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3 years ago

Determine the equation of quadratic function represented by the table of value below.

Mathematics

1 answer:

Svetllana [295]3 years ago

6 0

Answer:

Step-by-step explanation:

The general rule for the quadratic function is

$y=ax^2+bx+c$

Use the data from the table:

$y(0)=6\Rightarrow 6=a\cdot 0^2+b\cdot 0+c\\ \\y(1)=4\Rightarrow 4=a\cdot 1^2+b\cdot 1+c\\ \\y(-1)=10\Rightarrow 10=a\cdot (-1)^2+b\cdot (-1)+c$

We get the system of three equations:

$\left\{\begin{array}{l}c=6\\ \\a+b+c=4\\ \\a-b+c=10\end{array}\right.$

From the first equation

$c=6,$ then

$\left\{\begin{array}{l}a+b=-2\\ \\a-b=4\end{array}\right.$

Add these two equations:

$a+b+a-b=-2+4\\ \\2a=2\\ \\a=1$

So,

$b=-2-a=-2-1=-3$

The quadratic function is

$y=1\cdot x^2-3x+6\\ \\y=x^2-3x+6$

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A group of four components is known to contain two defectives. An inspector tests the components one at a time until the two def

Stells [14]

Answer:

when Y = 2, P(2) = 1/6 = 0.167

when Y = 3, P(3) = 2/6 = 0.333

when Y = 4, P(4) = 3/6 = 0.5

Step-by-step explanation:

Total number of possible ways to choose 2 components for defectives out of 4 components = 4C2 = 6

Y can only take values of 2, 3 and 4

So, Probability of Y = P(Y) = 1C(Y-1) / 6

when Y = 2, P(2) = 1/6 = 0.167

when Y = 3, P(3) = 2/6 = 0.333

when Y = 4, P(4) = 3/6 = 0.5

4 0

3 years ago

Find m ab <br> Find m acb

gulaghasi [49]

MAB = 110
mACB = 360 - 110 = 250

hope it helps

6 0

3 years ago

Find the expansion of cos x about the point x=0

ycow [4]

Answer:

Cos x = 1 - $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ - $\frac{x^6}{1!}$ + ...

Step-by-step explanation:

We use Taylor series expansion to answer this question.

We have to find the expansion of cos x at x = 0

f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x

Now we evaluate them at x = 0.

f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1

Now, by Taylor series expansion we have

f(x) = f(a) + f'(a)(x-a) + $\frac{f''(a)(x-a)^2}{2!}$ + $\frac{f'''(a)(x-a)^3}{3!}$ + $\frac{f''''(a)(x-a)^4}{4!}$ + ...

Putting a = 0 and all the values from above in the expansion, we get,

Cos x = 1 - $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ - $\frac{x^6}{1!}$ + ...

8 0

3 years ago

Given the following diagram, find the missing measure.<br>*

BigorU [14]

Option C:

x = 30

Solution:

The given image is a triangle.

angle 1, angle 2 and angle 3 are interior angles of a triangle.

angle 4 is the exterior angle of a triangle.

m∠4 = 2x°, $m\angle2=\frac{4}{3}x^\circ$ , m∠3 = 20°

Exterior angle theorem:

<em>In triangle, the measure of exterior angle is equal to the sum of the opposite interior angles.</em>

By this theorem,

m∠4 = m∠2 + m∠3

$$2x^\circ=\frac{4}{3}x^\circ+20^\circ$

Subtract $\frac{4}{3}x^\circ$ on both sides of the equation.

$$2x^\circ-\frac{4}{3}x^\circ=20^\circ$

To make the denominator same and then subtract.

$$\frac{6}{3}x^\circ -\frac{4}{3}x^\circ=20^\circ$

$$\frac{2}{3}x^\circ =20^\circ$

Multiply by $\frac{3}{2}$ on both sides of the equation.

x° = 30°

x = 30

Hence option C is the correct answer.

6 0

3 years ago

.) Find – 4.25 +2.5.

Arturiano [62]

The answer is -4 + 2 + -0.25 + 0.5.

3 0

3 years ago