Find the value of y.
Answers
You're working with two right triangles here.
The big one is the whole drawing. It's lying flat on its hypotenuse.
One side of the big triangle ... the left side ... has no label.
We'll be working with that side. Let's call it ' S ' .
The smaller triangle is the left piece of the big one.
Its height is 'y', and its base is 4. ' S ' is its hypotenuse.
Go to your toolbox and pull out the little box marked "Pythagoras".
Inside that box is the equation you need in order to work on this
problem, or any problem with right triangles. The equation is ...
(hypotenuse)² = (length of one leg)² + (length of the other leg)² .
In the big triangle, 'x' is one leg, and the hypotenuse is 16 .
(16)² = x² + S²
256 = x² + S²
Subtract x² from each side: S² = 256 - x²
Take the square root of each side: S = √(256 - x²)
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Now look at the small right triangle.
One leg is 4. The other leg is 'y'. The hypotenuse is ' S '.
S² = (4)² + y²
Subtract 16 from each side: y² = S² - 16
Writer in the value of S² that
we worked out before: y² = (256 - x²) - 16 .
y² = 240 - x²
Take the square root
of each side: y = √(240 - x²) .
That's what you're supposed to find. So we're done.
_________________________________________
Oh phooey ! Sometimes I am so stupid.
Forget almost everything I did up above, and
let's back up several steps:
==> Cut the picture along the line marked 'y', and throw away
the left piece, with the '4' on the bottom. We don't need it.
-- Now you have a right triangle that I didn't even notice before.
One leg is 12. The other leg is 'y'. The hypotenuse is 'x'.
Pythagoras says: (x²) = (12²) + (y²)
Subtract 12² from each side: y² = x² - 144
Take the square root of each side: y = √(x² - 144) .
Related Questions
Let f(x) = -x + 5 and g(x)=3x+ 2. Find f(x) – g(x).
Factorise fully 9x^2+3x^3
Can you help me can you help me
Please solve 5x - 1/4 = 3x - 5/4
Answers
Answer: B
Step-by-step explanation:
+ 5 = 0
= 4( + 5) = 4(0)
= x² + 20 = 0
= x² + 0x + 20 = 0
a=1, b=0, c=20
Answers
y=amount of adult tickets sold
2 times of children as adult
x=2y
total cost is 800
5x+10y=800
divide both sides by 5
x+2y=160
x=2y
2y+2y=160
4y=160
divie by 4
y=40
x=2y
x=2(40)
x=80
80 children tickets
40 adult tickets
Answers
Answer:
A is the answer
Step-by-step explanation:
Answer:
the answer is A.
Step-by-step explanation:
B. 104
C. 114
D. 124
Answers
Answers
Answers
Answer:
y= -1/2x
Step-by-step explanation:
Equation of the line is always in the form y=mx + c
where c is the y-intercept ( where the graph crosses the y-axis) and m is the gradient.
The straight line passes through the origin which are the points (0,0) hence
gradient= change in y÷ change in x
G= -2-0 ÷ 4-0 =-2÷4= -1/2x
y= 1/2x+c
-2=-1/2(4)+c
-2=-2+c
-2+2=c
c=0
∴ the equation of the line is y=-1/2x
Final answer:
The equation of the line passing through the origin and the point A(4,-2) is y = -0.5x.
Explanation:
In Mathematics, the equation of the line can be found using the point-slope form which is y = mx + c, where 'm' is the slope of the line and 'c' is the y-intercept. Since the line passes through the origin O(0,0), the y-intercept 'c' is 0. The slope 'm' of the line is found by the formula 'change in y/change in x'. Given the point A(4,-2), the change in y (the difference in the y-values of your two points) is -2 - 0 = -2, and the change in x (the difference in the x-values of your two points) is 4 - 0 = 4. Therefore, the slope 'm' is -2/4 = -0.5.
Substitute 'm' and 'c' values in the equation y = mx + c, we get the equation of the line OA as y = -0.5x.
Learn more about Equation of a Line here:
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