Answers
The angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.
What is unit circle in trigonometry?A circle having a radius of 1 that is centred at the origin of a coordinate plane is known as the unit circle. The sine, cosine, and tangent values for every angle in the unit circle are frequently defined in trigonometry.
A radian-measured angle that begins at the positive x-axis and rotates anticlockwise around the circle can be used to represent each point on the unit circle. (Cos, Sin) are the coordinates of the point on the unit circle that corresponds to the angle.
For the given triangle first determine the value of the height from, the player to the top of the baseball pole as follows:
10 - 5.8 = 4.2 units
Now, using the trigonometric identity of tangent we have:
tan θ = opposite / adjacent
tan θ = 4.2 / 15
θ = tan⁻¹(4.2 / 15)
Hence, the angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.
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Related Questions
Given the graph of y=f(x) below, find the value f(4).
Answers
The numeric value of the function at x = 4 is given as follows:
f(4) = 0.
How to obtain the numeric value of the function?The expression for the numeric value of the function in this problem is given as follows:
f(4).
This means that the input is given as follows:
x = 4.
Passing a vertical line through x = 4 the value of y in which the vertical line crosses the graph is given as follows:
y = 0.
Hence the numeric value is given as follows:
f(4) = 0.
Missing InformationThe graph is given by the image presented at the end of the answer.
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the volume of both of these trapezoid prisms is 24 cubic units. their heights are 6 and 8 units as labeled. What is the area of a trapezoidal base of each prism
Answers
the area of the trapezoidal base of the first prism is 9 square units, and the area of the trapezoidal base of the second prism is 16 square units.
What is Volume of both the trapezoidal prisms?
volume = area of cross section of object* height of object (A)
V = (1/2) * h * (b1 + b2) * H
For the first trapezoid prism, we have:
24 = (1/2) * 6 * (b1 + b2) * 8
Simplifying this equation, we get:
3 = (b1 + b2)
For the second trapezoid prism, we have:
24 = (1/2) * 8 * (b1' + b2') * 6
Simplifying this equation, we get:
4 = (b1' + b2')
A = (1/2) * h * (b1 + b2)
For the first trapezoidal prism:
A = (1/2) * 6 * 3
A = 9 square units
For the second trapezoidal prism:
A = (1/2) * 8 * 4
A = 16 square units
Therefore, the area of the trapezoidal base of the first prism is 9 square units, and the area of the trapezoidal base of the second prism is 16 square units.
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Plot the numbers -1 1/6 and 7/3 on the number line below.
Answers
The number line where we plotted -1 1/6 and 7/3 is added as an attachment
Plotting -1 1/6 and 7/3 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-1 1/6 and 7/3
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-7/6 and 7/3
Rewrite the denominators of the fractions
So, we have
-7/6 and 14/6
This means that we can plot -7/6 at -7 and 7/3 at point 14 where the difference in each interval is 1/6
Using the above as a guide, we have the following:
The number line is attached
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answers
2 + x = 5
x + 1 = 49
-5 + x = -2
Explanation:
Subtracting 2 from both sides of the equation 2 + x = 5 gives x = 3, which is the solution to the equation.
Subtracting 1 from both sides of the equation x + 1 = 49 gives x = 48, which is the solution to the equation.
Adding 5 to both sides of the equation -5 + x = -2 gives x = 3, which is the solution to the equation.
Use the following diagram to answer questions 11 – 16.
Name an acute angle and give its measure. (2 points)
Angle: ______ Measure: _____
Name an obtuse angle and give its measure. (2 points)
Angle: _____ Measure: _____
Answers
The answers to Q11 to 14 with the figure representing angles with protractor are as follows:
11.Acute angle= JEH & measure=25°
12.Obtuse angle=JEK & measure=75°
13.One right angle=DEJ
14.One straight angle=DEF
What is protractor ?
With the aid of the scale on it, it serves as a tool for measuring angles. Protractors often feature two sets of numbers that face each other. A protractor is a tool having a semicircular shape and markings from 0° to 180° on both its inner and outer scales. Angles come in many different shapes and sizes in geometry, including obtuse (>90), acute (90), right (90), reflex (180–270), complete (360), and straight (>90).(180).
11)Acute angles:
HEJ=25
JEK=50
KEF=40
HED=65
12)Obtuse angles:
KED=140
JEK=75
13)right angles:
JEF
JED
14)straight lines
DEF
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Prehistoric cave paintings were discovered in a cave in France. The paint contained
17% of the original carbon-14. Use the exponential decay model for carbon-14,
A=Age-0.000121t
to estimate the age of the paintings?
Answers
k = ln(1/2) / 5700
k = -0.000121
Now we can use the formula for exponential decay to find the age of the paintings:
0.17 = e^(-0.000121t)
ln(0.17) = -0.000121t
t = ln(0.17) / (-0.000121)
t ≈ 22,000 years
Therefore, the age of the paintings is approximately 22,000 years.
The second option is to issue new preferred stock at a market price of $56,000, with a $5.00 annual dividend. The net proceeds per share after paying flotation costs are $51.50.
Answers
The cost of capital for the second option, issuing new preferred stock, is 0.00356, or 0.356%. This means that for every dollar of capital raised through issuing preferred stock, the company will need to pay 0.356 cents in annual interest or dividend payments.
To calculate the cost of capital for the second option, we need to first calculate the cost of the preferred stock. The cost of preferred stock is the dividend yield, or the annual dividend divided by the market price of the stock. In this case, the annual dividend is $5.00 and the market price is $56,000.
Cost of preferred stock = Annual dividend / Market price of stock
Cost of preferred stock = $5.00 / $56,000
Cost of preferred stock = 0.000089
To calculate the cost of capital, we need to weight the cost of preferred stock with the proportion of capital that is financed by preferred stock. Let's assume that the preferred stock will finance 40% of the total capital.
Cost of capital = Cost of preferred stock * Proportion of capital financed by preferred stock
Cost of capital = 0.000089 * 0.40
Cost of capital = 0.0000356
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What is the probability that it will land on tails twice and heads once?
Answers
Answer:
3/8
Explanation:
I just know :) (;
PLS HELP 20 POINTS!
Below is a portion of the graph of a function, y = h(x):
If the graph of y = h(x-3) is drawn on the same set of axes as the graph above, then the two graphs intersect at one point. What is that point?
Answers
We are given the graph of
y = h(x)
Required;If the graph of y = h(x-3) is drawn on the same set of axes as the graph above, then the two graphs intersect at one point. What is that point?
Step-by-step solution;We begin by identifying two points on the graph of h(x).
These are;
P1(-2,3), P2(1,3)
next, we are told that the graph of y = h(x - 3) is drawn on the same axis, which means the graph of the function has been shifted 3 units to the right.
Therefore, the points identified above will now be;
P 1 Rightarrow (- 2 + 3, 3)
P_{1}' = (1, 3)
P 2 Rightarrow (1 + 3, 3)
P_{2}' = (4, 3)
In summary,
ANSWER:The point is
(1,3)Express the answers in simplest form. If a die is rolled one time, find the probability of (a) Getting a 6. (b) getting an even number (c) number greater than 3 (d) number greater than 0 (E) number greater than 4 and an odd number?
Answers
Answer:
a) 1/6
b) 1/2
c) 1/2
d) 1
e) 1/6
Step-by-step explanation:
a)Getting a six
=1/6
b)Gettingan even number =3/6=1/2
c)number greater than 3
=3/6=1/2
d)number greater than 0
=6/6=1
e)number greater than 4 and an odd number
=1/6
The volume of a rectangular prism is calculated using the formula V=Zoey, where V is the volume of the prism, I and W are the length and width base of the prism, respectively and h is the height of the prism
Answers
Answer:
I'm sorry, but there seems to be an error in the formula you provided. The correct formula for finding the volume (V) of a rectangular prism is V = l x w x h, where l, w, and h are the length, width, and height of the prism, respectively.
Exercise 6.2.8: Solve ′′′ + = 3( − 1) for initial conditions (0) = 1 and ′(0) = 0, ′′(0) = 0.
Answers
Answer:
Step-by-step explanation:
To solve the differential equation:
y′′′ + y = 3(y′ − 1)
we first find the characteristic equation:
r^3 + 1 = 0
The roots of this equation are:
r = -1, 0 ± i
So, the general solution of the homogeneous equation (y′′′ + y = 0) is:
y_h(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t)
To find a particular solution of the non-homogeneous equation (3(y′ − 1)), we assume a solution of the form:
y_p(t) = a t + b
Taking the first, second and third derivatives of y_p(t), we get:
y′_p(t) = a
y′′_p(t) = 0
y′′′_p(t) = 0
Substituting these into the differential equation, we get:
0 + (a t + b) = 3(a - 1)
Solving for a and b, we get:
a = 1
b = 2
Therefore, the particular solution of the non-homogeneous equation is:
y_p(t) = t + 2
So, the general solution of the non-homogeneous equation is:
y(t) = y_h(t) + y_p(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t) + t + 2
To find the values of c1, c2 and c3, we use the initial conditions:
y(0) = c1 + c2 + 2 = 1
y′(0) = -c1 + c2 + c3 = 0
y′′(0) = c1 - c2 = 0
Solving these equations simultaneously, we get:
c1 = c2 = 1/2
c3 = -1/2
So, the solution of the differential equation with initial conditions (0) = 1, ′(0) = 0, ′′(0) = 0 is:
y(t) = 1/2 e^(-t) + 1/2 cos(t) - 1/2 sin(t) + t + 2
Three different views of identical cubes are shown at right. What is on the face
opposite the black cirde? Explain/Prove your enswer completely.
A cylinder is sliced at an angle, leaving the shape shown at right. The shorter height
is 12 cm while the longer height is 18 cm. The radius of the base is 4 cm.
What is the volume of this sliced cylinder?
Answers
1) The opposite face of the black circle is, Plus +.
2) The volume of the sliced cylinder is 96π cubic cm.
We have to given that;
Three different views of identical cubes are shown at right.
Now, From first and third dice,
Star is just opposite to symbol ~.
Hence, From second and third dice,
The opposite face of the black circle is, +
2) For the volume of the sliced cylinder, we need to first find the volume of the full cylinder and then subtract the volume of the smaller cylinder that's left after the slice is made.
Hence, The volume of the full cylinder is given by:
V = πr²h
Where r is the radius of the base and h is the height of the full cylinder.
Using the given values, we can find:
V = π(4²)(18)
V = 288π cubic cm
Now, let's find the volume of the smaller cylinder. The shorter height of 12 cm tells us that the slice removed 6 cm from the top of the cylinder. So the height of the smaller cylinder is,
18 - 6 = 12 cm.
The radius remains the same at 4 cm.
Thus, the volume of the smaller cylinder is:
V = π(4²)(12)
V = 192π cubic cm
Finally, we can find the volume of the sliced cylinder by subtracting the volume of the smaller cylinder from the volume of the full cylinder;
⇒ V = (288π) - (192π)
⇒ V = 96π cubic cm
Therefore, the volume of the sliced cylinder is 96π cubic cm.
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math please help me on thissssssss hurry
Answers
The standard form based on the information given will be:
a) 2.35 x 10^-3 = 0.00235 (in standard form)
b) 2.35 x 10^3 = 2350 (in standard form)
How to explain the standard formIt should be noted that in mathematics and computer science, a normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.
Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way
he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.
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Find the value of x, y, and z in the rhombus below.
Answers
The value of x, y, and z in the rhombus below x = 20, y = -7, z = -11
How to find the values of x, y and z?Recall that a rhombus is an equilateral parallelogram with both pairs of opposite sides parallel and all sides the same length.
Sum of interior angles of a rhombus = 360°
The opposite angles of a rhombus are equal to each other.
The adjacent angles are supplementary (add up to 180°)
Therefore,
66 + (6x - 6) = 180
⇒ 66 + 6x - 6 = 180
⇒ 6x = 180 - 66 + 6
⇒ 6x = 120
⇒ x = 120 ÷ 6
⇒ x = 20
66 + (-10z + 4) = 180
⇒ 66 - 10z + 4 = 180
⇒ -10z= 180 - 66 - 4
⇒ -10z = 110
⇒ z = 110 ÷ -10
⇒ z = -11
(6x - 6) + (-10y - 4) = 180
⇒ 6x - 6 - 10y - 4 = 180
⇒ 120 - 6 - 10y - 4 = 180
⇒ -10y = 180 - 120 + 6 + 4
⇒ -10y = 70
⇒ y = 70 ÷ -10
⇒ y = -7
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1. Four family members attended a
family reunion. The table below
shows the distance each person
drove and the amount of time each
person traveled.
Family Reunion Travel:
•Name
Hank
Laura
Nathan
Raquel
•Distance
176 miles
150 miles
112.5 miles
286 miles
• Travel Time
3 hours 12 minutes
2 hours 30 minutes
2 hours 15 minutes
4 hours 24 minutes
If each person drove at a constant rate, who drove the fastest (in miles per hour)?
A. Hank
B. Laura
C. Nathan
D. Raquel
Answers
If each person drove at a constant rate, the person who drove the fastest (in miles per hour) is: C. Nathan.
What is speed?In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;
Miles per hour (mph).Kilometers per hour (kph).Meter per seconds (m/s).How to calculate the speed?In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
For Hank, we have:
Speed = 176/3.2 = 55 miles per hour.
For Laura, we have:
Speed = 150/2.5 = 60 miles per hour.
For Nathan, we have:
Speed = 112.5/2.25 = 50 miles per hour (Fastest).
For Raquel, we have:
Speed = 286/4.4 = 65 miles per hour.
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2as = vf2-vo2 despejar para a
Answers
Para despejar "a" de la ecuación 2as = vf^2 - vo^2, podemos seguir los siguientes pasos:
1. Sumar vo^2 a ambos lados de la ecuación:2as + vo^2 = vf^2
2. Dividir ambos lados de la ecuación por 2s:a = (vf^2 - vo^2) / 2s
Por lo tanto, la fórmula para calcular "a" a partir de la distancia de desplazamiento "s", la velocidad final "vf" y la velocidad inicial "vo" es:
a = (vf^2 - vo^2) / 2s
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Comparing Rates of Change Station Cards
Two students are texting.
●
Student A is texting at the rate given in the table.
Number of
Tests Sent
0
1
2
3
4
12
Number of Texts Sent
てん
0
10.
5
10
Student B is texting at the rate given in the graph.
15
20
2 3 4
Minutes
5
7+
What is the different in the texting rate of these two students?
what is student A's rate ?
Student B's rate ?
what is
Answers
Answer:
To compare the texting rates of Student A and Student B, we need to calculate their respective rates of change.
For Student A, we can use the formula for the slope of a line:
slope = (change in y) / (change in x)
In this case, the "y" variable represents the number of texts sent, and the "x" variable represents the number of tests sent. Looking at the table, we can see that Student A sent 10.5 texts after sending 1 test, and 10 texts after sending 2 tests. So the change in y is -0.5 (10.5 - 10), and the change in x is 1. Therefore:
slope = (-0.5) / 1 = -0.5
So Student A's texting rate is -0.5 texts per test.
For Student B, we can look at the graph and find the slope of the line connecting any two points. Let's choose the points (2, 15) and (5, 23) because they are easy to read off the graph. The change in y is 8 (23 - 15), and the change in x is 3 (5 - 2). Therefore:
slope = 8 / 3 = 2.67
So Student B's texting rate is 2.67 texts per minute.
To find the difference in their texting rates, we simply subtract:
difference = Student B's rate - Student A's rate
difference = 2.67 - (-0.5) = 3.17
So the difference in their texting rates is 3.17 texts per test.
Step-by-step explanation:
nd the compound interest and future value. Do not round intermediate steps. Round your answers to the neare Principal Rate Compounded Time $865 4% Annually 10 years The future value is $ and the compound interest is $ X Start over Ś
Answers
All the values are,
Compound interest = $1280.2
Future value = $1280.2 + $x
Given that;
P = $865
r = 4%
T = 10 years
Formula is,
Compound Interest = P(1 + r)^t
Where, Principal = P, Interest rate = r, Number of compounds = n, Interest time = t
Plug, p = 865, r = 0.04, t = 10
Compound Interest = 865 (1 + 0.04)¹⁰
Compound Interest = 865 (1.04)¹⁰
Compound Interest = 865 x 1.48
Compound Interest = 1280.2
Hence, We get;
Future value = Compound Interest + Principal
Future value = $1280.2 + $x
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Given that d is indirectly proportional to e+8, if d = 2 when e = 8, what is e when d = 4?
(A)-6
(B)-2
(9)0
(E) 10
Answers
4x Terry and Susan both detail cars. Terry chargers $75 for each car and Susan charges $70 for each car. This week Terry made an additional $65 in tips and Susan made an additional $95 in tips. Given that T and S represent the number of cars detailed by Terry (T) and Susan (S), which expression can be used to represent their combined earnings for the week?
Answers
The correct option- C: 75T + 70S + 160, represent their combined earnings of Terry and Susan for the week.
Explain about the variable:Every feature, number, or amount that can be gauged or quantified is referred to as a variable. An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown.
Given data:
T - number of cars detailed by Terry (T)
S - number of cars detailed by Susan (S).
Terry's charge - $75 for each car .
Total Terry's charge for T number of cars - 75T
Additional tip - $65
Susan's charge - $70 for each car.
Total Susan's charge for S number of cars - 70T
Additional tip - $95
Combined earnings = 75T + 65 + 70T + 95
Combined earnings = 75T + 70T + 160
Thus, 75T + 70S + 160, represent their combined earnings of Terry and Susan for the week.
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Complete question:
Terry and Susan both detail cars. Terry chargers $75 for each car and Susan charges $70 for each car. This week Terry made an additional $65 in tips and Susan made an additional $95 in tips. Given that T and S represent the number of cars detailed by Terry (T) and Susan (S), which expression can be used to represent their combined earnings for the week?
A: 145(T+S) + 160
B: 65T + 70S + 160
C: 75T + 70S + 160
D: 145TS + 160
How many possible winning number combinations a bettor may opt to select in a 6/42 Lottery? And based on this, what is the probability a bettor may win the lottery jackpot prize?
Answers
There are 5,245,786 possible winning number combinations in a 6/42 lottery, and for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.
What is the combinations?
Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order in which the items are selected. In other words, combinations are the different ways of choosing a group of items without taking into account their arrangement or order.
In a 6/42 lottery, there are 6 numbers drawn from a pool of 42 numbers. To determine the number of possible winning number combinations, we can use the formula for combinations:
C(n,r) = n! / (r! * (n-r)!)
where n is the total number of items in the set and r is the number of items being chosen.
In this case, we have 42 numbers in the pool and we need to choose 6 numbers, so the formula becomes:
C(42,6) = 42! / (6! * (42-6)!)
which simplifies to:
C(42,6) = 5,245,786
Therefore, there are 5,245,786 possible winning number combinations in a 6/42 lottery.
To calculate the probability of winning the jackpot prize, we need to divide the number of ways to win by the total number of possible outcomes. Since there is only one winning combination, the probability of winning the jackpot is:
1 / 5,245,786
which simplifies to approximately:
0.000019% or 1 in 5,245,786.
This means that for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.
hence, there are 5,245,786 possible winning number combinations in a 6/42 lottery, and for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.
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April shoots an arrow upward at the speed of 80 feet per second from a platform 50 feet high. The pathway of the arrow can be represented by using the equation h(t)=-16t^2+V₀t+h₀
a) What is the maximum height of the arrow?
b) About how many seconds will it take for the arrow it reach the ground?
c) How many seconds after launch will the arrow be 114 feet high?
I need this quickly please
Answers
h(2.5) = -16(2.5)^2 + 80(2.5) + 50 = 125 feet.
Therefore, the maximum height of the arrow is 125 feet.
b) To find how long it takes for the arrow to reach the ground, we need to find the value of t when h(t) = 0. Substituting h(t) = 0 and solving for t, we get:
0 = -16t^2 + 80t + 50
t^2 - 5t - 50/16 = 0
(t - 10/4)(t + 5/4) = 0
Therefore, t = 2.5 seconds or t = -1.25 seconds. Since the time cannot be negative, the arrow will hit the ground after approximately 2.5 seconds.
c) To find the time when the arrow is 114 feet high, we need to solve the equation h(t) = 114. Substituting h(t) = 114 and simplifying, we get:
-16t^2 + 80t + 50 = 114
-16t^2 + 80t - 64 = 0
t^2 - 5t + 4 = 0
(t - 4)(t - 1) = 0
Therefore, t = 1 second or t = 4 seconds. Since the arrow is at a height of 114 feet after it has been launched, the answer is t = 1 second.
Find the length of the third side of the right triangle 19, 21 and c
Answers
The length of the hypotenuse is 28.3
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.
If a and b are the legs of the triangle and c is the other side(hypotenuse) then,
c² = a²+b²
c² = 19² +21²
c² = 361+441
c² = 802
c = √802
c = 28.3
therefore , if the two legs are 19 and 21, the length of the other side is 28.3
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The length of the hypotenuse is 28.3
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.
If a and b are the legs of the triangle and c is the other side(hypotenuse) then,
c² = a²+b²
c² = 19² +21²
c² = 361+441
c² = 802
c = √802
c = 28.3
therefore , if the two legs are 19 and 21, the length of the other side is 28.3
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ASAPP Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
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identify one pair of verticle angles in the diagram below.
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Answer:
One pair of vertical angles is a and c.
Find the indicated measure. Lines that appear to be tangent are tangents(help pls)
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Step-by-step explanation:
This is basically an inscribed angle in a circle which encompasses twice as many degrees of arc (246) as the angle measure : angle 3 = 123 degrees
Calculate the height of the Zeta Tower as a percentage of the height of the Delta tower
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The height of the Zeta Tower as a percentage of the height of the Delta tower is the 94.72%
How to find the the height of the Zeta Tower as a percentage of the height of the Delta tower?Here we know that:
height of the Delta tower = 55mThe epsilon tower is 23% taller than the delta one, then the height is:
H = 55m*(1 + 0.23) = 67.65 m
And we know that the Zeta tower is 23 short than the epsilon one, then the height of this twoer is.
H' = 67.65m*(1 - 0.23) = 52.0905 m
The height of the delta tower is 55m, this is our 100%.
Then the height of the zeta tower written as a percentage will be:
(52.0905 m/55m)*100% = 94.72%
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Can someone please help me
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Answer:
Step-by-step explanation:
HELP PLEASE!!! Unit 10 circles homework central angles and arc measurements
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All the arcs are derived as given below.
How did to arrive at the figures above?5)
∡LO = 180°
so
∡KL = ∡ON = 180-90-67
∡KL = ∡ON = 23°
∡OM = 90 + 23 = 113°
∡ NL = 67 + 90 = 157°
7)
Where
(9x + 23) + 31 = 180
9x + 54 = 180
9x = 180-54
9x = 126
x = 126/9
x = 14
9.
(21x-9) = 90+27
21x - 9 = 117
21x = 117 + 9
x = 126/21
x = 6
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