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Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applie

Y_Kistochka [10]

Answer:

The coordinates of T' will be T'(13,-1)

Step-by-step explanation:

step 1

Find the rule of the translation

take any point of rectangle JKLM (pre-image)

The coordinate of point k(-3,2)

The coordinate of point k'(4,7)

so

The rule of the transformation

k(-3,2) -----> k'(4,7)

is equal to

(x,y) ------> (x+7,y+5)

That means ----> the translation is 7 units at right and 5 units up

step 2

Apply the rule of the translation at the coordinate T of trapezoid STUV

we have

T(6,-6)

(x,y) ------> (x+7,y+5)

T(6,-6) ------> T'(6+7,-6+5)

T(6,-6) ------> T'(13,-1)

therefore

The coordinates of T' will be T'(13,-1)

6 0

3 years ago

Let f(x) = x ^ 2 and g(x) = x - 3 . Evaluate (g?f)(0).

nignag [31]

Answer:

$g(f(0))=-3$

Step-by-step explanation:

we have

$f(x)=x^{2}$

$g(x)=x-3$

we know that

$(g o f)(x)=g(f(x))$

substitute the variable x in the function g(x) by the function f(x)

so

$g(f(x))=x^{2}-3$

Evaluate $g(f(0))$

For x=0

$g(f(0))=0^{2}-3$

$g(f(0))=-3$

5 0

3 years ago

A movie theater has a seating capacity of 387. The theater charges $5.00 for children, $7.00 for students, and $12.00 of

Rainbow [258]

Answer:

The attendance was 198 children, 90 students and 99 adults.

Step-by-step explanation:

We define:

c: children attendance

s: students attendance

a: adult attendance

The equation that describes the total ticket sales is:

$5c+7s+12a=2808$

We also know that the children attendance doubles the adult attendance:

$c=2a$

The third equation is the seating capacity, which we assume is full:

$c+s+a=387$

We start by replacing variables in two of the equations:

$c=2a\\\\s=387-c-a=387-2a-a=387-3a$

Then, we solve the remaining equation for a:

$5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99$

Then, we solve for the other two equations:

$c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90$

The attendance was 198 children, 90 students and 99 adults.

8 0

3 years ago

What is the absolute value of -3? 3 - 1/3 -3 1/3

Nezavi [6.7K]

The absolute value of -3 is 3 and -3 so both would be right

5 0

3 years ago

Graph the system of equations on your graph paper to answer the question

UNO [17]

Since we have to solve this system graphically, we'll have to draw both lines.

To draw a line, simply build a little tables with two x,y values: for the first line we have

$\begin{array}{c|c}x&-x+3\\0&3\\1&2\end{array}$

So, you can draw the points (0,3) and (1,2), connect them, and you'll have the graph of the line $y=-x+3$

For the second line we have

$\begin{array}{c|c}x&x+5\\0&5\\1&6\end{array}$

So, you can draw the points (0,5) and (1,6), connect them, and you'll have the graph of the line $y=x+5$

Finally, we have to check where the two lines cross. If your drawing is accurate enough, you'll see that the point you're looking for is (-1, 4)

7 0

3 years ago