Answer:
i recommend you watch videos on youtuube about equations and take notes.
Step-by-step explanation:
Suppose that equation of parabola is
y =ax² + bx + c
Since parabola passes through the point (2,−15) then
−15 = 4a + 2b + c
Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c
Since parabola passes through the point (−3,−5), then
−5 = 9a − 3b + c
Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5
Solving it we get that
a = −2, b = −4, c = 1
Thus, equation of parabola is
y = −2x²− 4x + 1
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Rewriting in the form of
(x - h)² = 4p(y - k)
i) -2x² - 4x + 1 = y
ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)
iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)
iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)
v) -3(x + 7/6)² = y - 445/36
vi) (x + 7/6)² = -⅓(y - 445/36)
(Shifting -⅓ to RHS)
vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p)
So, after rewriting the equation would be -
(x + 7/6)² = 4(-⅛)(y - 445/36)
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I hope this is what you wanted.
Regards,
Divyanka♪
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So the formula for the circumference of a circle is π x diameter
Since we know the the circumference already, we just divide that by π:
12π / π = 12
Now we halve the diameter to get the radius:
12 / 2 = 6
The area of a circle is π x radius²
So the area is:
·π x 6² = 36π· (or 113 not in terms of π)
t N.
In the figure shown below
Answer:
A horizontal line segment M K intersects with line segment J L at their midpoint N.
∠J N M =(5x+2)°
∠ LN M=3( x+ 14)°
So, ∠J N M + ∠ LN M =180°[ These two angles form linear pair.Angles forming linear pair are supplementary.]
⇒5 x+ 2+ 3 (x+ 14) =180 [ By Substitution]
⇒ 5 x+2 +3 x+42°= 180°
⇒ 8 x=180°-44°
⇒8 x= 136°
⇒x= 136°÷8
⇒x=17°
So, ∠J N M =5×17 +2=87°
∠ LN M= 3×(17 +14)=3×31=93
∠J N M =∠K N L [Vertically opposite angles]
∠K N L=87°
The correct answer is the option D, which is: <span>D. 78 cm; 39 cm; 30.3π cm
The explanation is shown above:
1-The formula for calculate the circumference of a circle is:
C=2</span>πr
78π=2πr
2- The radius is:
r=78π/2π
r=39 cm
3- The diameter is:
D=39 cm x 2
D=78 cm
4- The arc length is:
arc length=(140°π/180°)(39 cm)
arc length=30.3π cm
