Select the correct answer.

Which rule describes the composition of transformations that maps pre- image ABCD to final image A“B“C“D“?

Svetlanka [38]

Answer:

1. Reflection across the x-axis

2. Translation 6 units to the left and 1 unit up

Step-by-step explanation:

The quadrilateral ABCD has its vertices at points A(3,5), B(6,5), C(4,1) and D(1,1).

1. Reflect quadrilateral ABCD across the x-axis. This reflection has the rule:

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

then

$A(3,5)\rightarrow A'(3,-5)\\ \\B(6,5)\rightarrow B'(63,-5)\\ \\C(4,1)\rightarrow C'(4,-1)\\ \\D(1,1)\rightarrow D'(1,-1)$

2. Translate quadrilateral ABCD 6 units to the left and 1 unit up. This translation has the rule:

$(x,y)\rightarrow (x-6,y+1),$

then

$A'(3,-5)\rightarrow A''(-3,-4)\\ \\B'(6,-5)\rightarrow B''(0,-4)\\ \\C'(4,-1)\rightarrow C''(-2,0)\\ \\D'(1,-1)\rightarrow D''(-5,0)$

6 0

4 years ago

Read 2 more answers

PLEASE HELP ME

irina1246 [14]

Answer:

B) $(-1, -2)$

Step-by-step explanation:

3x + 1 = x - 1

-3x - 3x

___________

1 = −2x - 1

+1 + 1

_________

2 = −2x

_ ___

−2 −2

$x = -1$ [Plug this back into both equations above to get the y-coordinate of -2]; $-2 = y$

I am joyous to assist you anytime.

6 0

3 years ago

1) The two triangles are congruent. Find the missing side lengths and the missing angle measures.

gregori [183]

<u>Answers:</u>

Two <u>triangles are congruent</u> if they have the <u>same sides</u> and the <u>same size</u>.

In other words: they have the same shape and size, regardless of their position or orientation.

If we want to verify if two triangles are congruent, they must fulfill some conditions:

a) Two triangles are congruent if their three sides are respectively equal

b) Two triangles are congruent if two of their sides and the angle between them are respectively of equal length.

c) Two triangles are congruent if they have a congruent side and the angles with vertex at the ends of that side are also congruent.

d) Two triangles are congruent if they have two sides respectively congruent and the angles opposite the greater of the sides are also congruent

<h2>According to these criteria, it is not necessary to verify the congruence of the three sides and three angles of each triangle </h2>

Now, knowing these criteria, let’s answer the questions:

1) Here both triangles are<u> congruent</u> and are <u>Right Triangles</u> (have a right angle or a $90\º$ angle), as well.

This means angle $u=90\º$ and according to the <u>criterion b</u> listed above, the angle $t=35\º$ and angle $v=55\º$ .

This can be proven by the rule that states the sum of the three interior angles of a triangle is $180\º$ .

Then, according <u>criterion a</u>, $w=10.4m$ and $s=6m$ .

<u>This can be proven by the use of </u><u>two trigonometric functions,</u> sine and cosine:

$w=\frac{6m}{sin(35\º)}=10.4m$

Where $6m$ is the <u>Opposite side</u> to the $35\º$ angle and $w$ is the <u>hypotenuse</u>.

$s=cos(55\º)(10.4m)=5.9m$ ≅6m

Where $s$ is the <u>Adjacent side</u> to the $55\º$ angle and $10.4m$ is the <u>hypotenuse</u>.

<h2>Therefore, the answer is B: </h2>

$s=6m$ , $t=35\º$ , $u=90\º$ , $v=55\º$ , $w=10.4m$

2) According to the second figure shown, both triangles are congruent and fulfill the four criteria described above.

Therefore, the answer is:

3) “Knowing that line segment AB is the same length as line segment CD is enough to prove that triangles ABD and BCD are congruent”

This statement is <u>True</u>, because <u>both triangles share the line segment BD</u>.

<h2>This means <u>they have two equal sides</u>, and according to <u>criterion b</u> they are congruent </h2>

6 0

3 years ago

Ronald walks from home to Taco Bell to eat everyday. It takes him 30 minutes to walk the 2 mile distance. A) write a function fo

Alex777 [14]

A) We know that

$d=vt$

where d $y= \frac{1}{15}x$ = distance,
v = velocity,
t = time

In this case, d = 2 mi., t = 30 min. So we get

$2=30v$

Dividing both sides by 30, we get

$v= \frac{2}{30}= \frac{1}{15}$

Thus a function for his walk would be

$y= \frac{1}{15} x$
where y = distance and x = number of minutes he walks.

b) Domain of a function is a set of x-values on which the function defined. In this case, the number of minutes is 30 at maximum. So the domain of the function is [0, 30].

5 0

3 years ago

10y − 6y + 2y + 2y = 8

Volgvan

Step-by-step explanation:

$\tt{10y-6y+2y+2y=8 }$ ⠀