Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

${:[y=6x-30],[y=x^(2)-18 x+114]:} If (a,b) is the solution to the system of equations shown, what is the value of b ?$

$y=6 x-30$ $\newline$ $y=x^{2}-18 x+114$ $\newline$ If $(a, b)$ is the solution to the system of equations shown, what is the value of $b$ ?

View step-by-step help

View step-by-step help

Powers with decimal and fractional bases

Full solution

Q.

y=6 x-30

\newline

y=x^{2}-18 x+114

\newline

If

(a, b)

is the solution to the system of equations shown, what is the value of

b

?

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $y = 6x - 30$ $\newline$ $y = x^2 - 18x + 114$
Set Equal: Set the two equations equal to each other to find the $x$ -coordinate of the intersection point(s). $6x - 30 = x^2 - 18x + 114$
Rearrange & Solve: Rearrange the equation to set it to zero and solve for $x$ . $x^2 - 18x + 114 - 6x + 30 = 0$ $x^2 - 24x + 144 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ $(x - 12)^2 = 0$
Solve for x: Solve for x. $\newline$ $x - 12 = 0$ $\newline$ $x = 12$
Substitute & Find y: Substitute the value of $x$ into one of the original equations to find the value of $y$ . $\newline$ $y = 6x - 30$ $\newline$ $y = 6(12) - 30$ $\newline$ $y = 72 - 30$ $\newline$ $y = 42$

More problems from Powers with decimal and fractional bases

Question

\newline

2^2 =

Posted 1 year ago

Question

Evaluate. Write your answer as a fraction or whole number.

\newline

(\frac{1}{4})^4

Posted 9 months ago

Question

Which is equal to

9^{-61}

Posted 9 months ago

Question

\newline

Express your answer using positive exponents.

\newline

r^5 \cdot r^8

Posted 9 months ago

Question

Simplify. Express your answer using a single exponent.

\newline

(h^2)^6

\newline

Posted 9 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

(9p^5)(5p^8)

\newline

Posted 9 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

(2v^3)(4v)(5v)

\newline

Posted 1 year ago

Question

Simplify. Express your answer using a single exponent.

\newline

(5z^8)^2

\newline

Posted 9 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

r^9 \cdot r^8 \cdot r^{\text{-}5}

\newline

Posted 9 months ago

Question

Which expression is equivalent to

6 \times 6^8

\newline

\newline

\frac{1}{6^9}

\newline

6^8

\newline

\frac{1}{6^8}

\newline

6^9

Posted 1 year ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant