Consider a right triangle with a side of length x opposite angle A, a side of length y opposite angle B, and a hypotenuse of length z opposite the right angle. If [tex]sinB=1/sqrt(3)[/tex] and x=8, find the length of the other side (y) and the length of the hypotenuse (z).
Answers
Answer:
y = 4√2 ≈ 5.66z = 4√6 ≈ 9.80Step-by-step explanation:
From the sine of the angle, the other trig function values can be determined:
cos(B) = √(1 -sin²(B)) = √(1 -(1/√3)²) = √(2/3) = (√6)/3
tan(B) = sin(B)/cos(B) = (1/√3)/(√2/√3) = 1/√2 = (√2)/2
__
Then the unknown side can be found from ...
Tan = Opposite/Adjacent
tan(B) = y/x
y = x·tan(B) = 8·√2/2 = 4√2 ≈ 5.66
__
And the hypotenuse is ...
Cos = Adjacent/Hypotenuse
cos(B) = x/z
z = x/cos(B) = 8/√(2/3) = 8√(3/2) = 4√6 ≈ 9.80
Related Questions
Your first six-month auto insurance premium was $629.00. Based on your driving record, your renewal premium is $786.25. What percent increase did you see in your premium?
8%
20%
оооо
25%
32%
Answers
Hello!
Answer:
[tex]\Large \boxed{\sf 20\%}[/tex]
Step-by-step explanation:
→ We want to calculate the percentage increase we saw in our premium.
→ To calculate the percentage increase we saw in our premium, let's calculate the difference between our first six-month car insurance premium and our renewal premium:
[tex]\sf 786.25 - 629.00 = 157.25[/tex]
→ Calculate the percentage:
→ The formula used to calculate the percentage is:
[tex]\sf \dfrac{value}{total ~value} \times 100\%[/tex]
→ Apply this formula with value = 157.25 and total value = 786.25:
[tex]\sf \dfrac{157.25}{786.25} \times100\%[/tex]
→ Simplify the expression:
[tex]\sf \dfrac{157.25}{786.25} \times100\%\\\\\\= 0.2 \times100\%\\\\\\= 0.2 \times \dfrac{100}{100} \\\\\\= 0.2 \times 1\\\\\\= 0.2\\\\\\= \dfrac{20}{100} \\\\\\\boxed{\sf= 20\%}[/tex]
So the percentage increase we saw in our premium is 20%.
huong spent $20.83 on a magazine and seven candy bars. If the magazine cost $4.94, then how much was each candy bar?
Answers
Answer:
$2.27
Step-by-step explanation:
Huong's expense is the sum of the cost of the magazine and the cost of 7 candy bars. If c represents the cost of a candy bar, then Huong's expense was ...
$4.94 +7c = $20.83
7c = $15.89 . . . . . . . . subtract 4.94
c = $2.27 . . . . . . . . divide by 7
Each candy bar was $2.27.
can some one help i need to pass
Answers
When using estimates to make decisions,
A. It is important to always use a 95% confidence level
B. It is important to remember that you will never achieve certainty
C. It is important to calculate those estimates to at least six decimal places
D. It is important to use a 100% confidence level so as to achieve certainty
E. All of the above
F. None of the above
Answers
Answer:
C.
Explanation: I hope it's help you
The use of estimates to make the decisions It is important to calculate those estimates to at least six decimal places.
We have given the options that are
A. It is important to always use a 95% confidence level
B. It is important to remember that you will never achieve certainty
C. It is important to calculate those estimates to at least six decimal places.
D. It is important to use a 100% confidence level so as to achieve certainty.
E. All of the above
F. None of the above
We have to determine the correct decision.
What are the estimating values?
Any of numerous procedures used to calculate the value of some property of a population from observations of a sample drawn.
That is we are estimating the value up to 6 decimal places
Therefore option C is correct.
It is important to calculate those estimates to at least six decimal places.
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1. There are 1,200 students at Woodland Hills Elementary. Approximately 600 of
the students take the bus home. 50% of the students that do not take the bus
ride their bicycles home. Approximately how many students ride their bicycles
home?
A 100
B 200
С 300
D 400
E 500
Answers
1,200 divide by 600 = 2 students
2 students multiply by 50% is 100 students.
So, approximately 100 students ride their bicycles home.
(If not correctly, I am truly sorry)
In the following diagram,
A
∥
B
.
Use complete sentences to explain how the special angles created by the intersection of
A
and
B
by
D
can be used to solve for
x
.
Solve for
x
, showing all of your work.
Find the measure of
∠
6
.
Answers
Answer:
x=24
<6=79°
Step-by-step explanation:
We can see that if we add 3x+7 and 4x+5, it will total a 180-degree angle. This allows us to solve for x. 3x+7+4x+5=180 7x+12=180 7x=180-12 7x=168 x=24 We can also see that angle six is the same as the angle 3x+7. Since we know x=24, we can solve for those angles. 3(24)+7= 72+7=79 So <6=79 degrees
Answer choices:
A: y=x
B: y=1/4x -2
C: y= -x + 7/4
D: y= 7/4x -2
Answers
Answer:
b: y=1/4x -2
Step-by-step explanation:
It says the answer in the question. the slope on the graph is really just 1 though.
Complete the table by filling in the elapsed tine.
Help pls
Answers
Answer:
RADIUS
==================================
PROBLEM
Mary’s bicycle wheel has a circumference of 226.08 cm². What is its radius?
SOLUTION
We can solve this problem using the circumference formula in which π stands for ( 3.14 ), C stands for circumference itself and r stands for radius.
\bold{Formula \: || \: C = 2πr}Formula∣∣C=2πr
\tt{226.08 = 2(3.14) r}226.08=2(3.14)r
'Now to find the radius,Substitute 226.08 for c which is circumference in the formula.
\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{C = 2πr} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{226.08 = 2(3.14)\red{r}} \\ \\ \: \: \: \: \: \: \: \: \large \tt{ \frac{226.08}{6.28} = \cancel\frac{6.28 \red{r}}{6.28} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt\green{C = 36}}\end{gathered}
C=2πr
226.08=2(3.14)r
6.28
226.08
=
6.28
6.28r
C=36
To check:
\begin{gathered} \small\begin{array}{|c|}\hline \bold{circumference }\\ \\ \tt{C = 2πr} \\ \tt{C = 2(3.14) (36\:cm) } \\ \tt{C = 2(113.04\:cm) } \\ \underline{\tt \green{C = 226.08\:cm }} \\ \hline \end{array} \end{gathered}
circumference
C=2πr
C=2(3.14)(36cm)
C=2(113.04cm)
C=226.08cm
FINAL ANSWER
If Mary's Bicycle has a circumference of 226.08 cm then the radius is 36.
\boxed{ \tt \red{r = 36}}
r=36
==================================
#CarryOnLearning
Answer:
1 = 0.56
2 = 0.43
3 = 0.55
4 = 0.49
5 = 0.70
Step-by-step explanation:
I not sure
A computer and printer cost a total of $1101. The cost of the computer is two times the cost of the printer. Find the cost of each item.
Cost of computer:
Cost of printer:
Answers
Answer:
Cost of Computer: $734
Cost of Printer: $367
Step-by-step explanation:
These two equations can represent the costs; x = price of computer; y = price of printer.
x + y = 1101
2y = x
If you graph these, you get an intersection point of (734, 367). This means that the only place that both equations are fulfilled is on (734, 367).
Then you can check your work:
734+367=1101
367*2=734
how many feet is the answer?
Answers
Answer:
The Inch To Feet Calculator is available online here for free at BYJU'S. One inch is equal to 0.083333 feet. One foot is equal to 12 inches.
Step-by-step explanation:
.................................................................................................
Answers
Answer:
m<B = 141 degrees
Step-by-step explanation:
This shape is a heptagon meaning its angles should have a sum of 900 degrees.
we are given the degrees and we need to ad them up
148+90+120+129+130+142=749
then we subtract 749 from 900 which looks like
900-749=141
from subtracting 749 from 900 we get 141 hence we get our answer that m<B = 141 degrees
Consider the equation − 7 x − 6 y = − 18
Answers
Answer: The answer is simply O
Step-by-step explanation: In this algebraic problems is very common to find an answer like that since you step to step process is basically canceling out the terms. We make disappear X and Y because that’s gonna count as a 1 unit value so don’t write x and y. It’s only 0
5 people are in a line to withdraw money from the local Bank. All 5 withdrawal the same amount. The total withdrawn was $845. How much money did each withdraw? Set up an equation to find out how much money each person withdrew and then solve it.
Answers
845 / 5 = 169
Each person withdrew 169$ from their accounts.
hi! i need help finding the area of this shape! thank you
Answers
Answer: 7.5
Step-by-step explanation:
5x3 = 15 A = 1 half L x H
A = (3)(5)
A = 15
A = 15 x 1 half = 7.5
correct me if i am wrong.
CAN SOMEONE PLS ANSWER THIS QUESTION FAST
I WILL MARK BRAINLIEST
Answers
Answer:
20%
Step-by-step explanation:
add up all the values, then do 9 (alex's score) and divide it by 45 (total that was added up)
Answer:
A. 9
Step-by-step explanation:
Add all basketball shots then divide by 5
Which describes the combined variation in the formula h=2a/b?
h varies jointly with 2 and A and inversely with b.
h varies directly with A and inversely with b.
h varies jointly with A and b.
h varies inversely with A and b.
Answers
Step-by-step explanation:
h varies directly with a and inversely with b.
2 is the constant of variation.
what is 3.1 converted into a simplified fraction?
Answers
Answer:
31/10
Step-by-step explanation:
what is the value of x
Answers
Answer: x=17
Step-by-step explanation:(6x+x+4x)+(10+17-34)=180
we know this because triangles always equal 180o so the 3 angles equa; 180 so 187/11 + 17
PLEASE HELP PLEASE HELP I WILL BRAINLIEST
Answers
Answer:
65°
Step-by-step explanation:
<JKL=90°
<KJM+<JKL+<JML=360°
77°+90°+128°+<JML=360°
<JML=65°
A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white?
Answers
Answer:
3 participants
Step-by-step explanation:
7 + 6 + 5 = 18
21 - 18 = 3 participants
can someone please help me
Answers
Answer:
1.6
Step-by-step explanation:
There are 5 points from -1 to -2 if you count by 0.2 then you get 0.6 put that with the numbers on the line and you get 1.6
A picture frame measures 18 cm by 20 cm on the outside, and 168 cm?
of picture shows.
Find the width of the frame around the picture.
The width of the frame is
cm.
Answers
Answer:
hello
( 20 - 2 x ) ( 18 - 2 x )
= 360 - 40 x - 36 x + 4 x²
= 4 x² - 76 x + 360
Step-by-step explanation:
Use the drop-down menus to label the points on the number line.
Point A is at
.
Point B is at
.
Point C is at
.
Point D is at
.
Answers
Answer: B,D,C,A
Step-by-step explanation:
I hope that helps
Please mark me the brainiest !
Please Help ASAP (show work if you want its not needed i just need the answer)
Answers
[tex] \sin(60) = \frac{a}{4 \sqrt{3} } \\ [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{a}{4 \sqrt{3} } \\ [/tex]
[tex]a = 6[/tex]
_____________________________________________
[tex] \cos(60) = \frac{c}{4 \sqrt{3} } \\ [/tex]
[tex] \frac{1}{2} = \frac{c}{4 \sqrt{3} } \\ [/tex]
[tex]c = 2 \sqrt{3} [/tex]
_____________________________________________
[tex] \sin(45) = \frac{a}{b} \\ [/tex]
[tex] \frac{ \sqrt{2} }{2} = \frac{6}{b } \\ [/tex]
[tex]b = 6 \sqrt{2} [/tex]
_____________________________________________
[tex]d = a = 6[/tex]
Have a great day ♡
6 - 1 x 0 + 2 ÷ 2
Help meeee
Answers
Answer:
Answer is 1
Step-by-step explanation: 6-1= 5 5x0=0 0+2=2 2 divided by 2 is= 1
what is the area of the triangle
Answers
Answer:
Use this to answer your question :)
Step-by-step explanation:
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.
Answer:
54 units²
Step-by-step explanation:
Formula we use,
→ Area = ½ × b × h
Now the area of the triangle is,
→ ½ × b × h
→ ½ × 18 × 6
→ 9 × 6
→ 54 units²
Hence, the area is 54 units².
You were elected the student council president for the next year at your school. After vacation is over, you have to plan a school carnival for the new school year. You are studying last year’s event and know that 210 people attended last year’s school carnival. The total amount of money collected for tickets was $710. Prices were $5 for regular admission, $3 for students, and $1 for children. The number of regular tickets sold was 10 more than twice the number of children’s tickets sold. Determine how many of each kind of ticket were sold.
Answers
The number of regular tickets are 70, the number of student tickets are 110 and the number of children tickets are 30.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, you are studying last year’s event and know that 210 people attended last year’s school carnival.
The number of regular tickets sold was 10 more than twice the number of children’s tickets sold.
Let the number of children tickets be x.
Then, number of regular tickets be 2x+10
Let the number of student tickets be y.
You are studying last year’s event and know that 210 people attended last year’s school carnival.
x+2x+10+y=210
3x+y=200 --------(I)
The total amount of money collected for tickets was $710.
Now, 5(2x+10)+3y+x=710
10x+50+3y+x=710
11x+3y=660 --------(II)
Substitute y=200-3x in equation (II), we get
11x+3(200-3x)=660
11x+600-9x=660
2x=60
x=30
Substitute x=30 in equation (I), we get
3(30)+y=200
y=110
Number of regular tickets =2x+10
= 70
Therefore, the number of regular tickets are 70, the number of student tickets are 110 and the number of children tickets are 30.
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is 1.3 greater than 1.52
Answers
the median value for this data set is
Answers
Answer:
275
Step-by-step explanation:
because it is in between 270 and 280
Draw a pair of perpendicular lines
Answers
Answer:
+
perpendicular lines are lines that meet at a 90 degree angle
Step-by-step explanation: