What is x^2+8x-5 in vertex form? Please explain.
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Answer:13111111/200000000
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The altitude of the triangle whose base is 3 cm longer than its altitude is 7cm.
What is triangle?
Triangle is a plane figure with three straight sides and three angles such that the sum of the angles is 180°.
Given is a triangle whose base is 3cm longer than its altitude. The area of the triangle is 35 cm².
Assume that the altitude of the triangle is 'a' cm.
The area of a tringle is given by -
A [T] = 1/2 x base x height.
Now,
Altitude of triangle = a cm
Base of triangle = (a + 3) cm
Substituting the values in the formula of area, we get -
A [T] = 1/2 x base x height
A [T] = 1/2 x a x (a + 3)
a(a + 3) = 35 x 2
a(a + 3) = 70
a² + 3a - 70 = 0
On solving the above quadratic equation, you will get two values of x -
a = - 10 and a = 7
Altitude cannot be negative. Therefore, the altitude of the triangle is 7 cm.
Therefore, the altitude of the triangle whose base is 3 cm longer than its altitude is 7cm.
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Answer:
275 bicycles
Step-by-step explanation:
We are given the average cost per bicycle as;
C(x) = 0.2x² - 1.1x + 10.592
We will solve this by finding the derivative of the C(x) function which will give us the instantaneous slope. Thereafter, we will find the extremas which will occur when the instantaneous slope is equal to 0.
Thus, derivative of C(x) is;
C'(x) = 0.4x - 1.1
Equating to zero, we can find the extremas.
Thus;
0.4x - 1.1 = 0
x = 1.1/0.4
x = 2.75
To check if this is minimum of maximum, we will find the second derivative of C(x)
Thus;
C''(x) = 0.4
Thus is a positive value, and so it means the critical point is a minimum.
Thus, X = 2.75
We were told x is in hundreds of bicycles. Thus, X = 2.75 × 100 = 275 bikes
To Optimization minimize the average cost per bicycle, the shop should build 275 bicycles. This is determined by finding the x-coordinate of the vertex ('minimum point') of the parabolic graph represented by the average cost function .
The function is a quadratic function, and represents the average cost per bicycle. The shape of the graph of a quadratic function is a parabola.
In this case, because the coefficient of the x^2 term is positive, the parabola opens upwards,which means it has a minimum point.
Therefore, the minimum average cost per bicycle occurs at the vertex of the parabola.
To find the x-coordinate of the vertex (which is the number of bicycles), we use the formula , where a is the coefficient of the
term (0.2) and b is the coefficient of the x term (-1.1).
Plugging in these values gives hundreds of bicycles or 275 bicycles.
Therefore, the shop should build 275 bicycles to minimize the average cost per bicycle.
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Answer:
x=15 i think but im pretty sure
Step-by-step explanation: