Answer:
Step-by-step explanation:
first do this
Answer:
10/22
10 blue marbles/22 total marbles
(simplified = 5/11)
first we need to get rid of the ( ) so that we can see what the question really says
(3x³-5x² - 7+ 4x4) + (9x4 - 10x² - 5x³ + 3)
= 3x³-5x²-7+4x⁴+9x⁴-10x²-5x³+3
now all we need to do is add up the numbers with the same x's
<em>3x³</em>-5x²-7<u>+4x⁴+9x⁴</u>-10x²<em>-5x³</em>+3
= 13x⁴-2x³-15x²-4
Answer:
<em>The coordinates of the vertex are (-1,-4).</em>
Step-by-step explanation:
<u>Equation of the Quadratic Function
</u>
The vertex form of the quadratic function has the following equation:

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
We are given the function:

We must transform the equation above by completing squares:
The first two terms can be completed to be the square of a binomial. Recall the identity:

Thus if we add and subtract 1:

Operating:

The trinomial in parentheses is a perfect square:

Adding 4:

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).
The coordinates of the vertex are (-1,-4).
The ratio of the height (h) of the streetlight to its distance to the end of Laura's shadow is the same as the ratio of Laura's height to her distance from the end of her shadow.
.. h/(12+9) = 5'4"/9
.. h = (21/9)*5'4" = 12 4/9 feet
.. h = 12 ft 5 1/3 inches
The streetlight is 12 ft 5 1/3 inches tall.