Emmett has $90,000 in a savings account that earns 5% interest per year. The interest is
1 answer:
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The values of k for the different quadratic equation solutions are as follows
a the equation 2x² - x + 3k = 0 has two distinct real roots
- k < 1/24
b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots
- k = 3/5
ci the equation -x² + 3x + (k + 1) = 0 has real roots
- k > -3.25
d the equation 3kx² - 3x + 2 = 0 has no real solutions
- k < ± 1.633
Quadratic equations of the form ax² + bx + c = 0 is solved using the formula
OR
The equation b² - 4ac is called the discriminant and it is used as follows
To solve the equation and get two real roots: 2x² - x + 3k = 0
- b² - 4ac > 0
substituting the values gives
(-1)² - 4 * 2 * 3k > 0
1 - 24k > 0
1 > 24k
divide through by coefficient of k
k < 1/24
To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0
- b² - 4ac = 0
substituting the values gives
(-2)² - 4 * 5 * (2k - 1) = 0
4 - 40k + 20 = 0
-40k = -24
divide through by coefficient of k
k = 3/5
To solve the equation and get real roots -x² + 3x + (k + 1) = 0
- b² - 4ac > 0
substituting the values gives
(3)² - 4 * -1 * (k+1) > 0
9 + 4k + 4> 0
4k > -13
divide through by coefficient of k
k > -3.25
To solve the equation and get no real solutions 3kx² - 3x + 2 = 0
- b² - 4ac < 0
substituting the values gives
(-3)² - 4 * 3k * 2 < 0
9 - 24k² > 0
9 > 24k²
divide through by coefficient of k²
k² < 24/9
k < ± 1.633
Learn more about roots of quadratic equations: brainly.com/question/26926523
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Answer:
x = 28
Step-by-step explanation:
If the quadrilaterals are similar, there is a proportionality among their sides:
The top side in the large figure (70) is to the top side in the small figure (10) in the same ratio as the left side (x) in the large figure is to the left side in the small figure (4). This in math terms is written as:
We can then solve for the unknown "x" by multiplying both sides by 4: