Find three consecutive integers such that the sum of twice the smallest and 3 times the largest is 126.

Answers

Answer 1

Answer:

The addition is one of the four fundamental mathematical operations. The three consecutive terms are 24, 25, 26.

What is Addition?

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Let the first integer be represented by x. Then the other two integers will be (x+1) and (x+2).

Since it is given that the sum of twice the smallest and 3 times the largest is 126. Therefore we can write,

2x + 3(x+2) = 126

2x + 3x + 6 = 126

5x = 126 - 6

5x = 120

x = 120/5

x = 24

Thus, the three consecutive terms are,

x = 24

x + 1 = 25

x + 2 = 26

Hence, the three consecutive terms are 24, 25, and 26.

Learn more about Addition here:

brainly.com/question/14092461

#SPJ2

Answer 2

Answer: x-smallest
y middle
z largest

x+1=y
y+1=z
2x+3z=126

2x+ 3(y+1)=126
2x+3y+3=126
2x+3(x+1)=123
5x=120
x=24

y=25

z=26

Related Questions

What is the value of x in the equation 2x+7=1
Please help I need to know before tomorrow
In the past 4 years, a sporting goods store had two yearly losses of $28,000 and $42,000 and two yearly profits of $104,000 and $10,000. What was the net profit or loss over 4 years? A. –$70,000 B. $114,000 C. $44,000 D. –$44,000
Gold in the form of solid cylinders will be molded into solid blocks. Each cylinder has a diameter of 6.19 cm and a height of 6 cm. Each solid block will have a volume of 360 cm3. How many cylinders of gold will it take to mold one block of gold?
A 250 ml bottle of water treatment liquid will treat up to 625 litres of water. Given that 1 cubic meter=1000 litres, how much treatment liquid is needed to treat a water tank of 224m cubed when full. Please show workings. Many thanks

How many solutions can be found for the equation 3x − 2 = 3x + 5?a)zero
b)one
c)two
d)infinitely many

Answers

There is no solution to the equation, the sides are uneven. so, option A is correct.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given equation is;

3x − 2 = 3x + 5

Subtract 3x both sides;

3x − 2 - 3x = 3x + 5 - 3x

-2 = 5

Thus, there is no variable left in the equation.

Hence, there is no solution to the equation, the sides are uneven. so, option A is correct.

Learn more about equations here;

brainly.com/question/10413253

#SPJ2

Please help with geometry

Answers

Answer : 50 degree

To find angle 1 , we apply outside angle theorem . Refer to the diagram attached below.

Measurement of arc EF=140 degrees

Measurement of arc GH = 40

Angle D = angle 1

Theorem says

$angle D = (arc(EF)-arc(GH))/(2)$

Now we plug in the values

$angle 1 = (140-40)/(2)$

angle 1 = 50

Measurement of angle 1 = 50 degrees

Simplify the expression z2-z(z+3)+3z

Answers

$z^2-z(z+3)+3z=\n z^2-z^2-3z+3z=\n 0$

Solve. Good luck! Please do not try to google this. $(x^2+x-2)/(6x^2-3x) = √(2x) + (3x^2)/(2)$

Answers

$(x^(2) + x - 2)/(6x^(2) - 3x) = √(2x) + (3x^(2))/(2)$
$(x^(2) + 2x - x - 2)/(3x(x) - 3x(1)) = (2√(2x))/(2) + (3x^(2))/(2)$
$(x(x) + x(2) - 1(x) - 1(2))/(3x(x - 1)) = (2√(2x) + 3x^(2))/(2)$
$(x(x + 2) - 1(x + 2))/(3x(2x - 1)) = (2√(2x) + 3x^(2))/(2)$
$((x - 1)(x + 2))/(3x(2x - 1)) = (2√(2x) + 3x^(2))/(2)$
$((x - 1)(x + 2))/(3x(2x - 1)) = (2√(2x) + 3x^(2))/(2)$
$3x(2x - 1)(2√(2x) + 3x^(2)) = 2(x + 2)(x - 1)$
$3x(2x(2√(2x) + 3x^(2)) - 1(2√(2x) + 3x^(2)) = 2(x(x - 1) + 2(x - 1))$
$3x(2x(2√(2x)) + 2x(3x^(2)) - 1(2√(2x)) - 1(3x^(2))) = 2(x(x) - x(1) + 2(x) - 2(1)$
$3x(4x√(2x) + 6x^(3) - 2√(2x) - 3x^(2)) = 2(x^(2) - x + 2x - 2)$
$3x(4x√(2x) - 2√(2x) + 6x^(3) - 3x^(2)) = 2(x^(2) + x - 2)$
$3x(4x√(2x)) - 3x(2√(2x)) + 3x(6x^(3)) - 3x(3x^(2)) = 2(x^(2)) + 2(x) - 2(2)$
$12x^(2)√(2x) - 6x√(2x) + 18x^(4) - 9x^(3) = 2x^(2) + 2x - 4$
$12x^(2)√(2x) - 6x√(2x) = -18x^(4) + 9x^(3) + 2x^(2) + 2x - 4$
$6x√(2x)(2x) - 6x√(2x)(1) = -9x^(3)(2x) - 9x^(3)(-1) + 2(x^(2)) + 2(x) - 2(2)$
$6x√(2x)(2x - 1) = -9x^(3)(2x - 1) + 2(x^(2) + x - 2)$

Final answer:

To solve the given equation, first simplify both sides. Factor the numerator and denominator on the left side, then solve the quadratic equation obtained.

Explanation:

To solve the given equation:

$(x^2+x-2)/(6x^2-3x) = √(2x) + (3x^2)/(2)$

First, we need to simplify both sides of the equation. By factoring the numerator and denominator of the left side, we get:

x+22x.

Next, we can simplify the equation further by multiplying both sides by 2x. Finally, we solve the quadratic equation obtained by moving all terms to one side:

2x+4.

Therefore, the solution to the given equation is x = -2.

Learn more about Solving Equations here:

brainly.com/question/17595716

#SPJ12

Find the perimeter of the figure. Answer exactly or round to at least 2 decimal places.-width is 5 and height is 5

Answers

all you have to do is add up the angles total will equal up to 32.85

That's a square and a semicircle so we should calculate the perimeter for each one and then add them together.

Let's start with the easy one: the square
The perimeter of a square = 4x where x = one side of the square
Since the width of the shape is 5, that means the other three sides of the square should also be five so:

perimeter of square = 4(5)
perimeter of square = 20 units

Now let's find the perimeter of the semicircle.
That equation is this:

perimeter of semicircle = 1/2(π x diameter) + diameter

We know that the width is 5 which means the diameter is 5.
Let's plug that in!

perimeter of semicircle = 1/2(π x 5) + 5

Multiplying pi by 5 and dividing it in half will give us a decimal, so we have to round that to the second place:

perimeter of semicircle = 1/2(5π) +5
perimeter of semicircle ≈ 7.85 + 5
perimeter of semicircle ≈ 12.85 units

Like we said at the beginning, this is two shapes in one so we have to add the perimeter of the square to the perimeter of the semicircle

perimeter of square = 20 units
perimeter of semicircle ≈ 12.85 units

20 + 12.85 = 32.85 units

So the perimeter of the shape = 32.85 units

The length of one side of an equilateral triangle is 6 square root 3 meters. Find the length of one altitude of the triangle.