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3 years ago

Find the point, M, that divides segment AB into a ratio of 4:7 if A is at (-33,0) and B is at (0, 44).

Mathematics

1 answer:

Amanda [17]3 years ago

5 0

Answer:

(-21, 16)

Step-by-step explanation:

A is at (-33, 0) and B is at (0, 44),

A point that divides the line segment in a ratio of 4:7 also divides the differences of the x-and y-coordinates in the same ratio.

If we divide each distance into 11 equal parts and choose a length 4/11 of the distance, the other part will be 7/11 of the distance. The two parts will be in a ratio of 4:7.

For the x-coordinate,

x₂ - x₁ = 0 - (-33) = 0 + 33 = 33

(4/11) × 33 = 12

-33 + 12 = -21

The x-coordinate of M is (-21, 0).

For the y-coordinate,

y₂ - y₁ = 44 - 0 = 44

(4/11) × 44 = 16

0 + 16 = 16

The y-coordinate of M is (0, 16).

The coordinates of M are then (-21, 16).

The diagram below shows the point M that divides AB in a 4/7 ratio.

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-10.7474..... as a fraction

kondaur [170]

In fraction, it would be:

-107474/10000

6 0

2 years ago

The graph of F ( x ) = 4/x2 - 2x - 3 is shown <br> for which values of X is f ( x ) decreasing

Elza [17]

Hi there!

$\large\boxed{(-\infty, \sqrt[3]{-4}) \text{ and } (0, \infty) }$

We can find the values of x for which f(x) is decreasing by finding the derivative of f(x):

$f(x) = \frac{4}{x^2} - 2x - 3$

Taking the derivative gets:

$f'(x) = -\frac{8}{x^3} - 2$

Find the values for which f'(x) < 0 (less than 0, so f(x) decreasing):

0 = -8/x³ - 2

2 = -8/x³

2x³ = -8

x³ = -4

$x = \sqrt[3]{-4}$

Another critical point is also where the graph has an asymptote (undefined), so at x = 0.

Plug in points into the equation for f'(x) on both sides of each x value to find the intervals for which the graph is less than 0:

f'(1) = -8/1 - 2 = -10 < 0

f'(-1) = -8/(-1) - 2 = 6 > 0

f'(-2) = -8/-8 - 2 = -1 < 0

Thus, the values of x are:

$(-\infty, \sqrt[3]{-4}) \text{ and } (0, \infty)$

6 0

2 years ago

The first term of a geometric sequence is 8 and the fourth term is 216. What is the sum of the first 12 terms of the correspondi

Leokris [45]

Answer:

2,125,760

Step-by-step explanation:

The first term (a) is 8

The fourth term is 216

Hence the sum of the first 12 term can be calculated as follows

= 8-8(3)^12/1-3

= 8-24^12/-2

= 2,125,760

The sum of first 12 terms is 2,125,760

4 0

2 years ago

What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?

Helga [31]

Answer:

The sum of 8 geometric sequence is 959780

Step-by-step explanation:

We are given

this sequence is geometric

-4 , 24 , -144

First term is -4

so, $a_1=-4$

now, we can find common ratio

$r=\frac{24}{-4}=-6$

we can use formula

$S_n=a_1(\frac{1-r^n}{1-r} )$

n=8

now, we can plug values

$S_8=-4(\frac{1-(-6)^{8}}{1+6} )$

now, we can simplify it

and we get

$S_8=959780$

4 0

3 years ago

Consider the enlargement of the pentagon. A small pentagon has a bottom side length of x centimeters and left side length of 7 c

LuckyWell [14K]

When the pentagon is drawn to scale then its value of x will be x=3.3 cm

<h3>What is the pentagon?</h3>

The pentagon is defined as the shape having five sides connected together.

Now it is given in the question that

For small pentagone

Bottom =x

left =7 cm

For larger pentagone

Bottom=7cm

left=15cm

Now since the pentagon is actually dilated from its size to the new bigger size. It means that the equivalent ratio of both the pentagons will be equal.

For smaller pentagon

$\rm Equivalent \ Ratio = \dfrac{Bottom}{Left} =\dfrac{x}{7}$