While Dr. Andy operated, he thought of consecutive odd integers. His intensas
such that 4 times the sum of the first and fourth was 12 greater than 3 times them
the second and third. What were the first four integers on Dr. Andy's list?

Answers

Answer 1

Let's start with the two consecutive numbers. We don't know what are the two numbers that are side by side (consecutive), so we'll use variables but with a twist...instead of x and y, we'll use x for the first number and x+1 for the other number because the other number is 1 more than the value of x. So part of the problem looks like this: (x)+(x+1).

The problem says "the sum of one-third of the first and one-fourth of the second equal 9." One-third of the first would be 1/3(x) and one-fourth of the second would be 1/4(x+1) so if the sum is 9, then the problem is:

1/3(x)+1/4(x+1)=9.

 

Since we need to solve for x, we must remove the fractions. Right now they have different denominators so we need to make them the same. The least common denominator is 12 so that's the denominator to use, thus...

1/3x becomes 4/12(x) and 1/4(x+1) becomes 3/12(x+1).

 

Now the equation is 4/12(x)+3/12(x+1)=9

 

Multiply both sides by 12 so the denominators are gone:

 

[12•]4/12x+3/12(x+1)=9•12

4x+3(x+1)=108

 

Using distribution, it's now 4x+3x+3=108. Continuing on with the math...

7x+3=108

7x=105

x=15

 

We found x! If x=15 the the next number must be 16. Let's check the math: Does 1/3(15)+1/4(16)=9?

5+4=9 and 9=9 so YES! The numbers are 15 and 16


Related Questions

One year of membership at a rec center includes a fixed monthly cost and a one-time membership fee. The following table contains some of the ordered pairs for this linear relationship between the number of months enrolled and the total cost paid for the membership.
Which graph correctly represents this linear relationship?

PLS ANSWERR AND EXPLAIN HOW YOU GOT THE ANSWE PLSSS YOULL BE MARKED AS BRAINLIST.just plss helpp

Answers

Answer:

Graf 2 is correct

Step-by-step explanation:

The correct graph that represents the linear relationship is Graph B with a positive slope.

The table shows a linear relationship between the number of months enrolled and the total cost paid for the membership.

To determine which graph represents this relationship, we need to check if the cost increases or decreases as the number of months enrolled increases. If the cost increases, it means the graph should have a positive slope. If the cost decreases, it means the graph should have a negative slope.

Let's look at the table:

Number of Months Enrolled                                   Total Cost

1                                                                               75

2                                                                               100

3                                                                                 125

As the number of months enrolled increases, the total cost increases. Therefore, the graph should have a positive slope. From the given options, the graph that correctly represents this linear relationship is Graph B, which has a positive slope.

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What is 1 + 7k + k = -7? With work provided

Answers

Answer:

k=-1

Step-by-step explanation:

HELP! GIVING OUT BRAINLIEST!

find the probability that the sum of 2 randomly chosen numbers (0,1,2,3,4,5,6,7,8,9) is no greater than 10

Answers

Answer:

1 po iyan tama iyan trust mr

if 2y - 7 = 18 what is the value of 2y + 3

Answers

Hope it help, you need to solve the equation and found 2y. Once you did you just place the value of 2y on 2y+3. Like I did in the picture

A spinner included in a board game has four equally sized sections, as pictured below.

If a player spins and gets a 3, what is the probability they will get 3 on the next spin?
a. 0.25
b. 0.5
c. 0
d. 1

Answers

Answer:

.25

Step-by-step explanation:

Since it's a random and equal chance, you can completely disregard what he got previously. There is always a 1 in 4 chance no matter what. .025 is correct.

9514 1404 393

Answer:

  a.  0.25

Step-by-step explanation:

A spinner in an algebra problem is generally considered to have equal probabilities for equal areas. It is also generally considered to have the characteristic that the value produced by the next spin is independent of the value produced by the last spin.

With those assumptions in mind, the probability of getting a 3 is always 0.25. It is never anything else with this 4-section spinner.

If 2.2 is 1/5 of a fraction, what is 2.8 of a fraction?​

Answers

Answer:

the fraction of 2.8 is 14/5 u can simplify it bye dividing 14 by 5 and u will get a mixed number

Which of the following is a run on sentence

Answers

Answer:

It is defiantly either C or D.

Step-by-step explanation:

It's not A because it has a period with means there is 2 sentences and not 1.

It's not B because it does not have multiple commas.

It might most likely be C because it has the most amount of commas.

If I'm wrong about C, than try D.

Determine the slope and y-intercept of the linear function represented by the following scenario: Brooke and her friends decide to go bowling. The cost for the group is $15 for shoe rentals plus $4.00 per game.​

Answers

the slope is 4 because it is four per person so it can change

the y-intercept is 15 because it is the price to just go without anything

I’m not good at explaining but hope this helps!!

The equation is btw

y=4x+15

The slope of the given scenario will be 4.

The y - intercept of the given scenario will be 15.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The cost for the group is $15 for shoe rentals plus $4.00 per game.​

Now,

Let number of games = x

And, Total cost of the bowling's = y

Here, The cost for the group is $15 for shoe rentals plus $4.00 per game.​

So, We can formulate;

⇒ y = $4.00x + $15

⇒ y = 4x + 15

Compare with the standard form of equation of line y = mx + c, we get;

⇒ Slope = 4

And, The y - intercept = 15

Thus, The slope of the given scenario will be 4.

The y - intercept of the given scenario will be 15.

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Someone help please

Answers

Answer:

[tex]6^\frac{1}{10}[/tex]

It appears that the answer is 6 1/10 and I know because I aced the test all answers correct lol

Rewrite the equation below so that it does not have fractions.

3/4x-5=3/8

Do not use decimals in your answer

Answers

Answer:

6x-40=3

Step-by-step explanation:

3/4 x -5 =3/8

Multiply each side by 8 to get rid of the fractions.

8(3/4x -5 ) =8*3/8

Distribute

6x-40=3

>> Answer

_________

[tex] \: [/tex]

[tex] \frac{3}{4} x - 5 = \frac{3}{8} [/tex]

[tex] \frac{3}{4} x = \frac{3}{8} + 5[/tex]

[tex] \frac{3}{4} x = 5 \frac{3}{8} [/tex]

[tex] \frac{3}{4} x = \frac{43}{8} [/tex]

[tex]x = \frac{43}{8} \times \frac{4}{3} [/tex]

[tex]x = \frac{172}{24} [/tex]

[tex]x = \bold{7 \frac{1}{6}} [/tex]

help me on maths asap​

Answers

Answer:

x= 105°

Step-by-step explanation:

one interior angle of a hexagon is=120°

one interior angle of an octagon is=135° 360-255= 105

The size of the angle between the two regular polygons, marked x, is: 105°.

Interior Angle of a Regular PolygonAn interior angle of a regular polygon = [(n - 2)180]/n.Octagon has 8 sides, while hexagon has 6 sides.

Thus,

x° = 360 - sum of one interior angle of the regular octagon and hexagon.

One interior angle of octagon = [(8 - 2)180]/8 = 135°

One interior angle of hexagon= [(6 - 2)180]/6 = 120°

x° = 360° - 135° - 120°

x° = 105°

Therefore, the size of the angle between the two regular polygons, marked x, is: 105°.

Learn more about regular polygons on:

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what is -10 . -2 reflected to the y axis

Answers

(10, -2) is the answer when reflected to the y axis.

It costs $7 each way to travel to work each weekday by train. What is the weekly expense each way?

Answers

Answer:

it could either be 35 or 70

Step-by-step explanation:

Evaluate and simplify the
expression when x=10 and y=7.
?
5+ y
6x

Answers

5+y=12 and 6x=60
because 5+7=12 and 6x10=60

2 √7+3√7

can you guys give me the answer and explanation

Answers

Answer:

5[tex]\sqrt{7}[/tex]

Step-by-step explanation:

This is similar to collecting like term in algebra

2[tex]\sqrt{7}[/tex] + 3[tex]\sqrt{7}[/tex]

= (2 + 3)[tex]\sqrt{7}[/tex]

= 5[tex]\sqrt{7}[/tex]

is -4.9 bigger or smaller then 3.6

Answers

Answer:

Smaller

Step-by-step explanation:

On the number line, 3.6 is on the right side while -4.9 is on the left side. The closer to the right on the number line, the bigger the number.

Answer:

its smaller because negative numbers are to the left of positive numbers and when a number is to the left of another number its less than

A ball was thrown off of a 32 foot bridge and reached a maximum height of 50 feet after 3 seconds. How long
was the ball in the air?

a. 10 seconds
b. 6 seconds
c. 32 seconds
d. 8 seconds

Answers

Ok so if the ball reaches maximum height after 3 seconds and that height was 50 and your already 32 feet high 50-32= 18 than 18/3= 6 your rising and descending 6 feet per second so the answer is 68/6 which equals 11.3 so most likely it’s A

Use the following figure to answer the questions. Isosceles trapezoids ABCD and WXYZ are similar to each other.



Determine which of the following statements are NOT TRUE for similar isosceles trapezoids ABCD and WXYZ. Select all situations that apply.

Answers

Answer:

Step-by-step explanation:

Answer:

AD is not parallel to BC -- they are going opposite directions

AD does not equal DC -- there is nothing saying that they are congruent in length

YX is not parallel to ZW -- they are going opposite directions

The Quadratic equation y=0.5(x-1)(x-n) has an x - intercept at (1,0) and a vertex at (-2,4.5). what is the value of n A -5 B -2 C 2 D 5

Answers

Step-by-step explanation:

the point being that a quadratic equation has 2 x-intercepts (or solutions of x for y = 0).

the advantage of this nice form the equation is written in is, that we see immediately both conditions, when y can be 0 : one of the bracket expressions must be 0.

so, the point (1, 0) covers (x-1).

we get the solution for (x-n), when we consider that such a quadratic function is simply a parabola and is symmetric around its vertex point.

the x value of the vertex (-2) tells us, that it is 3 units on the left side of the (1, 0) x-intercept point.

due to the symmetry of the curve the second x-intercept point must be even further to the left with additional 3 units distance in x direction.

so, -2 - 3 = -5

and A is the correct answer option.

please help me if you can if your going to say I'm cheating i don't care cause i know I'm not thanks!!​

Answers

Answer:

13.9 sorry if I'm wrong just trying to help.

Step-by-step explanation:

first plug in your numbers

a*2+ b*2= c*2

12*12= 144

7*7=49

144+49= 193

square root of 193: 13.89244399

rounded to nearest tenth is 13.9

Please need help 15 points

Answers

A=sss……………………..okokokokokok

"Four is three times the sum of a number and two."
turn this into an equation

Answers

Answer:

4=3(n+2) or if you want the unknown variable to be x, then 4=3(x+2)

Step-by-step explanation:

Four is  :  4=

3 times the sum  :  3(_+_)

sum of a number and two  :  n+2

4=3(n+2)

Hello! :)

4=3(z+2)

Explanation:

4 is means 4=

3 times the sum of a number and two. There's a hint that tells us that we should multiply 3 by both the number and two, and here's how we indicate that:

3(z+2)

Let our number be z.

The sum of two numbers means we add the numbers together.

So, our equation looks like this:

4=3(z+2)

Hope it helps you!

If you have any query, feel free to ask!

~An excited gal

[tex]MagicalNature[/tex] here to help

Solve the equation for x.

5x = -60

Answers

Answer:

x=-12

Step-by-step explanation:

5x/5=1x = -60/5=-12

x=-12

Answer:

-12

Step-by-step explanation:

5x=-60

Divide both sides by 5 to isolate

X=-12

A cyclist rode at an average speed of 15 mph for 30 miles. How long was the ride? 0. 5 hours 1 hour 2 hours 3 hours.

Answers

Answer:

2 Hours

Step-by-step explanation:

using the relationship

distance = speed × time, then

time =[tex]\frac{distance}{speed}[/tex]  =[tex]\frac{30}{15}[/tex]  = 2 hours

Find the length of the hypotenuse of a right triangle where the perpendicular sides are 3 in. And 4in. In length

Answers

Answer:

5 inches

Step-by-step explanation:

To find the hypotenuse or any side of a right triangle, use the Pythagorean theorem. This is [tex]a^2+b^2=c^2[/tex] where a and b are the perpendicular sides and c is the hypotenuse. So, plugin  3 and 4 for a and b. This gives 9+16=c^2, which is equal to 25=c^2. Then, take the square of both sides to get c=5.

Another way to solve this is to know the triples. Triples are right triangles that have integers for all of their sides. The triple 3,4,5 is the smallest and most common triple.

Harry buys a wand for $12.50 plus 8% tax. Ron buys his sister a diary for $13 plus 8% tax. Write the sum, in dollars, that Harry and Ron paid, including tax.​

Answers

9514 1404 393

Answer:

  $27.54

Step-by-step explanation:

The straightforward way to do this is to compute the tax and total on each amount, then add those together. There is an easier way.

  ($12.50 + 0.08·12.50) + ($13.00 + 0.08·13.00) = $12.50·1.08 +13.00·1.08

  = 1.08($12.50 +13.00)

  = 1.08·$25.50

  = $27.54

Together, Ron and Harry paid a total of $27.54.

PLEASE HELP NUMBER 3 ASAP ILL GIVE BRAINLIEST THANKS

Answers

2 a’s bc 80 - 30 is 50 / 25 is 2

Answer:

Sarah gets 2 A's.

Step-by-step explanation:

Sarah's mother gives her $10 for each B she receives. She received 3 B's, so 3x10 is 30. You subtract 80-30. You get 50. She receives $25 for each A. You then divide 50 by 25, and are left with 2. The answer is that Sarah received 2 A's on her report card.

Hope you have a great day,

Ginny

Elizabeth wants to buy her mother a pair of pearl earrings for Mother’s Day. The earrings cost $50. The sales tax rate is 7.5%. What is the total amount Elizabeth will have to pay to purchase this gift?

Answers

Answer:

$46.25

Step-by-step explanation:

50 divided by 7.5% equals 3.75

Minus 3.75 from 50 to find the removed amount.

Answer:

Cost of the gift = $53.75

Step-by-step explanation:

Total cost of the gift = cost of the earrings + (cost of the earrings × sale tax)

Cost of the gift = $50 + ($50 × .075)                      7.5% = .075

Cost of the gift = $50 + $3.75

Cost of the gift = $53.75

Please help me! Thanks in advance

Answers

Answer:

the answer is

Step-by-step explanation:

that im not good with math so good luck

PLEASE HELP!!!

Find the slope of the line graphed below.

Answers

Answer:

slope = -8/5

Step-by-step explanation:

m= y2-y1/x2-x1

m=(4-(-4))/(-1-4)

m= 8/-5

Answer:

-8/5

Step-by-step explanation:

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