A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The vertex of the parabola will lie at (-3,2).
<h3>What is the Equation of a parabola?</h3>
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in the form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Comparing the given equation with the equation of a parabola, we will get,
y = a(x -h)² + k
y = -4(x+3)² + 2
Hence, the vertex of the parabola will lie at (-3,2).
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Since x=-3y+5, substitute x for -3y+5.
2(-3y+5)+8y=4
Distribute.
-6y+10+8y= 4
2y+10= 4
Subtract 10 on both sides.
2y=-6
Divide by 2.
y=-3
Plug in y=-3.
x=-3(-3)+5
x= 9+5
x=14
(14,-3)
We can check this.
2(14)+8(-3)=4
28-24=4
4=4 <== this works
I hope this helps!
~kaikers
The answer is 4,000 ft squared because since the sides are 100 ft and 80ft then we need to multiply them which is 8,000 then divide that by 2 since it’s a triangle which is 4,000 ft squared.
Answer:
(x-6)(x-4) = 0
Step-by-step explanation:
Subtract 5 from both sides to make the equation equal to 0. You will get the equation x2-10x+24=0. Now think of two numbers that multiply to get 24 but add to get -10. These numbers are -6 and -4. The factors of x2 are x and x which multiply to get x2. Now put two linear factors into parathesis to get (x-6)(x-4) = 0.
The value of the given variable x in the missing angles is; x = 12°
<h3>How to find alternate Angles?</h3>
Alternate angles are defined as the angles that occur on opposite sides of the transversal line and as such have the same size. There are two different types of alternate angles namely alternate interior angles as well as alternate exterior angles.
Now, from the question, we can see that ∠4 and ∠6 suit the definition of alternate angles and as such we can say that they are both congruent.
Since ∠4 = (8x + 4)° and ∠6 = (6x + 28)°, then we can say that;
(8x + 4)° = (6x + 28)°
Rearranging this gives us;
8x - 6x = 28 - 4
2x = 24
x = 24/2
x = 12°
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