Special Right Triangles
Isosceles Right Triangle
30-60-90 Triangle
help 1-12 please
Answers
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
1.
since it is a right-angled triangle, and one of the leg angles is 45°, then the other leg angle is also 45°.
which makes this an isoceles triangle.
so, the second leg is 6 too.
the baseline (Hypotenuse) is then per Pythagoras
baseline² = 6² + 6² = 36 + 36 = 72 or 2×36
baseline = sqrt(72) = 6×sqrt(2)
2.
this is then a 30-60-90 triangle.
the left leg (a) is then 2a/2 = 10/2 = 5.
and the bottom leg is 5×sqrt(3).
3.
isoceles triangle.
so, left and right legs (a) are both 3 (from the 3×sqrt(2)).
4.
30-60-90 triangle
upper leg is then 6×sqrt(3).
the baseline is 2 times the left leg : 2×6 = 12
5.
isoceles triangle
both legs are 2 (from the 2×sqrt(2)).
6.
30-60-90 triangle
left leg is 4 (from the 4×sqrt(3)).
the baseline is 2×4 = 8.
7.
isoceles triangle.
6 = a×sqrt(2)
a (both legs) = 6/sqrt(2)
8.
30-60-90 triangle
9 = a×sqrt(3)
a (left leg) = 9/sqrt(3)
baseline = 2a = 2×9/sqrt(3) = 18/sqrt(3)
9.
due to the equal leg angles this is an isoceles triangle.
4 = a×sqrt(2)
a (both legs) = 4/sqrt(2)
10.
30-60-90 triangle
the bottom leg (a) = 2a/2 = 6/2 = 3
the left leg is then 3×sqrt(3)
11.
isoceles triangle
left leg is also 5.
baseline is 5×sqrt(2)
12.
30-60-90 triangle
12 = a×sqrt(3)
a (left leg) = 12/sqrt(3)
the baseline is then 2a = 2×12/sqrt(3) = 24/sqrt(3)
Related Questions
Factor 5x2y + 22xy – 15y.
Answers
Answer:
5y(x^2 - 3)
Step-by-step explanation:
Hope this helps :)
What is the radius r of a circle with the circumference C of length 48.6 m
Answers
Answer:
r = 24.3/π m
r = 7.73 m
Step-by-step explanation:
C = 2πr
48.6 m = 2 × π × r
r = 48.6/(2π) m
r = 24.3/π m
r = 7.73 m
NEED HELP ASAP The salaries of Nathan and Trisha are in the ratio of 5:9. Trisha's salary is £16800 more than Nathan's. Find Nathan's salary.
Answers
Answer:
From the ratio
The difference is 9 - 5 = 4
Hence Trisha has 4 units more than Nathan and this resulted to 16800
Therefore 1 unit will be
16800 / 4 = 4200
Nathan’s salary is 5 units
5 * 4200 = 21000
Solve the following quadratic equations by any method. The solutions are:
f (x) = x 2 − 12x + 32
a.
(X - 4)(X - 8) this means that X = 4 and -8
b.
(X - 4)(X - 8) this means that X = -4 and -8
c.
(X - 4)(X - 8) this means that X = +4 and +8
d.
(X - 4)(X - 8) this means that X = -4 and +8
Answers
Answer:
Option C .
Step-by-step explanation:
We would like to solve the below quadratic equation ,
[tex]\longrightarrow f(x) = x^2-12x +32 [/tex]
Step 1 : Equate f(x) with 0 :-
[tex]\longrightarrow f(x) = 0\\[/tex]
[tex]\longrightarrow x^2-12x + 32=0[/tex]
Step 2 : Factorise the RHS :-
[tex]\longrightarrow x^2-8x - 4x +32=0\\[/tex]
[tex]\longrightarrow x(x-8)-4(x-8)=0\\[/tex]
[tex]\longrightarrow (x-8)(x-4)=0\\[/tex]
Step 3 : Equate each factor with 0 :-
[tex]\longrightarrow x - 8 = 0\\ \qquad x -4=0 [/tex]
[tex]\longrightarrow x = 8 \qquad x = 4 [/tex]
[tex]\longrightarrow \underline{\underline{\boldsymbol{ x = 8,4}}}[/tex]
Hence option C is correct .
no spammers pls and also giving brainliest to correct answer
Answers
you can tell from the angles being the same and the measurements of triangle c being 2/3s of triangle b's measurements.
The sides are in the ratio 3:2
And the angles and same: 37 degree, 53 degree and 90 degree
Two of the interior angles of a triangle are 84.0° and 30.0. Find the measure of the
third interior angle in degrees to one decimal place.
Answers
Answer:
66.0°
Step-by-step explanation:
The sum of the measures of the interior angles in a triangle is 180°.
Let "x" represent the measure of the third interior angle. We can use this to set up an equation:
84.0° + 30.0° + x = 180°
Add like terms:
114.0° + x = 180°
Subtract 114.0° from both sides:
x = 66°
The question asks for the answer to be in degrees to one decimal place, therefore:
x=66.0°
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
"When 85 is added to a number, the result is 45 more
than 6 times the number."
Answers
Answer:
136Step-by-step explanation:
85+45+6
136
this is solution ...
Need help with his geometry question. Find the value of x
Answers
Hey there!
Answer: [tex] \Rightarrow \boxed{\sf{x = 25}}[/tex]
[tex] \rightarrow \sf{ \frac{x}{20} = \frac{30}{24} }[/tex]
[tex] \rightarrow \: \boxed{ \sf{24x = 600}}[/tex]
[tex] \rightarrow \: \boxed{ \sf{ \frac{24x}{24} = \frac{600}{24}}} [/tex]
[tex] \rightarrow \boxed{ \bold{\sf{ x = 25}}}[/tex]
Hopes this helps
Estimate by rounding each decimal to the nearest whole number. 5.85+23.24
Answers
Answer:
Step-by-step explanation:
Can someone help me with this please
Answers
Answer:
6.46 seconds
Step-by-step explanation:
[tex] - 16 {t}^{2} + 65t + 248 = 0[/tex]
[tex]t = 6.46[/tex]
heresa earned scores of 88 points, 84 points, 88 points, and 91 points on four tests. What is the lowest score she can get on the fifth test and still finish with an average score of 90 points?
96 points
97 points
98 points
99 points
Answers
Answer:
99 points
Step-by-step explanation:
total of scores of 4 tests = 88 + 84 + 88 + 91 = 351
5 tests with an average score of 90:
⇒ total of scores = 5 × 90 = 450
Lowest score of 5th test = 450 - 351 = 99 points
Answer:
99 points
points scored:
88 points , 84 points, 88 points , 91 points, let the fifth test points be "n"
given score with an average 90 points[tex]\sf \rightarrow \dfrac{88 +84+88+91+n}{5} =90[/tex]
[tex]\sf \rightarrow 351+n =90 (5)[/tex]
[tex]\sf \rightarrow n =450-351[/tex]
[tex]\rightarrow \sf n = 99[/tex]
What angles are acute GFE mlk dbc dba
Answers
Answer:
d and a
Step-by-step explanation:
an acute is an angle less than 90 degrees. a 90 degree angle is a right angle (klm) the only 2 angles smaller than (klm) are (gfe) and (dba)
Help help help help
Answers
When spinning a penny, Claire believes the proportion of times the penny lands on heads is higher than 0.5. She spins a penny 50 times and it lands on heads 32 times. The P-value for the test of the hypotheses, H 0: p = 0.5, and H alpha: p greater-than 0.5, is 0.02, What is the correct interpretation of this value?
Answers
It depends on what the level of significance (alpha) is.
Since alpha is not stated, I'll assume that alpha = 0.05 by default.
Because the p-value is smaller than alpha, we reject the null hypothesis.
Therefore, we conclude that the alternative hypothesis is correct and the proportion of heads is greater than 0.5
A rectangle is shown with the area of 14/32 square in. Label two sides of the rectangle with appropriate fractions that would come up with the area of 14/32 square inches when multiplied together.
Answers
The dimensions of the rectangle that would have a value of 14/32 inches square are a length of 2/16 and a width of 31/2 inches.
What are the dimensions of the rectangle?
A rectangle is a 2-dimensional quadrilateral with four right angles that has a value of 360 degrees. It has two diagonals that bisect each other.
Area of a rectangle = length x width
2/16 x 7/2 = 14/32
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
Find all the common factors of 9 and 15.
A) 1, 3
B) 1, 3, 9
C) 1, 3, 5, 9
Answers
Answer:
A common factor is a whole number which is a factor of two or more numbers.
[tex]factors \: of \: 9 = 1 \times 3 \times 3[/tex]
[tex]factors \: of \: 15 = 1 \times 3 \times 5[/tex]
since both of the numbers have only 1 and 3 in common.
therefore ,
Option A is correct.
______________________________________
______________________________________
Additional information
★ The highest common factor (HCF) is the greatest factor that will divide into two or more numbers.
★ The lowest common multiple (LCM) is the smallest multiple that is common to two or more numbers.
hope helpful :D
In Steven's grade, 1/3 of the students have a sister. Of the students who have a sister, 3/5 also have a brother. What fraction of the students in Steven's grade have both a sister and a brother?
Answers
Answer:
You are looking for 1/2 OF 2/3
In word problems such as this OF
means to multiply.
(1/2)(2/3) = 2/6 = 1/3
Step-by-step explanation:
a student sketched some art on an 8 inch x 10 inch piece if paper he wants to resize it to fit an 4 inch x 6 inch frame. What percent of the original sketch was still able to be included?
(someone asked this question but all the answers were wrong, so I am letting you know that the correct answer is 83.3%)
Answers
Answer:
83.3%
Step-by-step explanation:
What is the area of the figure below?
A. 16
B. 45
C. 51
D. None of these
Answers
Answer:
C. 51
Step-by-step explanation:
For Square:
Length x Height
7 x 6 = 42
For Triangle:
Base x Height x 1/2
(6x3)1/2 = 9
42 + 9 = 51
The area of a rectangular field is 1.12×10^45 square feet. If the length of the field is 7×10^11 feet, and the width of the field can be written as 1.6×10x feet, what is the value of x?
Answers
Answer:
x = 10^34
Step-by-step explanation:
length × width = area
area/length = width
width = (1.12 × 10^45 ft²)/(7 × 10^11 ft)
width = 1.12/7 × (10^45)/(10^11) ft
width = 0.16 × 10^34 ft
width = 1.6 × 10^34 ft
width = 1.6 × x ft
x = 10^34
The value of x is [tex]10^3^2[/tex] or [tex]\rm x =10^3^2[/tex]
It is given that the area of a rectangular field is [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]
It is required to find the value of x
What is the area of the rectangle?It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.
The formula for finding the area of a rectangle is given by:
Area of rectangle = length × width
We have:
Area of rectangle = [tex]\rm 1.12\times10^4^5 \ feet^2[/tex]
The length of the rectangle = [tex]7\times 10^1^1[/tex] feet
The width of the rectangle = [tex]\rm 1.6\times 10x[/tex] feet
After putting the values in the formula, we get:
[tex]\rm 1.12\times10^4^5 =7\times 10^1^1\times\rm 1.6\times 10x[/tex]
[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\[/tex]
[tex]\rm x =\frac{1.12\times10^4^5}{7\times 10^1^1\times\rm 1.6\times 10} \\\\\rm x = 0.1\times 10^3^3[/tex]
[tex]\rm x =10^3^2[/tex]
Thus, the value of x is [tex]10^3^2[/tex]
Learn more about the area here:
https://brainly.com/question/14383947
Write the system below in the matrix form by using matrix multiplication:
x − 2y + z = 7
2x − y + 4z = 17
3x − 2y + 2z = 14
Answers
x-2y+Z=7
2x-y+ 42 = 17
3×-2y+2z=14
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answers
Answer:
B) B
Step-by-step explanation:
In this case, the first partial product will be 2 * 5 which is 10. The only option that shows this is option B, so this is our answer.
We can also check the answers as a whole,
2 * 5 = 10
80 * 5= 400
400 + 1 = 410
Again, only option B gives us this. This is means that option B is our answer.
Answer:
B
Step-by-step explanation:
82
5
--
5 x 2 = 0 (carry 1)
5 x 8 + 1 = 1 (carry 4 to bottom)
Solve for x.
5x = 25
=
x = [?]
=
Answers
4) A circle has a circumference of 219.8 yd. What is the diameter of the circle?
a) 35 yd
b) 70 yd
c) 30 yd
Answers
Answer:
70
Step-by-step explanation:
Circumference = pi × diameter
219.8 = pi × diameter
219.8/pi = diameter
Diameter = 69.96....
= 70yd
can someone please help me
Answers
Answer:
(2, 4)
Step-by-step explanation:
All you have to do is hop up 10 units on the grid from point P. 10 units up from -6 is 4. Therefore, your answer is (2, 4).
I hope this helps! Have a lovely day!! :)
Answer:
i belive its c
Step-by-step explanation:
you are shifting up 5 squares so you arrive at (2,4)
In the diagram above, what is point F called relative to ABC?
Answers
Answer:
Circumcenter
Step-by-step explanation:
The center that is created by intersection of the three perpendicular bisectors of your triangle sides.
which of the following is the equation of the one that passes through the point
Answers
Answer:
C
Step-by-step explanation:
the answer is C
( -6 , 1 )
y = -1/2x - 2
if x = -6
y = -1/2(-6) - 2
y = 3 - 2
y = 1
Rectangular rug has a perimeter of 3320 inches the length is 25 inches more than twice the width find the length and width of the rug
Answers
Answer:
length= 1115 inches
width= 545 inches
Step-by-step explanation:
The perimeter of the rectangular rug is the sum of the lengths of all its sides.
Start by defining the variables that we are going to use throughout our working.
Let the length and the width of the rug be L and W inches respectively.
Perimeter= 2(L +W)
Given that the length is 25 inches more than twice the width,
L= 2W +25 -----(1)
3320= 2(2W +25 +W)
Divide both sides by 2:
1660= 2W +W +25
1660= 3W +25
3W= 1660 -25
3W= 1635
Divide both sides by 3:
W= 1635 ÷3
W= 545
Substitute W= 545 into (1):
L= 2(545) +25
L= 1115
Thus, the length and width of the rug is 1115 and 545 inches respectively.
PLEASE HELP PLEASE PLEASE HELP
Answers
Answer:
Light
Step-by-step explanation:
Light can travel approximately 186,000 miles per second so the answer we are looking for in here is light.