Will mark brainliest for correct answer, due soon!

$= ( \sqrt{15x}) ( \sqrt{10x} ) \\ = \sqrt{(10x)(15x)} \\ = \sqrt{150 {x}^{2} } \\ = \sqrt{6(25 {x}^{2}) } \\ = (\sqrt{6} )( \sqrt{( {5x})^{2} } ) \\ = ( \sqrt{6} )(5x) \\ = 5x \sqrt{6}$

8 0

3 years ago

-2x^4y(3x^3-4x^2y^3)

Ilia_Sergeevich [38]

<span>x = {-1, 3}

Full explanation=

</span><span>Simplifying x + 2 = 3x + -1x2 + 5 Reorder the terms: 2 + x = 3x + -1x2 + 5 Reorder the terms: 2 + x = 5 + 3x + -1x2 Solving 2 + x = 5 + 3x + -1x2 Solving for variable 'x'. Reorder the terms: 2 + -5 + x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Combine like terms: 2 + -5 = -3 -3 + x + -3x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Combine like terms: x + -3x = -2x -3 + -2x + x2 = 5 + 3x + -1x2 + -5 + -3x + x2 Reorder the terms: -3 + -2x + x2 = 5 + -5 + 3x + -3x + -1x2 + x2 Combine like terms: 5 + -5 = 0 -3 + -2x + x2 = 0 + 3x + -3x + -1x2 + x2 -3 + -2x + x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 -3 + -2x + x2 = 0 + -1x2 + x2 -3 + -2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3 + -2x + x2 = 0 Factor a trinomial. (-1 + -1x)(3 + -1x) = 0 Subproblem 1Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1 Subproblem 2Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solutionx = {-1, 3}</span>

4 0

3 years ago

How tooo do thissss?

exis [7]

Step-by-step explanation:

m/s² = m/s / s

this is the slope of the line in the graph.

t = 2, that means it is in the first segment of 0 - 6 seconds

the slope in this segment is

(25-15)m/s / (6-0)s

10m/s / 6s = 10/6 m/s² = 5/4 m/s² = 1.25 m/s² ≈ 1.3 m/s²

the same thing for t = 12 in the third segment.

the acceleration or slope is negative here, but that's called here a "forbidden word", and is therefore also a positive number.

in that this segment the slope is

(0-25)m/s / (16-11)s

-25m/s / 5s = -5 m/s²

and so, the answer is 5 m/s².

for the total distance we need to calculate the area under the lines.

the line functions in the 3 segments are :

s(t) = 5/4 t + 15

s(t) = 25

s(t) = -5t + 25

the third one is simplified by moving it from the 11 to 16 seconds interval to a 0 to 5 seconds interval. this creates the same area under that line.

the area under the first line is the integral of the line function between 0 and 6.

that is

[5/8 t² + 15t] between 0 and 6.

and that is

5/8 × 36 + 90 - 5/8 × 0 - 15×0 = 45/4 + 90

= 45/4 + 360/4 = 405/4 = 101.25m

the area under the second segment is simply the area of the rectangle 5×25 = 125m

and the area under the third segment is the integral of the line function between 0 and 5 (remember, we shifted from 11 to 16 to the interval 0 to 5).

that is

[-2.5t² + 25t] in the interval 0 to 5.

and that is

-2.5×25 + 25×5 - -2.5×0 - 25×0 = -62.5 + 125 = 62.5m

as a control check this area is also the area of a right-angled triangle with legs of 5 and 25

the area is 25×5/2 = 125/2 = 62.5

so, it is correct.

the total area under the lines is therefore

101.25 + 125 + 62.5 = 288.75 m ≈ 288.8 m

the average speed is now simply

288.75 m / 16 s = 288.75/16 m/s = 18.046875 m/s ≈

≈ 18 m/s

but if we used the already rounded result of the total distance of 288.8 m, then we would get

288.8 / 16 = 18.05 m/s ≈ 18.1 m/s

3 0

3 years ago