All categories

3 years ago

If 2 X + 1 ,2 x-1 and 3 X + 4 are in AP find the value of x

Mathematics

1 answer:

julia-pushkina [17]3 years ago

6 0

Answer:

x = - 7

Step-by-step explanation:

Given that the terms are in AP , then

a₃ - a₂ = a₂ - a₁ , substitute values

3x + 4 - (2x - 1) = 2x - 1 - (2x + 1) ← distribute and simplify both sides

3x + 4 - 2x + 1 = 2x - 1 - 2x - 1

x + 5 = - 2 ( subtract 5 from both sides )

x = - 7

You might be interested in

_____ appear to never cross or meet and are always the same distance apart

Akimi4 [234]

Answer: parallel lines

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago

8 km<br> b<br> 17 km<br><br><br> What is the length of the missing leg?

Bond [772]

The answer is 15.

17^2-8^2=225
sr of 225= 15
:))

7 0

3 years ago

This question relates to concepts covered in Lectures 1 & 2. You can use any of the excel files posted to work through the q

liubo4ka [24]

Answer:

mean of this demand distribution = 100

Step-by-step explanation:

To find the mean of this demand distribution;

Mean = Expected vale = E[x]

for discrete provability function,

we say E[x] = ∑(x.p(x))

x p(x) x.p(x)

10 0.1 1

30 0.4 12

60 0.4 24

90 0.7 63

∴ ∑(x.p(x)) = ( 1 + 12 + 24 + 63 )

∑(x.p(x)) = 100

7 0

3 years ago

Could someone please help me

mamaluj [8]

The second attachment I solved in your another question.You may refer to that.

Apply Pythagorean theorem

x²=10²-6²

x²=100-36
x²=64
x=8cm

4 0

3 years ago

Read 2 more answers

If 2 X + 1 ,2 x-1 and 3 X + 4 are in AP find the value of x​

If 2 X + 1 ,2 x-1 and 3 X + 4 are in AP find the value of x