Triangle MRN is created when an equilateral triangle is folded in half.
Triangle N R M is shown. Angle N R M is a right angle. An altitude is drawn from point R to point S on side M N to form a right angle. The length of N S is 6, the length of S M is 2, the length of R M is x, the length of N R is y, and the length of R S is z.
What is the value of y?
2 StartRoot 3 EndRoot units
4 units
4 StartRoot 3 EndRoot units
8 units
Answers
The value of [tex]y[/tex] will be [tex]4\sqrt{3}[/tex] .
What is triangle ?Triangle is a three sides two dimensional surface having three angles.
We have,
[tex]\triangle MRN[/tex] , [tex]\triangle RSM[/tex] and [tex]\triangle RSN[/tex],
And, [tex]NS =6,\ SM=2,\ RM=x,\ NR=y,\ RS=z[/tex]
Now,
We have right angle [tex]\triangle MRN[/tex],
Using Pythagoras theorem,
[tex]x^2+y^2=8^2[/tex]
[tex]x^2+y^2+=64\[/tex] [tex].....(i)[/tex]
Now, We have right angle [tex]\triangle RSN[/tex],
Again Using Pythagoras theorem,
[tex]z^2+6^2=y^2[/tex]
⇒[tex]z^2=y^2-36[/tex] [tex].....(ii)[/tex]
Now, We have right angle [tex]\triangle RSM[/tex],
Again Using Pythagoras theorem,
[tex]z^2+2^2=y^2[/tex]
⇒[tex]z^2=x^2-4[/tex] [tex].....(iii)[/tex]
Now comparing equation [tex](ii)[/tex] and equation [tex](iii)[/tex],
We get,
[tex]x^2-4=y^2-36[/tex]
We get,
[tex]x^2-y^2=-36+4[/tex]
[tex]x^2-y^2=-32[/tex] [tex].....(iv)[/tex]
Now,
Adding equation [tex](i)[/tex] and equation [tex](iv)[/tex], i.e.
[tex]x^2+y^2+=64[/tex]
[tex]x^2-y^2=-32[/tex]
We get,
[tex]2y^2=96[/tex]
[tex]y^2=48[/tex]
[tex]y=\sqrt{48}[/tex]
[tex]y=4\sqrt{3}[/tex]
So, the value of [tex]y[/tex] is [tex]4\sqrt{3}[/tex]
Hence, we can say that the value of [tex]y[/tex] will be [tex]4\sqrt{3}[/tex] which is given in option (b).
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Answer:
its c
Step-by-step explanation:
taking test rn
Related Questions
given the following equation:
f(x)=(-7)x + -3
Find the following information: f(4) + f(4)
Answers
Answer:
-62
Step-by-step explanation:
In this question, we are going to solve the given expression.
We know that our f(x) equation is (-7)x - 3
Since we have to find what f(4) is, we would plug in 4 to x and solve.
Solve:
f(4) = -7(4) - 3
= -28 - 3
= -31
We are not done, we have to plug in our answer to the expression f(4 + f(4), since we now know what the value of f(4) is.
-31 - 31
-62
Your answer would be -62.
What does <,> mean please and if the number is bigger than another how do I know what symbol to use
Answers
Answer:
Imagine it is an alligator's mouth, the opening side eats the larger number because the alligator would want to eat the greater number then the less one, well, that's how I learned it.
-----____----____-----_____----____-----______------______-----_______-----___
IF THIS HELPED, PLEASE MARK ME AS BRAINLIEST!!!!!!!!16 + 7 + 9 = 7 + 9 + 16
A. commutative property of addition
B. additive identity property
C. multiplicative identity property
D. associative property of addition
Answers
Answer:
D
Step-by-step explanation:
I am trying to get 100 warns, pls help me
URGENT URGENT URGENT
Find the value of x.
Answers
Answer:
x = 5.
Step-by-step explanation:
x is the radius of the circle.
The line of length 4 bisects the chord of length 6 into 2 line segments of length 3.
If we draw a line from the centre to where the chord of length 6 meets the circle we have another radius.
This is also the hypotenuse (h) of a right triangle, so we have a right triangle whose legs are 3 and 4, then:
h^2 = 4^2 + 3^2 = 25
h = 5
x = 5 (as x and h are both radii).
Solution to 2 variable equations 2x+3y=12
Answers
Answer:
x= -3/2y + 6
Step-by-step explanation:
Let's solve for x.
2x+3y=12
Step 1: Add -3y to both sides.
2x+3y+−3y=12+−3y
2x=−3y+12
Step 2: Divide both sides by 2.
2x
2
=
−3y+12
2
On a certain hot summer's day, 73 people used the public swimming pool. The daily prices are for children are $1.25 and for adults are $2.25. The receipts for admission totaled $126.25. How many children and how many adults swam at the public pool that day?
Answers
Answer:
There were 35 children and 38 adults at the pool that day.
Step-by-step explanation:
You can use substitution to solve this answer. When solving equations with substitution, ask yourself "how many?" and "how much?" to create two equations:
1.25c+2.25a=126.25 (this equation tells us the dollar value)
c+a=73. (this equation tells us quantity, or how many)
1. Solve for 1 variable and plug it into the other equation.
a=73-c -----> 1.25c+2.25(73-c)=126.25
2. Simplify the equation above.
1.25c+164.25-2.25c=126.25
3. Simplify even more:
-1c+164.25=126.25
4. Subtract 164.25 from both sides to get:
-1c=-38
5. Divide both sides by -1.
c=38 (this means that there are 38 children)
6. Plug the new value for c back into the equation c+a=73.
38+a=73
7. Subtract 38 from both sides to solve for a:
a=35 (this means that there are 35 adults)
I hope this helps!
What are the solutions of x^2 - 2x + 10 = 0?
Answers
Answer:
C. x = 1 + 3i or x = 1 - 3i
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define
x² - 2x + 10 = 0
Step 2: Identify Variables
a = 1
b = -2
c = 10
Step 3: Find roots
Substitute [Quad Formula]: [tex]x=\frac{2\pm\sqrt{(-2)^2-4(1)(10)} }{2(1)}[/tex]Exponents: [tex]x=\frac{2\pm\sqrt{4-4(1)(10)} }{2(1)}[/tex]Multiply: [tex]x=\frac{2\pm\sqrt{4-40} }{2}[/tex]Subtract: [tex]x=\frac{2\pm\sqrt{-36} }{2}[/tex]Factor: [tex]x=\frac{2\pm\sqrt{-1} \sqrt{36} }{2}[/tex]Simplify: [tex]x=\frac{2\pm6i }{2}[/tex]Factor: [tex]x=\frac{2(1\pm3i) }{2}[/tex]Divide: [tex]x=1\pm3i[/tex]Point P is located at (–3, –2). P is reflected across the x-axis to create P'. What quadrant is P' in?
Answers
The quadrant of P' is (-3 , 2).
Here,
Point P is located at (–3, –2).
Point P is reflected across the x-axis to create P'.
We have to find the quadrant of P'.
What is Reflection across x-axis?
A point after reflection across the x-axis, the x- coordinate remains the same but y - coordinate is taken to be the additive inverse.
Now,
Point P is located at (–3, –2).
Point P is lie on third coordinates.
And, P is reflected across the x-axis to create P'.
Hence, Point P' is lie on second coordinates.
Since, The rule of the reflection across x- axis is,
(x, y) → (x, -y)
Hence, Quadrant of P' = (-3, -(-2)) = (-3, 2)
Therefore, The quadrant of P' is (-3 , 2).
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Answer quickly please
Answers
Answer:
C
Step-by-step explanation:
One tablet costs $249.00 and a company needs to buy k tablets. What is the relationship between the total cost, C, and the number of tablets? Determine the domain.
A. k=249C; The domain is C, the total cost of the tablets purchased.
B. k=249C; The domain is K, the number of tablets purchased.
C. C=249k; The domain is C, the total cost of tablets purchased.
D. C=249k; The domain is K, the number of tablets purchased.
Answers
Answer:
b
Step-by-step explanation:
Please help ASAP!!!
Chuck Stone is standing atop a high platform. He fires a rock up into the air with his slingshot. While it is in flight, the rock's distance in feet above the ground f(x) is a quadratic equation of time in seconds (x). This situation is modeled by the following function: f(x) = -5x^2 + 40x + 30.
a. How high above the ground is the platform?
30
b. How long does it take for the rock to hit the ground? Show all work to receive full credit!
is 30 correct for a? and please help me with b! Thank you!!!
Answers
Answer:
a) the platform is 110 feet above the ground.
b) It takes 8.69 sec for the rock to hit the ground
Step-by-step explanation:
This situation is modelled by the following function: [tex]f(x) = -5x^2 + 40x + 30\\[/tex]
We need to answer the following questions.
a) How high above the ground is the platform?
First we find x using the formula: [tex]x=-\frac{b}{2a}[/tex]
we have b = 40 and a = -5
Putting values and finding x
[tex]x=-\frac{b}{2a}\\x=-\frac{40}{2(-5)}\\x=-\frac{40}{-10}\\x=4[/tex]
Now putting x=4 in the function to find how high above the ground is the platform
[tex]f(x) = -5x^2 + 40x + 30\\Put\:x=4\\f(4)=-5(4)^2+40(4)+30\\f(4)=-5(16)+160+30\\f(4)=-80+160+30\\f(4)=110[/tex]
So, the platform is 110 feet above the ground.
b) How long does it take for the rock to hit the ground? Show all work to receive full credit!
We will factorise the given function [tex]f(x) = -5x^2 + 40x + 30[/tex] to find the time taken to hit the ground.
We can solve the equation using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a =-5, b=40, c=30
Putting values and finding x
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-40\pm\sqrt{(40)^2-4(-5)(30)}}{2(-5)}\\x=\frac{-40\pm\sqrt{1600+600}}{-10}\\x=\frac{-40\pm\sqrt{2200}}{-10}\\x=\frac{-40\pm46.9}{-10}\\x=\frac{-40+46.9}{-10},x=\frac{-40-46.9}{-10} \\x=-0.69,x=8.69[/tex]
So, we get values of x: x = -0.69 and x=8.69
As time cannot be negative, so we take x=8.69
So, It takes 8.69 sec for the rock to hit the ground
HELP ILL GIVE BRAINLIEST AND LOTS AND LOTS POINTS
Find the percent decrease. Where necessary round to the nearest tenth of a percent
3. from 64 to 24
4. from 6.5 to 4.8
5. The average cost of a gallon of gasoline was $1.29 in 1997 and $1.12 in 1998. Find the percent of decrease.
Answers
9514 1404 393
Answer:
3. 62.5% decrease
4. 26.2% decrease
5. 13.2% decrease
Explanation:
A percentage change is calculated from ...
percent change = ((new value) - (old value))/(old value) × 100%
When it is negative, the change is a decrease.
__
3. (24 -64)/64 × 100% = -40/64 × 100% = -62.5%, a 62.5% decrease
__
4. (4.8 -6.5)/6.5 × 100% = -1.7/6.5 × 100% ≈ -26.2%, a 26.2% decrease
__
5. (1.12 -1.29)/1.29 × 100% = -0.17/1.29 × 100% ≈ -13.2%, a 13.2% decrease
Which expression is not equivalent to 216 if the numbers look like they are apart is because they are supposed to be on the top of the number for example 6 2 the 2 should be on top of 6 on the side
A. 6 3
B. 6・6・6
C. 8・6 2
D. 3 3 ・8
Answers
Answer:
d
Step-by-step explanation:
hope this helps
−3x−6+(−1)
What is the answers and to do it step by step
Answers
Answer: -3x-7
Step-by-step explanation:
First, remove the parentheses,
-3x-6-1Then. simplify
-6-1=-7, so; -3x-7-3x - 6 - 1
-3x + (-6-1)
-3x - 7
Review Guide #3 16-27
Answers
Answer:
-11
Step-by-step explanation:
Susan has $188 and gets $25 for her birthday.
She earns $130 at her job. How much does she
have now?
Click to add text
Answers
Answer:
343
Step-by-step explanation:
the answer is that you add all of them
Giving brainliest & a thanks if you answer all of them
At a party store, packages of 12 noisemakers are $2 each. Packages of 9 party hats are $15 each. Mia wants to buy equal numbers of noisemakers and hats.
What is the least amount of money Mia can spend? ( IGNORE THIS QUESTION PLEASE)
To get that many noisemakers and hats:
How many packages of noisemakers does Mia need to buy?
How many packages of hats?
If Mia buys that many packages of each item, what is her total cost? Show your work.
Answers
Answer:
2) Mia needs to buy 3 packages of noisemakers
3)Mia needs to buy 4 packages of hats
4)Mia will dpend a total of $66
what is the lowest term of 49kg and 56kg
Answers
49/7 = 7
56/7 = 8
You could divide 7 by 7 but you can’t divide 8 by 7 and therefore that is the lowest you can go.
So the answer is: 49/56 = (7 /8)
Solve the equation. Check the solution.
9-17x-5-4x=7
Answers
Answer:
x = -1/7
Step-by-step explanation:
Solve for x
9-17x-5-4x=7
Combine like terms
-21x +4 = 7
Subtract 4 from each side
-21x-4+4 = 7-4
-21x = 3
Divide each side by -21
-21x/-21 = 3/-21
x = -1/7
Check
9 - 17(-1/7) -5 -4(-1/7) =7
9 + 17/7 -5 + 4/7 =7
4 +21/7 = 7
4+3 = 7
7=7
Please help due today!❤️❤️ thank you so much❤️❤️
The frequency table shows the number of points scored during 30 Bulldogs
basketball games. On a piece of paper, draw a histogram to represent the
data. Then determine which answer choice matches the histogram you drew.
Answers
Answer:
Step-by-step explanation:
C
Answer:
A.
Step-by-step explanation:
If you look closely you can see that A is the only one with 50-59 shaded up to 5 frequency and the other data is correct as well.
What's the answer to this?
Answers
what is the surface area of the triangular prism?
Answers
Answer:
300yd²
Step-by-step explanation:
Surface Area = area of triangles *2 + area of thhe 3 rectangles
SA= 2*( 9*4/2) + 5*12 + 8*12 + 9*12= 2*18 +5*12 + 8*12 + 9*12 =
36+60+96+108 = 300
Brainliest to whoever answers this correctly!
Answers
Answer:
I believe the answer is C
Step-by-step explanation:
Answer:
B. The rate of change of the cost of the taxi ride is $3.00 per minute.
Step-by-step explanation:
The slope is 3 so it is $3 per minute (x) and $2 is the flag down cost.
cassie measured the middle school and made a scale drawing. the scale of the drawing was 1 inch : 9 feet. the actual width of the gym is 45 feet. how wide is the gym in the drawing?
Answers
The wide is the gym in the drawing is 5
In the given statement is
Cassie measured the middle school and made a scale drawing. The scale of the drawing was 1 inch : 9 feet. the actual width of the gym is 45 feet.
To find how wide is the gym in the drawing
Now, According to the question
and, Based on the given conditions
=45 x1/9
=45/9
=5
Thus, The wide is the gym in the drawing is 5
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PLEASE HELP QUICK....... find X
Answers
Answer:
X=18
Step-by-step explanation:
Answer: 18
Step-by-step explanation:
we know that 6x+10 is equal with the angle above the one that is measured (5x-28)
we have 6x+10+5x-28=180 (a straight line)
11x=180+28-10
11 x=198
x=18
LMN with vertices L(4,8), M(4,3) and N(8,8) is rotated 270 clockwise about the origin what are the coordinates of L’?
Answers
Coordinates of L after rotation are (-8,4)
What are the rules of 270 degrees rotation of coordinates about the origin?
Assuming that the rotation is about (0,0)
then after 270° clockwise rotation (x, y) becomes (-y, x)
and after 270° anticlockwise rotation (x, y) becomes (y,-x)
Given that LMN with vertices L(4,8), M(4,3) and N(8,8) is rotated 270° clockwise about the origin
Then for L(4,8) as the rotation is 270° clockwise then
(x, y) = (4,8)
and after 270° clockwise rotation (x, y) becomes (-y, x)
Therefore new coordinates of L are (-8,4)
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I need help! I don’t understand!
Answers
Answer:
33
Step-by-step explanation:
just coint how much is on each side then multiply it by 3
Please answer this geometry question.
Answers
How are the triangles congruent?
Answers
Answer:
SSS
Step-by-step explanation:
it means side side side and the lines represent their congruecny with the other triangle, meaning that the two line dash is equal to the other two line dash and the one line dash is equal to the other one line dash and you know the last side is the same with eachother because they are sharing that side of the triange
hope it helps have a great day
im not having a great day i got 101 notifications. guess what they were. A MODERATOR DELETED ALL MY ANSWERS AND NOW I HAD TO START OVER I HAD 23 BRAINLIESTS AND 2983 POINTS AND NOW I HAVE -76 POINTS
Plz help me if ur still awake!!!!
Answers
Answer: I would post the answers in comment am unable to add the answer.
Step-by-step explanation:
1.F is the midpoint of AC, angle AFE = angle CFD and DF = EF (Given)
2.angle AFD = angle CFE ( A midpoint divides a segment into two congruent segments.)
3.angle DFE = angle DFE (Reflexive property)
4.angle A = angle C (Congruent angles subtracted from congruent angles form congruent angles )