Y=-2x-8 rate of change

Esterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?

Vladimir [108]

Answer:6 six graders were late. 10% would be 12, and half of that is 6. You need to divide that in half because 5 is half of 10.

8 0

2 years ago

Read 2 more answers

PLEASE HELP ME IM STUCK ON THIS QUESTION.

Vesna [10]

Answer:

You got it right. Triangle DAC

Step-by-step explanation:

Line segment DA is a perpendicular bisector(it cuts line segment CE perfectly in half making line segment AE an CA congruent. Since the triangle share line segment DA that makes them congruent by the SAS postulate

6 0

3 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

identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation descri

sertanlavr [38]

Answer: Random sampling

Step-by-step explanation:

A random sampling technique is a method of sampling in which each member for the sample is chosen randomly from the population.
Systematic sampling : It is a kind of random sampling in which the members get selected after a fixed interval but a random starting point.
Convenience sampling : It is a kind of random sampling in which the members get selected on the basis of researchers convenience.
Stratified sampling : It is a kind of random sampling in which the entire population is divided into a finite number of strata , the researcher select members for sample from each strata.
Cluster sampling : It is a kind of random sampling in which the entire population is divided into clusters. Then a random sample of cluster is drawn by researcher.

In the given situation , 784 adults are selected after their telephone numbers were randomly generated by a computer.

Therefore , the type of sampling used here is : random sampling

7 0

3 years ago

A triangle has angle measures 23° and 35°. What is the measure of the third angle ?

frozen [14]

23 + 35 + A=180
58 + a =180
-58 -58
-------------------
A = 122 degrees

7 0

3 years ago

Read 2 more answers