Please need help on this one

What is

Sergeeva-Olga [200]

Answer:

Standard form of the equation is:

∴ $3x+y=23$

Step-by-step explanation:

Given equation:

$y-2=-3(x-7)$

To convert the given equation to standard form of equation:

$A(x)+B(y)=c$

Using distribution.

$y-2=(-3x)+(-3\times-7)$

$y-2=-3x+21$

Adding 2 both sides.

$y-2+2=-3x+21+2$

$y=-3x+23$

Adding $3x$ to both sides.

$3x+y=3x-3x+23$

∴ $3x+y=23$

6 0

3 years ago

Simplify the Expression - 1/2 (8b+3)+3b=

Anna35 [415]

Answer:

-b -3/2

Step-by-step explanation:

-1/2(8b+3) + 3B (a negative times a positive equals a negative)

1. Mutiply -1/2 by 8b and then by 3

(-1/2 x 8b -1/2 x 3) + 3b

-4b - 3/2 + 3b

2. Add -4b + 3b = -b

-b - 3/2

5 0

2 years ago

Graph a triangle (STU) and reflect it over the y-axis to create triangle ST'U'.

lukranit [14]

The x-coordinates of $\triangle S'T'U'$ will be the negation of the x-coordinates of $\triangle STU$

The line segment from S to the y-axis equals the line segment from S' to the y-axis. Similarly, the line segment from T to the y-axis equals the line segment from T' to the y-axis

See attachment for $\triangle STU$ and $\triangle S'T'U'$

In order to solve this question, I will make the following assumptions.

Assume that the coordinates of $\triangle STU$ are

$S = (4,5)$

$T = (5,9)$

$U=(3,8)$

Refer to attachment for illustrations

(1) Reflect $\triangle STU$ over y-axis and describe the transformation

To reflect $\triangle STU$ across the y-axis, the following rule must be followed

$(x,y) \to (-x,y)$

This means that:

$S = (4,5) \to S' = (-4,5)$

$T = (5,9) \to T' = (-5,9)$

$U=(3,8) \to U'=(-3,8)$

The description of the transformation is as follows:

Notice that the signs of the x-coordinates $\triangle STU$ and $\triangle S'T'U'$ of both triangles are different.

In other words, if the x-coordinate of one is positive, then the other will have a negative x-coordinate; and vice versa.

(2) Compare the segments and the line of reflection

To reflect across the y-axis means that the reflecting line is the y-axis, itself.

The distance between a point to the y-axis is the absolute value of the x-coordinate.

So, the distance between S and the y-axis is:

$S = |4| = 4$

The distance between S' and the y-axis is:

$S' = |-4| = 4$

We can conclude that the two line segments are equal.

This is the same for other point T and T' because of the formula used above.

From T and T' to the y-axis is:

$T =|5| =5$

$T' =|-5| =5$