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4 years ago

6

Triangle END is reflected across the line y = x using the rule (x, y) → (y, x) to create triangle E′N′D′. If a line segment is d

rawn from point E to point E′, which statement would best describe the line segment drawn in relation to the line y = x?
A-Both are congruent to each other.
B- Both create diameters of concentric circles.
C- They are parallel.
D- They are perpendicular.

2 answers:

timama [110]4 years ago

8 0

Answer:

They are perpendicular.

Step-by-step explanation:

Step-by-step explanation:

For example, if we have the point E (1, 2) and E' (2, 1)

we can get the slope as follows

m' = (yE' - yE) / (xE' - xE)

⇒ m' = (1 - 2)/(2 - 1) = -1 / 1 = -1

Now we have the slope of the line y = x, which is m = 1

we can apply

m*m' = (1)*(-1) = - 1

we can say that they are perpendicular.

harina [27]4 years ago

5 0

the correct answer is that they are perpendicular.

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4t+3c=$81.00<br> 10t+3c=$135.00

muminat

$\left \{ {{4t+3c=81.00\:(I)} \atop {10t+3c=135.00\:(II)}} \right.$
<span>Simplify the first equation by (-1)
</span> $\left \{ {{4t+3c=81.00\:*(-1)} \atop {10t+3c=135.00\:\:\:\:\:}} \right.$
<span>Once simplified, cancel the opposing terms.
</span> $\left \{ {{-4t-\diagup\!\!\!\!3c=-81.00} \atop {10t+\diagup\!\!\!\!3c=135.00}} \right.$
Now find the value of "t".
$\left \{ {{-4t=-81.00} \atop {10t=135.00}} \right.$
-------------------------------
$6t = 54.00$
$t = \frac{54.00}{6}$
$\boxed{\boxed{t = 9.00}}\end{array}}\qquad\quad\checkmark$

Now find the value of "c", replace the found value of "t" in the first equation:
$4t+3c=81.00\:(I)$
$4*9+3c=81.00$
$36 + 3c = 81.00$
$3c = 81.00 - 36$
$3c = 45.00$
$c = \frac{45.00}{3}$
$\boxed{\boxed{c = 15.00}}\end{array}}\qquad\quad\checkmark$

Answer:
<span>The values of "t" and "c" satisfying the linear system are successively: $ 9.00 and $ 15.00</span>

3 0

3 years ago

Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

nalin [4]

Answer:

$y=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (\frac{5}{4})^x$

or

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

$y=a \cdot b^x$ , ( $b\neq 0$ ).

If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

So our function so far looks like this:

$y=8 \cdot b^x$

Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

$10=8 \cdot b^1$

$10=8 \cdot b$

Divide both sides by 8:

$\frac{10}{8}=b$

Reduce the fraction:

$\frac{5}{4}=b$

So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

$y=\frac{8}{16} \cdot 25$

$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

4 0

3 years ago

If the perimeter of a triangle is 45 cm and the ratio of the 3 sides is 2:3:4, find the length of all 3 sides

frozen [14]

Answer:

Below.

Step-by-step explanation:

2 + 3 + 4 = 9 so

the smallest side = 2/9 * 45, the next = 3/9 * 45 and the longest = 4/9 *45.

= 10, 15 and 20 cm.

5 0

3 years ago

A- CE=CD <br> B- CE = CA <br> C- BF=DF <br> D- DF=EF<br><br> please help!!

Oksana_A [137]

The perpendicular bisector theorem gives the statements that ensures

that $\overleftrightarrow{FG}$ and $\overleftrightarrow{AB}$ are perpendicular.

The two statements if true that guarantee $\overleftrightarrow{FG}$ is perpendicular to line $\overleftrightarrow{AB}$ are;

$\overline{CE} = \overline{CD}$

$\overline{DF} = \overline{EF}$

Reasons:

The given diagram is the construction of the line $\mathbf{\overleftrightarrow{FG}}$ perpendicular to line $\mathbf{\overleftrightarrow{AB}}$ .

Required:

The two statements that guarantee that $\overleftrightarrow{FG}$ is perpendicular to line $\overleftrightarrow{AB}$ .

Solution:

From the point <em>C</em> arcs <em>E</em> and <em>D</em> are drawn to cross line $\overleftrightarrow{AB}$ , therefore;

$\overline{CE} = \mathbf{\overline{CD}}$ arcs drawn from the same radius.

$\overleftrightarrow{FG}$ is perpendicular to line $\overleftrightarrow{AB}$ , given.

Therefore;

$\overline{DF} = \overline{EF}$ by perpendicular bisector theorem.

Learn more about the perpendicular bisector theorem here:

brainly.com/question/11357763

7 0

3 years ago

Celina and Richard spend a certain amount of money from their money box each month to buy plants.

loris [4]

Answer:

100

Step-by-step explanation:

5 0

3 years ago