Answer:A 30-60-90 right triangle is a special right triangle in which one angle measures 30 degrees and the other 60 degrees. The key characteristic of a 30-60-90 right triangle is that its angles have measures of 30 degrees (π/6 rads), 60 degrees (π/3 rads) and 90 degrees (π/2 rads). The sides of a 30-60-90 right triangle lie in the ratio 1:√3:2.
Step-by-step explanation:
The side lengths of a 30-60-90 triangle can be expressed as x, x√3, and 2x, where x is a positive constant.
We have,
In a 30-60-90 triangle, the angles measure 30 degrees, 60 degrees, and 90 degrees.
The side lengths of a 30-60-90 triangle have a specific ratio.
Let's denote the length of the shortest side as x, the length of the side opposite the 60-degree angle as y, and the length of the hypotenuse as z.
The ratios of the side lengths in a 30-60-90 triangle are as follows:
Shortest side: x
Side opposite 60-degree angle: y = x√3
Hypotenuse: z = 2x
Given this ratio, we can determine which set of values could be the side lengths of a 30-60-90 triangle.
The values must satisfy the above relationships.
Possible sets of values for the side lengths of a 30-60-90 triangle are:
Set 1:
x = 1
y = x√3 = √3
z = 2x = 2
Set 2:
x = 2
y = x√3 = 2√3
z = 2x = 4
Set 3:
x = 3
y = x√3 = 3√3
z = 2x = 6
Set 4:
x = k (where k is any positive constant)
y = x√3 = k√3
z = 2x = 2k
These sets of values satisfy the ratios for a 30-60-90 triangle.
Remember that the ratios are consistent, so any positive constant can be chosen for the length of the shortest side (x), and the other side lengths (y and z) will follow accordingly.
So,
Any set of values that satisfy the ratios given above could be the side lengths of a 30-60-90 triangle.
Thus,
The side lengths of a 30-60-90 triangle can be expressed as x, x√3, and 2x, where x is a positive constant.
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Somebody pls answer this fast!!!!
A new novel is 540 pages. Emily has read 192 pages in 6 hours. Maria has read 170 pages in 5 hours.
a. Who reads faster, Emily or Maria?
b. How long will it take Maria to read the entire novel at her current rate?
Answer:
maria reads faster (34 pages in a hour compared to 32) and might finish around 15.88 hours
Step-by-step explanation:
i dont think the second part is right
please help me with this! Thank youu
Answer:
y=-3x+2
y = [tex]\frac{1}{5}[/tex]x - 5
Step-by-step explanation:
Question 1
It is given that;
- one of the lines has an equation of; y = -3x-7
- the given line's y-int is (0, 2) ~(The y-int is when the line crosses the y axis, hence x is zero)
- these two lines are parallel
When two lines are parallel, their slope is the same, hence the equations of the given line would look like this;
y = -3x + 2
In the slope-intercept format (which is; y = mx + b, where "m" is the slope, and "b" is the y-intercept).
Questions 2
It is given that;
- one of the lines has an equation of y = -5x + 1
- the given line's y-int is (0, -5) ~(The y-int is when the line crosses the y axis, hence x is zero)
- these two lines are perpendicular
When two lines are perpendicular, their slopes are the negatives reciprocal of each other, hence the equations of the given line would look like this;
y = [tex]\frac{1}{5}[/tex]x - 5
In the slope-intercept format (which is; y = mx + b, where "m" is the slope, and "b" is the y-intercept).
Which is the best first step and explanation for solving this system of equations 3x + y = 7 x + y = 3
Answer: Add the two equations together to eliminate y
Step-by-step explanation:
X+y=3
4x-y=7
I would use elimination since one equation has +y and one equation has -y
Add the two equations together
X+y=3
4x-y=7
-------------------
5x = 10
solve inequality for v
Answer:
[tex]\displaystyle v > \frac{-28}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{-10}{7}v > 8[/tex]
Step 2: Solve for v
Divide both sides by [tex]\displaystyle \frac{-10}{7}[/tex]: [tex]\displaystyle v > \frac{-28}{5}[/tex]Here we see that any value v greater than [tex]\displaystyle \frac{-28}{5}[/tex] would work as a solution to the inequality.
What is the decay factor of the exponential function
represented by the table?
O1/3
O2/3
O 2
O 6
Fact: It is not 6!
And I swear I am not lying!
Answer:
A. 1/3
as x increases the values of the function all become one-third of each other !!
6 is 1/3 of 18
2 is 1/3 of 6
2/3 is 1/3 of 2
Ellen can read 3 pages in 7 minutes.
Rob can read 8 pages in 14 minutes.
Who is the faster reader? Justify your
answer.
Rob is the faster reader.
7 in half is 3.5, and 14 in half is 7. 8 is over 7, and 3 is under 3.5:
ur daddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
6. How much more is (6.48 x 10^5) than (3.2 x 10^2
Answer:
647680
Step-by-step explanation:
Answer:
Step-by-step explanation:
6.48x10^5 / 3.2 x 10^2=2.025 x 10^3
i divide 6.48/3.2
10^5/10^2=10^3
A builder needed to buy one hundred fifty-four boards for his latest project. If the board he needs comes in packs of three, how many packets will he need to buy
Answer:
51.3 packets or 51 1/3 packers
Step-by-step explanation:
From the above question:
The board he needs comes in packs of three. This means
1 pack = 3 boards
Hence:
3 boards = 1 packet
154 boards = x
Cross Multiply
3x = 154
x = 154/3
x = 51.333333333 packets
Approximately = 51.3 packets or 51 1/3 packers
The builder will need to buy 51.3 packets or 51 1/3 packers
A rectangle has a perimeter of 22cm with a length of 10m. What is the width of one side?
Step-by-step explanation:
We know that
1m = 100cm
according to question
perimeter of rectangle = 2 (l+b)
22cm = 2 (100+b)cm
2×(100+b)cm = 22cm
100+b cm = 22/2cm
100+b cm = 11 cm
b = 100 -11 cm
hence, breadth = 89 cm .thanks for ask question.
If <2 <4 what type of angle relationship do they have
Answer:
2
Step-by-step explanation:
This graph shows the solution to which inequality?
5
(3,2)
5
(-3,-6)
O A. yx-2
OB. ysx-2
O c. y< x-2
OD. y -2
Answer:
letss seeee
Step-by-step explanation:
c.
The graph shows the solution to y ≥ 2 and y < x inequality.
we have:
y ≤ 2
y ≥ 2
x > 2
y > 2
The graph is limited by a line; y = 2 (red line).
The part corresponds to the part in which y > 2.
The line is continuous, so 2 is also included in the interval
y ≥ 2
Then to find if it is "less than" (<) or "less than or equal to" (≤):
Since the line that limits this interval. The line is y = x, it is a dotted line, the extreme is not included.
In summary:
y < x
Answer is B. y ≥ 2 and y < x
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helP pls i’ll mark as brainliest if correcttt
Answer:
answer is 42 in²
:-)))
....
Answer the questions please
Answer:
The first one, As time increases, the number of Perennials sold has decreased
Step-by-step explanation:
Answer:
It's A or the first one on the top.
Step-by-step explanation:
3. The floor of building consists of 2000 tiles which are rhombus shaped and
each of its diagonals are 40 cm and 25 cm in length. Find the total cost of
polishing the floor, if the cost per m2 is Rs/5.
Answer:
Total cost of polishing the floor is Rs/500.
Step-by-step explanation:
The floor consists of 2000 tiles which have the shape of a rhombus.
Area of rhombus = [tex]\frac{d_{1} *d_{2} }{2}[/tex]
Where: [tex]d_{1}[/tex] and [tex]d_{2}[/tex] are the diagonals.
Given that:
[tex]d_{1}[/tex] = 40 cm = 0.4 m
[tex]d_{2}[/tex] = 25 cm = 0.25 m
Then,
Area of each tile = [tex]\frac{0.4*0.25}{2}[/tex]
= [tex]\frac{0.1}{2}[/tex]
= 0.05 [tex]m^{2}[/tex]
Area of each tile is 0.05 [tex]m^{2}[/tex].
Since there are 2000 tiles on the floor of the building, then;
Total area covered by the tiles = 0.05 x 2000
= 100 [tex]m^{2}[/tex]
The total cost of polishing the floor = 100 x Rs/5
= Rs/500
An expression is shown below:
the square root of 32 plus the square root of 2
Which statement is true about the expression?
the square root of 32 plus the square root of 2
It is rational and equal to 4 times the square root of 2.
It is irrational and equal to 4 times the square root of 2.
It is rational and equal to 5 times the square root of 2.
It is irrational and equal to 5 times the square root of 2.
Answer:
C or D...
im guessing
Answer:
√32=√(16*2)=4√2
4√2 + √2=5√2
That is why is irrational
Step-by-step explanation:
Carmen pays $20 to rent a scooter for 4 hours. The cost c, to rent a scooter is proportional to the number h of hours that she rents the scooter. Write an equation that represents the situation. How much would it cost Carmen to rent the scooter for 6 hours
Answer: 30$
Step-by-step explanation:
Equation
C=5h
c=5(6)
c=30
The hanger image below represents a balanced equation.
a
9.1
4
Write an equation to represent the image.
Answer:
2x = 3 hope that helps
Step-by-step explanation:
5,000 people visited a bookfair in the first week. The numbers increased by 10% in the second week. how many people visited the book fair the second week?
please show your work and explain
Answer:
5500
Step-by-step explanation:
5000 + (10 / 100) x 5000 = 5000 + (1/10) x 5000 = 5000 +500= 5500 people visted the book fair in the second week
Tabitha has a DVD rack which can hold 42 DVDS. She can fit 8 more DVDS on the rack before the rack is full. How many DVDS are on the rack?
Answer:
34
Step-by-step explanation:
42 dvds total but there is room for 8 more so
42 total size - 8 more can fit = 34 on the rack
i think im right unless i missunderstood the question
Answer:
34
MARK BRAINLIEST
pls help I literally don’t get this
According to the graph, what is the value of the constant in the equation below?
Answer:
36.
Step-by-step explanation:
plug in the numbers. height=constant/width
height=18
width=2
18=×/2
18×2=36 or 36/2=18
Please help 50 points if you can answer correctly
Answer:
A. -14. R.72. C.1. D.34
Step-by-step explanation:
I think that right
A salesman has a car for sale for $5000. He decides to increase the price by 40%. When no one buys the car, he decreases the new price by 10%.
What is the final price of the car?
Answer:
$6300
Step-by-step explanation:
original price: $5000
increase price by 40%: $5000×1.4=$7000
decrease new price by 10%: %7000×0.9=$6300
It says round all calculations to one decimal point
Pls show workings it due in a hour
Answer:
[tex]2\sqrt{5}+\sqrt{29}+\sqrt{53},\\\approx 17.14\:\mathrm{units}[/tex]
Step-by-step explanation:
The distance between two coordinates is given by:
[tex]d=\sqrt{(\Delta x)^2+(\Delta y)^2}[/tex], or [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
The distance between each of the coordinates of the triangle forms the sides of triangle. Therefore, we can add the distance between these coordinates to find the perimeter of the triangle.
The distance between [tex](3, -2)[/tex] and [tex](7, 0)[/tex] is:
[tex]d=\sqrt{(7-3)^2+(0-(-2))^2}=\sqrt{4^2+2^2}=\sqrt{20}=2\sqrt{5}[/tex]
The distance between [tex](3, -2)[/tex] and [tex](5, 5)[/tex] is:
[tex]d=\sqrt{(5-3)^2+(5-(-2))^2}=\sqrt{2^2+7^2}=\sqrt{53}}[/tex]
[tex]d=\sqrt{(7-5)^2+(0-5)^2}=\sqrt{2^2+5^2}=\sqrt{29}[/tex].
Therefore, the total perimeter of the triangle is:
[tex]\fbox{$2\sqrt{5}+\sqrt{29}+\sqrt{53}\:\checkmark$}[/tex].
Jacqui is selling scented candles as a fundraiser for a school field trip. Each cinnamon candle sells for $3.50 and each chocolate candle sells for $2.50. She raised a total of $94.50 for the trip. The number of chocolate candles that Jacqui sold is three less than twice the number of cinnamon candles. Let c represent the number of chocolate candles and let m represent the number of cinnamon candles. How many chocolate candles did Jacqui sell?
Answer:
Number of cinammon = 12
Number of chocolate = 21
Step-by-step explanation:
Given that:
Cost of Cinnamon candle , c = $3.50
Cost of chocolate candle , d = $2.50
Total amount raised, T = $94.50
d = 2c - 3
Total amount = (cost of Cinnamon * number sold) + (cost of chocolate * number sold)
94.50 = (3.50 * c) + (2.50 * (2c-3))
94.50 = 3.50c + 5c - 7.5
94.50 = 8.50c - 7.5
94.50 + 7.5 = 8.50c
102 = 8.50c
c = 102 / 8.50
c = 12
d = 2c - 3
d = 2(12) - 3
d = 24 - 3
d = 21
Answer:
D.) 21
Step-by-step explanation:
Can some one make question for me so I can get 4 more brainliest
Answer:
yeahhh no. go answer questions.
sure what should i call it?
can i have brainliest on this one?
kind of like were giving each other one?
1 meter of electric cord costs $3. How much do u pay for 2/3.
Answer:
2 dollars.
Step-by-step explanation:
1 meter costs 3 dollars
2/3 meter costs 2/3 * 3
2/3 * 3 = 2
So you would pay 2 dollars for 2/3 of a meter.
please help me! here’s a picture
Answer:
I would think the answer is 28?
im not really that sure
PLEASEEE HELP MEEE WITH THISS
Answer: The answer is D
Step-by-step explanation:
will give brainliest to right answer
Answer:
D
Step-by-step explanation:
Area of rectangle: 6 x 4 = 24
Area of triangle: 4(4)/2 = 8
Area of semi-circle: (πr²2)2 = 2π ≈ 6.28
24 + 8 + 6 = 38
