Use elimination to solve the system. The solution is ( , ). 3x+1/2y=3 6x-y=2

How do you graph this

Trava [24]

Answer:

=6

Step-by-step explanation:

hat is this passage mostly about?

Click for the passage, "Studies in Ice."

A. Studying nature

B. Storing and moving ice safely

C. Powering drills with the sun

D. Saving messages in ice

3 0

2 years ago

The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

so

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

so

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

so

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0

2 years ago

What is the opposite of 4?

Wittaler [7]

The opposite of 4 is negative 4, or -4

3 0

3 years ago

Please help me with this asap!!!!!!!!!!!!!!!!!!!!!!!!!!

drek231 [11]

Try the first four cards in order from left to right. It starts with the expression, plugs in 6 for t, does 6 * 3 first because of PEMDAS, and then does 27 - 18, which is 9.

3 0

2 years ago

The population of a city in the year 2000 was 4,400. In 2010, the population was 5,060. Find the percent increase in the populat

larisa86 [58]

Answer:

total population in the year 2000=4400

total population in the year 2010=5060

no of people increased=5060-4400

=660

increase percent=660/4400*100%

=3/20*100%

=15%

Step-by-step explanation:

15/100*5060

0.15*5060

759

in 2020 population will be

5060+759

5819

therefore the population will be 5819 in 2020

6 0

2 years ago

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