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3 years ago

What is the image of the point (2,3) after the transformation Ry-axis?

Mathematics

1 answer:

kiruha [24]3 years ago

4 0

Answer:

The image of the point (2, 3) after the reflection across the y-axis will be: (-2, 3)

Step-by-step explanation:

We know that when a point, let say P(x, y), is reflected across the y-axis, the sign of x-coordinate is reversed but y-coordinate remains the same.

In other words, the rule is:

P(x, y) → P'(-x, y)

Here, P'(x, y) is the image of the original point P(x, y) after the reflection across the y-axis.

Considering the point

A(2, 3)

Let us reflect the point A(2, 3) across the y-axis.

We know the rule:

P(x, y) → P'(-x, y)

A(2, 3) → A'(-2, 3)

Thus, the image of the point (2, 3) after the reflection across the y-axis will be: (-2, 3)

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At Gallicum Enterprises, all employees are in one of three categories: J, K, or L. The ratio of the numbers of employees in J to

MrRa [10]

Answer:

380.

Step-by-step explanation:

Given:

Total number of employees at Gallicum Enterprises are in the ratio,

J : k : L = 1 : 3 : 5 for some time.

Last month, 20 new J employees were hired, and no employees left and the new ratio of J to K is now 1 : 2.

Question asked:

What is the new total number of employees at Gallicum Enterprises ?

Solution:

As given, J : K : L = 1 : 3 : 5 

So, J : K = 1 : 3

$\frac{J}{K} = \frac{1}{3} \ (1)$

As last month, 20 new J employees were hired, new ratio of J to K is now

1 : 2.

So, $\frac{J+20}{K}=\frac{1}{2} \ (2)$

Dividing equation 1 and 2,

$\frac{J}{K}\div{\frac{J+20}{K} } = \frac{1}{3}\div{\frac{1}{2} }$

$\frac{J}{K}\times{\frac{K}{J+20} } = \frac{1}{3}\times{\frac{2}{1} }\\\\ \frac{J}{J+20} =\frac{2}{3} \\\\$

By cross multiplication:

$3J=2(J+20)\\3J=2J+40$

Subtracting both sides by $2J$

$J=40$

From equation 1.

$\frac{J}{K} = \frac{1}{3} \\\\ \frac{40}{K} =\frac{1}{3} \\\\$

By cross multiplication:

$K=40\times3\\\\ K=120$

As given, J : K : L = 1 : 3 : 5

So, K : L = 3 : 5

$\frac{K}{L} =\frac{3}{5} \\\\\\ \frac{120}{L} =\frac{3}{5}$

By cross multiplication:

$120\times5=3\times L\\600=3L$

Dividing both sides by 3

$L =200$

New total number of employees after hiring 20 new J employees :

New J + K + L = (New J = J + 20 = 40 + 20 = 60 )

60 + 120 + 200 = 380

Therefore, the new total number of employees at Gallicum Enterprises is 380.

4 0

3 years ago

Solve each component inequality and graph the solution

lord [1]

Solution: The value of x after solving both components is $2$ or $(2,11]$ .

Explanation:

From the first component it is clearly noticed that the value of x is greater than 2.

Simplify the second component.

$x-1\leq 10\\x\leq 11$

From the above inequality it is clearly noticed that the value of x is less than or equal to 11.

Solving both components we get $2$ and the graphical representation is shown in the figure.

The red portion shows the solutions of $x>2$ , blue portion shows the solution of $x-1\leq 10$ and purple portion which combination of red and blue portion shows the solution of both inequalities.

Therefore, value of x after solving both components is $2$ or $(2,11]$ .

5 0

3 years ago

I have two questions. Solve for x : 7x + 3 ≤ -35 Solve for n : -9n + 7 < -11

kvv77 [185]

Answer:

x≤−38 /7

n>2

Step-by-step explanation:

mathpapa.com is v helpful for this kind of stuff :)

dont worry doe, i did da math so u should b good

3 0

3 years ago

How do you find the length of an equilateral triangle with the area?

max2010maxim [7]

Formula used for an equilateral triangle is
Root3 a^2/4
Hope this helps.!!

7 0

3 years ago

edwardo wants to find the height of a building using the sun, his height, and similar triangles. He goes out during his noon lun

FrozenT [24]

You can indeed use similar triangles to get a side of another similar triangle.

let's say Edwardo stood next to the building and his shadow was 20ft, he's 4ft tall, and the building cast a shadow of 125ft, then, check the picture below.

8 0

3 years ago