Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

13 X is a point inside triangle
PQR. It is
3cm from
P, and
4cm from Q. How far is
X from
R ?

$13 X$ is a point inside triangle $P Q R$ . It is $3 \mathrm{~cm}$ from $P$ , and $4 \mathrm{~cm}$ from Q. How far is $\mathrm{X}$ from $\mathrm{R}$ ?

View step-by-step help

View step-by-step help

Transformations of functions

Full solution

Q.

13 X

is a point inside triangle

P Q R

. It is

3 \mathrm{~cm}

from

P

, and

4 \mathrm{~cm}

from Q. How far is

\mathrm{X}

from

\mathrm{R}

?

Identify Problem: Identify the problem as finding the distance from point $X$ to vertex $R$ in triangle $PQR$ , where distances from $P$ to $X$ and $Q$ to $X$ are known.
Use Triangle Inequality Theorem: Use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Apply Theorem: Apply the theorem: Let's denote the unknown distance from X to R as $d$ . According to the triangle inequality: $\newline$ $1$ . $PX + XR > PR$ $\newline$ $2$ . $QX + XR > QR$ $\newline$ $3$ . $PX + QX > PQ$ $\newline$ Given $PX = 3$ cm and $QX = 4$ cm, we can write: $\newline$ $1$ . $3 + d > PR$ $\newline$ $2$ . $4 + d > QR$ $\newline$ $3$ . $3 + 4 > PQ$
Additional Information Needed: Since we don't have the values for $PR$ , $QR$ , or $PQ$ , we cannot directly calculate $d$ using these inequalities. We need additional information about the triangle or a different approach to solve for $d$ .

More problems from Transformations of functions

Question

g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

Posted 2 months ago

Question

What does the transformation

f(x) \mapsto f(x - 4)

do to the graph of

f(x)

\newline

\newline

\text{translates it } 4 \text{ units right}

\newline

\text{translates it } 4 \text{ units down}

\newline

\text{translates it } 4 \text{ units left}

\newline

\text{translates it } 4 \text{ units up}

Posted 2 months ago

Question

What does the transformation

f(x) \mapsto f(4x)

do to the graph of

f(x)

\newline

\newline

[A] stretches it vertically

\newline

[B] stretches it horizontally

\newline

[C]shrinks it horizontally

\newline

[D]shrinks it vertically

Posted 1 month ago

Question

g(x)

g(x)

is the translation

9

f(x) = 10x + 8

\newline

\newline

g(x) = 10x - 82

\newline

g(x) = 10x + 98

\newline

g(x) = 10x - 1

\newline

g(x) = 10x + 17

Posted 2 months ago

Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

\newline

\text{[D]translation 10 units right}

Posted 1 month ago

Question

y=x^{2}

is scaled vertically by a factor of

7

. What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted down by

6

units and to the right by

5

\newline

What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted up by

2

units and to the right by

3

\newline

What is the equation of the new parabola?

\newline

y=

Posted 1 month ago

Question

y=x^{2}

is reflected across the

x

-axis and then scaled vertically by a factor of

5

\newline

What is the equation of the new parabola?

\newline

y=\square

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

\frac{1}{10}

\newline

What is the equation of the new parabola?

\newline

y=

Posted 3 months ago