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3 years ago

Find the rule for the function x, -1, 0, 1, 2 y, 3, 1, 1/3, 1/9

Mathematics

1 answer:

Katyanochek1 [597]3 years ago

5 0

The function is y = $\frac{1}{3}^{x}$

This can be found by using the base equation for exponential y = $ab^{x}$ . Now we can use the second ordered pair (0, 1) to find the value of a.

y = $ab^{x}$

1 = $ab^{0}$

1 = a(1)

1 = a

Now that we have a, we can solve for b using any other ordered pair.

y = $ab^{x}$

$\frac{1}{3}$ = $(1)b^{1}$

$\frac{1}{3}$ = (1)(b)

$\frac{1}{3}$ = b

Now we can use these in the same equation.

y = $\frac{1}{3}^{x}$

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Given the quadratic equation <img src="https://tex.z-dn.net/?f=y%20%3D%202%28x%20-1%29%5E%7B2%7D%20%2B%208" id="TexFormula1" tit

Sunny_sXe [5.5K]

Answer:

Part 1) "a" value is $2$

Part 2) The vertex is the point $(1,8)$

Part 3) The equation of the axis of symmetry is $x=1$

Part 4) The vertex is a minimum

Part 5) The quadratic equation in standard form is $y=2x^{2}-4x+10$

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

if a > 0 then the parabola open upward (vertex is a minimum)

if a < 0 then the parabola open downward (vertex is a maximum)

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

$x=h$

In this problem we have

$y=2(x-1)^{2}+8$ -----> this is the equation in vertex form of a vertical parabola

The value of $a=2$

a>0 then the parabola open upward (vertex is a minimum)

The vertex is the point $(1,8)$

$(h,k)=(1,8)$

The equation of the axis of symmetry is $x=1$

The equation of a vertical parabola in standard form is equal to

$y=ax^{2}+bx+c$

Convert vertex form in standard form

$y=2(x-1)^{2}+8$

$y=2(x^{2}-2x+1)+8$

$y=2x^{2}-4x+2+8$

$y=2x^{2}-4x+10$

see the attached figure to better understand the problem

7 0

3 years ago

What is the coefficient in the expression 4x + 2 <br>O2<br>O4<br>Ox<br>O+

Amiraneli [1.4K]

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x).

The 2 and + are out since they don't have variables(and the + is just a +).

So 4 and x are left. x is a variable, not a coefficient, so the last(and correct) answer is 4.

---

hope it helps

8 0

3 years ago

Tom planted 1/2 of an 8-ft by 9-ft garden with vegetables. He planted tomatoes in 1/3 of the vegetable garden and corn in the re

ser-zykov [4K]

Answer:

Corn was planted in 24 sq.ft. of the vegetable garden.

Step-by-step explanation:

Length of garden = 9 ft

width of garden = 8 ft

Hence we will first find the total area of garden.

Total area of garden = length × width = $8 \times 9 = 72ft^2$

He planted 1/2 of the garden with vegetables.

Hence.

Area of Vegetables garden = $\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2$

He planted tomatoes in 1/3 of the vegetable garden and corn in the rest

Area in which tomatoes was planted = $\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2$

Hence Area in which corn were planted = Area of Vegetables garden - Area in which tomatoes was planted = $36ft^2-12ft^2=24ft^2$

Hence Area of vegetable garden in which corn was planted is 24 sq.ft.

7 0

3 years ago

What's 532 over 315 simplified

jok3333 [9.3K]

Your answer should be 76/45

8 0

2 years ago

Read 2 more answers

What is 12 dollars an hour

Reptile [31]

Answer:

I think you are missing something from the question, but if you were to find out how much you would get paid for a certain amount of hours from $12 per hour, then the formula would be:

Step-by-step explanation:

Let h = no. of hours worked

$12 * h

8 0

2 years ago