Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the value of $𝑥$ in the solution to the system of equations? $\newline$ $2x+2y=11$ $\newline$ $4x-y=28$

View step-by-step help

View step-by-step help

Transformations of functions

Full solution

Q. What is the value of

𝑥

in the solution to the system of equations?

\newline

2x+2y=11

\newline

4x-y=28

Simplify Equation: Simplify the first equation by dividing all terms by $2$ to make calculations easier. $\newline$ $\frac{2x + 2y}{2} = \frac{11}{2}$ $\newline$ $x + y = 5.5$
Substitution Method: Use substitution method to solve for x. Substitute $y = 5.5 - x$ into the second equation. $\newline$ $4x - (5.5 - x) = 28$ $\newline$ $4x - 5.5 + x = 28$ $\newline$ $5x - 5.5 = 28$
Solve for x: Solve for x by isolating x on one side. $\newline$ $5x = 28 + 5.5$ $\newline$ $5x = 33.5$ $\newline$ $x = \frac{33.5}{5}$ $\newline$ $x = 6.7$

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