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Masja [62]
3 years ago
9

Consider the function ƒ(x) = (x + 1)2 – 1. Which of the following functions stretches ƒ(x) vertically by a factor of 4?

Mathematics
1 answer:
laila [671]3 years ago
5 0

Answer:

C f(x) = 4(x+1)2-1

Step-by-step explanation:

factor of 4 = 2^2

(x+1)2-1 = 4(x+1) 2-1 = with x

           =   4(+1) 2-1  = without x

           =  (4 - 4) 2 = individual products of -1

           =  (8 - 8 ) = individual products of 2

           =   8 - 8  = 2^2 -2^2

           =  2^2 - 2^2

(x+1)2-1 = 4(x+1)2-1 = with x

            = 2x^2 -2^2

          -x = 2^2 -2^2

            x = -2^2-2^2

            x = 4

which proves f(x) is a factor of 4

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Write the equation of the line which contains all images of point C.
Elena-2011 [213]

Answer:

A. y = \frac{1}{4}x - 2

Step-by-step explanation:

7 0
3 years ago
(A journey by bus takes 45 minutes at 60 km per hour. How fast must a car go to do the same
Vlad [161]

Answer:

The car must drive at 108 km/h to cover the same journey.

Step-by-step explanation:

Given that:

Time taken by bus journey = 45 minutes = \frac{45}{60} = 0.75\ hour

Speed of bus = 60 km/h

Distance of the journey = Speed * Time

Distance of the journey = 60 * 0.75 = 45 km

The car needs to cover 45 km in 25 minutes.

25 minutes = \frac{25}{60}\ hour

Distance = Speed * Time

45 = \frac{25}{60}*Speed

Speed = 45*\frac{60}{25}

Speed = 108 km/h

Hence,

The car must drive at 108 km/h to cover the same journey.

7 0
3 years ago
Write an EQUATION that represents what is seen in the figure and then find the value of x.
Nadusha1986 [10]
(180-144)° + 3x + 90° = 180°
36 + 3x + 90° = 180°
x = 18°
8 0
3 years ago
Graph the line given by 5x+6y=12 and the circle given by x²+y²=1.Find all solutions to the system of equations.
kenny6666 [7]

Answer:

The system has no real solution.

Step-by-step explanation:

Hi there!

We have the following system of equations:

x² + y² = 1

5x + 6y = 12

The solutions of the system are those (x,y) pairs that satisfy both equations.

Let´s take the second equation and solve it for y:

5x + 6y =12

subtract 5x to both sides of the equation

6y = 12 - 5x

divide by 6 both sides

y = (12- 5x)/6

Now, let´s replace the y in the first equation:

x² + y² = 1

x² + [(12- 5x)/6]² = 1

Apply distributive property

x² + (12 - 5x)²/36 = 1

x² + (12 - 5x)(12 - 5x)/36 = 1

Apply distributive property

x² + (144 - 120x + 25x²)/36 = 1

Apply distributive property

x² + 4 - 10/3 · x + 25/36 · x² = 1

subtract 1 to both sides

61/36 · x² - 10/3 · x + 3 = 0

Using the quadratic formula, let´s find the solutions to this quadratic equation:

a = 61/36

b = -10/3

c = 3

[-b ± √(b² - 4ac)]/2a

[10/3 ± √(100/9 - 4(61/36)(3))]/2(61/36)

(10/3 ± √-83/9)/61/18

This expression has no real solution because √-83/9 is not defined in the set of real numbers. This means that both curves don´t intersect (see attached figure).

Have a nice day!

3 0
3 years ago
6^7 divided by 6^5= what? 36....got my answer
jok3333 [9.3K]

Yep, 36 is correct.

3 0
3 years ago
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