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3 years ago

Use the explicit rule given to write recursive rule for the geometric sequence:

Mathematics

2 answers:

yKpoI14uk [10]3 years ago

8 0

Answer:

Option B

Step-by-step explanation:

A) a1 = 3

a2 = 3×20

an = 3 × 20^(n-1)

B) a1 = 20

a2 = 20×3

an = 20 × 3^(n-1)

C and D are not geometric

andreev551 [17]3 years ago

6 0

Answer:

see below

Step-by-step explanation:

You know the relationship between the explicit rule and the recursive rule for a geometric sequence is ...

$\text{explicit rule: }a_n=a_1\cdot r^{n-1}\\\\\text{recursive rule: }a_n=a_{n-1}\times r,\ \text{$a_1$ is the same}$

The given explicit rule tells you a1 = 20, r = 3, so you know the recursive rule is the one shown below.

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If a line has a slope of -4 and a u intercept of 1, which of the following is it's graph?

3241004551 [841]

Well. I can't see the picture. But it would be decreasing at a rate of 4 so pick a point on the any line move over to the right one, then down four. And for the y intercept the line would intersect the y axis at positive one. Sorry if that's confusing

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3 years ago

Directions: Find the complemen

andre [41]

Given:

The angles are:

Example $54^\circ$

1. $63^\circ$

2. $87^\circ$

3. $45^\circ$

4. $72^\circ$

5. $5^\circ$

To find:

The complimentary angle of the given angles.

Solution:

If two angles are complimentary, then their sum is 90 degrees.

Example: Let x be the complimentary angle of $54^\circ$ , then

$x+54^\circ=90^\circ$

$x=90^\circ -54^\circ$

$x=36^\circ$

Similarly,

1. The complimentary angle of $63^\circ$ is:

$90^\circ -63^\circ=27^\circ$

2. The complimentary angle of $87^\circ$ is:

$90^\circ -87^\circ=3^\circ$

3. The complimentary angle of $45^\circ$ is:

$90^\circ -45^\circ=45^\circ$

4. The complimentary angle of $72^\circ$ is:

$90^\circ -72^\circ=18^\circ$

5. The complimentary angle of $5^\circ$ is:

$90^\circ -5^\circ=85^\circ$

Therefore, the complimentary angles of $54^\circ, 63^\circ, 87^\circ, 45^\circ, 72^\circ, 5^\circ$ are $36^\circ, 27^\circ, 3^\circ, 45^\circ, 18^\circ, 85^\circ$ respectively.

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3 years ago

Katie gives Maggie half of her pencils. Maggie keeps 5 pencils and gives the rest to Jamil. A. Write an expression for the numbe

Alexandra [31]

Here's what I mean when I write x/2 JUST IN CASE.

а.

Let the total number of pencils be x, then this implies that Maggie received x/2 pencils from Katie. Maggie keeps 5 and give the rest to Jamil, this means

that Jamil receives

x/2-5 pencils.

b. Expression of pencils given to Jamil is: x/2-5

Substitute x=16 in this expression: x/2-5

Simplify and evaluate: = 8-5= 3

Maggie gives 3 pencils to Jamil.

c. Expression of pencils given to Jamil is: x/2-5 to

Equate this expression with 1 to form an equation and solve for x all, the total

number of pencils if Jamil received 1 pencil:

x/2 - 5 = 1

Solve for x:

x = 2(1+ 5)

Evaluate:

x = 2(6) = 12

Katie had 12 pencils if Jamil received 1 pencil.

RESULT

a. Expression of number of pencils given to Jamil is x/2-5, where x is total number of pencils.

b. Maggie gives 3 pencils to Jamil.

c. Katie had 12 pencils if Jamil received 1 pencil.

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3 years ago

What equation represents y=2x^2+24x+85 in vertex form

Andrej [43]

Y=a(x-h)^2+k

vertex form is basically completing the square

what you do is
for
y=ax^2+bx+c
1. isolate x terms
y=(ax^2+bx)+c
undistribute a
y=a(x^2+(b/a)x)+c
complete the square by take 1/2 of b/a and squaring it then adding negative and postive inside
y=a(x^2+(b/a)x+(b^2)/(4a^2)-(b^2)/(4a^2))+c
complete square
too messy \
anyway

y=2x^2+24x+85
isolate
y=(2x^2+24x)+85
undistribute
y=2(x^2+12x)+85
1/2 of 12 is 6, 6^2=36
add neagtive and postivie isnde
y=2(x^2+12x+36-36)+85
complete perfect square
y=2((x+6)^2-36)+85
distribute
y=2(x+6)^2-72+85
y=2(x+6)^2+13

vertex form is
y=2(x+6)^2+13

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3 years ago

Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of so

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I believe this is an equation that could help solve your problem 2.99x+12.99y=43.92

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3 years ago

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