The quadratic equations and their solutions are;
9 ± √33 /4 = 2x² - 9x + 6.
4 ± √6 /2 = 2x² - 8x + 5.
9 ± √89 /4 = 2x² - 9x - 1.
4 ± √22 /2 = 2x² - 8x - 3.
Explanation:
- Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.
- We have to solve all of the five equations to be able to match the equations with their solutions.
- 2x² - 8x + 5, here a = 2, b = -8, c = 5. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4. 24 can also be written as 4 × 6 and √4 = 2. So x = 8 ± 2√6 / 2×2= 4±√6/2.
- 2x² - 10x + 3, here a = 2, b = -10, c = 3. x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.
- 2x² - 8x - 3, here a = 2, b = -8, c = -3. x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4. 88 can also be written as 4 × 22 and √4 = 2. So x = 8 ± 2√22 / 2×2 = 4± √22/2.
- 2x² - 9x - 1, here a = 2, b = -9, c = -1. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4. x = 9 ± √89 / 4.
- 2x² - 9x + 6, here a = 2, b = -9, c = 6. x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4. x = 9 ± √33 / 4 .
Answer:
4
Step-by-step explanation:
Where on the X-axis do they intersect? 4
For A: 1 senior; 1 infant; 2 children; 4 adults, out of 8 people
for B: 1 senior; 3 infants; 6 children; 6 adults, out of 16 people
for D: $43.75
for E: $76.25
1 kilogram (kg) equals to 1000 grams (g). Since you have 6.42 kilograms, divide 6.42 kilograms to 1000 grams. Your final answer is 6420 grams in total.
9514 1404 393
Answer:
- slope: cost per mile
- y-intercept: fixed base cost
Step-by-step explanation:
The y-intercept is the value of y when x=0. The problem statement tells you that x is the number of miles driven, and y is the rental cost.
When the number of miles driven is zero, the rental cost is ...
y = 2.25×0 +70
y = 70
The cost of renting the truck is $70 when it isn't driven anywhere. The y-intercept ($70) is the basic, fixed cost of truck rental.
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If x=1 (1 mile driven), then 2.25 is added to the cost of the truck rental. The slope (2.25) is the cost per mile driven. (That mileage cost is added to the basic rental cost.)
