} represents f(x) moved left by (a) units.
4) {f(x – a)} indicates f(x) moved right by (a) units.
Given information:
f(x) = x²
g(x) = (x-5)² + 1
By comparing the transformation from f(x) to g(x) with the translation rules
It can be concluded that g(x) represents f(x) through a translation of 5 units to the right and 1 unit upwards (rules 1 and 4)
Refer to the attached image, which illustrates the graphs of both f(x) and g(x)
As depicted, g(x) intersects (2, 10), has a vertex at (5, 1), and crosses through (8, 10)
Question 1
Total budget sums up to 180 + 475 + 15 + 50 + 65 + 25 + 150 + 30 = $990.
Actual expenditure amounts to 182 + 475 + 12 + 65 + 68 + 12.50 + 150 + 36 = $1000.5.
Mae Green surpassed her designated budget.
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Question 2
Eleanor:
Earned = 380.48
Spent = 16.50
Peter:
Earned = 120 + 13.65 + 100 = 233.65.
Combined total income = 233.65 + 380.48 - 16.50 = 597.63.
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Question 3
Aggregate expenditure = 540 + 48.55 + 34.15 + 12.80 + 18.95 + 38.60 + 2 + 6.50 = 701.55.
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Question 4
Marie's updated balance = 250.65 - [21.95+48.50+75.60] + 55 = $159.50.
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Question 5
[235/825] × 100 = 28.48%
In the ratio of miles traveled, Mr. Storey and Mrs. Storey's journey is represented as mr: mrs = 3: 1. The total of these ratio units equals 4 (3+1), which means each unit corresponds to 3200 divided by 4, resulting in 800 miles. Mr. Storey drove 3 multiplied by 800, equating to 2400 miles, while Mrs. Storey drove 1 multiplied by 800, totaling 800 miles.
To derive the function that characterizes the bee population:
1) Initially, there are 9,000 bees in the first year.
2) In the second year, a reduction of 5% occurs => 9,000 - 0.05 * 9,000 = 9,000 * (1 - 0.05) = 9,000 * 0.95
3) Each subsequent year sees a 5% decline => 9,000 * (0.95)^(number of years)
4) Let x represent years and f(x) signify the bee count, then: f(x) = 9,000 (0.95)^x.
Evaluation of the claims:
<span>1) The function f(x) = 9,000(1.05)x applies to the scenario.
FALSE: WE ESTABLISHED IT AS f(x) = 9,000 (0.95)^x
2) The function f(x) = 9,000(0.95)x applies to the scenario.
TRUE: THIS IS THE RESULT OF OUR PRIOR ANALYSIS.
3) After 2 years, the farmer projects approximately 8,120 bees will be left.
Calculating:
f(2) = 9,000 * (0.95)^2 = 9,000 * 0.9025 = 8,122
Thus, this statement is TRUE
4) After 4 years, the farmer can predict there will be roughly 1,800 bees left.
f(4) = 9,000 * (0.95)^4 = 9,000 * 0.81450625 = 7,330
This statement is therefore FALSE
5) The domain values contextual to this situation are restricted to whole numbers.
FALSE: DOMAIN VALUES INCLUDE ALL NON-NEGATIVE REAL NUMBERS. FOR INSTANCE, THE FUNCTION IS VALID AT X = 5.5
6) The range values pertinent to this situation are restricted to whole numbers.
TRUE: FRACTIONS OF BEES CANNOT EXIST.
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