This is a quadratic equation with a general equation of ax^2 + bx + c.
The quadratic formula can help to get the roots of the equation. We know the highest degree of that equation is 2; so there will be also two roots.
The quadratic formula is
x = [-b ± √(b^2 - 4ac)] / 2a
With a = 1, b = 7, c = 2,
x = {-7 ± √[(7)^2 - 4(1)(2)]} / 2(1) = (-7 ± √41) / 2
So the two roots are
x1 = (-7 + √41) / 2 = -0.2984
x2 = (-7 - √41) / 2 = 0.2984
This is also another way of factorizing the equation
(x + 0.2984)(x + 0.2984) = x^2 + 7x + 2
Answer: 427 miles
Step-by-step explanation:
if the jeep averages 30.5 miles per gallon, and you have 14 gallons, then you will need to multiply 30.5*14 to get your answer, which is 427
28/80 and then you simplify it by dividing the numerator and denominator by 4 and you get 7/20.
B. 7/20 is the correct answer
Using translation concepts, the transformations are given as follows:
a) The function is horizontally compressed by a factor of 3 and shifted down one unit.
b) The function is shifted right 3 units and vertically stretched by a factor of 2.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Item a:
The transformations are:
- x -> 3x, hence the function is horizontally compressed by a factor of 3.
- y -> y - 1, hence the function is shifted down one unit.
Item b:
The transformations are:
- x -> x - 3, hence the function is shifted right 3 units.
- y -> 2y, hence the function is vertically stretched by a factor of 2.
More can be learned about translation concepts at brainly.com/question/4521517
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Answer:
125.6 cm²
Step-by-step explanation:
Area of the shaded region = area of larger circle - area of the smaller circle
Area of the smaller circle = πr²
π = 3.14, r = 3 cm
Area of smaller circle = 3.14*3² = 3.14*9 = 28.26 cm²
Area of larger circle = πr²
π = 3.14, r = 7
Area of larger circle = 3.14*7² = 3.14*49 = 153.86 cm²
Area of the shaded region = 153.86 - 28.26 = 125.6 cm²
