<h3>
Answer:</h3>
1. Solutions: x = 3.4, 10.6
2. Solutions:
, ![\textsf{$x = \dfrac{-7}{2}$} - \dfrac{i\sqrt{15}}{2}](https://tex.z-dn.net/?f=%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-7%7D%7B2%7D%24%7D%20-%20%5Cdfrac%7Bi%5Csqrt%7B15%7D%7D%7B2%7D)
3. Solutions: x = -1, 11
<h3>
Step-by-step explanation:</h3>
Quadratic formula: ![\large \textsf{$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$}](https://tex.z-dn.net/?f=%5Clarge%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%24%7D)
Quadratic equation: ax² + bx c = 0, where a ≠ 0
1. x² - 14x + 36 = 0
a = 1, b = -14, c = 36
Substitute the given values into the formula:
![\normalsize \textsf{$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$}\\\\\normalsize \textsf{$x = \dfrac{-(-14) \pm \sqrt{(-14)^2-4(1)(36)}}{2(1)}$}\\\\\normalsize \textsf{$x = \dfrac{14 \pm \sqrt{196-144}}{2}$}\\\\\normalsize \textsf{$x = \dfrac{14 \pm \sqrt{52}}{2}$}\\\\\normalsize \textsf{$x = \dfrac{14 \pm 7.21}{2}$}](https://tex.z-dn.net/?f=%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-%28-14%29%20%5Cpm%20%5Csqrt%7B%28-14%29%5E2-4%281%29%2836%29%7D%7D%7B2%281%29%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B14%20%5Cpm%20%5Csqrt%7B196-144%7D%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B14%20%5Cpm%20%5Csqrt%7B52%7D%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B14%20%5Cpm%207.21%7D%7B2%7D%24%7D)
Separate into two cases:
and ![\normalsize \textsf{$x = \dfrac{14 - 7.21}{2}$}\\\\\normalsize \textsf{$x = \dfrac{6.79}{2}$}\\\\\normalsize \textsf{$x = 3.395$}\\\\\textsf{Nearest tenth: 3.4}](https://tex.z-dn.net/?f=%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B14%20-%207.21%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B6.79%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%203.395%24%7D%5C%5C%5C%5C%5Ctextsf%7BNearest%20tenth%3A%203.4%7D)
2. x² + 7x + 16 = 0
a = 1, b = 7, c = 16
Substitute the given values into the formula:
![\normalsize \textsf{$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$}\\\\\normalsize \textsf{$x = \dfrac{-7 \pm \sqrt{7^2-4(1)(16)}}{2(1)}$}\\\\\normalsize \textsf{$x = \dfrac{-7 \pm \sqrt{49-64}}{2}$}\\\\\normalsize \textsf{$x = \dfrac{-7 \pm \sqrt{-15}}{2}$}\\\\\normalsize \textsf{$x = \dfrac{-7 \pm i\sqrt{15}}{2}$}](https://tex.z-dn.net/?f=%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-7%20%5Cpm%20%5Csqrt%7B7%5E2-4%281%29%2816%29%7D%7D%7B2%281%29%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-7%20%5Cpm%20%5Csqrt%7B49-64%7D%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-7%20%5Cpm%20%5Csqrt%7B-15%7D%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-7%20%5Cpm%20i%5Csqrt%7B15%7D%7D%7B2%7D%24%7D)
Imaginary number rule: For any positive real number "k", ![\large \textsf{$\sqrt{-k} = i\sqrt{k}$}](https://tex.z-dn.net/?f=%5Clarge%20%5Ctextsf%7B%24%5Csqrt%7B-k%7D%20%3D%20i%5Csqrt%7Bk%7D%24%7D)
Notes: Two imaginary solutions indicate that the graph will not intersect the x-axis. As a result, it has no real roots.
Separate into two cases:
3. x² - 10x - 11 = 0
a = 1, b = -10, c = -11
Substitute the given values into the formula:
![\normalsize \textsf{$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$}\\\\\normalsize \textsf{$x = \dfrac{-(-10) \pm \sqrt{(-10)^2-4(1)(-11)}}{2(1)}$}\\\\\normalsize \textsf{$x = \dfrac{10 \pm \sqrt{100+44}}{2}$}\\\\\normalsize \textsf{$x = \dfrac{10 \pm \sqrt{144}}{2}$}\\\\\normalsize \textsf{$x = \dfrac{10 \pm 12}{2}$}](https://tex.z-dn.net/?f=%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-%28-10%29%20%5Cpm%20%5Csqrt%7B%28-10%29%5E2-4%281%29%28-11%29%7D%7D%7B2%281%29%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B10%20%5Cpm%20%5Csqrt%7B100%2B44%7D%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B10%20%5Cpm%20%5Csqrt%7B144%7D%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B10%20%5Cpm%2012%7D%7B2%7D%24%7D)
Separate into two cases:
and ![\normalsize \textsf{$x = \dfrac{10 - 12}{2}$}\\\\\normalsize \textsf{$x = \dfrac{-2}{2}$}\\\\\normalsize \textsf{$x = -1$}](https://tex.z-dn.net/?f=%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B10%20-%2012%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20%5Cdfrac%7B-2%7D%7B2%7D%24%7D%5C%5C%5C%5C%5Cnormalsize%20%5Ctextsf%7B%24x%20%3D%20-1%24%7D)
Hope this helps!
Learn more about quadratic equation here:
brainly.com/question/27729447
Answer:
1 cm
Step-by-step explanation:
We know that the formula for perimeter is<u> 2(l+w) or l+l+w+w</u>
We know that the height is 5 cm so that means <em><u>w= 5</u></em> also that there is 5 cm on both sides of the rectangle. So 5+5=10 so that means that the length of the rectangle is <em><u>1 cm</u></em> if you add the length together you 2 when you add the width you get 10. <em>10+2=12.</em>
Answer:
Step-by-step explanation:
<u>The difference in interest amount is:</u>
- $500*4*(4.5 - 2.5)/100 = $40
Jason received $40 more than Alistair
It was 0.16 cents a pencil just divide 1.92 by 12
answer is 2720
solution below
First, converting R percent to r a decimal
r = R/100 = 4.5%/100 = 0.045 per year.
solving our equation:
A = 2000(1 + (0.045 × 8)) = 2720
A = $2,720.00
the total amount accrued, principal plus interest, from simple interest on a principal of $2,000.00 at a rate of 4.5% per year for 8 years is $2,720.00