part 4. Find the missing sides for the 30 60 90 triangles. Please show work for each
Answers
10. tan(30) = l / 6√3
l = tan(30) x 6√3
l = 6
cos(30) = 6√3 / y
y = 6√3/cos(30)
y = 12
11. tan(30) = c/30
c = 30 x tan(30)
c = 10√3
cos(30) = 27/w
w = 27/cos(30)
w = 18√3
12.
sin(60) = 36/y
y = 36/sin(60)
y = 24√3
tan(60) = 36/x
x = 36/tan(60)
x = 12√3
Answer:
10. (l, y) = (6, 12)
11. (c, w) = (9√3, 18√3)
12. (x, y) = (12√3, 24√3)
Step-by-step explanation:
Side ratios, shortest to longest, in a 30°-60°-90° triangle are ...
1 : √3 : 2
__
10. l : 6√3 : y = 1 : √3 : 2
multiply by 6
= 6 : 6√3 : 12
l = 6, y = 12
__
11. c : 27 : w = 1 : √3 : 2
multiply by 27/√3 = 9√3
= 9√3 : 27 : 18√3
c = 9√3, w = 18√3
__
12. x : 36 : y = 1 : √3 : 2
multiply by 36/√3 = 12√3
= 12√3 : 36 : 24√3
x = 12√3, y = 24√3
__
This is easier when the triangle is drawn to clearly differentiate the lengths of the sides. The long leg is opposite the 60° angle; the short leg is opposite the 30° angle.
Related Questions
Please help me with my question!!
Answers
Answer:
Step-by-step explanation:
y = 10x + 50
x ---> no of weeks
y - intercept = 50
what number times there self eqaul to 64
Answers
Answer:
8
Step-by-step explanation:
8 times 8 = 64
Order the simplification steps of the expression below using the properties of rational exponents. [tex]\sqrt[3]{7}=7^{\frac{1}{3}}[/tex]
A.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7^{\frac{1}{3}}\cdot ^{\frac{1}{3}}\cdot ^{\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7\\[/tex]
B.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7\cdot 7^{\frac{1}{3}}=3\cdot \frac{1}{3}\cdot 7=1\cdot 7=7[/tex]
C.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}}+\:^{\frac{1}{3}}+\:^{\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7[/tex]
D.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7\cdot \left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)=7\cdot \frac{3}{3}=7\cdot 1=7[/tex]
Answers
The answer is C.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7[/tex]
what you plug in for calculator
\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7
y=-3x + 6
y = 9
What is the solution to the systems of equations
Answers
Answer:
-1,9
Step-by-step explanation:
You use the equal values method to combine the two equations
-3x+6=9
then subtract 6 on both sides of the equal sign
nine minus six is 3
-3x=3
divide negative three on both sides to isolate the x value
to get....
x=-1
then plug the x value back in to find the y value
(you can plug in to one of them but I would plug into both of them just for double checking) ALWAYS CHECK YOUR WORK
3+6 is 9
9=9 check!
Answer:C -(-1,9)
Step-by-step explanation:
Given: 3x < -6. Choose the solution set.
A. {x | x < -2}
B. {x | x > -2}
C. {x | x < 2}
D. {x | x > 2}
Answers
Answer:
When we divide the inequality by 3 we get x < -2 so the answer is A.
a food scientist wants to know if increasing the amount of lemon juice in a hummus recipe by 10% will increase the shelf life of the product, so he prepares 100 Badges of the recipe - 50 following the old recipe and 50 with extra lemon juice –and?checks each batch once per day to see how long it stays fresh. What type of data source is this?
Answers
Answer:
b. Experiment
Step-by-step explanation:
Setting up conditions so that you can examine the outcome is called an "experiment."
Answer:
[tex]\fbox{\begin{minipage}{10em}Option B-Experiment\end{minipage}}[/tex]
Step-by-step explanation:
As described, the food scientist performs the research based on the actual data, without using a computer or any simulation devices.
=> The data source is not generated from a computer simulation.
=> Option A-Simulation is incorrect.
The food scientist intentionally prepares the research by conducting an experiment, in which 100 badges are used, 50 badges following the old recipe and 50 badges with extra lemon juice.
=> This is not a subjective process, but a purposely attempting to observe the amount of lemon juice in a specific manner.
=> This is not a survey.
=> Option C-Survey is incorrect.
=> Option B-Experiment is correct.
Hope this helps!
:)
HELP ME!!! Find the y intercept of the line y=2x-11
Answers
Answer:
It would intercept the y-axis at y = -11
Step-by-step explanation:
Here is the work
Answer:
Step-by-step explanation:
the y interception is -11
Y=mx+b formula the b is for the y intercept and the m is the slope.
y varies directly as x and inversely as z. If y = 5 when x = 3 and z = 4, find y when x = 6 and z = 8.
Answers
Answer:
y= 201/40
Step-by-step explanation:
y=k (x÷z)
5 = (3÷4)k
cross multiply
20=3k
k= 6.7 or 67÷10
y = 6.7 (x÷z) the law
y = (6÷8) × 6.7
y = 0.75 ×6.7
y= 5.025 or 201÷40
Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold. What expression represents the profit?
A. 27x – 650
B. 27x + 390
C. 33x – 650
D. 33x + 390
Answers
Answer:
We need to subtract both equations. 2x3+30x-130-2x3+3x+520
that gives
30x-130+3x + 520
33x+390
D is answer
Answer:
D. 33x + 390
Step-by-step explanation:
Profit is the difference between revenue and cost so subtract the given polynomials:
2x³ + 30x – 130 - (2x³ – 3x – 520) = 2x³ + 30x – 130 -2x³+3x+520
combine like terms: 33x +390
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!
Answers
When Jonathan bought 12 peaches and pears, at $1.50 per peach and
at $1.60 per pear, the total price was $18.50.
How many peaches and pears did he buy, respectively?
Fill in the blanks provided and solve for the answer.
Answers
Explanation: you will need to make two equations to represent the problem
X being for peaches and y for pears
x+y= 12
1.5x + 1.6y= 18.5
We are going to use the elimination method and so we need to cancel either x or y in this case x. So we multiple the top equation by -1.5
-1.5x - 1.5y = -18
1.5x + 1.6y = 18.5
Then we can cancel the x since they are opposite and we can add the rest
0.1y =0.5
Y= 5
Then we can substitute the y into one of the equations
x + 5= 12
x= 7
Which is a correct first step in solving 5 - 2x < 8x - 3?
5 < 6x-3
3x < 8x-3
5 < 10x - 3
2 - 2x < 8x
Answers
Answer:
5 < 10x-3
Step-by-step explanation:
5 - 2x < 8x - 3
Add 2x to each side
5 - 2x+2x < 8x - 3+2x
5 < 10x-3
Answer:
The answer is C.
Step-by-step explanation:
Trust me, I got you.
What is the range of the function?
A. (3)
B. {3, 9, 12)
C. (-2, 2, 3, 4, 9, 12)
O D. {-2, 2, 3, 4
Answers
The range is all the possible y values, so the set with all the arrows.
Answer: B. {3,9,12}
Answer:
B
Step-by-step explanation:
The range means the y coordinates or output
In this the output are the numbers on the right.
We can also find the answer by eliminating.
Option A could not be the answer because it is only one of the numbers from the range.
Option B is the answer because it includes all the numbers from the range.
Option C and Option D could not be the answer because they include other numbers from the domain (which we are not trying to find).
This is an example here below
Hope this helped!!
Mr Hassan gave his year 7 class a test on Friday. the highest possible mark for the test was 10.
Answers
Answer:
To solve this question, we just need to observe the given graph.
(A) How many pupils scored more than 8 in the test?
Each little square is equivalent to 0.5 units, so there are 5 students who fot more than 8. Specifically, 1 got 8 points and 4 students got 10.
(B) How many pupils are there in Mr. Hassan's Year 7 class?There are 33 pupils in total, remember that each little square is equivalent to 0.5 units.
(C) What assumption have you made in answering part b)?The assumption was that the majority of pupils scored less than 8.
Write as an algebraic expression
Answers
Answer:
17. [tex]2^{6}[/tex]
19. 2 * 5
21. 8²
a 150 adults complete a survey 80 of them a woman what the ratio
Answers
Answer:
The number of men to number of women be 7 : 8 .
Step-by-step explanation:
Answer:
7:8
Step-by-step explanation:
The table shows the scores of a biology test in Mrs. Smiths class . Find the mean of the data without Kim’s score.
A- 80
B- 87.2
C- 90
D- 84.5
Answers
That will give you B
Hope this helps! :)
Answer:
87.2
Step-by-step explanation:
90+93+87+83+86+90+82=611
611/7=87.29
answer is b
There are three routes from a person's home to her place of work. There are four parking lots where she works, three entrances into her building, two elevators to her floor, and one route from each elevator to her office door. a) How many ways can she go from her home to her office? [2 marks] b) If she makes her various choices at random, what is the probability that she will take Morningside Drive, park in lot A, use the south entrance, and take elevator 1? [3 marks] c) As she starts her car one morning, she recalls parking lots A and B are closed for repair. What is the probability that she will take Industrial Avenue, park in lot D, use the north entrance, and take elevator 2?
Answers
Answer:
a) 72
b) 1/72
c) 1/36
Step-by-step explanation:
a) number of ways she can choose route= 3C1 = 3
number of ways she can choose parking lots= 4C1 = 4
number of ways she can choose entrances= 3C1 = 3
number of ways she can choose elevators= 2C1 = 2
number of ways she can go to office= number of ways she can choose route×number of ways she can choose parking lots×number of ways she can choose entrances×number of ways she can choose elevators
number of ways she can go to office= 3×4×3×2
= 72
b) Probability of morning side= number of morning side/ total number of routes= 1/3
probabiltiy of Parking lot A= number of parking lot A/ total number of parking lot= 1/4
probability of south entrance= number of south entrance/ total number of entrances= 1/3
probablity of elevator 1= number of elevator 1/ total number of elevator= 1/2
combine probability= 1/3× 1/4×1/3×1/2 = 1/72
c) Probability of Industrial Avenue= number of industrial avenue/ total number of avenue= 1/3
Probability of parking lot D= number of parking lot D/ total number of parking lot after deducting number of parking lots A and B = 1/2
Probability of north entrance= number of north entrance/ total number of entrance= 1/3
probablity of elevator 2= number of elevator 2/ total number of elevator
= 1/2
combine probability= 1/3 × 1/2 × 1/3 ×1/2
= 1/36
Given the regular octagon, what is the length of any side?
Answers
Answer:110
Step-by-step explanation:x^2+17x=15x+35
x^2+17x-15x-35=0
x^2+2x-35=0
delta=2^2-4*1*(-35)=4+140=144
x1=(-2+V144)/2=(-2+12)/2=10/2
x=5
so 15*5+35=75+35=110
Answer:
110Step-by-step explanation:
In a regular polygon, each side has the same length.
Therefore we have the equation:
[tex]x^2+17x=15x+35[/tex]
We must specify the domain:
[tex]x^2+17x>0\ \wedge\ 15x+35>0\\\\x(x+17)>0\ \wedge\ 15x>-35\\\\(x<-17\ \vee\ x>0)\ \wedge\ x>-\dfrac{7}{3}\Rightarrow x>0[/tex]
[tex]x^2+17x=15x+35\qquad\text{subtract}\ 15x\ \text{from both sides}\\\\x^2+17x-15x=15x-15x+35\\\\x^2+2x=35\qquad\text{add 1 to both sides}\\\\x^2+2x+1=35+1\\\\x^2+2(x)(1)+1^2=36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=36\to x+1=\pm\sqrt{36}\\\\x+1=\pm6\qquad\text{subtract 1 from both sides}\\\\x+1-1=\pm6-1\\\\x=-7\ \vee\ x=5[/tex]
[tex]x<-7\notin\text{domain};\ x=5\in\text{domain}[/tex]
The length of a side:
[tex]x^2+17x=5^2+17(5)=25+85=110\\\\15x+35=15(5)+35=75+35=110[/tex]
Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written using
function notation?
f(y) = -1/3y+4/3
f(x) = -3x+4
f(x) = -1/3x + 4/3
f(y) = -3y+4
Answers
9x + 3y =12
3y = -9x +12
y = -3x + 4
f(x)= -3x+4
Then, the answer is B
*I WILL MARK YOU BRAINLIEST!!!!!*
Answers
-3
Explanation:
Rate of change in the interval
X=0 to X=3 is given by,
[tex]r = \frac{f(3) - f(0)}{3 - 0} \\ here \\ f(3) = 1 \\ f(0) = 10 \\ r = \frac{1 - 10}{3} \\ \: \: \: = \frac{ - 9}{ 3} \\ \: \: \: \: = - 3 \\ hope \: it \: helps.....[/tex]
Find the missing exponet
Answers
Mrs. Meyer's soap is $3.99 for 12 ounces. What is the cost per ounce?
Answers
Answer:
It's about 33 cents per ounce. The exact answer would be 0.3325
Step-by-step explanation:
Answer:
0.33
Step-by-step explanation: i did it on a piece of paper
A multi level parking lot has 6 levels and there are total of 1,327 parking spots. There are 162 parking spots on the first level. The rest of the parking spots are distributed equally on the other 5 levels. How many parking spots are there on the top level? *
Answers
Answer:
233 parking spots
Step-by-step explanation:
1327 - 162 = 1165
1165 ÷ 5 = 233
OA= (1,3,-1) and OD=(-1,0,n) find the value of n for which the length of AD is 7 units
Answers
Answer:
n = 5
Step-by-step explanation:
0A = (1,3,-1) and OD=(-1,0,n)
AD = √ (-1-1)^2 + (0-3)^2 + (n-(-1))^2
7 = √ (-2)^2 + (-3)^2 + (n+1)^2
7 = √4 + 9 + (n+1)^2
Now squaring both sides we have :
7^2 = (√4 + 9 + (n+1)^2)^2
49 = 4 +9 + (n+1)^2
49 = 13 + (n+1)^2
49 -13 = (n+1)^2
36 = (n+1)^2
Taking the square root of both sides we have :
√36 = √(n+1)^2
6 = (n+1)
6 = n + 1
6 - 1 = n
5 = n
Therefore n = 5
3х + y = 8
x - Зу = 11
Answers
Answer:
y = 8-3x and y = -11/3 + x/3
For the first equation you have to subtract 3x from both sides of the equation. for the second equation you have to move all terms that doesn't contain y to the right side and solve
My question is 3x + (2− 4x)
Answers
Answer:
3x+(2-4x)
= 2 (3x+4x)
=2 (7x)
=2/7x
=7x/2
=3.5
Step-by-step explanation:=3.5
Which of the following is an equivalent equation to find w
Answers
[tex]answer \\ w = \frac{ {8x}^{2} - 2y }{y} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Please help! Correct answers only!
There is a raffle with 200 tickets. One ticket will win a $550 prize, one ticket will win a $510 prize, one ticket will win a $280 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
Answers
Answer:
" Expected Payoff " = $ 6.70
Step-by-step explanation:
Consider the steps below;
[tex]Probability of Winning the 550 Dollar Prize - 1 / 200,\\Probability * Money Won = " Expected Payoff " For The 550 Dollar Prize,\\\\1 / 200 * 550,\\" Expected Payoff " - 2.75 Dollars,\\\\Probability of Winning the 510 Dollar Prize - 1 / 200,\\\\1 / 200 * 510,\\" Expected Payoff " - 2.55 Dollars,\\\\Probability of Winning the 280 Dollar Prize - 1 / 200,\\\\1 / 200 * 280,\\" Expected Payoff " - 1.4 Dollars,\\\\[/tex]
[tex]Conclusion ; Expected Payoff = 6.70 Dollars[/tex]
Which graph represents y<-3x?
Answers
Step-by-step explanation:
Desmos Graphing Calculator
