Solve: 2(x+2)-5=3(x-1)

1 answer:

7 0

Answer:
x = 2

Explanation:
2(x+2)-5=3(x-1)
1) Use distributive property (multiply the 2 by x+2 and the 3 by x-1)
2x+4-5=3x-3
2) Combine like terms
2x-1=3x-3
3) Subtract 2x on both sides
-1=x-3
4) Add 3 on both sides
2=x

hope this helps!

You might be interested in

ПОЖАЛУЙСТА ПОМОГИТЕ РЕШИТЬ ДАЮ 23 ОЧКА!!!

posledela

(Простите, пожалуйста, мой английский. Русский не мой родной язык. Надеюсь, у вас есть способ перевести это решение. Если нет, возможно, прилагаемое изображение объяснит достаточно.)

Use the shell method. Each shell has a height of 3 - 3/4 y ², radius y, and thickness ∆y, thus contributing an area of 2π y (3 - 3/4 y ²). The total volume of the solid is going to be the sum of infinitely many such shells with 0 ≤ y ≤ 2, thus given by the integral

$\displaystyle 2\pi \int_0^2 y \left(3-\frac34 y^2\right) \,\mathrm dy = 2\pi \left(\frac32 y^2 - \frac3{16} y^4\right)\bigg|_0^2 = 6\pi$

Or use the disk method. (In the attachment, assume the height is very small.) Each disk has a radius of √(4/3 x), thus contributing an area of π (√(4/3 x))² = 4π/3 x. The total volume of the solid is the sum of infinitely many such disks with 0 ≤ x ≤ 3, or by the integral

$\displaystyle \pi \int_0^3 \left(\sqrt{\frac43x}\right)^2 \,\mathrm dx = \frac{2\pi}3 x^2\bigg|_0^3 = 6\pi$

Using either method, the volume is 6π ≈ 18,85. I do not know why your textbook gives a solution of 90,43. Perhaps I've misunderstood what it is you're supposed to calculate? On the other hand, textbooks are known to have typographical errors from time to time...

8 0

3 years ago

A hot tub has capacity of 1458 liters 487 liters and 750 ml were put in how much more needs to be put in

Colt1911 [192]

Well the easiest way we can do it is convert liters in to milliliters and since there are 1000 milliliters in a liter multiply 1458 by 1000 and 487 by 1000 which will get you 1458000 milliliters of capacity and the 487 liters turns into 487000 mililiters we add this to the 750 milliliters to get 487750 milliliters. Now it is all a matter of subtracting to find out how much more needs to be put in. 1458000-487750=970250 milliliters. So the amount needed to fill the hot tub is 970250 ml or if you want to convert it back to liters 970.250 l

5 0

3 years ago

If perpendiculars from any point within an angle on its arms are equal, prove that it lies on the bisector of that angle

Oxana [17]

Your question can be quite confusing, but I think the gist of the question when paraphrased is: Prove that the perpendiculars drawn from any point within the angle are equal if it lies on the angle bisector?

Please refer to the picture attached as a guide you through the steps of the proofs. First. construct any angle like ∠ABC. Next, construct an angle bisector. This is the line segment that starts from the vertex of an angle, and extends outwards such that it divides the angle into two equal parts. That would be line segment AD. Now, construct perpendicular line from the end of the angle bisector to the two other arms of the angle. This lines should form a right angle as denoted by the squares which means 90° angles. As you can see, you formed two triangles: ΔABD and ΔADC. They have congruent angles α and β as formed by the angle bisector. Then, the two right angles are also congruent. The common side AD is also congruent with respect to each of the triangles. Therefore, by Angle-Angle-Side or AAS postulate, the two triangles are congruent. That means that perpendiculars drawn from any point within the angle are equal when it lies on the angle bisector