The three-digit number "ab5" is divisible by 3. How many different three-digit numbers can "ab5" represent?

Answers

Answer 1

Answer:

30

Step-by-step explanation:

I can't prove this, but I can tell you the answer.

30.

a = 100 s  digit

b = 10 s digit

5 is always the units digit.

I'm pretty sure that 30 is the correct answer.

What an interesting question. If I find out how it is done, I'll post it in the comments.

I can say this much.

a + b + 5 must be divisible by 3.

a = 1     b = 9     + 5

a = 1     b = 6     + 5

a = 1     b = 3     + 5

a = 1     b = 0 +  5

===============

Three more are obtained by interchanging the 100s and 10s digit except for b = 0

a = 9     b=1    + 5

a = 6     b =1   + 5

a = 3     b= 1   + 5

==================

a = 2    b = 2 + 5

a = 2    b = 5  + 5

a = 2    b = 8  + 5

only 2 more are obtained by interchanging the 10s and 100s digit

=============

a = 3   b = 4    +5

a = 3   b = 7    +5

You can't go any further. You get 2 more by interchanging the b and a digits.

=============

I hope you see what I've done here. I don't think this is an exact proof, but it is an exhaustive search.


Related Questions

Justin and his children went into a grocery store and he bought $18 worth of bananas and mangos. Each banana costs $0.60 and each mango costs $1.50. He bought 2 more bananas than mangos. Graphically solve a system of equations to determine the number of bananas, x, and the number of mangos, y, that Justin bought.

Write an answer in y=mx+b form, please.
Two equations.

Answers

Answer:

x=10 and y= 8.

Step-by-step explanation:

Given that the cost of 1 banana = $0.60

Cost of 1 mango = $1.50.

Total cost= $ 18  

Here, x be the number of bananas and y be the numbers of mangos,

As the number of bananas is 2 more than the number of mangos,

So, x=y+2

[tex]\Rightarrow y=x-2 \cdots(i)[/tex]

Cost of x bananas [tex]=\$ 0.60 \times x[/tex]

Cost of y mangos [tex]=\$ 1.50 \times y[/tex]

Total cost = 0.6x+1.5y

[tex]\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).[/tex]

Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.

Both the graphs intersect at the point (10,8) as shown in the graph.

So, the solution of both the equations is, (x,y)=(10,8). i.e

The number of bananas = x= 10 and

the number of mangos = y = 8.

Maliah goes to an electronics store. Let y represent the price of a laptop and let z represent the price of a television. The equation
y=32 + 12 relates the prices.

Answers

Answer:

hi

Step-by-step explanation:

use the graph below to determine how many cakes mary sells after 4 hours

Answers

Answer:

8

Step-by-step explanation:

follow the graph

Answer:

D. 8

Step-by-step explanation:

Look for 4 the x axis and go up until you see the dot. Whatever is on the y-axis is your answer(8)

simplify the expression -9x-8+4x+7

Answers

Answer: 5x - (-1)

Step-by-step explanation:

Answer:

-5x-1

Step-by-step explanation:

First combine like terms

-9x-8+4x+7 combine -9 and 4

-5x-8+7 then combine -8 and 7

-5x-1

Kyle deposited $1200 in a savings account that earns 4.25% simple annual interest. If kyle keep the money in the account for 4 years what is the new balance?

Answers

Answer:

If kyle keeps the money in the account for 4 years, the new balance is $1,417.37.

Step-by-step explanation:

You can use the formula to calculate the future value to find the money in the account after 4 years:

FV=PV*(1+i)^n

FV= future value

PV= present value=$1,200

i= interest rate=4.25%=0.0425

n=number of periods of time=4

FV=1,200*(1+0.0425)^4

FV=1,200*(1.0425)^4

FV=1,417.37

According to this, the answer is that if kyle keeps the money in the account for 4 years, the new balance is $1,417.37.

f(0) = 3 and f(1) = 15.

Answers

Answer:

Step-by-step explanat

Given=F(0) = 3 and f(1) = 15.

So f(X)=12x+3

When X=0, f(0)=12x0+3=3

When X=1, f(1) = 12x1+3= 15

So f(X)=12x+3 is the solution o

Guys plz help Answer this QUESTION!!!

Answers

Answer:

I beliEve it is D

Step-by-step explanation:

Listen Rachel babysat three children for five hours if they were paid $2.50 per hour for each child and divided their earnings equally how much did each girl receive

Answers

Answer: Each girl will receive $18.75.

Step-by-step explanation:

Given: Two girls babysat three children for five hours.

Hourly pay for each child = $2.50

Payment for 5 hours per child = [tex]5\times\$2.50=\$12.5[/tex]

Payment to 3 children for 5 hours = [tex]3\times \$12.5=\$37.5[/tex]

So, the amount received by each girl  = [tex]\dfrac{\text{Payment to 3 children for 5 hours}}{2}[/tex]

[tex]=\dfrac{37.5}{2}=\$18.75[/tex]

Hence, each girl will receive $18.75.

an equation of the line with a slope of 2/3 and y-intercept of −8.

Answers

Answer:

y = 2/3x - 8

Step-by-step explanation:

Use the slope intercept form, y = mx + b, where m is the slope and b is the y intercept

Plug in the slope and y intercept:

y = mx + b

y = 2/3x - 8

So, y = 2/3x - 8 is the equation of the line.

round 6.24159 to the nearest hundredths

Answers

Answer:

6.24

you look at the number behind the hundredth place which is 1

Please help !!

What is the general equation to the √x?

Answers

x^1/2 or x to the 1/2 power

Stores open at the craziest hours on Black Friday Some
even open for their big sale on Thanksgiving Read the
conversation below to figure out when coch store opens
and fill in the table with opening times below.
"It boks like we are going to have to start our shopping of ter
our Thanksgiving meal. Our guests are leaving at four pm, right
when Old Navy opens, and Toys R Us opens one hour later
"Okay, but we need to be at Best Buy to get the great deal on
that TV an hour later."
"But what about the cheap tool set at Target? They open at the
some tmeos Best Buy! We can't be in two ploces at once."
"Well, I saw that Lowe's has the same set for even cheaper, and
they open hours AFTER Target does. We will be able to get
some sleep bettre we head there!"
"Okay, two hours of ter Lowe's opens, we will head to Som's
Club and check out their great deals on cameras
"Sounds good. But an hour ofter Sam's opens, we need to be at
Gander Mountain Sports to buy that new jacket I wanti"
DAY OPEN
TIME OPEN
Thanksgiving 4:00 pm
OLD NAVY
GANDER MOUNTAIN SPORTS
TARGET
LOWE'S
5:00 am
TAVE DHE

Answers

Answer:

Happy Thanksgiving, my friends.

Step-by-step explanation:

I need help!!!!

Write an equation of the line that passes through the points.

(0, −2), (4, −2)

Answers

First you need to find the slope:  (y2 - y1)/(x2 -x1) = (-4 -(-4))/(0-2) = 0.  So the line is horizontal, which means the y coordinate is constant and equal to -4, so the equation of the line is y = -4.

So...I'm stuck on this. HELP

Answers

Answers:

Yes the data can be modeled with a linear equation.

Processing fee = 42 dollars; Daily fee = 102 dollars

Max number of days you can rent house = 11 days

========================================================

Explanation:

Part 1

Let

x = number of days

y = total cost in dollars

Note how each time x goes up by 2, y goes up by 204 (since 450-246 = 204). This consistent pattern directly tells us we have a linear equation going on. The next section goes into more detail.

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

Part 2

The daily fee is directly tied to the pattern mentioned earlier. We have the cost going up by $204 each time 2 days go by. So the daily fee is 204/2 = 102 dollars per day.

You could also use the slope formula with say the first two columns of the table

m = (y2-y1)/(x2-x1)

m = (450-246)/(4-2)

m = 204/2

m = 102

This confirms the daily fee is $102.

You can use any two columns of the table that you want to get the slope. It doesn't have to be the first two columns.

Now use (x,y) = (2,246) along with m = 102 to find the y intercept. Like before you can use any column you want to form the (x,y) value.

y = mx+b

246 = 102*2+b

246 = 204+b

246-204 = b

42 = b

b = 42

The equation is y = 102x+42. The initial processing fee is $42. If you stayed at the house for x = 0 days, you still have to pay the fee y = 42.

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

Part 3.

Plug in y = 1200 and solve for x

y = 102x+42

1200 = 102x+42

1200-42 = 102x

1158 = 102x

102x = 1158

x = 1158/102

x = 11.3529411764706

x = 11

We round down to the nearest whole number. This way we clear the hurdle.

Note that if x = 11, then,

y = 102x+42

y = 102*11+42

y = 1164

which is under the $1200 budget

In contrast, plugging in x = 12 leads to

y = 102x+42

y = 102*12+42

y = 1266

which is over the 1200 dollar budget. This shows that x = 11 is the max number of days you can rent the house.

it for dreelliot only 2+2 = ? ​

Answers

Answer:

4

Step-by-step explanation:

+

that is as simple as I could put it you literally just need to count the skulls

1) In a survey, Eric, the team manager, asked all 120 soccer players in the league which drink they preferred during
and after the game.
Drink During Game After Game
Sports Beverage 70
10
Juice
10
80
Water
40
30
Directions: For each statement below, tell if it accurately represents the information from the survey AND
explain how you made each decision. (SHOW YOUR THINKING)
a. During the game, players prefer juice to water by a ratio of 4 to 1.
b. 25% of the players prefer water after the game.
c. More than half of the players prefer a sports drink during the game.

Answers

Your answer would be B
If this helped can I please get brainliest

what are the solutions of the following system?

[tex]\left \{ {{x -2y = -6} \atop {-2x + 4y = -3}} \right.[/tex]

Answers

Step-by-step explanation:

x-2y=-6 ...(1)

-2x+4y=-3 ...(2)

Multiply equation (1) by 2

So,

2x-4y=-12 ...(3)

Now add equation (2) and (3).

-2x+4y + 2x-4y = -3+(-12)

0=-15

It means that there is no solution of the given equations.

What is a possible solution set to x + 7 ≤ -9 ?

Answers

Answer:

Step-by-step explanation:

x + 7 ≤ -9 subtract 7 from both sides

x≤-16  this is your answer

If you're plotting it will be (-∞,-16]

Answer:

Step-by-step explanation:

For this equation, all it is asking is to replace the unknown value with a number that completes the equation. However, the number must make the equation valid. Here is a few examples that could be a valid solution to this problem:

1. -55 + 7 < -9

(you don't need to solve this equation to tell that it's less than negative nine.)

2. 22 + (-98) + 7 < -9

(this is more complicated, but you can still tell that the sum is less than negative nine.)

So, basicly all that you have to do is replace the missing value with a number that gives the eqquation a sum less than negative nine. Hope this helped!!! :)

PLEASE HELP ME LIKE IM GOING TO CRY ILL give you brainliest if the answer is correct and 20/40 points..............Ben participated in a race. During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. What equation could you write to solve for the number of hours Ben ran during each half of the race? Let y represent the number of miles in half the race. Write two equations, one for the first half of the race and one for the second half. How could you transform these two equations to be the same as the original equation you wrote to solve for x? What do you think this means about solving for the variables in a situation represented by two equations?

Answers

Answer:

Answer are at the bottom!

Step-by-step explanation:

First equation: y=5x

Second equation: y=5.5x

Unit rate:

x/5.5

5.5/5.5

x/1

Hope this helps!

5.(A.3A) The table represents some points on the graph
of a linear function. What is the slope of this
function?
х у
-6-7
0-10
6-13
12-16

Answers

Answer:

3

Step-by-step explanation:

Can you help with this problem

Answers

Answer:

The value of w is 3.

Step-by-step explanation:

Parallelograms have equal opposite side measures.

so,

6w = w +15

6w - w = 15

5w = 15

w = 3

Answer:

w=3

Step-by-step explanation:

The opposite arms of parallelogram are equal

So the equation is

6w=w+15

=>6w-w=15

=>5w=15

=>w=15/5

Therefore

w=3

If you find my answer helpful.then please mark me as brainliest

Unit 2 lesson 5 practice problem 3 in math workbook

You get 15 points if you answer this.

Answers

Answer:

what do you need help with???

Which of the following best describes the function graphed below? (1 point) A graph shows a straight slanting line that starts at a point on the y-axis and goes down to touch the x-axis. Question 14 options: 1) Nonlinear increasing 2) Nonlinear decreasing 3) Linear increasing 4) Linear decreasing

Answers

Answer:

linear decreasing

Step-by-step explanation:

cause it is a straight line and it's going down so it's decreasing.

Answer:

linear decreasing

Step-by-step explanation:

the answer that will appear before mine is right

What is the sum of 6 and y

Answers

Answer:

6+y

Step-by-step explanation:

6+y is the ans as the question has asked to sum of them but it has not given any other clues

Answer:

i got 6y

Step-by-step explanation:

The height reached by a model rocket can be calculated using the equation h= -16t2 + vt +
where t is the time the rocket is in flight, vis the rocket's velocity, and n is the rocket's beginning
height.
Calculate the height, h at 3 seconds given that the rocket travels 85 feet per second and starts on a
launch pad 15 feet off the ground.
Knowns:
t = 3 seconds
v = 85 feet per second
n = 15 feet
If we plug all those values in, our Formula becomes h= (–16.32) + (85.3) + (15).
Solve for h

Answers

Answer:

Step-by-step explanation:

9.0

The height (h) reached by model rocket will be equal to 126 ft.

It is given that the height reached by a model rocket can be calculated using the equation h = - 16 [tex]t^{2}[/tex] + ( v × t ) + n

We have to calculate the height (h) at 3 seconds.

What is algebra ?

Algebra is the branch of mathematics that deals with various symbols and the arithmetic operations such as multiplication , division , etc.

As per the question ;

h = - 16 [tex]t^{2}[/tex] + ( v × t ) + n   ---------- Equation 1

t = time rocket is in flight = 3 seconds

  v = velocity at which rocket travels = 85 ft. per second

  n = height of rocket at beginning = 15 ft

Putting these values in equation 1 , we get.

h = - 16 × ( 3² ) + (85) × (3) + 15

h = - 16 × 9 + 255 + 15

h = -144 + 270

h = 126 ft.

Thus , the height (h) reached by model rocket will be equal to 126 ft.

To learn more about algebra click here ;

https://brainly.com/question/19253676

#SPJ2

What is the length of a segment with endpoints at (-3,4) and (4,4)

Answers

Answer:

The length is 8

Step-by-step explanation:

please help me please please nice brainly people pls

Answers

Answer:

I think your answer is B= 12.

Step-by-step explanation:

Its x times 1 .33333 = y

brainliest?

B=12 its x time 1.33333 = y

Natalie wants to start a business, she is going to make bracelets. She spends $40 for a braiding device and materials to start her business. Each times she makes a bracelet it costs her $8 in materials and packaging. Natalie sells her bracelets for $8 each.

Answers

y=9+9 because when you take that factor off you add 8 + 1

The area of a square is 1,521 cm2. Find the length of a side of the square by
prime factorisation method.​

Answers

9514 1404 393

Answer:

  39 cm

Step-by-step explanation:

  1521 = 3·3·13·13 = (3·13)² = 39²

The length of the side of the square is 39 cm.

If 20 apples cost $7, what is the unit cost?

Answers

Answer:

35 cents per apple

Step-by-step explanation:

its 7 / 20 and you get 0.35

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