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eduard
2 years ago
10

Graph the function. G(x)=2(x+2)(x+6)

Mathematics
1 answer:
sergey [27]2 years ago
5 0

Answer:

Step-by-step explanation:

Distribute 2(x+2):

2(x) + 2(2) = 2x + 2

Use the FOIL method to multiply (2x + 2)(x+6)

(2x + 2)(x+6)

2x(x) = 22x^{2}

2x(6) = 12x

2(x) = 2x

2(6) = 12

22x^{2} + 12x + 2x + 12 = 22x^{2} + 14x + 12

Graph the following equation on a graphing calculator, and then you should know how to graph it on paper.

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If 1st and 4tg terms of G.p are 500 and 32 respectively it's second term is ?
bixtya [17]

Answer:

T_{2} = 200

Step-by-step explanation:

Given

Geometry Progression

T_1 = 500

T_4 = 32

Required

Calculate the second term

First, we need to write out the formula to calculate the nth term of a GP

T_n = ar^{n-1}

For first term: Tn = 500 and n = 1

500 = ar^{1-1}

500 = ar^{0}

500 = a

a = 500

For fought term: Tn = 32 and n = 4

32 = ar^{4-1}

32 = ar^3

Substitute 500 for a

32 = 500 * r^3

Make r^3 the subject

r^3 = \frac{32}{500}

r^3 = 0.064

Take cube roots

\sqrt[3]{r^3} = \sqrt[3]{0.064}

r  = \sqrt[3]{0.064}

r = 0.4

Using:  T_n = ar^{n-1}

n = 2     r = 0.4     and a = 500

T_{2} = 500 * 0.4^{2-1}

T_{2} = 500 * 0.4^1

T_{2} = 500 * 0.4

T_{2} = 200

<em>Hence, the second term is 200</em>

5 0
3 years ago
How to solve these 3 problems
Bingel [31]

Answer:

  1. a. decay; b. growth; c. decay; d. neither
  2. r = 4; a = 1; y = 1·4^x
  3. a. an = 3(5^(n-1)); b. f(x) = (3/5)(5^x); c. exponential growth; d. y-intercept: 3/5; first term: 3.

Step-by-step explanation:

There are two kinds of exponential problems here.

  1. exponential functions of the form f(x) = a·b^x
  2. exponential sequences of the explicit form an = a1·r^(n-1)

The second problem gives you a table that suggests the sequence form, but it asks for the exponential function form. The third problem does something similar.

__

<h3>1.</h3>

In an exponential function of the form f(x) = a·b^x, the function grows if b>1 and decays if b<1. Using this check, we can easily answer ...

  a. 0.4 < 1 . . . decay

  b. 1.3 > 1 . . . growth

  c. 1/2 < 1 . . . decay

  d. 1 = 1 . . . neither growth nor decay; the function is constant: j(x) = 1.

__

<h3>2.</h3>

The value of x is given starting at 1, so we can consider this a geometric sequence. The common ratio is r = 16/4 = 4. The first term is a1 = 4, so the explicit formula for the sequence is ...

  an = 4·4^(n-1)

When this is expanded to get rid of the constant in the exponent, we have ...

  an = 4·(4^n)·(4^-1) = 1·4^n

We recognize this form as matching the functional form f(x) = a·r^x. The multiplier of the exponential factor is a=1. In summary, ...

  r = 4; a = 1; f(x) = 1·4^x

__

<h3>3.</h3>

The first term of this geometric sequence is a1 = 3. The common ratio is r = 15/3 = 5. Using the explicit formula, we have ...

 a. explicit form: an = 3·5^(n-1)

Using the method of question 2 to write the functional form, we find ...

  an = 3(5^n)(5^-1) = (3/5)(5^n)

  b. functional form: f(x) = (3/5)(5^x)

  c. function family: exponential growth functions

 d. y-intercept: (3/5) . . . . read this from the f(x) form

     1st term: the first term listed in the given sequence is 3

_____

<em>Additional comment</em>

The "y-intercept" of a sequence is irrelevant (undefined), as the sequence term numbering starts with 1, not 0. The domain of the explicit formula is <em>natural numbers</em>, which does not include 0.

Similarly, the "first term" of a function f(x) needs further definition. Here, we've answered the question by saying the first term is f(1). There is no conventional definition of a "first term" for a continuous function.

3 0
2 years ago
Please help.. (This is meant to be infinite, so I can't use a calculator)
Alex17521 [72]

Answer:

5

Step-by-step explanation:

→ Let x = √20 + √20 .....

x

→ Square both sides

x² = 20 + √20 +√20 + √20

→ Replace √20 +√20 + √20 with x

x² = 20 + x

→ Move everything to the left hand side

x² - 20 - x = 0

→ Factorise

( x + 4 ) ( x - 5 )

→ Solve

x = -4 , 5

→ Discard negative result

x = 5

7 0
2 years ago
Read 2 more answers
Question on the photo
IrinaVladis [17]

Answer:

C

Step-by-step explanation:

Since it is only addition and subtraction, you can rearrange the order of the equations. This is what the three eqautions will look like after the arrangement:

1.6z + 8.3 z = ? (9.9z)

6.2y - 5.1y = ? (1.1y)

4.3x + 5.5x = ? (9.8x)

Then you just add and subtract.

8 0
3 years ago
On a map, the distance between two towns is 2.5 inches, and 1 inch represents 6 miles.
MAXImum [283]
So it's 2.5 inches, so it would be 15 miles, because 6+6+3=15.
8 0
3 years ago
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