A triangle with angles of 30, 60, and 90 degrees is a unique and special type of right triangle known as a 30-60-90 right triangle, which has consistent properties and side ratios in Euclidean geometry.
Yes, a triangle with angles of 30, 60, and 90 degrees is a unique triangle, known as a 30-60-90 right triangle. This classification is based on the fact that in Euclidean geometry, the sum of the angles in any triangle is exactly 180 degrees. Since one of the angles is given as 90 degrees, this indicates it is a right triangle, and the remaining angles must add up to 90 degrees. Given that the other two angles are 30 and 60 degrees, this satisfies the requirement exactly, making it a specific type of right triangle with consistent properties.
For example, the sides of a 30-60-90 triangle are always in the ratio 1:√3:2. The side opposite the 30-degree angle is the shortest; the side opposite the 60-degree angle is √3 times longer; and the hypotenuse, opposite the 90-degree angle, is twice as long as the shortest side. These proportions and the angles create the unique properties of the 30-60-90 triangle, and they can be applied in trigonometric calculations and proofs. This distinct set of angles and side ratios is what makes the 30-60-90 triangle a special and unique case in geometry.
If the area of a triangle is 18 units (squared 2 to the power), and a side of a triangle is 6, what is the other side?
Answer:
The other side is 6 units long.
Step-by-step explanation:
Area of a Triangle = (1/2)(Base)(Height)
18 = (1/2)(6)(x)
Note that x is the other side of the triangle.
18 = 3x
x = 6
The other side is 6 units long.
The distance around tim's rectangular book is 48 cm. The length of each longer side is 14 cm? What is length of each shorter ...
14+14= 28= 48-28= 20/2= 10
What is the probability?
Answer:
(C) is 0.14 that is your probability
Step-by-step explanation:
Consider the graph of the quadratic graph y=-x^2 -10x+24 ,what is the y-value of the vertex
-51
First, find the axis of symmetry, or the x value where the line switches directions. This is also the x value of the vertex. Find this by using the equation -b/2a. In this case, -10 is b, and 1 is a.
-(-10)/2(1)
10/2
5
So, the x value of the vertex is 5. Now, find the y value by putting the x value back into the equation.
y = -(5)^2 - 10(5) + 24
y = -25 - 50 + 24
y = -75 + 24
y = -51
So, the y value of the vertex is -51.
Which answer describes the transformation?
Horizontal translation 1 unit to the left
If 2500 sheets of paper make a stack that is 3/4 foot(9in.) tall, how many sheets of paper would fit in one of terry’s trays? Round your answer to the nearest 100
Answer:
694.44 sheets of paper
Step-by-step explanation:
we know that
The height of terry’s trays is [tex]h=2\frac{1}{2}\ in=\frac{2*2+1}{2}=\frac{5}{2}\ in[/tex]
using proportion
2,500/9=x/(5/2)
x=2,500*(5/2)/9
x=694.44 sheets of paper
A cube has a volume of 300 cm3. If all the side lengths are multiplied by 7, what will the resulting volume be?
For this case we have that by definition, the volume of a cube is given by:
[tex]V = l ^ 3[/tex]
Where "l" is the length of the side.
We have to:
[tex]l ^ 3 = 300\\l = \sqrt [3] {300}\\l = 6,69432950[/tex]
If we multiply the sides by 7, we will have:
[tex]l '= 6,69432950 * 7\\l '= 46.86030650[/tex]
Then, the new volume will be:
[tex]V '= l' ^ 3\\V '= 102900 \ cm ^ 3[/tex]
Answer:
[tex]102900 \ cm ^ 3[/tex]
Use the list method to write "The perfect square integers between 1 and 80 inclusive".
{1, 4, 9, 16, 25, 36, 49, 64, 80}
{4, 9, 16, 25, 36, 49, 64}
{1, 4, 9, 16, 25, 36, 49, 64}
ANSWER
{1, 4, 9, 16, 25, 36, 49, 64}
EXPLANATION
The perfect square integers between 1 and 80 inclusive are obtained by squaring the natural numbers from 1 to 8
[tex] {1}^{2} = 1[/tex]
[tex] {2}^{2} = 4[/tex]
[tex] {3}^{2} = 9[/tex]
[tex] {4}^{2} = 16[/tex]
[tex] {5}^{2} = 25[/tex]
[tex] {6}^{2} = 36[/tex]
[tex] {7}^{2} = 49[/tex]
[tex] {8}^{2} = 64[/tex]
The square of the next number does not fall within the given range.
Therefore "The perfect square integers between 1 and 80 inclusive" are
{1, 4, 9, 16, 25, 36, 49, 64}
(1,9,16,25,36,49,64)Answer:
Step-by-step explanation:
Graph the line with slope2/3 passing through the point(-2, 1)
Answer:
The graph in the attached figure
Step-by-step explanation:
step 1
Find the equation of the line into point slope form
The equation of the line is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute the given values
[tex]y-1=(2/3)(x+2)[/tex]
step 2
To graph the line find the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y-1=(2/3)(0+2)[/tex]
[tex]y=(4/3)+1[/tex]
[tex]y=(7/3)[/tex]
The y-intercept is the point (0,7/3)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
[tex]0-1=(2/3)(x+2)[/tex]
[tex]-1=(2/3)x+(4/3)[/tex]
[tex](2/3)x=-(4/3)-1[/tex]
[tex](2/3)x=-(7/3)[/tex]
[tex]2x=-7[/tex]
[tex]x=-7/2[/tex]
The x-intercept is the point (-7/2,0)
step 3
Plot the intercepts to graph the line
see the attached figure
What’s the slope between -14,-10 and 12,18
[tex]\bf (\stackrel{x_1}{-14}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{18}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{18-(-10)}{12-(-14)}\implies \cfrac{18+10}{12+14}\implies \cfrac{28}{26}\implies \cfrac{14}{13}[/tex]
Answer:
28/26
Step-by-step explanation:
We can find the slope using the equation
y2-y1/x2-x1
We are give two points so lets plug them into the equation above
18-(-10)/12-(-14)
= 18+10/12+14
=28/26
A 25ft ladder is placed 7 feet from the wall, as shown. How high up the wall with the ladder reach?
Answer:
24 ft up the wall
Step-by-step explanation:
We can use the Pythagorean theorem to solve, letting the 25 ft ladder be the hypotenuse
a^2 +b^2 = c^2
7^2 +b^2 = 25^2
49 + b^2 = 625
Subtract 49 from each side
49-49 +b^2 = 625-49
b^2 = 576
Take the square root of each side
sqrt(b^2) = sqrt(576)
b = 24
We only take the positive solution since length cannot be negative
The ladder will reach 24 ft up the wall
If the function rule is to add 6, and an output value is 6, what is the input value?
The answer is 0! The input value would be 0!
the function rule is to add 6, so:
y = x + 6 (y is the output, x is the input)
Since they gave you an output value of 6, you can plug it into the equation
y = x + 6 Plug in 6 for y
6 = x + 6 Subtract 6 on both sides to find the input value
0 = x
Mrs. Garcia owns a day-care. She brought 8 toy truck's 6toy cars 4 toy boats 6 toy planes is she combines the transportation toys and places an eaual number into 3 containers, how many will be in each container?
It’s going to be 8 because you add all the toys together and divide that by the container number
Answer:
There will be 8 transportation toys
Step-by-step explanation:
So first you would all the toys up. Then divide it by 3.
6+4=10 + 6= 16 +8=24
24 / 3 = 8
The price of a shirt with a $5 tax. The original shirt price is g dollars.
Select the correct answer.
Question 2 options:
5g
g - 5
g + 5
Final answer:
The price of the shirt after including a $5 tax is represented by the expression 'g + 5', where 'g' is the original price of the shirt.
Explanation:
When calculating the price of an item after tax, you simply add the tax amount to the original price of the item. In this case, the original shirt price is represented by the variable g dollars, and a $5 tax is added to this price. Therefore, the correct answer to the question 'The price of a shirt with a $5 tax. The original shirt price is g dollars.' is g + 5.
shakia has five days to read a 200 page book if she wants to read the same numbee of pages each day how many pages should she read each day
Answer:
40
Step-by-step explanation:
Since she has a total of 200 pages and 5 days you would divide to get 40.
3x+1+5x=7+15+7x what is x?
Answer: x=21
Step-by-step explanation:
To solve for x you must first combine you like terms on each side of the equal sign. So you problem will become 8x+1=22+7x. Then get your x on one side and your numbers on the other by taking the one away from the right side and 1 away from 22. Then take away 7 from the left side to cancel it out. Then take 7x away from 8x to leave you with x. making your answer x=21
Answer:
x = 21Step-by-step explanation:
3x + 1 + 5x = 7 + 15 + 7x combine like terms
(3x + 5x) + 1 = (7 + 15) + 7x
8x + 1 = 22 + 7x subtract 1 from both sides
8x = 21 + 7x subtract 7x from both sides
x = 21
The answer is A right?
Answer: it is c
Step-by-step explanation:
[tex]d. \: 35m + 50 + 25 \\ \\ 1. \: 35m + (50 + 25) \\ 2. \: 35m + 75[/tex]
what is the slope of the line described by the equation below?
y= -x + 8
Answer: The slope is -1
Step-by-step explanation:
The slope of the line in Slope-intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
You can observe that the equation of the line [tex]y= -x + 8[/tex] is written in Slope-intercept form. Therefore, you can identify that the slope of the line described by this equation is:
[tex]m=-1[/tex]
And the y-intercept is:
[tex]b=8[/tex]
A cube has an edge measuring 7 inches. What is the volume of the cube, in inches³?
Answer:
343 in^3
Step-by-step explanation:
The volume of a cube is found by V = s^3. Here s = 7. So the volume is 7*7*7 = 343 in^3.
Final answer:
The volume of a cube with an edge length of 7 inches is 343 cubic inches.
Explanation:
The volume of a cube is calculated by multiplying the length, width, and height of the cube. Since all sides of a cube are equal, we simply need to cube the length of one side.
In this case, the edge (length, width, and height) of the cube is 7 inches.
The volume of a cube with an edge length of 7 inches can be calculated as follows:
Volume = edge length³Volume = 7³Volume = 7 x 7 x 7 = 343 cubic inchesTherefore, the volume of the cube is 343 cubic inches.
Raul had $60. Mike had $30. Each boy donated 1 tenth of his money.
Which statement is true?
Raul donated more money than Mike did.
Mike donated more money than Raul did.
The boys donated an equal amount.
Answer:
raul donated more money than mike did is
Step-by-step explanation:
raul donated 1/10 of 60 so
1/10*60=6
mike donated 1/10 of 30 so
1/10*30=3
so raul donated more money than mike did is the correct statement
Answer: B.
Step-by-step explanation:
So it's B because...
So if they donated 1/10th of their money, that means they donated 10%. So, 10% of 60 is 6 and 10% of 30 is 3. which means that Raul donated more money than Mike did.
10 % of 60 = 6
10% of 30 = 3
ANSWER → B
* Hopefully this helps:) Mark me the brainliest:)!!
∞ 234483279c20∞
What is 2% of 50??????
Answer:
1
Step-by-step explanation:
2%= 0.2
0.2*5= 1
When finding Percent of whole multiply.
To figure this out you must do a proportion. Typically you would do [tex]\frac{part}{whole}[/tex]
This means that you would set up your proportions like this:
[tex]\frac{x}{50} =\frac{2}{100}[/tex]
^^^you want to find 2% of 50, so 50 is the "whole" and x (what you are looking for) is the part. The reason there is the 100 is because % are always taken out of 100% , and therefore 100 is the "whole". 2 is on top of 100 because it is a "part" of 100
the next step is cross multiplication so you would get:
100x= (50*2) ---> 100x = 100
^^^you then solve this like a normal algebra equation to get x = 1
Hope this helped! Let me know if there is anything else I can do!
The circumference of oC is 56 cm. What is the length of AB (the minor arc)?
Answer:
Length of arc AB is 14. So, option E is correct
Step-by-step explanation:
Circumference of circle == 56 cm
We need to find length of arc AB?
Formula used will be l = rФ
We know, C = 2πr
56 = 2πr
56/2π = r
=> r = 8.91
Ф = 90° = 1.57 radians
So, l= rФ
l = 8.91 * 1.57
l = 13.98 = 14
So, Option E is correct
Answer:
Length of arc AB is 14. So, option E is correct
Step-by-step explanation:
if it take 10 hours to get 50% how many hours are 32%
ANSWER
6.4 hours
EXPLANATION
if it takes 10 hours to get 50%, then it will take less number of hours to get 32%
We use proportion to solve this question.
If less more divides.
The number of hours it will take to get 32% is
[tex] = \frac{32\% \times 10}{50\%} [/tex]
[tex] = 6.4[/tex]
Hence it will take 6.4 hours to get 32%
An angle measures 148° less than the measure of a supplementary angle. What is the measure of each angle?
PLEASE HELP!!
Answer:
164 and 16
Step-by-step explanation:
5(x–9)–7(3x+6)=25
Please help me.
Answer:
x=-3 10/16
Step-by-step explanation:
5x-9-21x-42=25 (opening parenthesis)
-16x-33=25
16x+58=0
x=-58/16=-3 10/16
-1 3/5 ÷-2/3 as a mixed number
[tex]\text{Hey there!}[/tex]
[tex]-1\frac{3}{5}\div\frac{2}{3}[/tex]
[tex]-1\frac{3}{5}=-\frac{8}{5}[/tex]
[tex]\text{Problem becomes:}-\frac{8}{2}\div\frac{2}{3}[/tex]
[tex]\text{Solve that, and you will get:}\frac{-4}{5}\div{\frac{3}{1}}[/tex]
[tex]-4\times1=-4[/tex]
[tex]5\times3=15[/tex]
[tex]\rightarrow =\frac{-4}{15}[/tex]
[tex]\boxed{\boxed{\boxed{\bf{Answer:\frac{-4}{15}}}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
For every $10 worth of candy student council sells, they get to keep $5. This can be represented with variables.
1. What are the variables?
2. What letter can you use to represent each?
3. How are they related>
4. Create an equation relating them to each other. One that you could use to find out the amount of money student council will make for any amount of candy they sell.
1. The variables are “money sold total ($10)” and “money kept by student council($5)”
2. The “money sold total ($10)” can be represented by T. (For Total)
The “money kept by student council($5)” can be represented by K. (for kept)
3. As T increases, K increases.
4. K= t/2
Good luck!
The variables in this problem are the amount of candy sold and the amount of money student council keeps. They are related by the equation m = 0.5c. This equation allows us to find out the amount of money student council will make for any amount of candy they sell.
Explanation:The variables in this problem are the amount of candy sold and the amount of money student council keeps.
We can represent these variables with the letters 'c' for candy sold and 'm' for money kept by student council.
The relationship between the variables is that for every $10 worth of candy sold, student council keeps $5. So, the amount of money student council keeps is half of the amount of candy sold.
We can express this relationship with the equation m = 0.5c.
This equation allows us to find out the amount of money student council will make for any amount of candy they sell.
For example, if they sell 20 worth of candy, we can substitute c = 20 into the equation and solve for m: m = 0.5(20) = 10.
Therefore, student council will make $10 for selling $20 worth of candy.
What is XxYx4-34=?????
Answer:
4XY-34
Step-by-step explanation:
1. x*y=xy
2.xy*4=4xy
3. 4xy-34
given a triangle with sides measuring 18 inches,21 inches 14 inches find the measure of the anglewith the greatest
ANSWER
[tex]A = 80.98 \degree[/tex]
EXPLANATION
The angle with the greatest measure corresponds to the longest:
Since we know the three side lengths, we use the cosine rule to obtain;
[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(A) [/tex]
where a=21, b=18 and c=14
[tex] {21}^{2} = {18}^{2} + {14}^{2} - 2 \times 18 \times 14\cos(A) [/tex]
[tex]44 1= 324+ 196 - 504\cos(A) [/tex]
[tex]44 1= 520 - 504\cos(A) [/tex]
[tex]44 1 - 520 = - 504\cos(A) [/tex]
[tex] - 79 = - 504\cos(A) [/tex]
[tex]\cos(A) = 0.1567[/tex]
[tex]A = \cos ^{ - 1} (0.1567) = 80.98 \degree[/tex]
correct to the nearest hundredth.
Solve 2/3 + 5/8 and put answer in simplest form.
Answer:
1 and 7/24
Step-by-step explanation:
2/3 + 5/8
= 16/24 + 15/24
= 31/24
= 1 and 7/24
Hope this helps!
For this case we must simplify the following expression:
[tex]\frac {2} {3} + \frac {5} {8}[/tex]
Then, we add the fractions making cross product:
[tex]\frac {2} {3} + \frac {5} {8} = \frac {8 * 2 + 3 * 5} {3 * 8} = \frac {16 + 15} {24} = \frac {31 } {24}[/tex]
Thus, the fraction can not be simplified.
How mixed number we have:
[tex]\frac {31} {24} = 1 \frac {7} {24}[/tex]
ANswer:
[tex]\frac {31} {24}[/tex]