<span><span>Solve <span>x5 + 3x4 – 23x3 – 51x2 + 94x + 120 </span></span>><span><span> 0</span>. </span></span><span>First, I factor to find the zeroes:<span><span>x5 + 3x4 – 23x3 – 51x2 + 94x + 120</span><span>= (x + 5)(x + 3)(x + 1)(x – 2)(x – 4) = 0</span></span><span>...so </span><span>x = –5, –3, –1, 2,</span><span> and </span>4<span> are the zeroes of this polynomial. (Review how to </span>solve polynomials, if you're not sure how to get this solution.)<span>To solve by the Test-Point Method, I would pick a sample point in each interval, the intervals being </span>(negative infinity, –5)<span>, </span>(–5, –3)<span>, </span>(–3, –1)<span>, </span>(–1, 2)<span>, </span>(2, 4)<span>, and </span>(4, positive infinity). As you can see, if your polynomial or rational function has many factors, the Test-Point Method can become quite time-consuming.<span>To solve by the Factor Method, I would solve each factor for its positivity: </span><span>x + 5 > 0</span><span> for </span><span>x > –5</span>;<span>x + 3 > 0</span><span> for </span><span>x > –3</span><span>; </span><span>x + 1 > 0</span><span> for </span><span>x > –1</span><span>; </span><span>x – 2 > 0</span><span> for </span><span>x > 2</span><span>; and </span><span>x – 4 > 0</span><span> for </span><span>x > 4</span>. Then I draw the grid:...and fill it in:...and solve:<span>Then the solution (remembering to include the endpoints, because this is an "or equal to" inequality) is the set of </span>x-values in the intervals<span> [–5, –3]<span>, </span>[–1, 2]<span>, and </span>[4, positive infinity]</span>. </span>
As you can see, if your polynomial or rational function has many factors, the Factor Method can be much faster.
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</span>
Answer:
13
Step-by-step explanation:
x² = 5²+12²
x² = 25+144
x² = 169
x² = 13²
x = 13
Answer:
y = 2x+5
Step-by-step explanation:
rearrange the equation to make y the sof
y = 1/2x - 3
to find gradient of perpendicular line
1/2 ÷ ( - 1 )
y = -2x + c , the replace the coordinates (-3,-1)
y = 2x + 5
Answer:
<em>Mrs. Adams will earn $3,120 of interest at the end of year 8.</em>
Step-by-step explanation:
<u>Simple Interest</u>
In simple interest, the money earns interest at a fixed rate, assuming no new money is coming in or out of the account.
We can calculate the interests earned by an investment of value A in a period of time t, at an interest rate r with the formula:
Mrs. Adams deposited an amount of A=$12,000 into an account that earns an annual simple interest rate of r=3.25%. We must find the interest earned in t=8 years. The interest rate is converted to decimal as:
The interest is then calculated:
Mrs. Adams will earn $3,120 of interest at the end of year 8.
