Answers
The value of sinα in the right angle triangle is [tex]\frac{16\sqrt{281} }{78961}[/tex]
What is a right-angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle. The right triangle plays an important role in trigonometry.
sin α = opposite/hypotenuse
opposite = 16, hypotenuse [tex]\sqrt{281}[/tex]
sin α = [tex]\frac{16}{\sqrt{281} }[/tex]
By rationalizing, the denominator which means multiply the fraction by [tex]\frac{\sqrt{281} }{\sqrt{281} }[/tex]
[tex]\frac{16}{\sqrt{281} }[/tex] x [tex]\frac{\sqrt{281} }{\sqrt{281} }[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
sin [tex]\alpha[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
In conclusion, the value of sin[tex]\alpha[/tex] = [tex]\frac{16\sqrt{281} }{78961}[/tex]
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Related Questions
For a given set of rectangles, the length is inversely proportional to the width. In one
of these rectangles, the length is 25 and the width is 3. For this set of rectangles,
calculate the width of a rectangle whose length is 5.
Answers
Answer:
Step-by-step explanation:
Answer:
The width is 8 units
Step-by-step explanation:
This is a variation problem we are to work with.
Length is inversely proportional to width, let length be l and width be w
modeling the statement mathematically, we have lw = k where k is the proportionality constant
Now let’s get k from l = 12 and w = 6
k = 12 * 6 = 72
Now for the second rectangle also;
lw = k given l = 9
9w = 72
w = 72/9
w = 8
What is the value of sin E?Give your answer as a simplified fraction.
Answers
For this problem we first use the pythagorean theorem to find QH
[tex]\begin{gathered} QH^2+HE^2=QE^2 \\ QH^2=QE^2-HE^2=101^2-99^2=400 \\ QH=20 \end{gathered}[/tex]Then
[tex]\sin (E)\text{ =}\frac{QH}{QE}=\frac{20}{101}[/tex]Can I get an answer please?
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the rule is reflextive
here(x, y) is changing into (x , -y)
the process is called translation
Find the slope between the points:(1,7)(-2,3)
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Using the formula,
[tex]m=\frac{7-3}{1-(-2)}\rightarrow m=\frac{4}{1+2}\rightarrow m=\frac{4}{3}[/tex]Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 7 ) and (x₂, y₂ ) = (- 2, 3 )
m = [tex]\frac{3-7}{-2-1}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
The birth weights of the 908 babies born at Valley Hospital in 2019 were normally
distributed with a mean of 7.2 pounds with a standard deviation of 1.5. Use the Z-
Score Table from the book to determine the number of babies that weighed more
than 10 pounds.
Answers
The number of babies that weighed more than 10 pounds is 43 using Z-
Score Table.
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a "bell curve."
Given that total number of babies is 908.
The mean of the normal distribution is 7.2 pound.
The standard deviation of the normal distribution is 1.5 pound.
The formula of z score is z = (x - μ)/σ
In the given question x = 10, μ = 1.5, σ = 7.2
z score = (10 - 7.2)/1.5 = 1.86667
P-value from Z-Table:
P(x<10) = 0.96903
P(x>10) = 1 - P(x<10) = 0.030974
The number of babies that weighed more than 10 pounds is ( 0.030974 × 908) = 43.39 = 43 (approx.)
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What is the solution to the system of equationsy = 3x - 2 and y = g(x) where g(x) is defined bythe function below?y=g(x)
Answers
we need to write the equation of the graph
it is a parable then the general form is
[tex]y=(x+a)^2+b[/tex]where a move the parable horizontally from the origin (a=negative move to right and a=positive move to left)
and b move the parable vertically from the origin (b=negative move to down and b=positive move to up)
this parable was moving from the origin to the right 2 units and any vertically
then a is -2 and b 0
[tex]y=(x-2)^2[/tex]now we have the system of equations
[tex]\begin{gathered} y=3x-2 \\ y=(x-2)^2 \end{gathered}[/tex]we can replace the y of the first equation on the second and give us
[tex]3x-2=(x-2)^2[/tex]simplify
[tex]3x-2=x^2-4x+4[/tex]we need to solve x but we have terms sith x and x^2 then we can equal to 0 to factor
[tex]\begin{gathered} 3x-2-x^2+4x-4=0 \\ -x^2+7x-6=0 \end{gathered}[/tex]multiply on both sides to remove the negative sign on x^2
[tex]x^2-7x+6=0[/tex]now we use the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a is 1, b is -7 and c is 6
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(1)(6)}}{2(1)} \\ \\ x=\frac{7\pm\sqrt[]{49-24}}{2} \\ \\ x=\frac{7\pm\sqrt[]{25}}{2} \\ \\ x=\frac{7\pm5}{2} \end{gathered}[/tex]we have two solutions for x
[tex]\begin{gathered} x_1=\frac{7+5}{2}=6 \\ \\ x_2=\frac{7-5}{2}=1 \end{gathered}[/tex]now we replace the values of x on the first equation to find the corresponding values of y
[tex]y=3x-2[/tex]x=6
[tex]\begin{gathered} y=3(6)-2 \\ y=16 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=3(1)-2 \\ y=1 \end{gathered}[/tex]Then we have to pairs of solutions
[tex]\begin{gathered} (6,16) \\ (1,1) \end{gathered}[/tex]where green line is y=3x-2
and red points are the solutions (1,1)and(6,16)
the approximate weights of two animals are 8.16 x 10 4 lbs. and 9.2 x 10 4 lbs. find the total weight of the two animals. write the final answer in scientific notation with the correct number of significant digits. 1.2 x 103 lbs. 1.19 x 103 lbs. 11 x 102 lbs. 5.8 x 102 lbs.
Answers
The scientific notation of weight of animal is 1.736 × 10^5.
What is scientific notation?
The scientific notation helps us to represent the numbers which are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small. Learn power and exponents for better understanding.
The numbers can be written as a×10ⁿ.
Given, the weight of one animal is 8.16 × 10^4 and other animal is 9.2×10^4
Therefore, the sum of the weights in scientific notation is
=8.16 × 10^4 +9.2×10^4
Since they have same power of exponent, hence
=(8.16+9.2)10^4 =17.32×10^4
or we can write it as
1.732×10^5.
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A bus traveled on a level road for 6 hours at an average speed of 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 2 hour find the average speed on the level road if the entire trip was 360 miles.
Answers
Given:
A bus traveled on a level road for 6 hours at an average speed of 20 miles per hour .
The distance is calculated as,
[tex]\begin{gathered} d_1=r\times t \\ d_1=6\times20 \\ d_1=120\text{ miles} \end{gathered}[/tex]The distance covered by bus on level road is faster than it raveled on a winding road.
The time spent on the winding road was 2 hour. So, the distance is,
[tex]\begin{gathered} d_2=r\times t \\ d_2=2r\text{ miles} \end{gathered}[/tex]The total distance was 360 miles.
[tex]\begin{gathered} d_1+d_2=360 \\ 120+2r=360 \\ 2r=360-120 \\ 2r=240 \\ r=120 \end{gathered}[/tex]Answer: the average speed on the level road is 120 mph
QuestionThe width of a rectangle is 6 less than the length, let L represent the length of the rectangle, Write an expression for thewidth of the rectangle
Answers
Since L represents the length and the width is 6 less the length, if w denotes the width, we have
[tex]w=L-6[/tex]that is, the width measures L-6
experimental and theoretical
Answers
Spinning a three:
experimental = 11/50
theoretical = 1/5
Spinning an even number:
experimental = 21/50
theoretical = 2/5
Spinning an odd number:
experimental: 29/50
theoretical: 3/5
Spinning a number less than 5:
experimental: 21/25
theoretical: 4/5
2. Fill in the blanks below to show the sum of (2x2 + 4x) and (x2 + 8).
Answers
Given the function (2x^2+4x) and (x^2+8), we are to find the sum of both functions. This is as shown below;
(2x^2+4x) + (x^2+8) [sum means addition]
Next is to collect the like terms based on the power
= (2x^2+x^2)+4x +8
Evaluate the expression in parenthesis
= 3x^2 + 4x + 8
Hence the sum of (2x2 + 4x) and (x2 + 8) is 3x^2 + 4x + 8
You will have to fil the blanks with the corresponding coefficient of x^2 and x and the constant.
The first blank will be 3 (coefficient of x^2)
The second blank will be 4 (coefficient of x)
The third blank will be 8 (the constant value)Y
I am a rectangle with an area of 100 cm, what is the area of the one of my triangles A. 50 in B. 50 cm C. 100 cm D. 25 cm
Answers
the area of a triangle is half the area of the rectangle:
100 cm / 2 = 50 cm
match the property to the correct step in the problemA.) addition property of equality. B.) subtraction property of equalityC.) distributive property
Answers
In the first step
It is distributive property because we multiplied 10 by 2x and 10 by 4
1. C
In the second step
We add 6x to both sides, then
It is addition property of equality
2. A
In the third step
We subtract 40 from both sides, then
It is the subtraction property of equality
3. B
fill in the blank summataion notation
Answers
we have the sequence
5+9+13+...
we have an arithmetic sequence
a1=5
a2=9
a3=13
a2-a1=9-5=4
a3-a2=13-9=4
the common difference is d=4
the general expression is equal to
[tex]a_n=a_1+d\cdot(n-1)[/tex]we have
a1=5
d=4
substitute
[tex]\begin{gathered} a_n=5+4\cdot(n-1) \\ a_n=4n+1 \end{gathered}[/tex]therefore
the notation is equal to
see the attached figure
please wait a minute to fill the image
The polar equation r=8sin(4θ) graphs as a rose.What is the length of the petals of this rose?
Answers
Polar equations of rose curves follow the pattern:
[tex]r=a\text{ }sin\text{ }n\theta\text{ }[/tex]where:
a = represents the length of the petals
n = represents the number of petals.
Based on the given polar equation, the value of "a" is 8. Since "a" represents the length of the petals, then the length of the petals of this rose is 8 units.
What is the perimeter of the composite figure?6 cm9 cm2 cm10 cm
Answers
As the given figure can be considered as two rectangles,
Consider the first rectangle,
The length is, 9-2 = 7 cm,
The width is, 10-6 = 4 cm.
Therefore, the perimeter is,
[tex]P=2(l+w)=2(7+4)=22\text{ cm}[/tex]For the second rectangle,
[tex]P=2(l+w)=2(10+2)=24\text{ cm}[/tex]Therefore, the total perimeter is,
22 cm + 24 cm = 46 cm.
Cindy is riding her bicycle six miles ahead of Tamira. Cindy is traveling at an average rate of 2 miles per hour. Tamira is traveling at an average rate of 4 miles perhour. Let a represent the number of hours since Tamira started riding her bicycleWhen will Tamira be ahead of Cindy? Write an inequality to represent thissituation
Answers
Given:
Cindy is riding her bicycle six miles ahead of Tamira at an average rate of 2 miles per hour.
Let 'a' represents the number of hours.
Distance travellled by Tamira in a hours = 4a
Distance travelled by Cindy in a hours=2a
[tex]4a>2a+6[/tex]What are the coordinates of the point on the directed line segment from (-1,1) to (8, 10) that partitions the segment into a ratio of 2 to 1?
Answers
Point 1 = (x1,y1)= (-1,1)
Point 2 = (x2,y2)= (8,10)
xp,yp= ? (coordinates of the point)
a:b= 2:1
xp= x1+ a/a+b (x2-x1)
xp= -1+ 2/2+1 (8-(-1))
xp= -1+2/3 (8+1)
xp= -1+2/3(9)
xp= -1+ 6
xp= 5
yp= y1 + a/ a +b (y2-y1)
yp= 1 +2/3 (10-1)
yp =1+2/3 (9)
yp=1+6
yp=7
xp,yp = (5,7)
when you compare the 2016-2017 season with the 2017-2018 season, what was the percent increase in the number of games that the Lakers won ? show your work.
Answers
In order to calculate the percent increase in the number of games that the Lakers won from the 2016-2017 season with the 2017-2018 season we would have to make the following calculation:
percentage of increase=100* (games won 2017-2018-games won 2016-2017)/ (games won 2016-2017)
percentage of increase=100*(35-26)/(26)
percentage of increase=100*0.34615
percentage of increase=34.615%
The percent increase in the number of games that the Lakers won from the 2016-2017 season with the 2017-2018 was 34.615%
In the rectangle below, SU= 4x – 2, RT = 5x-10, and m Z VSR=26°.Find RV and m ZVTS.Rm
Answers
SU and RT are the diagonals of the rectangle and are thus equal.
We the equate them to find x
SU = RT = 4x - 2 = 5x - 10
subtracting 4x from both sides gives:
4x - 2 - 4x = 5x - 10 - 4x
-2 = x - 10
Adding 10 to both sides give:
10 - 2 = x - 10 + 10
x = 8
RV is half of RT
where = RT = 4(8) - 2 = 32 - 2 = 40
Therefore, RV = 40/2 = 20
To calculate angle VTS, we consider that it is in an isosceles triangle with its angle equal to angle VST. Same angle VST is complementary with angle VSR
Therefore, angle VTS = VST = 90 - 26 = 64 degrees (sum of angles in a right angle)
VTS = 64 degrees
In a class of students, the following data table summarizes how many students playan instrument or a sport. What is the probability that a student chosen randomlyfrom the class does not play a sport?Plays an instrument Does not play an instrumentPlays a sport34Does not play a sport136
Answers
First, let's calculate the total number of students in the class:
[tex]3+4+13+6=26[/tex]Out of those 26 students we have
[tex]13+6=19[/tex]19 that do not play a sport.
Therefore the probability that a student chosen randomly
from the class does not play a sport is:
[tex]\frac{19}{26}[/tex]determine the solution to the system. Explain which method you used to determine your solution. 2x+y=-15y-6x=7
Answers
This is the system.
We will use the method of elimination to solve it.
So we will multiply the first equation by 3 and add it to the second one, this will gives us.
[tex]8y=4\rightarrow y=\frac{1}{2}[/tex][tex]2x+\frac{1}{2}=-1\rightarrow2x=-\frac{3}{2}\rightarrow x=-\frac{3}{4}[/tex]how do u solve 6=×+3_2
Answers
To solve the equation, we should isolate x on one side and the numerical term on the other side
So we have to multiply both sides by 2 to cancel the denominator 2 from the right side
[tex]\begin{gathered} 6\times2=\frac{(x+3)}{2}\times2 \\ 12=x+3 \end{gathered}[/tex]Now want to move 3 from the right side to the left side
Subtract 3 from both sides
[tex]\begin{gathered} 12-3=x+3-3 \\ 9=x \end{gathered}[/tex]The solution is x = 9
Solve: -2y ≥ 10y ≤ -5y ≤ 5y ≥ -5y ≥ 5
Answers
Given
[tex]-2y\ge10[/tex]Solution
Recall: Dividing by a negative number means you reverse the inequality symbol
[tex]\begin{gathered} -2y\ge10 \\ divide\text{ both sides by -2} \\ -\frac{2y}{-2}\ge\frac{10}{-2} \\ \\ y\leq-5 \end{gathered}[/tex]The final answer
[tex]y\leq-5[/tex]You have to deliver medicines 1 mile away. In order to do that, you have to which drone to use depending on the size of the blade in the drone. The equation that gives the relationship between the size of the blade (b) in inches and speed (miles/hour) is as follows: Speed = 50-2b In order to deliver the medicine in time, the drone must travel faster than 37 miles/hour. Check the box underneath the blade that you would like to use. Then write the speed of the drone using this blade.
Answers
From the information given,
The equation representing the relationship between the size of the blade (b) in inches and speed (miles/hour) is given as
Speed = 50-2b
Also, the required drone must travel faster than 37 miles/hour.
For the small blade, b = 4 inches
speed = 50 - 2 * 4 = 50 - 8
speed = 42 miles/hour
For the medium blade, b = 6 inches
speed = 50 - 2 * 6 = 50 - 12
speed = 38 miles per hour
For the large blade, b = 8
speed = 50 - 2 * 8 = 50 - 16
speed = 34 miles per hour
Since the speed of the drone with small blade is greater than 37 miles per hour and it is the greatest among the three drones,
The speed of the drone will be 42 miles per hour
9+9x=10x+2 Solve for x
Answers
This problem is about linear equations.
To solve it, we need to find the value of x.
[tex]9+9x=10x+2[/tex]First, we need to organize the equation, all terms without variables at the right side, and all terms with variables at the left side
[tex]9x-10x=2-9\text{ }\rightarrow-x=-7[/tex]Finally, we multiply the equation by -1 to get the proper answer
[tex]x=7[/tex]Therefore, the answer is 7.given : f(x) = x2 - 5 and g(x) = 3x - 1 Find 2g (f(-5))
Answers
The given functions are
f(x) = x^2 - 5
g(x) = 3x - 1
To find 2g(f(- 5)), we would first find f(- 5)
To find f(- 5), we would substitute x = - 5 into f(x) = x2 - 5. It becomes
f(- 5) = (- 5)^2 - 5
f(- 5) = 25 - 5
f(- 5) = 20
Then, we would substitute f(- 5) = 20 into g(x) = 3x - 1
Thus,
g(f(- 5) = 3*20 - 1
g(f(- 5) = 60 - 1
g(f(- 5) = 59
Therefore,
2g(f(- 5)) = 2 * 59 = 118
Find the 10th term of the geometric sequence whose common ratio is 3/2 and whose first term is 3.
Answers
ANSWER:
59049/512
EXPLANATION:
Given:
Common ratio(r) = 3/2
First term(a) = 3
Number of terms(n) = 10
To find:
The 10th term of the geometric sequence
We can go ahead and determine the 10th term of the sequence using the below formula and substituting the given values into it and evaluate;
[tex]\begin{gathered} a_n=ar^{n-1} \\ \\ a_{10}=3(\frac{3}{2})^{10-1} \\ \\ a_{10}=3(\frac{3}{2})^9 \\ \\ a_{10}=3(\frac{19683}{512}) \\ \\ a_{10}=\frac{59049}{512} \end{gathered}[/tex]Therefore, the 10th term of the sequence is 59049/512
This is all the information I was given. O. 2.5.
Answers
The equation of a line in the slope-intercept form is y = mx + b, where m is the slope and b the y-intercept.
If it is known:
- The equation of a parallel line
- One point of the equation
To find the equation of the line, follow the steps:
1. Parallel lines have the same slope. So, use the slope of the parallel line to find the slope of the line.
2. Substitute the point in the equation to find b.
3. Since m and b are known, you found the equation of the line.
Solve for y.2x – 8y = 24
Answers
Answer:
[tex]y=\frac{1}{4}x-3[/tex]Explanation:
Given the equation:
[tex]2x-8y=24[/tex]To solve for y, we follow the steps below:
Step 1: Rearrange to Isolate the term containing y.
[tex]8y=2x-24[/tex]Step 2: Divide both sides by 8.
[tex]\begin{gathered} \frac{8y}{8}=\frac{2x-24}{8} \\ y=\frac{2x-24}{8} \end{gathered}[/tex]Step 3: Simplify
[tex]\begin{gathered} y=\frac{2x}{8}-\frac{24}{8} \\ y=\frac{1}{4}x-3 \end{gathered}[/tex]