(2 x 10^2)(4 x 10^3)

Work out 5 x 10^6 / 4 x 10^4 Give your answer as an ordinary number.

Angelina_Jolie [31]

Answer:

$1.25 \times {10}^{2} = 125$

Step-by-step explanation:

$\frac{5 \times {10}^{6} }{4 \times {10}^{4} } = \frac{5}{4} \times \frac{ {10}^{6} }{ {10}^{4} } = 1.25 \times {10}^{2} = 125$

5 0

3 years ago

A circle is translated 4 units to the right and then reflected over the x-axis. Complete the statement so that it will always be

irga5000 [103]

Answer:

The statement is now presented as:

$\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}$

In other words, this mathematical statement can be translated as:

There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r.

Step-by-step explanation:

Let $C = (h,k)$ the coordinates of the center of the circle, which must be transformed into $C'=(h', k')$ by operations of translation and reflection. From Analytical Geometry we understand that circles are represented by the following equation:

$(x-h)^{2}+(y-k)^{2} = r^{2}$

Where $r$ is the radius of the circle, which remains unchanged in every operation.

Now we proceed to describe the series of operations:

1) Center of the circle is translated 4 units to the right (+x direction):

$C''(x,y) = C(x, y) + U(x,y)$ (Eq. 1)

Where $U(x,y)$ is the translation vector, dimensionless.

If we know that $C(x, y) = (h,k)$ and $U(x,y) = (4, 0)$ , then:

$C''(x,y) = (h,k)+(4,0)$

$C''(x,y) =(h+4,k)$

2) Reflection over the x-axis:

$C'(x,y) = O(x,y) - [C''(x,y)-O(x,y)]$ (Eq. 2)

Where $O(x,y)$ is the reflection point, dimensionless.

If we know that $O(x,y) = (h+4,0)$ and $C''(x,y) =(h+4,k)$ , the new point is:

$C'(x,y) = (h+4,0)-[(h+4,k)-(h+4,0)]$

$C'(x,y) = (h+4, 0)-(0,k)$

$C'(x,y) = (h+4, -k)$

And thus, $h' = h+4$ and $k' = -k$ . The statement is now presented as:

$\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}$

In other words, this mathematical statement can be translated as:

There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r.

4 0

3 years ago

Find the median of the data

kicyunya [14]

The median is the middle number of the data plot. Since there 30 numbers, there isn't a exact middle. To find the median you must add the two middle number then divide by 2.
In this case you must add 87 and 88 which gives 175.
Then divide 175 by 2 which gives 87.5
87.5 is the median

5 0

2 years ago

Please answer this question for brainliest!

kkurt [141]

The original side length is given as 3.00

Multiply the original length by the scale factor:

3.00 x 0.75 = 2.25

The answer is B. 2.25 cm

3 0

2 years ago

A bag contains red, yellow and green sweets.2/5 of the sweets are red and 1/4 of the sweets are yellow. What fraction of the swe

Sauron [17]

Answer:

Let x = the number or green sweets

Let x + 8 = the number of red sweets

red/green: (x + 8)/x = 5/3 Cross multiply

5x = 3(x + 8)

5x = 3x + 24

2x = 24

x = 12 green sweets

3 0

3 years ago