Show that 3 · 4n + 51 is divisible by 3 and 9 for all positive integers n.

Answers

Answer 1

Answer:

4^1 + 17 = 21 , which is divisible by 3. 4^k + 17 and 3 * 4^k are both divisible by 3, so 4^k + 17 + 3 * 4^k is divisible by 3 as well. 3 * (4^n + 17) would be divisible by 9


Related Questions

Nancy drew a scale drawing of a theater. In the scale Nancy used for the drawing, 1 inch represents 3 feet. The stage is 16 inches long in the drawing. How long in feet is the actual stage?

Answers

Answer:

The answer to this question is 48 feet

Step-by-step explanation:

You would see that 1 inch is 3 feet then you would multiply 3 and 16 to receive 48

In a survey of 100 people, some of them jog for exercise, some of them ride a bike, some do both, and 15 do not jog or ride a bike. If 46 of the people surveyed job and 21 of them both jog and ride a bike, how many of the people surveyed only ride a bike?

Answers

Answer:

Bike alone = 39

Step-by-step explanation:

Given that:

Total number = n(T) = 100

Jog= n(J)

Bike = n(B)

Bike and jog = n(BnJ) = 21

Number who jog = 46

Jog alone = 46 - 21 = 25

Neither jog nor bike = 15

Let bike alone = x

Hence,

Jog alone + bike alone + jog and bike + none of the two = 100

25 + x + 21 + 15 = 100

x = 39

if profit is ppersent and cost peice is cp qhat will ne the selling price​

Answers

Answer:

selling price will be sp

--------------------------

convert the following fraction to the lowest term 0.4​

Answers

Answer:

2/5.

Step-by-step explanation:

Hope this helps. S

Answer:

2/5 is the answer of this question

Fracción equivalente de 1/3

Answers

Answer:

2/6

Step-by-step explanation:

1/3 times 2

I'm confused there is only i answer is it B or D?

Answers

Answer:

B

Step-by-step explanation:

Answer:

Where the question?

Step-by-step explanation:

Write the decimal expansion for 4/9.

Answers

Answer:

0.4

Step-by-step explanation:

Heather made $299 for 13 hours of work.
At the same rate, how much would she make for 18 hours of work?

Answers

Answer:

$414

Step-by-step explanation:

We know that Heather made $299 for 13 hours of work.

So, to find how much Heather will make for 18 hours of work at the same rate, we can write and solve for the following proportion:

[tex]\frac{299}{13}=\frac{x}{18}[/tex]

Notice that we align the rates vertically and the measurements horizontally (dollars in the numerator and hours in the denominator).

So, to find how much Heather will make for 18 hours, we will solve for x. Cross-multiply:

[tex]13x=5382[/tex]

Divide both sides by 13:

[tex]x=\$414[/tex]

So, Heather will make $414 for 18 hours of work.

And we're done!

Please help! I am supposed to write a recursive and an explicit function for the geometric sequence but this one is really frustrating me. Thank you!

Answers

Step-by-step explanation:

Initially, there's only 1 letter.

Tania sends the letter to 4 friends.

Each friend sends a letter to 4 more friends (4 × 4 = 16).

Each of those friends sends to 4 more friends (16 × 4 = 64).

The pattern is 1, 4, 16, 64, etc.

This is a geometric sequence.  The first term is 1 and each term is 4 times the previous term.

a₁ = 1

aₙ = 4 aₙ₋₁

The explicit formula is:

aₙ = 1 (4)ⁿ⁻¹

Which is the point-slope equation of a line with a slope of 1/2 that contains (4,7)

My answer choices are
A= Y - 7 = 1/2 (x+4)
B= Y - 7 = 1/2 (x-4)
C = Y - 7 = - 4 + (1/2)
D = y + 7 = 1/2 (x+

Answers

Answer:

B

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = [tex]\frac{1}{2}[/tex] and (a, b) = (4, 7) , thus

y - 7 = [tex]\frac{1}{2}[/tex](x - 4) → B

Can someone help me photo is above

Answers

Answer: 9x + (-1)

Step-by-step explanation:

(7x + 2x) + (2 -3)

9x + (-1)

Answer:

14x²-17x-6

Step-by-step explanation:

multiply (7x+2)(2x-3)

(1) multiply 7x and 2x =14x²

(2) multiply 7x and -3 = -21x

(3) multiply 2 and 2x= 4x

(4) multiply 2 and -3 = -6

Last step: add all answers from step 1 to 4

: 14x² +(-21x)+4x+(-6)

answer: 14x²-17x-6

Which statement is true?
7 < 65 <8
4< 13 < 5
6 < 33 < 7
o 9 < 91 < 10

Answers

Answer:

→ All statement are false................

Given the function g(x)=-x^2+6x+12g(x)=−x
2
+6x+12, determine the average rate of change of the function over the interval -3\le x \le 5−3≤x≤5.

Answers

Answer:

4

Step-by-step explanation:

edge

The average rate of the function is 4.

What is average rate of function?

The average rate of change of a function f(x) over an interval [a, b] is defined as the ratio of "change in the function values" to the "change in the endpoints of the interval". i.e., the average rate of change can be calculated using [f(b) - f(a)] / (b - a). In other words, the average rate of change (which is denoted by A(x)) is the "ratio of change in outputs to change in inputs". i.e.,

A(x) = (change in outputs) / (change in inputs)

= Δy / Δx

= [f(b) - f(a)] / (b - a)

given function:

f(x) = -x² + 6x + 12

Now,

let a= -3, b = 5

and, f(b)= -(5*5) + 6*5 + 12

 =-25+ 30 +12

 = 17

f(a) = -(- 3 * (-3))+6(-3) +12

  = -9-18+12

  = -15

Now,

f(b)- f(a) / (b-a)

=17 -(-15))/5-(-3)

=32/ 8

=4

Learn more about rate of change here:

https://brainly.com/question/23715190

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Use the graph to determine which statement describes f(x)
O A. f(x) does not have an inverse function, because its graph fails the
horizontal line test.
O B. f(x) has an inverse function, because its graph passes the
horizontal line test.
C. f(x) has an inverse function, because its graph passes the vertical
line test.
D. f(x) does not have an inverse function, because its graph fails the
vertical line test.

Answers

Answer:

f(x) does not have an inverse function, because its graph fails the horizontal line test. ⇒ A

Step-by-step explanation:

The vertical line test is used to show that the graph represents a

function or not

If the vertical line crosses the graph in more than one point, then the graph does not represent a functionIf the vertical line crosses the graph in only one point in different positions, then the graph represents a function

The horizontal line test is used to show that the function has an

inverse or not

If the horizontal line crosses the graph of a function in more than one point, then the function has no inverseIf the horizontal line crosses the graph of a function in only one point in different positions, then the function has an inverse

Let us look at the given graph

→ The graph represents a parabola, which represents the function f(x)

∵ Any horizontal line drawn will cross the graph in more than one point

∴ f(x) has no inverse

f(x) does not have an inverse function, because its graph fails the

  horizontal line test.

SORRY I NEED HELP AGAIN! 5 cans of soda cost $3.75. At this rate, how much do 3 cans of soda cost?
Type your answer here..

Answers

Answer:

So if 5 soda cost $3.75 per can, multiply 3 times $3.75 and that would be your answer:  $11.25

Step-by-step explanation:

PLEASE HELP!!! AND HURRY, I HAVE 15 MIN TO FINISH!!!!!

Which best describes this inheritance pattern?
The diagram shows the results when two parents are
crossed. The letters represent alleles for a trait that is
controlled by three different genes.
o multiple allele because a trait is controlled by three
different genes
polygenic because the offspring have alleles from
both parents
multiple allele because the offspring have alleles
from both parents
polygenic because a trait is controlled by three
different genes

Answers

Answer:its b i think

Step-by-step explanation:

Answer: D, polygenis because a trait is controlled by three different genes.

Step-by-step explanation: I got 100 of the test ^^

What is the equation of the line passing through the points (2, -1) and (5, -10) in slope-intercept form?

A. y=-3x-5
B. y=-3x+5
C. y=3x-5
D. y=3x+5

Answers

Answer:

b. y=-3x+5

Step-by-step explanation:

If you find the slope(y-y/x-x) I found that the slope is -3. from using the slope and graphing this out, the y-intercept is +5 giving me the answer of y=-3x+5.

I hope this helps have a great day:)

Answer:

y = -3x + 5

Step-by-step explanation:

The answer is correct because I just took the test and I got a 100%.

7.13 x 6.2 = 44.206
write down two more multiplications with an answer of 44.206

Answers

22.103 x 2
44.206 x 1
11.0515 x 4

what is the x coordinate​

Answers

Answer:

the x coordinate is the horizontal line wich is going in a straight line.

Step-by-step explanation:

The coordinates of

A are (0.5,4)

B are (-3,0)

C are (-1,1)

The formula for coordinates is (x,y).

The x coordinates are the ones that are on the horizontal line.

The y coordinates are the ones that are on the vertical line.

Jennifer added the product 125 and 58 to the product of 357 and 42 what is the sum?

Answers

Answer:

22244

Step-by-step explanation:

(125*58)+(357*42)=22244

ASAP PLS ILL GIVE BRAINLIEST

coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f'. Where are points A' and B' located after dilation, and how are lines f and f' related? A) The locations of A' and B' are A' (0, 2) and B' (6, 0); lines f and f' intersect at point A. B) The locations of A' and B' are A' (0, 6) and B' (2, 0); lines f and f' intersect at point B. C) The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f' are the same line. D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

Answers

Answer:

D (0,6) (6,0)

Step-by-step explanation:

when you multiply it you do the x coordinates first then the y.

so (0,2)  x 3 = (0,6)

(2,0) x 3 = (6,0)

These coordinates are parralel to each other.

The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel, the correct option is D.

What is Transformation?

Transformation is the process of changing the graph to a new graph by Rotation, Reflection, Translation, and Dilation.

Dilation is a process in which the object or the graph is enlarged or compressed by a scale factor.

The coordinates of A( 0, 2)

The coordinates of B(2,0)

The scale factor is 3

The center of dilation of f is at the origin to create line f'.

The points A and B lie on the line f, when line f is dilated, the coordinates will also get dilated.

The coordinate of A after dilation is 3 * (0,2)

A' = (0,6)

The coordinate of B after dilation is 3 * (2,0 )

B' = (6,0)

The line f' will be parallel to the line f.

To know more about Transformation

brainly.com/question/11709244

#SPJ5

i need to know asap

Answers

Answer:

16/25 = 0.64

6/7 = 0.857142

Step-by-step explanation:

Convert the fraction to a decimal by dividing the numerator by the denominator.

Oct 09, 11:40:51 AM
Solve the following inequality for f. Write your answer in simplest form.
9f + 5(-8f +1) < 3f +7 – 10
fi
Submit Answer
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attempt out of 2
Copyright 2020
DIL

Answers

get it sis 57
11 23 fhsjjdjrjr

round 75.0794 to 2 decimal places​

Answers

Answer:

75.08

Step-by-step explanation:

Focus on the 2nd digit to the right of the decimal point (it is 7).  The next digit is 9.  Because of this (nex digit 5 or greater), we round the 7 up to 8 and obtain the answer

75.08

20 POINTS AND BRAINLIST
restaurant has 22 bags of potatoes weighing 363 pounds. If the weight of the bags of potatoes varies directly with the number of bags of potatoes, how much will 15 bags weigh?
a 247.5
b 330
c 115.5
d 315

Answers

A - i hope so


363 divided by 22 is 16.5

16.5 x 15 is 247.5

Expand and simplify: 2(x-4^2)+7

Answers

Answer:
2x-25

Explanation:
2(x-4^2)+7
1) Find the exponent
=2(x-16)+7
2) Use the distributive property on the parentheses
=2x-32+7
3) Subtract 32 and 7
=2x-(32-7)
=2x-25

I hope this helps! Please comment if you have any questions.

HELPPPPPPPPPP ITS DUEEEEEEEEEEEEEEEE

Answers

Answer:

Look below.

Step-by-step explanation:

1.) Alternate exterior

2.) Alternate interior

3.) Same-side interior

4.) Vertical

5.) Corresponding

6.) Alternate exterior

2 1/3+3 1/3? (2 and 1/3+ 3 and 1/3)

Answers

Answer: 5 2/3

Step-by-step explanation:

Answer:

5.6666666667

Step-by-step explanation:

2 1/3 + 3 1/3

= 7/3 + 10/3

= 7/3 + 10/3

= 17/3

= 5.6666666667

is a letter or symbol that represents the unknown value (term)​

Answers

Variable

Step-by-step explanation:

Wally's grandmother started a college savings account for him with
$3,000. What is the total amount of money in the account after 5 years if
the annual simple interest rate is 3%?
I need this plz help explain the proses thx ASAP

Answers

Answer:

$450

Step-by-step explanation:

You want to calculate the interest on $3000 at 3% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $3000.00.

r is the interest rate, 3% per year, or in decimal form, 3/100=0.03.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 3000 × 0.03 × 5 to get that:

The interest is: $450.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),

or 3000.00 + 450.00 = 3450.00.

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