9. SAILING The sail on Milton's schooner is the shape of a 30°-60°-90°triangle. The length of the hypotenuse is 45 feet. Find the lengths of thelegs. Round to the nearest tenth.
Answers
The triangle is shown below:
Notice how this is an isosceles triangle.
We can find the lengths of the hypotenuse by using the trigonometric functions:
[tex]\sin \theta=\frac{\text{opp}}{\text{hyp}}[/tex]Then we have:
[tex]\begin{gathered} \sin 45=\frac{21}{hyp} \\ \text{hyp}=\frac{21}{\sin 45} \\ \text{hyp}=29.7 \end{gathered}[/tex]Therefore the hypotenuse is 29.7 ft.
Related Questions
Enter your solution as an ordered pair, with no spaces and with parentheses. OR the answer could be: Infinitely many OR No Solution
Answers
Given the equation system:
[tex]\begin{gathered} 1)y=4x \\ 2)3x+2y=55 \end{gathered}[/tex]The first step is to replace the first equation in the second equation
[tex]3x+2(4x)=55[/tex]With this, we have a one unknown equation. Now we can calculate the value of x:
[tex]\begin{gathered} 3x+8x=55 \\ 11x=55 \\ \frac{11x}{11}=\frac{55}{11} \\ x=5 \end{gathered}[/tex]Now that we know the value of x, we can determine the value of y, by replacing x=5 in the first equation
[tex]\begin{gathered} y=4x \\ y=4\cdot5 \\ y=20 \end{gathered}[/tex]This system has only one solution and that is (5,20)
Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 7.25x − 36.25, where x is the number of bracelets he sells. What is the value of Q(5), and what is its interpretation?
Q(5) = 0; If Quincy sells 0 bracelets, he will earn $5.
Q(5) = 0; If Quincy sells 5 bracelets, he will earn $0.
Q(5) = 5.69; If Quincy sells 5.69 bracelets, he will earn $5.
Q(5) = 5.69; If Quincy sells 5 bracelets, he will earn $5.69.
Answers
The value of Q(5) is zero and represents the zero profit on selling 5 bracelets thus option (B) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given,
Daily profit function Q(x) = 7.25x − 36.25 where x is the number of bracelets he sells.
At x = 5 ( selling 5 bracelets)
Q(5) = 7.25(5) - 36.25
Q(5) = 36.25 - 36.25 = 0
It means selling 5 bracelets doesn't give any profit.
Hence "The value of Q(5) is zero and represents the zero profit on selling 5 bracelets".
For more about the function,
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the Anderson are going on a long sailing trip during the summer however one of the sails on their sailboat ripped and they have to replace it the sail is pictured below if the sailboat sails are sale for 2$ per square foot how much will the new sail cost?
Answers
Firs we need to calculate the area of a triangle
[tex]A=\frac{b\cdot h}{2}[/tex]b= base
h=heigth
in our case
b=8ft
h=12ft
[tex]A=\frac{8\cdot12}{2}=\frac{96}{2}=48ft^2[/tex]then we will calculate the total cost
1 square foot ----- $2
48 square feet ----- x
the total cost is 48*2=96
total cost is $96
I thought of a number. from ²/₇ parts of that number I subtracted 0,4 and got ⅗. The number is: A: ²⁄₇ B: ⅖ C: 3,5D: 4,5
Answers
Note : The use of comma as number separator represent point in this solution
Step 1: Let the number be x, thus, 2/7 parts of the number means
[tex]\frac{2}{7}x[/tex]Step 2: Subtract 0,4 from 2/7 parts of x
[tex]\frac{2}{7}x-0,4\Rightarrow\frac{2}{7}x-\frac{4}{10}[/tex]Step 3: Equate the expression above to 3/5
[tex]\frac{2}{7}x-\frac{4}{10}=\frac{3}{5}[/tex]Step 4: Simplify the equation above
[tex]\begin{gathered} \frac{2}{7}x-\frac{4}{10}=\frac{3}{5} \\ \frac{20x-28}{70}=\frac{3}{5}(\text{cross multiply)} \\ 5(20x-28)=70(3) \\ 100x-140=210 \\ 100x=210+140 \\ 100x=350 \\ \frac{100x}{100}=\frac{350}{100}(\text{Divide both side by 100)} \\ x=3,5 \end{gathered}[/tex]Hence, the number is 3,5
Option C is correct
On December 13, 2007, one South African rand was worth 0.15 U.S. dollars.(a) On that date, how many rand was 44.11 dollars worth?Round your answer to the nearest hundredth of a rand.rand(b) On that date, how many dollars was 168.18 rand worth?Round your answer to the nearest hundredth of a dollars. I need help with this math problem.
Answers
Explanation
Part A
Given that one South African rand was worth 0.15 U.S. dollars. 44.11 dollars will be worth
[tex]\frac{44.11}{0.15}=294.07[/tex]Answer: 294.07 rands
Part B
On that date, how many dollars was 168.18 rand worth?
[tex]168.18\times0.15=25.23[/tex]Answer: 25.23 dollars
Maggie has $30 in an account. The interest rate is 10% compounded annually.To the nearest cent, how much will she have in 1 year?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Solution:
Using the formula;
[tex]\begin{gathered} B=p(1+r)^t \\ \\ \text{ Where }B=balance,p=principal,r=rate,t=time \end{gathered}[/tex][tex]p=30,r=10\text{ \%}=0.1,t=1[/tex]Thus;
[tex]\begin{gathered} B=30(1+0.1)^1 \\ \\ B=33 \end{gathered}[/tex]ANSWER: $33
Which of the following numbers are greater than 6 and less than 8? Explainhow you know.
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Let's analyze each case and see if they are less than 8 first:
[tex]7<8,therefore(7)^{\frac{1}{2}}<8[/tex][tex]\sqrt[]{64}=8[/tex]thus
[tex]\sqrt[]{60}<\sqrt[]{64}=8[/tex][tex]\sqrt[]{60}<8[/tex]Finally,
[tex]64<80[/tex][tex]\sqrt[]{64}<\sqrt[]{80}[/tex]thus
[tex]8<\sqrt[]{80}[/tex]In sumary, the first two options are less than 8, but not the third.
Now let's see if they are greater than 6
[tex]9>7[/tex][tex]\sqrt[]{9}>\sqrt[]{7}[/tex][tex]3>\sqrt[]{7}[/tex]and
[tex]6>3>\sqrt[]{7}[/tex]thus
[tex]6>\sqrt[]{7}[/tex]Now
[tex]36<60[/tex][tex]\sqrt[]{36}<\sqrt[]{60}[/tex]and so
[tex]6<\sqrt[]{60}[/tex]Finally
[tex]\sqrt[]{80}>\sqrt[]{60}>6[/tex]thus
[tex]\sqrt[]{80}>6[/tex]In conclussion, the second and third options are greater than 6, but not the first.
which transformation occurred to create the graph shown below from square root parent function?
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Solution:
Given the function:
[tex]f(x)=\sqrt{x+4}[/tex]whose graph is shown below:
Suppose that the parent function is expressed as
[tex]f(x)=\sqrt{x}[/tex]This implies that the parent function is transformed by a horizontal shift to the left by four spaces.
The correct option is
solve for missing variable: 11y-36=63
Answers
The equation can be solved as,
[tex]\begin{gathered} 11y-36=63 \\ 11y=63+36 \\ 11y=99 \\ y=\frac{99}{11} \\ y=9 \end{gathered}[/tex]Therefore, the value of y is 9.
find the sum to infinity 16,4,1,1/4
Answers
Answer:
The sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]Explanation:
From the given series, we can see that the series is a Geometric Progression (GP) because it has a common ratio;
[tex]\begin{gathered} r=\frac{4}{16}=\frac{1}{4} \\ r=0.25 \end{gathered}[/tex]The formula to calculate the sum to infinity of a GP is;
[tex]\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ \text{For;} \\ 0Where;a = first term = 16
r = common ratio = 0.25.
substituting we have;
[tex]\begin{gathered} S_{\infty}=\frac{16}{1-0.25}=\frac{16}{0.75} \\ S_{\infty}=21\frac{1}{3} \\ S_{\infty}=21.33 \end{gathered}[/tex]Therefore, the sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]Two airplanes are flying in the air at the same height. Airplane A is flying east at 451 mi/h and airplane B is flying north at 494 mi/h. If they are both heading to the same airport, located 3 miles east of airplane A and 3 miles north of airplane B, at what rate is the distance between the airplanes changing?
Answers
The rate at which the distance between the airplanes is changing is 668.2 mi/h.
In the given question,
Speed of Airplane A:
dA/dt = 451 mi/h
and the Speed of Airplane B:
dB/dt = 494 mi/h
Aircraft A and B will form a right triangle because Aircraft A is flying east and Aircraft B is flying north, and we can use Pythagoras' theorem to calculate their distance from one another.
Let P be the distance.
P² = A² + B²
Differentiating the above equation with respect to t,
2P(dP/dt) = 2A(dA/dt) + 2B(dB/dt)
Dividing each side of the equation by 2,
P( dP/dt ) = A( dA/dt ) + B( dB/dt ) ..........(1)
Where dP/dt is the rate of change in distance between the two aircraft.
Now,
P² = A² + B²
P = √(A² + B²)
Substituting, A = 3 miles and B = 3miles;
P = √(3² + 3²)
P = √( 9+ 9)
P = √18
P = 3√2 miles
Substituting the value in the equation (i)
3√2 (dP/dt) = (3× 451) + (3× 494)
3√2 (dP/dt) = 2835
4.2426 × dP/dt = 2835
dP/dt = 2835/4.2426
dP/dt = 668.2 mi/h
Therefore, the rate at which the distance between the airplanes is changing is 668.2 mi/h
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Which is equal to 2 over 5? A. 2%B. 2.5%C. 20%D. 25%E. 40%
Answers
Calculating the value of 2 over 5 in percentage, we have:
[tex]\begin{gathered} \frac{2}{5}=\frac{20}{50}=\frac{40}{100}=40\text{\%} \\ or \\ \frac{2}{5}=0.4=40\text{\%} \end{gathered}[/tex]So the correct option is E.
The dog looked at the cat warily A with interestb viciously c hungrily d with caution
Answers
Answer
Option D is correct.
The dog looked at the cat with caution.
is the same as
The dog looked at the cat warily.
Explanation
The word warily means 'using caution' or 'cautiously'.
Hope this Helps!!!
Please help i need the answers for a test and how to work em out for the future
Answers
Given: The angles as shown in the image
[tex]\begin{gathered} m\angle DEY=105^0 \\ m\angle DEF=27x+3 \\ m\angle YEF=6x+3 \end{gathered}[/tex]To Determine: The measure of angle DEF
Solution
It can be observed that
[tex]\begin{gathered} m\angle DEY+m\angle YEF=m\angle DEF \\ Therefore \end{gathered}[/tex][tex]\begin{gathered} 105^0+6x+3=27x+3 \\ 105=27x-6x+3-3 \\ 105=21x \\ x=\frac{105}{21} \\ x=5 \end{gathered}[/tex][tex]\begin{gathered} m\angle DEF=21x+3 \\ =21(5)+3 \\ =105+3 \\ =108 \end{gathered}[/tex]Question 12
Given:
[tex]\begin{gathered} m\angle UIJ=x+43 \\ m\angle HIJ=66 \\ m\angle HIU=x+37 \end{gathered}[/tex]To Determine: The measure of angle HIU
Solution:
It can be observed that
[tex]m\angle UIJ+m\angle HIU=m\angle HIJ[/tex][tex]\begin{gathered} x+43+x+37=66^0 \\ Collect-like-terms \\ x+x+43^0+37^0=66^0 \\ 2x+80^0=66^0 \\ 2x=66^0-80^0 \\ 2x=-14^0 \\ x=-\frac{14^0}{2} \\ x=-7^0 \end{gathered}[/tex]Therefore, the measure of angle HIU would be
[tex]\begin{gathered} m\angle HIU=x+37^0 \\ m\angle HIU=-7+37^0 \\ m\angle HIU=30^0 \end{gathered}[/tex]Hence, the measure of angle HIU is 30⁰
2. Simba pays $15 per month
for the phone he bought. His cell phone plan costs $49
per month and includes 15GB of
data. He also pays $5 for each additional 1GB
of data he uses over the 15GB limit. Using x to represent the GB of data
he uses over 15 GB, write an equation to represent Simba's monthly cell
phone bill and determine how much he will pay if one month he uses
23GB of data.
Answers
The equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
What is an linear equation is one variable?
An linear equation is an equation of degree one. the highest exponent is 1 and one variable is number of variable is 1 in the equation
We are given that, Simba pays $15 per month for the phone he bought. His cell phone plan costs $49 per month.
He pay additional $5 for 1 gb data after 15gb data limit got over
Let the number of gb's used be x
Hence the total bill will be given by the equation
B= 15+49+5x
B= 64+5x
If he uses 23 gb of data the first 15 Gb are covered in his phone plan
And he has to pay $5 for each gb
The total cost is 8*5=$40
Hence the total phone bill is B=64+40
B=$104
Hence the equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
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Find the rational number halfway between and 1/6 and 3/4
Answers
In order to find the middle number between them we can simply add them together and divide the result by 2 as follows:
[tex]\begin{gathered} \frac{1}{6}+\frac{3}{4}=\frac{11}{12} \\ Now_{\text{ }}divide_{\text{ }}by_{\text{ }}2: \\ \frac{11}{12}\div2=\frac{11}{24} \end{gathered}[/tex]Answer:
11/24
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.A) Create an equation to represent their total earnings in each situation. Explain what each of the variables represent.
Answers
Given:-
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.
To find:-
An equation to represent their total earnings in each situation.
A math teacher said that 18 out of 25 students passed the test. What percent of thestudents did NOT pass the test?C.72%A.18%D.28%B.82%
Answers
Let's begin by listing out the given information:
18 students passed
Total students = 25
Number of people who did not pass = 25 - 18 = 7
7 out of 25 students did not pass. This has its percentage as:
[tex]\begin{gathered} \frac{7}{25}\cdot100\text{\%}=28\text{\%} \\ \Rightarrow28\text{\%} \end{gathered}[/tex]Therefore, 28% of the students did not pass
PLS HELP WILL ASAP WILL GIVE BRAINLIST
Answers
Answer:
if the bottom side is 4n + 15, then n=8
n times 5 is 40
40+7=47
Step by step
The parallelogram rule says the opposite sides are equal length so our equation is
4n + 15 = 5n + 7
Subtract 5n from both sides to combine variable
4n - 5n + 15 = 5n - 5n + 7
Combine
-n + 15 = 7
Subtract 15 from both sides to solve
-n + 15 -15 = 7 -15
-n = -8
n = 8
Now substitute 8 for n in the KL expression
5n + 7
5(8) + 7
40 + 7 = 47
Side KL is 47 units
Solve for x. Then find m
(8x+4)°
(10x-6)°
Both lines are intersecting and the two equations are vertical pairs
Answers
Answer:
x = 5
m∠QRT = 44
Step-by-step explanation:
8x + 4 = 10x - 6
-10x -10x
------------------------
-2x + 4 = -6
-4 -4
---------------------
-2x = -10
÷-2 ÷-2
--------------------
x = 5
m∠QRT
8x + 4
8(5) + 4
40 + 4 = 44
I hope this helps!
From the image, [tex](8x + 4 )° = (10x - 6)°[/tex]
Reason: Vertically opposite angles are equal.
Now, we solve for x
[tex]8x + 4 = 10x - 6[/tex]
collect like terms
[tex] 4 + 6 = 10x - 8x[/tex]
[tex]→ 10 = 2x[/tex]
Divide both sides by the coefficient of x to find the value of x
[tex] x = 5[/tex]
Now, substitute for the value of x in the expression for m∠QRT to find the degree
[tex](8x + 4 )° → (8(5) + 4)°[/tex]
Therefore: m∠QRT = 44°
I hope this helpsThe line plot below shows the number of minutes dog owners in a certain neighborhood spent walking their dogs last month.Which statement describes the data shown?The data has a range of 150 to 40, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 20, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.The data has a range of 150 to 20, with a peak at 90 and gaps at 50 and 60. The median of the data is 110.The data has a range from 150 to 40, with a peak at 80 and gaps at 50 and 60. The median of the data is 100.
Answers
Looking at the graph, the minimum value is 40 and the maximum value is 150, therefore the range is between 150 and 40.
Also, we have a total of 27 points on the graph, which means the median is the 14th value of the data set in crescent order.
Counting the points from the left to the right, the 14th point has a value of 100, therefore the median is equal to 100.
So the correct option is
what does y= 75-29 equal?
Answers
Starting with the expression:
[tex]y=75-29[/tex]Substract the numbers to find the value of y:
[tex]y=46[/tex]Answer:
if y = 75-29 the we subtract 29 from 15
75-29=46
y=46
If the function rule is to add 6, and an output value is 6, what is the input value?options:01-612
Answers
Given,
If the function rule is to add 6, and an output value is 6.
To find: What is the input value?
Solution:
When we add 0 to any number, we got the same number.
So adding 0 with 6 we get the same number 6.
[tex]6+0=6[/tex]Thus, the answer 0 is the correct option.
find the missing value in the given equivalent ratios 9:5=__:35
Answers
First, let's express the proportion as an equation, where the blank space is the variable x.
[tex]\frac{9}{5}=\frac{x}{35}[/tex]To find the value of x, we multiply both sides by 35.
[tex]\begin{gathered} \frac{9}{5}\cdot35=\frac{x}{35}\cdot35 \\ x=63 \end{gathered}[/tex]Therefore, the missing value is 63.The diagram shows two similar polygonsN51P224048MR3016.5SFigures not drawn to scale.What is the length of CS?
Answers
Notice the correspondence between the vertices of the polygons:
[tex]VQRGX\approx CNPMS[/tex]Corresponding segments of similar polygons are proportional. Then:
[tex]\frac{CS}{VX}=\frac{PM}{RG}[/tex]Substitute VX=48, PM=22 and RG=16.5 and solve for CS:
[tex]\begin{gathered} \Rightarrow\frac{CS}{48}=\frac{22}{16.5} \\ \Rightarrow CS=\frac{22}{16.5}\times48 \\ \Rightarrow CS=64 \end{gathered}[/tex]Therefore, the length of CS is 64.
Given that p = 6 and q = 2, which yields a quotient greater than -9? ОА -3 a -р B 3 O a O С Зр. (-9) (0) D (-p) (-39)
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About how much more is the total weight of the pacific halibut and conger than the weight of the yellowfin tuna ? Explain
Answers
The weight of pacific halibut is 459 pounds and weight of yellowfin tuna is 387 pounds.
There is 72 pounds more is the total weight of pacific halibut than the yellowfin tuna.
Which phrase best describes the translation from the graph y = 2(x-15)² + 3 to the graph of y = 2(x-11)² + 3?O4 units to the left4 units to the rightO 8 units to the leftO 8 units to the rightMark this and returnSave and ExitNextSubmit
Answers
Given:
it is given that a graph of the function y = 2(x-15)^2 + 3 is translated to the graph of the function y =2(x - 11)^2 + 3
Find:
we have to choose the correct option for the given translation.
Explanation:
we will draw the graphs of both the functions as following
The graph of the function y = 2(x - 15)^2 + 3 is represented by red colour and the graph of the translated function y = 2(x - 11)^2 + 3 is represented by blue colour in the above graph.
From, the graphs of both functions, it is concluded that the graph of the translated function is shifted 4 units to the left.
You purchase a TV set that is originally valued at $1090. You receive a 45% discount on the purchase of a promo. Your sales tax rate is 7%. What is the total cost of the merchandise?
Answers
Answer:
The answer would be $641.47 I believe.
Step-by-step explanation:
How do you solve this?
Answers
Answer: I thought you already asked this question.
Step-by-step explanation:
