MATHEMATICS COLLEGE

What is the effect on the graph of the function f(x)=x when f(x) is replaced with -1/2f(x)?

Answers

Answer 1

Answer:

Answer:

For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression

Step-by-step explanation:

Parent function is f(x)= x

We need to find the effect of the graph when f(x) is replaced with -1/2f(x)

When negative sign is multiplied outside f(x) like -f(x), then there will be a reflection over x-axis

When negative sign is multiplied inside f(x) like f(-x) then there will be a reflection over y-axis

When a number is multiplied outside f(x) then there will be a vertical stretch or compression

Here 1/2 is multiplied outside f(x). $(1)/(2)$ is less than 1 so there will be a vertical compression

For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression

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Answers

1. 2300 divided by 45= 51
2.357 divided by 21= 17
3. 1215 divided by 15= 81
4.360 divided by 24= 15

Answer:

51.111, 17, 81, 15

Step-by-step explanation:

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, ifc=2b, a=12?

Answers

b = 4√3

using Pythagoras' identity in the given triangle

c² = a² + b² ( substitute c = 2b and a = 12 into the equation )

(2b)² = 12² + b²

4b² = 144 + b² ( subtract b² from both sides )

4b² - b² = 144

3b² = 144 ( divide both sides by 3 )

b² = 48 ( take the square root of both sides )

b = √48 = √( 16 × 3 ) = √16 × √3 = 4√3 ' exact value '

Toy company produces rubber balls that have a radius of 1.7 cm.A sphere has a radius of 1.7 centimeters.
What is the volume of one rubber ball? Round to the nearest hundredth of a centimeter.

Answers

Answer:

The volume of one rubber ball is 20.58 cubic centimeters.

Step-by-step explanation:

The rubber ball has a spheric format.

A sphere with radius r has volume given by the following equation:

$V = (4\pi r^(3))/(3)$

In this question:

r = 1.7 cm.

The radius is in centimeters, so the volume will be in cubic centimeters.

What is the volume of one rubber ball?

$V = (4*\pi*(1.7)^(3))/(3) = 20.58$

The volume of one rubber ball is 20.58 cubic centimeters.

Answer:

1) 20.58 cm

2) $0.09

3) $0.41

Step-by-step explanation:

Find the rectangular coordinates of the point ( -3, 1/2 π)

Answers

Answer:

$x = -3 cos ((\pi)/(2))= 0$

$y = -3 sin ((\pi)/(2))= -3$

And then the rectangular coordinates for this case are :

$(x = 0 , y = -3)$

Step-by-step explanation:

We have the following point given $P = (-3, (\pi)/(2))$ and we want to conver from polar to rectangular coordinates and we need to use the following formulas:

$x = r cos \theta$

$y = r sin \theta$

For this case we have that:

$r = -3$

And:

$\theta = (\pi)/(2)$

Replacing we got:

$x = -3 cos ((\pi)/(2))= 0$

$y = -3 sin ((\pi)/(2))= -3$

And then the rectangular coordinates for this case are :

$(x = 0 , y = -3)$

Mr.ward and mr. heskey are racing toy cars and Mr. heskey wants to give mr. ward an 8 ft head start because his car is 2 seconds slower. mr. ward's car travels 4 feet per second and mr. he's key's car travels 6 ft per second.which inequality could be used to determine after how many seconds, 's mr. heskey's car will be head of mr. ward's car?

please show how you got the answer.

Answers

Answer:

F. 6s > 4s +8

Step-by-step explanation:

From a reference point at the beginning of the track, Ward's car will be located 4s+8 feet down the track after s seconds. That is, it starts 8 feet down the track, and increases its distance by 4 feet every second.

From the same reference point, Heskey's car will be located 6s feet down the track after s seconds. Its distance starts from zero and is increasing at the rate of 6 feet every second.

For Heskey's distance to exceed Ward's distance you want ...

6s > 4s +8 . . . . . . matches choice F

The perimeter of a rectangle is 80 cm. The width is 10 cm more than twice the length. Whatis the length and width of this rectangle? P=2W+2L