Why are standardized units of measure important to scientists?

5. Please write the equation of a line in y=mx+b format. Find the SLOPE first then find the Y-INTERCEPT (b) Your answer

castortr0y [4]

Answer:

y = $\frac{5}{3}x-1$

Step-by-step explanation:

Let the equation of the line is,

y = mx + b

Here m = slope of the line

b = y-intercept

Slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is,

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

From the graph attached,

Since, the given line passes through (0, -1) and (3, 4),

Slope 'm' = $\frac{4+1}{3-0}$

m = $\frac{5}{3}$

y - intercept 'b' = -1

Therefore, equation of the line will be,

y = $\frac{5}{3}x-1$

5 0

3 years ago

Sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0

andreev551 [17]

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0

sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2

sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ

… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π

… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5

sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ

… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π

… … … … … ==> x = nπ or x = (2n + 1)π/2

cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ

… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ

… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ

(where n is any integer)

5 0

3 years ago

How can I describe an angles measure

Yanka [14]

The question is too general....but it could be acute, obtuse

3 0

4 years ago

How are lines best fit and other trend lines used with scatter plots?

skad [1K]

- Line of Best Fit. A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points.

6 0

3 years ago

True or false? (Picture below)

faltersainse [42]

Answer:

i think its false

Step-by-step explanation:

6 0

3 years ago

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