When adding integers with the same sign, you add and __________

1. Points A and B are to be mapped onto a number line according to two equations. The solution to the equation 2/3 A= -24 is the

OleMash [197]

<span>The solution to the equation 2/3 A= -24 is the coordinate of point A.

2/3 A = -24
A = -24 / 2/3
A = -24 * 3/2
A = -72/2
A = -36

The solution to the equation 20=-b/0.5 is the coordinate of point B

20 = -b/0.5
20 * 0.5 = -b
10 = -b
10/-1 = -b/-1
-10 = b

A = -36 and B = -10

The distance between the two letters is 26 units. </span>

4 0

2 years ago

Write functions for each of the following transformations using function notation. Choose a different letter to represent each f

joja [24]

Answer:

1. Translation: g(x) = f(x-a)+b.

2. Reflection around y-axis: h(x) = f(-x)

3. Reflection around x-axis: k(x) = -f(x)

4. Rotation of 90° : $R_{90} (x,y)=(-y,x)$

5. Rotation of 180° : $R_{180} (x,y)=(-x,-y)$ .

6. Rotation of 270° : $R_{180} (x,y)=(y,-x)$ .

Step-by-step explanation:

Let us assume that the transformations namely translation, reflection are applied to a function f(x) and the rotation is applied to the point ( x,y ).

So, according to the options:

We know that 'translation moves the image in horizontal and vertical direction'.

1. As we have to translate the function f(x) 'a' units to the right and 'b' units up. So, the new form of the function becomes g(x) = f(x-a)+b.

Further, we know that 'reflection means to flip the image around a line'.

2. As, we have to reflect the function f(x) around y-axis. The new form of the function is h(x) = f(-x).

3. As, we have to reflect the function f(x) around x-axis. The new form of the function is k(x) = -f(x).

Since, 'rotation turns the image around a point to a certain degree'.

4. As, we have to rotate ( x,y ) counter-clockwise to 90° about the origin, the new form of the function is $R_{90} (x,y)=(-y,x)$ .

5. As, we have to rotate ( x,y ) counter-clockwise to 180° about the origin, the new form of the function is $R_{180} (x,y)=(-x,-y)$ .

6. As, we have to rotate ( x,y ) counter-clockwise to 270° about the origin, the new form of the function is $R_{180} (x,y)=(y,-x)$ .

5 0

2 years ago

Lola is making greeting cards, which she will sell by the box at an arts fair. She paid $50 for a booth at the fair, and the mat

Schach [20]

At some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)

<h3> How did we figure this out?</h3>

Lola is making greeting cards, which she will sell by the box at an arts fair. She paid $50 for a booth at the fair, and the materials for each box of cards cost $8. She will sell the cards for $10 per box of cards.

We are going to use 50, 8 and 10 to find are answer.

Therefore, we are going to divide the numbers:

$\boxed{50/10}$