HELP!!! Which of the following sets of ordered pairs is a function?

Write in the form p(x+q)²+r 2x²-5x+1

Eva8 [605]

$\text{Let}\ f(x)=ax^2+bx+c,\ \text{then}\ f(x)=a(x-p)^2+k,\ \text{where}\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\-----------------\\\\\text{We have}\ f(x)=2x^2-5x+1\to a=2,\ b=-5,\ c=1.\\\\\text{Substitute:}\\\\h=\dfrac{-(-5)}{2(2)}=\dfrac{5}{4}\\\\k=f\left(\dfrac{5}{4}\right)=2\left(\dfrac{5}{4}\right)^2-5\left(\dfrac{5}{4}\right)+1=2\left(\dfrac{25}{16}\right)-\dfrac{25}{4}+1\\\\=\dfrac{25}{8}-\dfrac{25\cdot2}{4\cdot2}+\dfrac{8}{8}=\dfrac{25-50+8}{8}=-\dfrac{17}{8}\\\\\text{Therefore we have}$

$f(x)=2\left(x-\dfrac{5}{4}\right)-\dfrac{17}{8}=\boxed{2\left(x+\left(-\dfrac{5}{4}\right)\right)^2+\left(-\dfrac{17}{8}\right)}$

$q=-\dfrac{5}{4},\ k=-\dfrac{17}{8}$

4 0

3 years ago

Stacy wants to build a patio with a small, circular pond in her backyard.The pond will have a 6-foot radius. She also wants to i

solong [7]

First we are going to find the Area of the pond using the area of a circle formula: $A= \pi r^2$
where
$A$ is the area of the circle
$r$ is the radius of the circle
We know for our problem that the pond will have a 6-foot radius, so $r=6$ . Lets replace that value on our area formula:
$A= \pi r^2$
$A= \pi (6)^2$
$A=113.1ft^{2}$
We know that the cost of installing the pond is $0.62 per square foot, so lets multiply the area we just found by the cost:
Total cost of pund= $(0.62)(113.1)=70.12$ dollars

Now, let $x$ be the width the rectangle, so its length will be $x+13$ . Remember that the area of a rectangle is width times length, so:
$A=x(x+13)$
$A=(x^2+13x)ft^2$
Since the cost of installing ties is $1, the cost of installing ties in our rectangle will be x^2+13x dollars.

Stacy can spend no more than $536 on this project, so we can setup an inequality relating the cost of the pound and the cost of installing ties:
 $70.12+x^2+13x \leq 536$
$x^2+13x \leq 465.88$

We can conclude that the inequality that can be used to fin the width, $x$ , of the patio is $x^2+13x \leq 465.88$

6 0

3 years ago

Jack Matthew bought a new diamond ring for $20,000. Sales tax is 5% with a 10% excise tax. The total price including taxes that

Blizzard [7]

Jack paid $ 23000 for the ring.

Solution:

Given that, Jack Matthew bought a new diamond ring for $20,000

Sales tax is 5% with a 10% excise tax

To find: total price including taxes

Given that sales tax is 5% of 20,000

$\begin{array}{l}{\text { Sales tax }=5 \% \times \text { cost price }} \\\\ {\text { Sales tax }=\frac{5}{100} \times 20000=5 \times 200=1000}\end{array}$

Also given that excise tax is 10%

$\begin{array}{l}{\text { Excise tax }=10 \% \times \text {cost price }} \\\\ {\text { Excise tax }=\frac{10}{100} \times 20000=10 \times 200=2000}\end{array}$

Total price = cost price + sales tax + excise tax

Total price = 20,000 + 1000 + 2000

Total price = 23000

Hence, jack paid $ 23000 for the ring.

5 0

4 years ago

What is the value of the 3 in the number 61.83

melamori03 [73]

Answer:

three occupies the hundredths place (it is 3/100 of a whole number)

8 0

3 years ago

Consider the graph below.

kramer

Answer:

$f(x)=\begin{cases}x^2 + 3; & \text{ } x$

Step-by-step explanation:

The y-intercept (when x = 0) on the quadratic graph is 3, the upper quadratic graph does not intersect the x-axis, and the endpoint of the function has an open circle that stops at x = 1. The starting point extends to the boundaries of the graph

Therefore, the piecewise function shown in the quadratic graph is given as follows;

f(x) = x² + 3; x < 1

The straight line graph has a negative slope and starts at x = 1, with a closed circle, extending to higher values of x to the boundaries of the graph

Two points on the straight line graph are (1, 3) and (5, -5), therefore, the slope is (-5 - 3)/(5 - 1) = -2

The equation of the function is y - 3 = -2·(x - 1)

∴ y = f(x) -2·x + 2 + 3 = -2·x + 5

f(x) = -2·x + 5; x ≥ 1

4 0

3 years ago