What kind of transformation is illustrated between the triangle XYZ and XYZ?

Slav-nsk [51]

It leaves Chicago at 11:49 am and takes 2 hrs 26 min.
So in central time, that gets you to Denver at 2:15 PM.
Since mountain time is one hour behind central time, your answer would be 1:15 PM.

5 0

3 years ago

Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are

Galina-37 [17]

Answer:

$B' = (-3,6)$

Step-by-step explanation:

Given

$A(4,5)$

$B(0,5)$

$C(3,-1)$

Translation: 3 units left and 1 unit right

Required

Determine the new coordinates of B

Write out the coordinates of B

$x = 0$

$y = 5$

When a function is shifted to the left, we have to subtract the unit from the x value of the function;

Shifting by 3 units left, the new x becomes

$New\ x = 0 - 3$

$New\ x = -3$

When a function is shifted upward, we have to add the unit to the y value of the function;

Shifting by 1 unit up, the new y becomes

$New\ y = 5 + 1$

$New\ y = 6$

Hence, the new coordinates of B is

$B' = (-3,6)$

5 0

3 years ago

Find the length of AB

aniked [119]

FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula = $\sqrt{ (x_{2}- x_{1})^{2} + ( y_{2} - y_{1} )^{2} }$

Now, plug the values into the formula, So,
distance = $\sqrt{ (6- 2)^{2} + ( 2 - (-4))^{2} }$

= $\sqrt{ (6- 2)^{2} + ( 2 +4))^{2} }$

= $\sqrt{ (4)^{2} + ( 6))^{2} }$

= $\sqrt{ 16+36}$

= $\sqrt{52}$

= $2 \sqrt{13}$

So, the length of AB is $2 \sqrt{13}$ .

THIRD QUESTION
Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = $(\frac{ x_{1}+ x_{2} }{2} , \frac{ y_{1}+ y_{2} }{2} )$

$(1, 1)=(\frac{ 3+ a }{2} , \frac{ -2+b }{2} )$

Now, equaling the ordered pair, we have,

$1=\frac{ 3+ a }{2}$ .............equation (1)

$1=\frac{ -2+b }{2}$ ................equation (2)

Now, taking equation (1)
$1=\frac{ 3+ a }{2}$

$1*2=3+a$

$2-3=a$

$a=-1$

Now, taking equation (2)
$1=\frac{ -2+b }{2}$

$1*2=-2+b$

$2+2=b$

$b=4$

So, the co ordinates of C are (a, b) which is (-1 , 4)


SECOND QUESTION:
Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4

6 0

3 years ago

If x^y = z is there any way to find y if you know x and z?

Rzqust [24]

We make use of $y = \log_x(z)$ to solve for y, when you know x and z

<h3>How to solve for y?</h3>

The expression is given as:

x^y = z

The above expression is an exponential expression.

Start by taking the logarithm of both sides

y log(x) = log(z)

Divide both sides by log(x)

$y = \log_x(z)$

Hence, we make use of $y = \log_x(z)$ to solve for y, when you know x and z

Read more about exponential functions at:

brainly.com/question/11464095

#SPJ1

6 0

2 years ago

seven less than the product of twice a number is greater than 5 more the same number which integer satisfies this inequality

JulsSmile [24]

To answer this question, we would have to use algebra.

Let the unknown number be A.

Now, as per the question, we have the equation ->
2A - 7 > 5 + A
==> 2A - A > 5+7
==> A > 12

So, the final answer is --> A > 12

4 0

3 years ago

Read 2 more answers