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3 years ago

Rotate 90 degrees clockwise about (0,0)

1 answer:

4 0

Rotation of point through 90° about the origin in clockwise direction when point M (h, k) is rotated about the origin O through 90° in clockwise direction. The new position of point M (h, k) will become M’ (k, -h).

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two times a number is subtracted from 25 the result is the same as when it is added to six times.find the number

ExtremeBDS [4]

Answer:

6.3

Step-by-step explanation:

1. 25 - 2n = n + 6

2. 25 = 3n + 6

3. 3n = 19

4. n = 6.3

8 0

2 years ago

What two numbers multiply to -126 and add up to -65

Airida [17]

Xy = -126
x + y = -65

$xy = -126$
$\frac{xy}{x} = \frac{-126}{x}$
$y = \frac{-126}{x}$

$x + y = -65$
$x + \frac{-126}{x} = -65$
$\frac{x^{2}}{x} + \frac{-126}{x} = -65$
$\frac{x^{2} - 126}{x} = -65$
$-65x = x^{2} - 126$
$0 = x^{2} + 65x - 126$
$x = \frac{-(65) \+ \sqrt{(65)^{2} - 4(1)(-126)}}{2(1)}$
$x = \frac{-65 \± \sqrt{4225 + 504}}{2}$
$x = \frac{-65 \± \sqrt{4729}}{2}$
$x = \frac{-65 \± 68.8}{2}$
$x = \frac{-65 + 68.8}{2}$ $or$ $x = \frac{-65 - 68.8}{2}$
$x = \frac{3.8}{2}$ $or$ $x = \frac{-133.8}{2}$
$x = 1.9$ $or$ $x = -66.9$

x + y = -65
  1.9 + y = -65
- 1.9   - 1.9
y = -66.9
  (x, y) = (1.9, -66.9)

or

  x + y = -65
  -66.9 + y = -65
+ 66.9 + 66.9
y = 1.9
  (x, y) = (-66.9, 1.9)

The two numbers that add up to -65 and can multiply to -126 are the numbers -66.9 and 1.9.

3 0

3 years ago

Rewrite the product as a sum: 10cos(5x)sin(10x)

mote1985 [20]

Answer:

10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]

Step-by-step explanation:

In this question, we are tasked with writing the product as a sum.

To do this, we shall be using the sum to product formula below;

cosαsinβ = 1/2[ sin(α + β) - sin(α - β)]

From the question, we can say α= 5x and β= 10x

Plugging these values into the equation, we have

10cos(5x)sin(10x) = (10) × 1/2[sin (5x + 10x) - sin(5x - 10x)]

= 5[sin (15x) - sin (-5x)]

We apply odd identity i.e sin(-x) = -sinx

Thus applying same to sin(-5x)

sin(-5x) = -sin(5x)

Thus;

5[sin (15x) - sin (-5x)] = 5[sin (15x) -(-sin(5x))]

= 5[sin (15x) + sin (5x)]

Hence, 10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]

8 0

3 years ago

Jamie owns about 3 times as much books as Carly. Jamie owns 42 books write an equation and use it to estimate the number n of bo

Marina CMI [18]

Answer:

Carly owns 14 books.

Step-by-step explanation:

42/3= 14

hope this helps!!! (:

4 0

3 years ago

8n-13=13-8n can someone answer with steps, please?

NARA [144]

Answer:

1.625

Step-by-step explanation:

Add 13 to both sides

8n = 26 - 8n

Add 8n to both sides

16n = 26

Divide both sides by 16

Your answer is 1.625

Hope I helped :)

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(unless the other person does a better job)

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4 0

3 years ago