All categories

3 years ago

Can somebody explain how to do this quickly. Already know how to solve it but it takes me a long time

Mathematics

1 answer:

steposvetlana [31]3 years ago

7 0

Answer:

n = 8

Step-by-step explanation:

Initial point: (1, -2)

Final point: y = x

Blue light translation:

4 units right, 5 units down
Number of translations = n

Red light translation:

1 unit left, 4 units up
Number of translations = 15

Final point is going to be:

x = 1 + 4n - 15*1 = 4n - 14
y = -2 - 5n + 15*4 = -5n + 58

Since the coordinates of final point are same, we have:

4n - 14 = -5n + 58
4n + 5n = 58 + 14
9n = 72
n = 72/9
n = 8

You might be interested in

The point ( - 14,12) is on the graph of y = f(x). Find the corresponding point on the graph of y= qe), where gex) = arcus.

liubo4ka [24]

Answer:

$(-14,4)$

Step-by-step explanation:

Given

$(-14,12)$ $\to$ $y =f(x)$

$g(x) = \frac{1}{3}f(x)$

Required

The corresponding point on $y = g(x)$

$(-14,12)$ $\to$ $y =f(x)$ means:

$12 = f(-14)$

$f(-14)=12$

$g(x) = \frac{1}{3}f(x)$ is calculated

$g(-14) = \frac{1}{3} * f(-14)$

$g(-14) = \frac{1}{3} * 12$

$g(-14) = 4$

So, the corresponding point on $y = g(x)$ is: $(-14,4)$

7 0

3 years ago

Data Set: {60, 30, 35, 30,25}

GrogVix [38]

30 is the correct answer

3 0

3 years ago

Hi guys actually I have forgotten the steps do it yesterday my online school opened so I don't how to solve it can you help me p

cestrela7 [59]

Answer:

(i) (x +4)^3 = x^3 +12x^2 +48x +64

(ii) (2m +1)^3 = 8m^3 +12m^2 +6m +1

(iii) (a -2b)^3 = a^3 -6a^2b +12ab^2 -8b^3

Step-by-step explanation:

Powers of a binomial have a pattern. The coefficients of the terms of the expanded product are the numbers in the corresponding row of Pascal's Triangle. Here, you want the 3rd power, so the coefficients of interest are ...

1, 3, 3, 1

The pattern is ...

(a +b)^2 = a^2 +2ab +b^2

(a +b)^3 = a^3 +3a^2b +3ab^2 +b^3

The total of powers of the variable is equal to the exponent of the binomial. The powers of the first variable decrease to 0 while the powers of the second variable increase from zero.

When 'a' or 'b' is something with a coefficient, that whole term is raised to the appropriate power.

i) (x+4)^3 = x^3 +3·4x^2 +3·4^2x +4^3

(x +4)^3 = x^3 +12x^2 +48x +64

ii) (2m +1)^3 = (2m)^3 +3·1·(2m)^2 +3·1^2·(2m) +1^3

(2m +1)^3 = 8m^3 +12m^2 +6m +1

iii) (a -2b)^3 = a^3 +3·a^2·(-2b) +3·a·(-2b)^2 +(-2b)^3

(a -2b)^3 = a^3 -6a^2b +12ab^2 -8b^3

_____

Additional comment on Pascal's triangle

The numbers in each row are the sums of the two numbers immediately above. For binomial expansion, you're only interested in the contents of a row. The "patterns" shown in the attachment are an extra added attraction, not particularly relevant to binomial expansion.