Two sets of three consecutive integers have a property that the product of the larger two is one less than seven times the smallest.set up and solve an equation that can be used to find both sets of integers

Answers

Answer 1

Answer:

(x + 1)(x + 2) = 7x - 1

{1, 2, 3} and {3, 4, 5}

Step-by-step explanation:

Let the three consecutive integers be x, x + 1, and x + 2.

(x + 1)(x + 2) = 7x - 1

x² + 3x + 2 - 7x + 1 = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0

x - 3 = 0  or  x - 1 = 0

x = 3  or  x = 1

For x = 1,

x = 1, x + 1 = 2, x + 2 = 3

For x = 3,

x = 3, x + 1 = 4, x + 2 = 5

Answer: {1, 2, 3} and {3, 4, 5}


Related Questions


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1.‌ ‌What‌ ‌fraction‌ ‌of‌ ‌the‌ ‌big‌ ‌rectangle‌ ‌does‌ ‌the‌ ‌
small‌ ‌rectangle‌ ‌represent?‌ ‌Explain‌ ‌your‌ ‌
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Answers

Answer:

1. 1/4

2. 1/2

Step-by-step explanation:

1. Without measuring I can't be 100% sure, but it looks like the smaller rectangle is 1/4 of the big rectangle, as the side lengths of the smaller rectangle are half those of the big rectangle.

2. If he delivered 3/8 of his newspapers in the first hour, then he had:

1 - 3/8 = 5/8 of his newspapers left to deliver after the first hour.

If he delivered 4/5 of the remaining newspapers in the second hour:

4/5 ths of 5/8 = 4/5 x 5/8 = 20/40 = 1/2

He delivered 1/2 of all the newspapers in the second hour

One inch on a map equals
150 miles. What do 3 1/2 inches
represent?

Answers

If 1 inch = 150 miles, we can use fractions (ratios) to determine what 3 1/2 inches would be

Since 1 is correlated to 150, they would be on the same fraction

1/150 (it really doesn’t matter which one is on top and which one is on the bottom)

And since 1 and 3 1/2 are both inches, they both go on the same side of the fraction. X would be a placeholder value for the miles

1/150 = 3.5/x

Multiply x

x • 1/150 = 3.5

Divide by 1/150 or multiply by 150 (they are the same in this case)

x = 525 miles

Or, more simply in this case, just multiply 3.5 inches by 150 miles

3.5 • 150 = 525 miles

y = -3x+5

which of the following equations would create a system of equations with INFINITE SOLUTIONS?


A.y=5+ -3x
B.y=5x+3
C.y=3+5x
D.y=1/3x-5

Answers

Answer:

A. y=5+ -3x that should be the answer

Please help me with this please and thank you please actually help me

Answers

Answer:

-5, -8, and -11

Step-by-step explanation:

We can see it is becoming negative so, it is going -3.

Find the equation of the line that passes through (1,3) and is perpendicular to 2y=2x-1
Leave your answer in the form of y=Mx+c

Answers

Answer:

y = -x + 4

lmk if it's wrong lol

If the discriminant is zero how many solutions are there:.

Answers

Answer: 1

If the discriminant is zero, there is only one solution with a multiplicity of two.

Which statements are accurate about the dilation? Check all that apply. The dilation is a reduction. The scale factor is between 0 and 1. A is the image of A' Point O is the center of dilation. OB = BB'.

Answers

Answer:

A,B,D

Step-by-step explanation:

Trust me just did it on edge

Answer:

A, B, D is your answer...

Step-by-step explanation:

In the diagram below, FG is parallel to CD. If the length of C D is the same as the
length of FE, CE = 17, and FG = 6, find the length of FE. Figures are not
necessarily drawn to scale. State your answer in simplest radical

Answers

Answer: sqrt(102)

Step-by-step explanation:

We know that triangles GFE and DCE are similar by AA.

If we let CD=FE=x, then we can set up a proportion. Namely,

CE/FE = CD/FG

17/x = x/6

x^2 = 102 -> x=sqrt(102)

what is the resolution war about?

Answers

Answer:

The War Powers Resolution requires the president to notify Congress within 48 hours of committing armed forces to military action and forbids armed forces from remaining for more than 60 days, with a further 30-day withdrawal period, without congressional authorization for use of military force (AUMF) or a declaration ...Step-by-step explanation:

If g (x) = -x + 2 and d (x) = x 2 + 2, what is d (g(x))?
+

Answers

Answer : x^2-4x+6
Solution in pic

Need help math question about Two Lines and Transversals
The right and accurate answer will get brainiest and a thanks!

Answers

Corresponding angles

pls help ill give brainliest i put pictute down

Answers

Answer:

Option D

Step-by-step explanation:

Given the following question:

Airline makes $98,410
Truck driver makes $38,200

Annually means in a year so the airline makes $98,410 and the truck driver makes $38,200 in a year.

Now in order to find the amount the two make in 20 years we have to multiply:

[tex]98410\times20=1968200[/tex]
[tex]38200\times20=764000[/tex]

Now since the question asks "how much MORE" does the airline make we have to subtract:

[tex]1968200-764000=1204200[/tex]
[tex]=1204200[/tex]

The airline makes "$1,204,200 more dollars" than the truck driver, or option D.

Hope this helps.

Answer:

The answer is either D or B

Step-by-step explanation:

98,410 x 20 is 1,968,200 so

it might be closer to D or B instead.

Sorry if this is wrong.

But If it is right Can I get brainlest pls.

help? The ratio of 1000 ml to 2 liters is??

Answers

We know that, 1 litre = 1000 ml

Then, 2 litres = 2000 ml

Hence, the required ratio of 1000 ml to 2000 ml be

= 1000 : 2000

= 1 : 2

1 litres =1000ml

then

1000:2000

1:2

I don't understand the question.

Answers

Answer:

Distribution means to spread the product throughout the marketplace such that alarmed number of people can buy it.

When solving an ______, use inverse operations to undo the operations.

Answers

equation/algebraic equation

Someone please help me with this I can’t get it wrong

Answers

Answer:

a = 7

Step-by-step explanation:

Using the Cosine rule in the triangle

a² = b² + c² - (2bc cosA )

   = 2² + (5[tex]\sqrt{3}[/tex] )² - (2 × 2 × 5[tex]\sqrt{3}[/tex] × cos30° )

  = 4 + 75 - (20[tex]\sqrt{3}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) ← exact value of cos30°

 = 79 - ( 10 × 3)

 = 79 - 30

 = 49 ( take square root of both sides )

a = [tex]\sqrt{49}[/tex] = 7

 

Answer:

a = 7

Step-by-step explanation:

a² = b² + c² - 2bc × cos α

a² = 2² + ( 5√3 )² - 2 × 2 × 5√3 × [tex]\frac{\sqrt{3} }{2}[/tex]

a² = 49

a = 7

A bag contains 16 blue marbles, 12 red marbles, and 12 green marbles. If Malik randomly draws a marble from the bag (and puts it back) 25 times, how many times should he expect to pull a blue marble? Enter your answer as a number, like this: 42

Answers

The expected number of times he picks a blue marble is the mean of the blue marbles

Malik should expect to pick a blue marble 10 times when he picks 25 marbles

How to determine the expected times

The given parameters are:

Blue = 16

Red = 12

Green = 12

The total number of marbles is:

Total = 16 + 12 + 12

So, we have:

Total = 40

When he picks 25 marbles, the expected number of blue marble is:

Expected = Blue/Total * 25

So, we have:

Expected = 16/40 * 25

Evaluate the product

Expected = 10

Hence, he should expect to pick a blue marble 10 times when he picks 25 marbles

Read more about expected values at:

https://brainly.com/question/15858152

What lines are lines of symmetry of a rectangle?

Question 5 options:

Line x and y


Line x only


Line x, y, and m


Line x, y, m, and p

Answers

The answer is A. Line x and y


Mr. Smith bought 7 apples, 5 mangoes and 8 oranges. What fraction of the fruits are mangoes? ​

Answers

Answer:

1/4

Step-by-step explanation:

First we need to find the total of the fruit

7+5+8 = 20

The fraction of the fruit that is mangoes is the number of mangoes over the total.

mangoes / total = 5/20 = 1/4

5/20

Explanation: Add 7+5+8 which means the bottom number is 20 and if there are 5 mangos it equals 5\20

There is a bag filled with 2 blue, 4 red and 3 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?

Answers

Answer:

.753

Step-by-step explanation:

Let Ps = probability both marbles are the same color.

Let Pd = probability both marbles are a different color.

Pd = 1 -Ps

Let Pb = probability both marbles are blue

Let Pr = probability both marbles are red.

Let Pg = probability both marbles are green

Pb= 2/9 * 1/9 = 2/81

Pr= 4/9 * 3/9 = 12/81

Pg=.3/9 * 2/9= 6/81

Ps = Pb + Pr +Pg= 20/81

Pd =1-Ps= 61/81 = .753

Is this correct?


Find the Perimeter of the figure below, composed of a rectangle and a semicircle.
Round to the nearest tenths place.

Answers

Answer:

53.7

Step-by-step explanation:

Rectangle: lenth = 14, width = 2 * 5 = 10

perimeter of reactangle (3 sides) = 14 + 10 + 14 = 38

perimeter of semicircle = π * 5 = 3.14 * 5 = 15.7

Total perimeter = 38 + 15.7 = 53.7

Answer:

Step-by-step explanation:

Rectangle:

Length = 14 units

Width = diameter of the semicircle = 2*5 = 10 units

Circumference  of circle = πr = 3.14 * 5 = 15.7 units

Perimeter of the figure = 14 + 10 + 14 + 15.7 = 53.7 units

.It makes sense to measure the number of students in a class in partial quantities.
True or False

Answers

maybe it’s true? try it

only one question today

Answers

Answer:

c) Solve for the second equation for y and then substitute this value int the first equation.

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

always choose the equation where the variable is alone.

second equation has a lone 'y' and all that needs to be done is subtracting 2x from both sides of equal sign.

find area of shaded regions​

Answers

Answer:

140.8584073

Step-by-step explanation:

Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape. The result is the area of only the shaded region, instead of the entire large shape. In this example, the area of the circle is subtracted from the area of the larger rectangle.

please help with this quesriom

Answers

Answer:

True

Step-by-step explanation:

Just a guess

HELPPPP PLSS help me and i willl give u brainlylist

Answers

Answer : 34.5

A= Length * Width
you need to do the square root of 1190 since all sides of a square are equal. You get a number that is very long but it says to round to the tenths place and that gives 34.5 mm to be the answer .

What is the solution to this equation?

−4(2m − 7) = 3(52 − 4m)

Answers

Answer:

m = 32

Step-by-step explanation:

-4(2m-7) = 3(52 - 4m)

-8m + 28 = 156 - 12m

-8m + 12m = 156 - 28

4m = 128

m = 32 Ans...

The required solution is m = 32 to the given equation −4(2m − 7) = 3(52 − 4m).

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given an equation as

⇒ -4(2m-7) = 3(52 - 4m)

Apply the distributive of multiplication,

⇒ -8m + 28 = 156 - 12m

Rearrange the terms of m in the above equation,

⇒ -8m + 12m = 156 - 28

Apply the subtraction operation,

⇒ 4m = 128

Divided by 4 both sides of the equation, we get

⇒ m = 32

Therefore, the solution is m = 32 to the given equation −4(2m − 7) = 3(52 − 4m).

Learn more about the equation here:

brainly.com/question/13947055

#SPJ2

help plssssss
hsjehwhabsb

Answers

um i cant see it clearly

Find the unit rate
12 boxes can hold 96 books

Answers

Answer

8 books per box

Step-by-step explanation:

one box can hold 8 books

solve the following inequality

Answers

Answer:

X>30

Step-by-step explanation:

you add 9 to both sides to get X by itself, then add 9+21 and get 30. That’s the answer

♪Answer :x - 9 ≥ 21 x ≥ 21 + 9 x 30
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