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3 years ago

If you get the answers right you will get brainliest and get a thanks :-)

Mathematics

1 answer:

sergejj [24]3 years ago

5 0

5. 3, 12, 48, 192, 768, ...

You can find the 15th term by using the formula $a_n = a_1 *r^{n-1}$ , where $a_1$ is the first term of the sequence, r is the common ratio, and n is the number of the term you want to find.

 $a_n = a_1 *r^{n-1}$ Plug in your information (the common ration is x4)
 $a_{15} = 3 * 4^{14}$ Simplify the exponent
$a_{15} = 3 * 268435456$ Multiply
$a_{15} = 805306368$

The 15th term of the sequence is 805306368.

6. 200, 40, 8, 1.6, ...
Using guess and check, I found that the pattern here is ÷5, ÷5, ÷5, .... That can also be written as × $\frac{1}{5}$ , × $\frac{1}{5}$ , × $\frac{1}{5}$ , ... When you are multiplying the terms of a sequence, that is a geometric sequence.

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The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____.

Kryger [21]

Using the triangle of pascal we have that the expression equivalent to (x + y) ^ 6 is given by:
x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
Therefore, the coefficients of the expansion are given by:
1, 6, 15, 20, 15, 6, 1
Answer:
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1

5 0

3 years ago

Read 2 more answers

Convert -18° to radians.

Fiesta28 [93]

0.314159

Is the answer

5 0

3 years ago

4(2x + 1) = 12x + 3 - 4x +1

gayaneshka [121]

Answer:4(2x + 1) = 12x + 3 - 4x +1=0

Step-by-step explanation:

group like terms =4(2x+1)=12x-4x+3+1

add similar elements=4(2x+1)=8x+3+1

add the numbers=4(2x+1)=8x+4

expand=8x+4=8x+4

subtract 4 from both sides 8x+4-4=8x+4-4

simplify=8x=8x

subtract 8x both sides=0

5 0

3 years ago

On a coordinate plane, kite W X Y Z is shown. Point W is at (negative 3, 3), point X is at (2, 3), point Y is at (4, negative 4)

xz_007 [3.2K]

Answer:

$P = 10 + 2\sqrt{53}$ units

Step-by-step explanation:

Given

Shape: Kite WXYZ

W (-3, 3), X (2, 3),

Y (4, -4), Z (-3, -2)

Required

Determine perimeter of the kite

First, we need to determine lengths of sides WX, XY, YZ and ZW using distance formula;

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

For WX:

$(x_1, y_1)\ (x_2,y_2) = (-3, 3),\ (2, 3)$

$WX = \sqrt{(-3 - 2)^2 + (3 - 3)^2}$

$WX = \sqrt{(-5)^2 + (0)^2}$

$WX = \sqrt{25}$

$WX = 5$

For XY:

$(x_1, y_1)\ (x_2,y_2) = (2, 3)\ (4,-4)$

$XY = \sqrt{(2 - 4)^2 + (3 - (-4))^2}$

$XY = \sqrt{-2^2 + (3 +4)^2}$

$XY = \sqrt{-2^2 + 7^2}$

$XY = \sqrt{4 + 49}$

$XY = \sqrt{53}$

For YZ:

$(x_1, y_1)\ (x_2,y_2) = (4,-4)\ (-3, -2)$

$YZ = \sqrt{(4 - (-3))^2 + (-4 - (-2))^2}$

$YZ = \sqrt{(4 +3)^2 + (-4 +2)^2}$

$YZ = \sqrt{7^2 + (-2)^2}$

$YZ = \sqrt{49 + 4}$

$YZ = \sqrt{53}$

For ZW:

$(x_1, y_1)\ (x_2,y_2) = (-3, -2)\ (-3, 3)$

$ZW = \sqrt{(-3 - (-3))^2 + (-2 - 3)^2}$

$ZW = \sqrt{(-3 +3)^2 + (-2 - 3)^2}$

$ZW = \sqrt{0^2 + (-5)^2}$

$ZW = \sqrt{0 + 25}$

$ZW = \sqrt{25}$

$ZW = 5$

The Perimeter (P) is as follows:

$P = WX + XY + YZ + ZW$

$P = 5 + \sqrt{53} + \sqrt{53} + 5$

$P = 5 + 5 + \sqrt{53} + \sqrt{53}$

$P = 10 + 2\sqrt{53}$ units

6 0

3 years ago

The 7 a.m. flight from Dallas to Chicago is on time 75% of the time. Fran created this spinner to simulate the scenario.

Elena-2011 [213]

Answer:

CORRECT OPTION is (C) The flight will be late on one of the three days.

Step-by-step explanation:

The 7am flight from Dallas to Chicago is on time 75% of the time.

A spinner with four sections was created by Fran to simulate this scenario.

Since the 4 sections were equal, it means each section was 25% of the spinner.

3 sections were shaded. That implies 25 × 3 = 75% of the spinner was shaded area.

This coincides with the 75% probability that the flight is on time on a given day.

In other words, if the spinner's pointer lands on shaded area, the flight will be on time. If the pointer lands on an unshaded portion, the flight will be late.

Now Fran spun the spinner 3 times so she has 3 outcomes. The outcomes are:

- Shaded - Shaded - Unshaded

CORRECT OPTION is (C) The flight will be late on one of the three days.

4 0

3 years ago