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2 years ago

(6m^3 -16m^2 + 15m - 40) / (2m^2 + 5)

Mathematics

1 answer:

Helen [10]2 years ago

4 0

6m3 - 16m2 + 15m - 40 Simplify ————————————————————— 2m2 + 5 Checking for a perfect cube :

4.1 6m3 - 16m2 + 15m - 40 is not a perfect cube

Trying to factor by pulling out :

4.2 Factoring: 6m3 - 16m2 + 15m - 40

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 15m - 40
Group 2: -16m2 + 6m3

Pull out from each group separately :

Group 1: (3m - 8) • (5)
Group 2: (3m - 8) • (2m2)
 -------------------
Add up the two groups :
 (3m - 8) • (2m2 + 5)
Which is the desired factorization

3m-8 is the answer

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The coordinates for three points of a rectangle are (2, 6) (2, 9) and (8, 6). What is the coordinate for the fourth point in the

saw5 [17]

Answer:

(8,9)

Step-by-step explanation:

Given

$A = (2,6)$

$B = (2,9)$

$C = (8,6)$

Required

Determine the 4th point

The coordinate point of a horizontal or a vertical rectangle is given as:

(x1,y1), (x2,y2), (x3,y3), (x4,y4)

Where:

$x_1 = x_2$ $x_3 = x_4$ $y_1 = y_3$ $y_2 = y_4$

So, we have:

$A = (2,6)$ --- $(x_1.y_1)$

$B = (2,9)$ ---- $(x_2.y_2)$

$C = (8,6)$ ---- $(x_3,y_3)$

Using the above equations:

$x_3 = x_4$ $=8$

$y_2 = y_4$ $= 9$

Hence, the coordinate of the 4th point is:

$(x_4,y_4) = (8,9)$

4 0

3 years ago

given MP m(-12 -5) and p(9,-12) if N lies on MP such that the ratio of MN to NP is 3:4, Find the coordinates of N

Nataly_w [17]

Answer:

The coordinates of N are (-3,-8)

Step-by-step explanation:

Here, we are going to use the internal division to find the coordinates of the point split the line segment MP in the ratio 3:4

Mathematically, that would be;

(x,y) = (nx1 + mx2)/(m + n), (ny1 + my2)/(m + n)

we have;

m = 3 and n = 4

M is (x1,y1) while N is (x2,y2)

we have;

(x,y) = (4(-12) + 3(9))/(3+4) , (4(-5) + 3(-12))/(3+4)

(x,y) = (-48 + 27)/7, (-20 -36)/7

(x,y) = (-21/7 , -56/7)

(x,y) = (-3,-8)

8 0

2 years ago

50 POINTS AND BRAINLIEST! What is the area of this figure?

oksian1 [2.3K]

Answer:

42 units²

Step-by-step explanation:

The figure is composed of a rectangle ( middle section) and 2 triangles with the same length base and height

Area of rectangle = 7 × 4 = 28 units²

Area of 2 triangles = 2 × $\frac{1}{2}$ × 7 × 2 = 14 units²

Area of figure = 28 + 14 = 42 units²

5 0

2 years ago

Read 2 more answers

Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side

maria [59]

Answer:

cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = $-\frac{1}{3}$

cos(b) = $-\frac{1}{4}$

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = $-\sqrt{1-(-\frac{1}{3})^2}$ [Since, sin(a) = $\sqrt{(1-\text{cos}^2a)}$ ]

= $-\sqrt{\frac{8}{9}}$

= $-\frac{2\sqrt{2}}{3}$

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be negative.

sin(b) = $-\sqrt{1-(-\frac{1}{4})^2}$

= $-\sqrt{\frac{15}{16}}$

= $-\frac{\sqrt{15}}{4}$

By substituting these values in the identity,

cos(a + b) = $(-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})$

= $\frac{1}{12}-\frac{\sqrt{120}}{12}$

= $\frac{1}{12}(1-\sqrt{120})$

= $\frac{1}{12}(1-2\sqrt{30})$

Therefore, cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

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2 years ago

When given the two points (2,-3) and (2,-4) how do you write an equation in standard form

Nadusha1986 [10]

Answer:

2,-4

-2,-3

_____

Step-by-step explanation:

That is how write the equation because you have to line them up by the higher x or y value

7 0

2 years ago