The perpendicular bisector of the of the hypotenuse side forms a right
triangle with the hypotenuse and the longer leg of the of the triangle.
The ratio, of the length of the segment cut from the perpendicular bisector by the hypotenuse and the longer leg to the length of the longer leg, is 1 : 3
Reason:
The given parameters are;
An acute angle of the right triangle = 30°
Let R represent the length of the hypotenuse side, we have;
The length of the longer leg, [tex]L_{ll}[/tex] = R × cos(30°) = [tex]\dfrac{\sqrt{3} }{2} \cdot R[/tex]
The perpendicular bisector forms a right triangle with a leg length = R/2
The length of the hypotenuse formed by the bisector is therefore;[tex]R_{bisector} = \dfrac{\dfrac{R}{2} }{cos(30^{\circ})} = \dfrac{\dfrac{R}{2} }{\dfrac{\sqrt{3} }{2} } = \dfrac{R}{\sqrt{3} }[/tex]
The length, L, of the segment cut by the hypotenuse and the longer leg is therefore;
[tex]L= R_{bisector} \times sin(30^{\circ}) = \dfrac{1}{2} \times \dfrac{R}{\sqrt{3} } = \dfrac{R}{2 \cdot \sqrt{3} }[/tex]
The ratio, of the length of the segment cut from this perpendicular bisector by the hypotenuse and the longer leg to the length of the longer leg, r, is therefore;
[tex]r = \dfrac{L}{L_{ll}} = \dfrac{ \dfrac{R}{2 \cdot \sqrt{3} }}{\dfrac{\sqrt{3} }{2} \cdot R} = \dfrac{2 \cdot R}{2 \cdot \sqrt{3} \times \sqrt{3} \times R } = \dfrac{1}{3}[/tex]
The ratio, of the lengths, r = [tex]\dfrac{1}{3}[/tex], therefore, r = 1:3
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Answer:
1:3
Step-by-step explanation:
If the shorter leg is equal to x, AB is 2x and AC is x root 3.
AE is half of AB which is x.
Angle ADE is 90-30=60 degrees.
DE is x/root 3.
[tex]\frac{\frac{x}{\sqrt{3}} }{x\sqrt{3}} = 1:3[/tex]
Will give correct answer brainliest
Answer:
(2,-5)
(-6,-7)
(-7,-4)
these are the coordinates after the transformation
Please help! I will mark brainliest!
Answer:
1. is 283.9953
Step-by-step explanation:
360 degrees - 76.0047 degrees is 283.9953
can y'all help me with this one I'm stumped, 1 + k over 5 equals -1
Answer:
k=-10
Step-by-step explanation:
first subtract the 1 from both sides
so then you have k/5=-2
then multiply by 5 on both sides
which gives you k=-10
A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in threehours.
Answer:
50 (mph) = rate of passenger train
Step-by-step explanation:
Let the rate of the freight train = R
Let the rate of the passenger train be R + 30
The freight train has been traveling for 2 + 3 = 5 hours
And the passenger train has been traveling for 3 hours
And they have traveled the same distance when the passenger train overtakes the freight train
So using rate * time = distance we have that
R(5) = (R + 20) 3 simplify
5R = 3R + 60 subtract 3R from both sides
2R = 60 divide both sides by 2
R = 30 (mph) = rate of freight train
R + 20 = 50 (mph) = rate of passenger train
Which graph matches the equation 4x² + 25y^2 = 100?
graph b matches the equation
I NEED HELP PLEASEEE
Answer:
b = [tex]\sqrt{333}[/tex]
Step-by-step explanation:
1. We can use the Pythagorean Theorem to find the missing side, b.
[tex]14^2 + b^2 = 23^2[/tex]2. (Solving)
Step 1: Simplify both sides of the equation.
[tex](14*14)+b^2 =(23*23)[/tex] [tex]196 + b^2 = 529[/tex]Step 2: Subtract 196 from both sides.
[tex]196 + b^2 - 196 = 529 - 196[/tex] [tex]b^2 = 333[/tex]Step 3: Take square root of both sides.
[tex]\sqrt{b^2} = \sqrt{333}[/tex] [tex]b = \sqrt{333}[/tex]Step 4: Check if solution is correct.
[tex]14^2 + \sqrt{333^2} = 23^2[/tex] [tex](14*14)+(\sqrt{333} *\sqrt{333})=23*23[/tex] [tex]196 + 333 = 529[/tex] [tex]529 = 529[/tex]Therefore, b = [tex]\sqrt{333}[/tex].
Answer:
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^2\\14^2 + b^2 = 23^2\\\\196 + b^2 = 529\\\\b^2 = 333\\b = 18.2482875909[/tex]
PLS HELP I'LL DIRECTLY MARK YOU BRAINLIST !!!
Answer:
[tex]12 \div \frac{3}{4} = 12 \times \frac{4}{3} = 12 \times 4 \div 3 = 4 \times 4 = 16 \\ 16 \times 5 = 80 \: ft \: [/tex]
first you must know how many 3/4 do you have
because of scale
and after that multiply to 5 to get actual length
(solve equation)
7b=84
Answer:
b = 12
Step-by-step explanation:
7b = 84
We can break down 7b as 7 x b
7 x b = 84
We divide both sides by 7:
7 x b ÷ 7 = 84 ÷ 7
b = 12
-Chetan K
Write the verbal phrase
as an
algebraic expression.
1.
the sum of d and 7
Answer:7
Step-by-step explanation:
I graduate from Harvard
Which of the following is the solution to 17 - 2x=-11?
03
O-14
14
-3
Answer:
17-2x=-11 ---> 14
Step-by-step explanation:
plug in the "answers"
17-2(14)=-11
Find the equation of the line passing through the points (22,37) and (-33,-23). Write your answer in the form
y
=
m
x
+
b
.
y
=
m
x
+
b
.
Answer:
y = 12/11x + 13
Step-by-step explanation:
Slope: (-23-37) / (-33-22) = -60/-55 = 12/11
b = 37 - (12/11)(22) = 13
I dont understand this plz help me
Answer:
Step-by-step explanation:
9e - 7 = 7e - 11
solve for e
Answer:
e = -2
Step-by-step explanation:
9e - 7 = 7e - 11
Subtract 7e from both side
2e - 7 = -11
Add 7 to both sides
2e = -4
Divide by 2 to isolate e
e = - 2
Answer:
e = -2
Step-by-step explanation:
9e - 7 = 7e -11
9e - 7e - 7 = -11
9e - 7e = -11 + 7
2e = -4
e = -2
Feel free to mark this as brainliest! :D
Francine and Cheryl receive equal scores on a test made up of multiple choice questions for an essay. Francine got 34 multiple choice questions correct and received 14 points for her essay. Cheryl got 30 multiple choice questions correct and received 22 points for her essay.
Answer:
hello I would like to help you but you don't give us the question? how do you expect people to help you if you don't actually give the question
The perimeter of a rectangle is 28cm it’s length is more than 10cm more than it’s widith which equation can be used to find the dimensions
P = 2((10 + x) + x)
The perimeter of a rectangle is the sum of the length and width multiplied by 2
P = 2(l + w)
[to simplify the expression]
P = 2 × (l + w)
[using x to represent the width]
w = x
l = x + 10
P = 2 × ((10 + x) + x)
P = 2((10 + x) + x)
Solve by
substitution or elimination
2x-y=10
4x-2y=21
A school had 180 boys and 240 girls attending
(a) What is the ratio of boys to girls?
(b) What is the ratio of girls to boys?
(c) What is the ratio of students to boys?
(d) What is the ratio of girls to students?
Answer:
a) 3 : 4
b) 4 : 3
c) 7 : 3
d) 4 : 7
Step-by-step explanation:
(just a side note: you can write ratios in fraction form as well!)
To find the ratio between boys to girls, we would write it like this:
180/240 or 180 : 240 or 180 to 240
Although that is right, that isn't simplified.
Thus, we need to find a common factor that both the numerator and denominator share!
180 and 240 are both divisible by 60!
180 ÷ 60 = 3
240 ÷ 60 = 4
Therefore, you would get a simplified ratio of 3 : 4! For every 3 boys. there are 4 girls!
For part b, you simply switch the 4 and 3 around so you get 4 : 3. For every 4 girls, there are 3 boys.
Now part c involves the total amount of students...
Basically, add the number of boys and the number of girls together, and you would get 420.
420 : 120 shows the amount of students there are to boys...but it is not in its simplest form!!
Like we did before, we have to find a common factor between the two...which is 60!
420 ÷ 60 = 7
120 ÷ 60 = 3
Thus, there are 7 students for every 3 boys (7 : 3)
Finally, part d! Simply the ratio:
420 : 240
Divide both by 60 and...
You get 4 :7! For every 4 girls, there are 7 students
Hope this helps! Let me know if you have any other questions :D
Answer:
(a) 3:4
(b) 4:3
(c) 7:3
(d) 4:7
Step-by-step explanation:
(a) 3:4
180:240 = 3:4 (after simplification)
(b) 4:3
240:180 = 4:3 (after simplification)
(c) 7:3
Total number of students = 240 + 180 = 420
420:180 = 7:3 (after simplification)
(d) 4:7
Total number of students = 240 + 180 = 420
240: 420 = 4:7 (after simplification)
what is plzz help me 3[x-6]
Answer: if this is distribution it would be 3x-18
Step-by-step explanation:
what is the slope in y + 4 = -2(x - 9)?
Answer:
is y=−2x+14
Step-by-step explanation:
because yo.multipli
Answer:
y- y1 =m(x -x1)
comparing these; -y1= 4;y1 = -4
m= -2 ;x1 = 9
The slope is -2
Step-by-step explanation:
PLS MARK BRAINLIEST
work out x pls anwser pls
Answer:
66?
Step-by-step explanation:
180 degrees in a triangle, add 79 and 35 together = 114
180 - 114 = 66
Answer:
66°
Step-by-step explanation:
All angles in a triangle add up to 180° . Therefore you will need to add up 79° and 35° then subtract it from 180° in order to find the missing angle x.
12r-5 61°
R
A) 790
C) 140°
B) 70°
D) 970
Answer:
79 because x = 7 so 12 x7 - 5 =79
a carpenter is fitting some bookcases to an alcove, using as much of the space as possible from floor to ceiling, a height of 2.5 m. The books to be fitted into the shelves are 210 mm high and a gap of at least 30 mm is necessary above each book so that they can be removed. The shelves are 20 mm thick. The alcove is 1.2 m wide. The bottom shelf should not be less than 300 mm from the ground, as the house-owner cannot bend down easily. How many shelves can be fitted into the alcove?
The number of shelves that fit in the alcove is given by the height of each shelve and the height of the bookshelf above the ground
The number of bookshelves that fit into alcove, is 8 bookshelves
Reason:
Height of the alcove = 2.5 m
Height of the books = 210 mm = 0.21 m
The gap above each book = 30 mm = 0.03 m
The thickness of the shelves = 20 mm = 0.02 m
Width of the alcove = 1.2 m
Height of the bottom shelf above the ground = 300 mm = 0.3 m
Required:
The number of shelves that can be fitted into the alcove
Solution;
Let x, represent the number of shelves that can be fitted into the alcove
We have;
An initial height of the bookshelves above the ground = 0.3 m
Height of a shelve, H = Height of books + Gap above books + Thickness of shelves
Height above ground, including the bottom shelve = 0.3 m
[tex]x = \dfrac{2.5 - (0.3)}{0.02 + 0.03 } = 8\frac{6}{13}\approx 8.46[/tex]Therefore, the maximum number of whole bookshelves that can be fitted into alcove, x ≈ 8 bookshelves
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Solve for h in terms of g and u
4u²(2u²) /g = -2u²h -gh²/2 +h
9514 1404 393
Answer:
h = (1 -2u² ± √(1 -4u²-12u⁴))/g
Step-by-step explanation:
This is a quadratic in h, so there are two solutions.
Written in standard form, the given equation is ...
(-g/2)h² +(1-2u²)h -8u⁴/g = 0
The quadratic formula tells you the solution for h is ...
h = (-(1 -2u²) ±√((1 -2u²) -4(-g/2)(-8u⁴/g)))/(2(-g/2))
h = (2u² -1 ± √(4u⁴ -4u² +1 -16u⁴))/-g . . . . . simplify
h = (1 -2u² ± √(1 -4u²-12u⁴))/g . . . . . . . . collect terms
I need help with this:
Answer:
I need you hahaah
Step-by-step explanation:
Answer:
38_kaksfhdksks ejdjdjdk sjdjdjs
Pls I need help and a explanation
Answer:
20) 7/16 = 0.4375
21) 1/6 = 1.6 repeating
22) 2 4/5 = 2.8
23) 98 2/3 = 98.6 repeating
24) 0.8 = 4/5
25) 26 1/5
26) 72.1 repeating = 72 1/9
27) 0.505 = 101/200
Explanation:
To convert fraction into decimal, divide the numerator by the denominator and that's your answer. For example:
7 ÷ 16 = 0.4375.
To convert a decimal into a fraction, place the number after the decimal point over the number place it's in. For example: If you look at 0.8 , 8 is in the tenths place, so you place it over 10 like this 8/10, and then you simplify. Half of 8 is 4 , and half of 10 is 5, so you'd have 4/5.
For #27, since 505 in 0.505 , is in the thousandths place, you'd put it over 1,000 like this 505/1000 and then you simplify. Look at image above to learn how to simplify 505/1000.⤴⤴⤴
Any experts, help please.
Solve. 39 divided by 11
O A) 3 5/11
O B) 3 6/11
O C) 11 1/2
O D) 6 3/11
At the beginning of the week, Aksa’s parents deposited $20 into Aksa’s lunch account. The amount of money Aksa had left after each day is shown in the table, where x is the number of days and y is the remaining balance.
a. What are the x- and y-intercepts?
b. What do the x- and y-intercepts represent?
Here we need to plot x and y co-ordinates from the given table.
What are x and y co-ordinates and intercepts ?This is 2D co-ordinate geometry here we have an x axis and a y axis we use co-ordinate geometry to plot lines and curves according to the gives question.when the question consist of linear equations they form straight lines and when questions consists of quadratic and higher degree polynomials they form curves.
a. Here the the days are represented by x and remaing balance are represented by y.
So, when x = 0, y = 20 is co-ordinate form we can represent this as (0,20)
similarly the other co-ordinate points are (1,16), (2,12), (3,8), (4,4), (5,0).
b. x- and y- intercepts represnts the value of one variable corresponding to the other variable.
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I need help again you guys hehe plz help :)
What is 5x+4=8x-71? SHOW WORK!!!!
Answer:
x=25
Step-by-step explanation:
5x + 4 = 8x-71
-5x = -5x
4 = 3x-71
+71 = +71
75 = 3x
75/3 = 3x/3
25 = x