Which expression is equivalent to 3\tfrac{1}{3}-8\tfrac{2}{3}3

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

3 years ago

Kofi wants to find the most-liked snacks to put in the vending machine at his office so the most people will buy from it.

Whitepunk [10]

Answer:

The correct option is B

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

State the probability that justifies each statement. 11. If 2x+19=27, then 2x=8

Liono4ka [1.6K]

Answer:

100% true....

subtracting 19 from both sides brings you to 2x=8, so x=4

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the answer to the question

S_A_V [24]

The equation of the parallel line is y = –2x – 11.

Solution:

Given equation of the line is y = –2x – 5.

Slope of this line is $(m_1)$ = –2

To write the equation parallel to this line and passes through (–4, –3).

If two lines are parallel, then they have the same slope.

$\Rightarrow m_1=m_2$

$\Rightarrow m_2 =-2$

Point-slope formula:

$y-y_1=m(x-x_1)$

Substitute the given values in the formula, we get

$y-(-3)=-2(x-(-4))$

$y+3=-2(x+4)$

$y+3=-2x-8$

Subtract 3 from both sides of the equation.

$y+3-3=-2x-8-3$

$y=-2x-11$

Hence the equation of the parallel line is y = –2x – 11.

5 0

3 years ago

A large home improvement store is considering expanding its selection of moving products, such as cardboard boxes and packing ta

fiasKO [112]

Answer:

The store can be 90% confident that the interval from 0.293 to 0.355 captures the proportion of all customers of this store who have moved in the past 5 years.

Step-by-step explanation:

The confidence interval provides a range of values (lower and upper bound) based on a certain confidence level at which the true proportion or mean value of a given sample mean or proportion exists. In the scenario above, the confidence level is 90% and the confidence interval is 0.293 to 0.355. Hence, we can be 90% confident that the true proportion of all customers of the store who have moved within the last five years exists within this interval.

8 0

3 years ago