All categories

3 years ago

If the given sequence is a geometric sequence, find the common ratio.

Mathematics

1 answer:

Tcecarenko [31]3 years ago

3 0

Answer:

d. 1/4

Step-by-step explanation:

The ratio of adjacent terms is the common ratio:

(3/12)/(3/3) = 3/12 = 1/4

You might be interested in

A line passes through the points (2,4) and (5,6) .

Alenkinab [10]

Answer:

Option B and D are correct.

Step-by-step explanation:

Given: A line passes through the points (2,4) and (5,6).

* Case 1:

If a line passes through the points (2, 4) and (5, 6)

Point slope intercept form:

for any two points $(x_1,y_1)$ and $(x_2, y_2)$

then the general form $y -y_1=m(x-x_1)$ for linear equations where m is the slope given by:

$m =\frac{y_2-y_1}{x_2-x_1}$

First calculate slope for the points (2, 4) and (5, 6);

$m = \frac{y_2-y_1}{x_2-x_1} =\frac{6-4}{5-2} = \frac{2}{3}$

then, by point slope intercept form;

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

* Case 2:

If a line passes through the points (5, 6) and (2, 4)

First calculate slope for the points (5, 6) and (2, 4);

$m = \frac{y_2-y_1}{x_2-x_1} =\frac{4-6}{2-5} = \frac{-2}{-3}= \frac{2}{3}$

then, by point slope intercept form;

$y-6=\frac{2}{3}(x-5)$

Yes, the only equation of line from the given options which describes the given line are;

$y-4=\frac{2}{3}(x-2)$ and $y-6=\frac{2}{3}(x-5)$

8 0

3 years ago

What is the answer to this and how do I do this problem?

DaniilM [7]

Answer:

B) 25.1 units

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides of the triangle. The length of the side BC that is vertical can be found by finding the difference of y-coordinates:

BC = 5 -(-2) = 7

The lengths of the other two sides can be found using the given distance formula. Fill in the coordinate values and do the arithmetic.

AB = √((4-(-4))^2 +(5-(-1))^2) = √(8^2 +6^2) = √(64+36)

AB = √100 = 10

AC = √((4-(-4))^2 +(-2-(-1))^2) = √(8^2 +(-1)^2) = √(64 +1)

AC = √65 ≈ 8.06

So, the perimeter is ...

P = AB +BC +AC

P = 10 + 7 + 8.06 = 25.06 ≈ 25.1 . . . . matches choice B

5 0

2 years ago

HEEEEEELLLPPPPPPPP!!!!!!!!!!!!

ivann1987 [24]

The standard form would be y = 7x^2 - 42x + 67

8 0

2 years ago

Write the equation of the line in Point-Slope Form

katrin [286]

17.

The point-slope form:

$y-y_1=m(x-x_1)$

We have slope=m=8, and the point (-5, -3). Substitute:

$y-(-3)=8(x-(-5))\\\\\boxed{y+3=8(x+5)}$

18.

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (3, 4) and (15, 10). Substitute:

$m=\dfrac{10-4}{15-3}=\dfrac{6}{12}=\dfrac{1}{2}$

The point-slope form:

$\boxed{y-4=\dfrac{1}{2}(x-3)}$

$\boxed{y-10=\dfrac{1}{2}(x-15)}$

4 0

2 years ago

Sharon purchased a used car for $24,600. The car depreciates exponentially by 8% per

Tju [1.3M]

Answer:

The value of car after 5 years of exponentially depreciation is $16,213.36

Step-by-step explanation:

The initial amount of the car = i = $24,600

The depreciates rate of interest applied = r = 8%

Let The value of car after n years = A

The number of years = n = 5 years

Now,According to question

The value of car after n years = initial price of car × $(1-\dfrac{\textrm rate}{100})^{\textrm time}$

Or, The value of car after 5 years = i × $(1-\dfrac{\textrm r}{100})^{\textrm n}$

Or, $A = $24,600 × $(1-\dfrac{\textrm 8}{100})^{\textrm 5}$

Or, $A = $24,600 × $(0.92)^{5}$

Or, $A = $24,600 × 0.65908

Or, $A = $16,213.36

So, The value of car after 5 years = A = $16,213.36

Hence , The value of car after 5 years of exponentially depreciation is $16,213.36 . Answer

5 0

3 years ago