Insert the “equal” sign or the “not equal” sign (= or #) to make each statement true.

Find the y intercepts of 3x^2+24x-51. quadratic formula

julia-pushkina [17]

Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , with a = x^2 coefficient, b = x coefficient, and c = constant.

Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:

$y=3*0^2+24*0-51\\y=0+0-51\\y=-51$

Your y-intercept is (0,-51).

Next, using our equation plug the appropriate values into the quadratic formula:

$x=\frac{-24\pm \sqrt{24^2-4*3*(-54)}}{2*3}$

Next, solve the multiplications and exponent:

$x=\frac{-24\pm \sqrt{576-(-648)}}{6}\\\\x=\frac{-24\pm \sqrt{576+648}}{6}$

Next, solve the addition:

$x=\frac{-24\pm \sqrt{1224}}{6}$

Now, simplify the radical using the product rule of radicals as such:

Product Rule of Radicals: √ab = √a × √b

√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34

$x=\frac{-24\pm 6\sqrt{34}}{6}$

Next, divide:

$x=-4\pm \sqrt{34}$

The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).

Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

$x=-4+ \sqrt{34},-4- \sqrt{34}\\x\approx 1.83, -9.83$

The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).

5 0

3 years ago

3 feet long and 2 feet wide is what in square inches when area conversion with whole number

mixer [17]

The area is 864 square, or 6 square feet.

3 0

3 years ago

Read 2 more answers

The laws that established an official system of slavery in the American colonies

expeople1 [14]

Good Morning!

C)made it legal to keep enslaved people for their entire lives.


It was legal, for the system of slavery sustained in the British colonies - and also in the Spanish and Portuguese, as in the case of Brazil - to maintain a person as a slave throughout his life. There was no time limit, children were also enslaved - daughters of slaves.

Hugs!

5 0

3 years ago

What is the y-intercept of this line?

GaryK [48]

12, 8, 4, 0

Step-by-step explanation:

Thank Me. Super.

4 0

3 years ago

Find the midpoint of the segment with the following endpoints. (2,9) and (8,1)

vazorg [7]

Answer:

$\displaystyle (5,5)$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Midpoint Formula: $\displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

Step 1: Define

Point (2, 9)

Point (8, 1)

Step 2: Identify

(2, 9) → x₁ = 2, y₁ = 9

(8, 1) → x₂ = 8, y₂ = 1

Step 3: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Substitute in points [Midpoint Formula]: $\displaystyle (\frac{2+8}{2},\frac{9+1}{2})$
[Fractions] Add: $\displaystyle (\frac{10}{2},\frac{10}{2})$
[Fractions] Divide: $\displaystyle (5,5)$

7 0

3 years ago