Final answer:
To find the smallest angle in a right triangle with side lengths of 5.0 m, 12 m, and 13 m, we use the inverse tangent function with the shortest leg over the adjacent leg, yielding an angle of approximately 22.6 degrees.
Explanation:
The subject of the question is mathematics, and it pertains to high school level geometry. The question is asking to determine the smallest angle in a right triangle with sides measuring 5.0 m, 12 m, and 13 m. To find the smallest angle, we can use trigonometry, specifically the inverse tangent function.
Step-by-Step Explanation
Identify the sides of the triangle. In this case, we know that the sides are 5.0 m, 12 m (which could be interpreted as legs), and 13 m (the hypotenuse).
Because we are looking for the smallest angle, we will use the smallest leg, which is 5.0 m, and the next largest leg, which is 12 m.
Use the tangent function, which relates the opposite side to the adjacent side in a right triangle. The smallest angle, which we will call θ, will have the opposite side of 5.0 m and an adjacent side of 12 m.
Calculate θ using the inverse tangent function (also known as arctangent). θ = tan-1(5.0/12).
Perform the calculation using a calculator to find the nearest degree. θ = tan-1(5.0/12) ≈ 22.6°.
Therefore, the smallest angle in the triangle is approximately 22.6 degrees.
What is the place value of the 4 in the number 5,679.04
Find the cost per pound of a "house blend" of coffee that is made from 20 lb of Central American coffee that costs $7 per pound and 30 lb of South American coffee that costs $4.50 per pound
The first three values in a selected series are 3, 6, and 9. what are the next three va;ies that will be inserted by autofill?
Answer:
the answer is 12, 15. and 18.
Step-by-step explanation:
Is 25/99 a terminating or repeating decimal
The graph of y = –3x + 4 is:
A. a point that shows the y-intercept.
B. a line that shows the set of all solutions to the equation.
C. a point that shows one solution to the equation.
D. a line that shows only one solution to the equation.
Answer: The answer is B, just got this one on a test.
Step-by-step explanation:
Suppose you buy a piece of office equipment for $9,000.00. After 5 years you sell it for a scrap value of $2,000.00. The equipment is depreciated linearly over 5 years. The value of the piece of equipment after 2 years is (rounded to the nearest whole dollar)
The value of the piece of equipment after 2 years is $6,200.00.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
The equipment is depreciated linearly, which means that its value decreases at a constant rate each year. We can find the rate of depreciation by subtracting the scrap value from the purchase price, and then dividing by the number of years of useful life:
Rate of depreciation = (Purchase price - Scrap value) / Useful life
Rate of depreciation = (9000 - 2000) / 5
Rate of depreciation = 1400
This means that the equipment loses $1,400 of value each year. After 2 years, the value of the equipment will be:
Value after 2 years = Purchase price - (Rate of depreciation x Number of years)
Value after 2 years = 9000 - (1400 x 2)
Value after 2 years = 6200
Therefore, the value of the piece of equipment after 2 years is $6,200.00.
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Last year, Amanda had
$10,000
to invest. She invested some of it in an account that paid
6%
simple interest per year, and she invested the rest in an account that paid
10%
simple interest per year. After one year, she received a total of
$760
in interest. How much did she invest in each account?
Greg drank 5 cups of water on Monday. He drank 4 cups of water on Tuesday. How many 1/4 cup servings of water did Greg drink on Monday and Tuesday combined?
At full power, how long would it take for the car to accelerate from 0 to 64.0 mph ? neglect friction and air resistance. express your answer in seconds.
x+2y=8 in slope intercept form
[tex]x+2y=8[/tex] can be written in a slope-intercept form as [tex]y = 4-\dfrac{x}{2}[/tex].
SlopeA slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
Given to us,[tex]x+2y=8[/tex]
To find the slope-intercept formTo find the function, simply isolate y.
[tex]x+2y=8\\2y = 8-x\\y = \dfrac{8-x}{2}\\\\y = \dfrac{8}{2}-\dfrac{x}{2}\\\\y = 4-\dfrac{x}{2}[/tex]
Hence, [tex]x+2y=8[/tex] can be written in a slope-intercept form as [tex]y = 4-\dfrac{x}{2}[/tex].
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For a fixed loan amount, what happens to the monthly payment as the annual rate increases? a. as the annual rate increases, the monthly payment increases c. as the annual rate increases, the monthly payment stays the same b. as the annual rate increases, the monthly payment decreases d. no correlation
Each side of a square is increasing at a rate of 5 cm/s. at what rate is the area of the square increasing when the area of the square is 49 cm2? 70 cm2/s
X/2-18=(-28)
What is x?
X=?
30 + (.0825 x 30) + (15% x 30) =
You purchase three packs of batteries at $11.99/pack. You have a coupon for 10% off and the sale tax is 7% how much is the total cost of your purchase?
The answer is 34.64. C.
The entire purchase of the three items cost about $34.
How to determine the total cost?The given parameters are:
The cost of one packs of batteries is $11.99/pack.
Coupon = 10% off
The total cost is then calculated using:
Total = (three packs of batteries) * (1 - Coupon)
So, we have:
Total = (11.99 + 11.99 + 11.99 ) * (1 - 10%)
Evaluate,
Total = 34.47
Approximate
Total = 34
Hence, the entire purchase of the three items cost about $34.
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Find two numbers with a sum of 20 and a difference of 14.
Suppose that f(t)f(t) is continuous and twice-differentiable for t≥0t≥0. further suppose f′′(t)≤3f″(t)≤3 for all t≥0t≥0 and f(0)=f′(0)=0f(0)=f′(0)=0. using the racetrack principle, what linear function g(t)g(t) can we prove is greater than or equal to f′(t)f′(t) (for t≥0t≥0)?
(x) is continuous and twice differentiable for ±≥ 0. Suppose f”( ±) ≤ 5 for all ±≥ 0 and f (0) = f’(0) = 0. The linear function with a derivation of 0 is y = 0. Thus we have g(t) = 0. The quadratic function with concavity 5 and initial slope 0 is y = 5/2 x^2 + 0x. Therefore, h(t) = (5/2)x^2
Given the conditions, the function g(t)=3t is always greater than or equal to f'(t), as it represents the maximum possible velocity considering the maximum constant acceleration of 3 over time.
Explanation:Given that f(t) is a continuous and twice-differentiable function for t≥0 and that f''(t)≤3 for all t≥0, the function f(t) represents the position of an object over time, with f'(t) and f''(t) being the velocity and acceleration, respectively. Further, given that f(0)=f'(0)=0, it is stated that at time t=0, the object is at the origin and is at rest.
Using the Racetrack Principle, we know that velocity must be less than or equal to the maximum acceleration times time. In plain terms, the actual speed of a body at a time 't' (f'(t)) could not be more than the distance it would have covered if it was accelerating at the maximum possible rate from rest. Since f''(t)≤3, the maximum possible acceleration is 3.
Thus, for all t≥0, if we consider the linear function g(t)=3t, we can say g(t) is greater than or equal to f'(t). Because even if the acceleration was at the maximum value of 3 for the entire duration, the velocity wouldn't exceed 3t.
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The price of 6 pretzels is $5.10. Simon and Sofia bought 8 pretzels and shared the cost equally. How much did each person pay?
which pair of fractions is equivalent to this pair : 3/5 and 2/7
a. 21/35 & 10/35
b. 10/35 & 7/35
c. 7/35. & 5/35
d. 24/35 & 12/35
You are planning a party and want to know how many cans of soda to buy. a genie offers to tell you either the mean number of cans guests will drink
a square has the side measurment of s = 2 3 over 2 using the formula 1= s^2 find the area of the square
The point(3,7) is reflected in the y axis what are the coordinates now
Two negative integers are five minutes apart on the number line, and their product is 126. What is the sum of the two integers?
"sam's furniture was destroyed by a fire. the furniture cost $1200 when it was purchased, but similar new furniture now costs $1800. assuming the furniture was 50 percent depreciated, what is the actual cash value of sam's loss?"
The actual cash value of Sam's furniture loss is $600.
To calculate the actual cash value of Sam's furniture loss, we first determine the amount of depreciation applied to the original purchase price. Since the furniture was 50 percent depreciated, we calculate this amount to be 50% of $1200, which is $600. This means the depreciated value of the furniture is $1200 - $600 = $600. However, because the replacement cost of new, similar furniture is now $1800, this does not affect the actual cash value of the lost furniture, which remains at the depreciated value of $600. So the actual cash value of Sam's loss is $600.
Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose the entire history of Earth is represented with a 1000-meter-long timeline, with the birth of Earth on one end and today at the other end.
2 billion years is represented by how many meters of the timeline?
10 11/12 + 7 1/4 =
A. 3 8/12
B. 3 2/3
C. 17 1/4
D. 18 1/6
1. 3/5x -7 = 23
A. x = 40
B. x = 45
C. x = 50
D. x = 55
2.When Patrick and Cameron went bowling at Victory Lanes, they spent a total of $42. This included rental of shoes at $3.50 per pair. Patrick bowled 2 games, and Cameron bowled 3 games.
How much did each game cost?
A. $6.00
B. $7.00
C. $7.70
D. $8.75
3.A local movie theater offers a special deal for birthday parties. The price, which covers the cost of the tickets and a box lunch, includes a flat fee of $75 plus $5 per ticket. Sarah’s parents spent $150 altogether at the theater to celebrate her birthday.
Which equation can be used to determine how many children, x, were in the group?
A. 75/150=5x
B. 150/75=5x
C. 150 = 5x – 75
D. 150 = 5x + 75
4. 35 + 0.25x = 53.75
A. x = 75
B. x = 140
C. x = 215
D. x = 250
5.T he perimeter of this isosceles triangle is 47 cm.
top point. (B) left bottom point (A) right bottom point (C) in between 12cm
What is the length of each of its legs (it doesn't have legs)?
A. 15 cm
B. 17.5 cm
C. 19.5 cm
D. 35 cm
-3.1 * (- 2.9) Please help! Math.
Convert 604,800 seconds to weeks using Dimensional analysis
Bob is a high school basketball player. his probability of making a free throw is 0.70. let x denote the number of hits in 10 shots. . find the probability that bob makes at least 9 hits. the probability is _____________.