Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

8y=4x^(2)-12 x+46

y=(3)/(2)x+(5)/(4)
If
(a,b) is the solution to the system of equations shown, what is the value of
a ?

$8 y=4 x^{2}-12 x+46$ $\newline$ $y=\frac{3}{2} x+\frac{5}{4}$ $\newline$ If $(a, b)$ is the solution to the system of equations shown, what is the value of $a$ ?

View step-by-step help

View step-by-step help

Evaluate recursive formulas for sequences

Full solution

Q.

8 y=4 x^{2}-12 x+46

\newline

y=\frac{3}{2} x+\frac{5}{4}

\newline

If

(a, b)

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

a

?

Substitute $y$ into first equation: We have a system of two equations: $\newline$ $1$ ) $8y = 4x^2 - 12x + 46$ $\newline$ $2$ ) $y = \frac{3}{2}x + \frac{5}{4}$ $\newline$ To find the solution to the system, we need to substitute the second equation into the first one to solve for $x$ .
Distribute $8$ on left side: Substitute $y$ from the second equation into the first equation: $\newline$ $8\left(\frac{3}{2}x + \frac{5}{4}\right) = 4x^2 - 12x + 46$
Rearrange equation and solve: Distribute $8$ on the left side of the equation: $\newline$ $8 \times \left(\frac{3}{2}\right)x + 8 \times \left(\frac{5}{4}\right) = 4x^2 - 12x + 46$ $\newline$ $12x + 10 = 4x^2 - 12x + 46$
Divide and simplify: Rearrange the equation to set it to zero and solve for $x$ : $4x^2 - 12x - 12x - 10 + 46 = 0$ $4x^2 - 24x + 36 = 0$
Factor the quadratic equation: Divide the entire equation by $4$ to simplify: $\newline$ $x^2 - 6x + 9 = 0$
Set factors equal to zero: Factor the quadratic equation: $\newline$ (x - \(3)(x - $3$ ) = $0$
Find $x$ value: Set each factor equal to zero and solve for $x$ : $x - 3 = 0$ $x = 3$
Final solution for $a$ : We found the value of $x$ to be $3$ . Since we are looking for the value of $a$ , and $(a,b)$ is the solution to the system, $a = x$ .

More problems from Evaluate recursive formulas for sequences

Question

Find the sum of the finite arithmetic series.

\sum_{n=1}^{10} (7n+4)

\newline

Posted 9 months ago

Question

Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`

Posted 5 months ago

Question

Type the missing number in this sequence: `2, 4 8`, ______,`32`

Posted 5 months ago

Question

What kind of sequence is this?

2, 10, 50, 250, \ldots

Choices:Choices:

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 5 months ago

Question

What is the missing number in this pattern?

1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_

Posted 7 months ago

Question

Classify the series.

\sum_{n = 0}^{12} (n + 2)^3

\newline

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 5 months ago

Question

Find the first three partial sums of the series.

\newline

1 + 6 + 11 + 16 + 21 + 26 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 7 months ago

Question

Find the third partial sum of the series.

\newline

3 + 9 + 15 + 21 + 27 + 33 + \cdots

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

S_3 =

Posted 7 months ago

Question

Find the first three partial sums of the series.

\newline

1 + 7 + 13 + 19 + 25 + 31 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 9 months ago

Question

Does the infinite geometric series converge or diverge?

\newline

1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots

\newline

\newline

\text{[A]converge}

\newline

\text{[B]diverge}

Posted 5 months ago

Related topics

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