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2 years ago

Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k

Mathematics

1 answer:

V125BC [204]2 years ago

7 0

Answer:

Option A (3).

Step-by-step explanation:

First step in this question is to identify f(x). Since f(x) is a linear function, therefore, the equation of the straight line is given by the following formula:

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1); where (x, y) is the general point, (x1, y1) is the first point on the line, and (x2, y2) is the second point on the line.

From the graph, it is given that (x1, y1) = (3, 2) and (x2, y2) = (2, 0):

(y - 2)/(x - 3) = (0 - 2)/(2 - 3).

(y - 2)/(x - 3) = (-2)/(-1).

(y - 2)/(x - 3) = 2.

Cross multiplying:

(y - 2) = 2(x - 3).

y - 2 = 2x - 6.

y = 2x - 4.

This the equation of f(x) in the y = mx + c form. To calculate g(x), it is important to note that f(0) = g(k*0) because this simplifies to f(0) = g(0). This means that y-intercept of both the equations is same. The y-intercept of f(x) is -4. Which means that y-intercept of g(x) is -4. This is one point (0, -4). From the graph, another point which passes through g(x) is (1, 2).

it is given that (x1, y1) = (0, -4) and (x2, y2) = (1, 2):

(y - (-4))/(x - 0) = (2 - (-4))/(1 - 0).

(y + 4)/(x) = (6)/(1).

(y + 4)/x = 6

Cross multiplying:

y + 4 = 6x

y = 6x - 4.

In short, f(x) = 2x - 4 and g(x) = 6x - 4

It is given that g(x) = f(k*x). Since f(k*x) = 2*kx - 4, therefore:

6x - 4 = 2*kx - 4.

6x = 2*kx.

2k = 6.

k = 3.

Therefore, Option A is the correct choice!!!

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EF is located at E (x,y) and F (7,-10) and was rotated around the origin. EF became E’F’ with coordinates E’ (4,5) and For (10,7

monitta

Answer:

90° CCW

Step-by-step explanation:

If we assume you intend F'(10, 7), point F has been transformed by the rule ...

(x, y) ⇒ (-y, x)

The transformation rule (x, y) ⇒ (-y, x) represents a 90° CCW rotation.

5 0

2 years ago

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3

butalik [34]

Answer:

The answer is below

Step-by-step explanation:

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3 miles.

a) Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.

a) A house is located 5 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?

Answer:

Let the center of the town represent the origin (0,0). Also 1 unit = 1 mile. Since the cell tower is located 3 miles east and 4 miles north of the center of a small town, it is represented by A(3, 4)

The cell tower has a coverage of radius 3 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius. Hence:

(x - 3)² + (y - 4)² = 3²

(x - 3)² + (y - 4)² = 9

The diagram is drawn using geogebra.

b) The house is 5 miles north. It can be represented by y = 5 line.

To find the distance east of the house we have to substitute y = 5 and solve for x, hence:

(x - 3)² + (y - 4)² = 9

(x - 3)² + (5 - 4)² = 9

(x - 3)² + 1 = 9

(x - 3)² = 8

(x - 3) = √8

x - 3 = ±2.83

x = 3 ± 2.83

x = 5.83 or 1.83

Since it is to the east to the cell tower, hence x = 5.83.

Therefore the house is located 5.83 miles to the east of the cell tower

8 0

2 years ago

The percentage of U.S. college freshmen claiming no religious affiliation has risen in recent decades. The bar graph shows the

emmainna [20.7K]

Answer:

0.5%/year

24.2%

Step-by-step explanation:

Estimate the average yearly increase in the percentage of first-year college females claiming no religious affiliation

Percentage of females by year:

1980 = 6.2%

1990 = 10.8%

2000 = 13.6%

2012 = 21.7%

Average yearly increase :

Percentage increase between 1980 - 2012 :

2012% - 1980% = ( 21.7% - 6.2%) = 15.5% increase over [(2012 - 1980)] = 32 years

15.5 % / 32 years = 0.484375% / year = 0.5%/year

b. Estimate the percentage of first-year college females who will claim no religious affiliation in 2030,

Given an average increase of 0.484375% / year

(2030 - 1980) = 50 years

Hence by 2030 ; ( 50 years × 0.484375%/year) = 24.218% will claim no religious affiliation.

=24.2% (nearest tenth)

3 0

2 years ago

Noor wants to spend less than $20 on condiments. Each kilogram of salt costs $1.50, and each kilogram of pepper costs 2.50.

nata0808 [166]

Answer:

1.5s+2.5p<20

Step-by-step explanation:

Multiply by each kilo and then make sure it adds up to less than 20!

3 0

2 years ago

A circle with radius of \greenD{4\,\text{cm}}4cmstart color #1fab54, 4, start text, c, m, end text, end color #1fab54 sits insid

mario62 [17]

Answer:

The area of the shaded region is $329.87\ cm^2$

Step-by-step explanation:

<u><em>The correct question is</em></u>

A circle with radius of 4cm sits inside a circle with a radius of 11cm. What is the area of the shaded region?

The shaded region is the area outside the smaller circle and inside the larger circle

we know that

To find out the shaded region subtract the area of the smaller circle from the area of the larger circle

$A=\pi r_a^{2} -\pi r_b^{2}$

simplify

$A=\pi (r_a^{2} -r_b^{2})$

where

r_a is the radius of the larger circle

r_b is the radius of the smaller circle

we have

$r_a=11\ cm\\r_b=4\ cm$

substitute

$A=\pi (11^{2} -4^{2})$

$A=\pi (105)\ cm^2$

assume

$\pi=3.1416$

substitute

$A=(3.1416)(105)=329.87\ cm^2$

7 0

2 years ago