Answer: a. 126.20 gallons.
b. 2740 miles.
Step-by-step explanation:
We will use unitary method in this question.
a) ∵ 310 miles can be covered by a car with the help of 15.5 gallons of gasoline
∴ 1 mile can be covered = gallons
∴2524 miles can be covered =
= 126.20 gallons
b). ∵ With 15.5 gallons of gasoline car can be driven = 310 miles
∴ With 1 gallon of gasoline car can go = 310/15.5 miles
∴ With 137 gallons can can go = (310×137)/15.5 miles
= 2740 miles.
9514 1404 393
Answer:
7. odd angles, 143°; even angles, 37°
8. odd angles, 159°; even angles, 21°
9. even angles, 34°; odd angles, 146°
10. even angles, 29°, odd angles, 151°
Step-by-step explanation:
Angles 1 and 3 are vertical angles, so are congruent. The same can be said of angles 2 and 4. Each odd-numbered angle is supplementary to each even-numbered angle.
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7. m∠1 = m∠3 = 143°, m∠2 = m∠4 = 180° -143° = 37°
8. m∠1 = m∠3 = 159°, m∠2 = m∠4 = 180° -159° = 21°
9. m∠2 = m∠4 = 34°, m∠1 = m∠3 = 180° -34° = 146°
10. m∠2 = m∠4 = 29°, m∠1 = m∠3 = 180° -29° = 151°
<h3>
Answer: Approximately 119.76 meters</h3>
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Work Shown:
x = starting length of the shadow
y = height of the pole
tan(angle) = opposite/adjacent
tan(58) = y/x
1.6003345 = y/x
1.6003345x = y
x = y/1.6003345
x = (1/1.6003345)y
x = 0.62486936y
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When the angle changes, the adjacent side gets 90 meters longer
tan(angle) = opposite/adjacent
tan(36) = y/(x+90)
0.72654253 = y/(0.62486936y+90)
0.72654253(0.62486936y+90) = y
0.453994166y + 65.3888277 = y
65.3888277 = y-0.453994166y
65.3888277 = 0.546005834y
0.546005834y = 65.3888277
y = 65.3888277/0.546005834
y = 119.758478075162
y = 119.76
The height of the pole is about 119.76 meters.
Answer:
about 13.73 square feet
Step-by-step explanation:
We presume you want the area of the figure.
It can be decomposed into a triangle with base 3.6 ft and height 4.8 ft, together with a semicircle of diameter 3.6 ft.
The area of the triangle is given by ...
A = 1/2bh
For the given base and height, this is ...
A = (1/2)(3.6 ft)(4.8 ft) = 8.64 ft²
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The radius is half the diameter, so the radius of the semicircle is 1.8 ft. The area of a whole circle of radius 1.8 ft is given by ...
A = πr² = π(1.8 ft)² = 3.24π ft²
We want the area of half the circle, so its area will be ...
semicircle area = (1/2)(3.24π ft²) = 1.62π ft² ≈ 5.089 ft²
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Then the total area of the figure is ...
total area = triangle area + semicircle area
= 8.64 ft² + 5.09 ft²
total area = 13.73 ft²
Log5(x)+log5(4x-1)
As the bases are the same the number doesn't matter
Log (a) + log(b) =log (ab)
Log(4x^2-x)
(x )(4x-1)
x=0.25 or x=0
Log(4×0.25^2-0.25) = log(0) = Infinity
Same with 0. So no answer