All categories

2 years ago

BRE

Mathematics

1 answer:

zvonat [6]2 years ago

5 0

Answer:

2nd option

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = $\frac{A'C'}{AC}$ = $\frac{9}{6}$ = $\frac{3}{2}$ = 1 $\frac{1}{2}$

You might be interested in

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

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

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

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

$0.028x=0.68$

$x=24.3$

Alternative method

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

$0 \leq x \leq 48.6\ ft$

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

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

If the area of a triangular kite is 6 square feet and its base is 4 feet, find the height

KonstantinChe [14]

The height of the kite is 3 feet. Here’s
why;
We know that BH=2A (base times height is equal to 2 times the area) of any given triangle.
Lets plug in values;
BH=2A
4(H)=2(6)
Then simplify;
4(H)=12
Flip the equation to find the missing value;
12 divided by 4 is 3.
Check your work;
4(3)=6(2):
12=12
The height of the kite is 3 feet.

4 0

2 years ago

Hellllllllllllllllllllllllllp

murzikaleks [220]

Answer:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Step-by-step explanation:

Slope-intercept form of a linear equation:

$\boxed{y=mx+b}$

where:

m is the slope.
b is the y-intercept (where the line crosses the y-axis).

Slope formula

$\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}$

Equation 1

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(-1, 6)$

$\textsf{Let }(x_2,y_2)=(0, 1)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5$

From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=-5x+1$

Equation 2

Define two points on the line:

$\textsf{Let }(x_1,y_1)=(1, 1)$

$\textsf{Let }(x_2,y_2)=(0, -4)$

Substitute the defined points into the slope formula:

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5$

From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

$y=5x-4$

Conclusion

Therefore, the system of linear equations shown by the graph is:

$\begin{cases}y=-5x+1\\y=5x-4 \end{cases}$

Learn more about systems of linear equations here:

brainly.com/question/28164947

brainly.com/question/28093918

5 0

1 year ago

Read 2 more answers

1. The radioisotope Iodine-123 is used in thyroid therapy. The half-life of this isotope is 13.27 hours.

Mandarinka [93]

1. Answer: D. A = 100 (1/2)^t/13.27

Exponent equation formula would be an= a0( 1+r)^t
In this question, the radio isotopes will become half of its weight after the half-life. So, the ratio would be -0.5 (r= -0.5)
The halftime is 13.27 hours, so the time will be divided by that number. The result would look like this:
an= a0( 1+r)^t
an= a0( 1-0.5)^t/13.27
an= a0( 1/2)^t/13.27

2. Answer: x= 74°

The ladder and the building will make a right triangle with the ladder as the hypotenuse.
The foot of the ladder is 2 feet from the building, so the adjacent side is 2ft.
It reaches a point 7 feet high on the building, so the opposite side is 7ft
You can find the angle by using the tan equation

tan x= opposite / adjacent
tan x= 7/2= 3.5
x= 74°

7 0

3 years ago

before cam broke his right arm he was able to text 9 words per minute on his phone after he broke his arm he had to use his left

mojhsa [17]

He textes less because hes not useed to texting with that arm so it lot harder

3 0

2 years ago