Solve Quadratic Equations by Factoring: Solve by factoring and using the Zero Product Property:
1. 2x^2+3x-5=x^2+4x-5
2. 16x^2+5=4
3. X^2+45=20-10x
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Answers
Answer:
- x = 0 or 1
- x = ±i/4
- x = -5 (twice)
Step-by-step explanation:
Factoring is aided by having the equations in standard form. The first step in each case is to put the equations in that form. The zero product property tells you that a product is zero when a factor is zero. The solutions are the values of x that make the factors zero.
1. x^2 -x = 0
x(x -1) = 0 . . . . . x = 0 or 1
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2. 16x^2 +1 = 0
This is the "difference of squares" ...
(4x)^2 - (i)^2 = 0
(4x -i)(4x +i) = 0 . . . . . x = -i/4 or i/4 (zeros are complex)
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3. x^2 +10x +25 = 0
(x +5)(x +5) = 0 . . . . . x = -5 with multiplicity 2
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Answers
An, ( y=5/2×0+5 ) as you know if i multiply number to zero you get zero so "x" change to the zero you get
( y=0+5 )= ( y=5 ) that is your answer
Answers
x² / (9/4) + y² / 9 = 1
This is an ellipse. Equation is: x²/a² + y²/b² = 1
a² = 9/4 ⇒ a = 3/2
b² = 9 ⇒ b = 3
The axis of symmetry are the x and y axis, or the lines: y = 0 and x = 0.
Graph is in the attachment.
The lines of symmetry for the graph of equation 4x² + y² = 9 are the x-axis and the y-axis.
To determine the lines of symmetry of the graph of equation 4x² + y² = 9, we need to analyze the form of the equation.
The given equation represents an ellipse, as it contains terms for both x² and y².
Comparing this with the given equation 4x² + y² = 9, we can rewrite it as:
(2x)²/3² + y²/3² = 1
By comparing the equations, we can deduce that a² = 3² and b² = 3². This means that the major axis has a length of 2a = 2(3) = 6 and the minor axis has a length of 2b = 2(3) = 6.
Since the ellipse is symmetric with respect to both the x-axis and the y-axis, there are two lines of symmetry.
Learn more about ellipses here:
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Answers
9 and 1 over 2 plus 1 over 4
9 and 1 over 2 minus 1 over 4
9 and 1 over 2 divided by 1 over 4
Answers
x = (9 1/2) / (1/4)......9 and 1/2 divided by 1 over 4 <===
x = (19/2) / (1/4)
x = 19/2 * 4
x = 76/2 = 38 days is how long he went jogging
Answer:
Question:
George jogged a total distance of 9 and 1 over 2 miles during the months of October and November. If George only jogged 1 over 4 mile every day, which expression shows the number of days in which he went jogging?
We know:
He jogged 9 1/2 miles during October and November
1/4 mile every day
Answer:
9 and 1 over 2 divided by 1 over 4
Answers
Final answer:
Partial fractions are used in numerous aspects of everyday life, especially in fields requiring mathematical calculations. This includes engineering, calculus, computer science, signal processing, and electrical circuits. While we may not directly observe their use, their applications make many of our daily operations possible.
Explanation:
The concept of partial fractions is widely used in numerous aspects of our daily life, especially in fields that require mathematical calculations. Partial fractions make complex mathematical processes simpler and easier to solve.
For instance, in the field of engineering, partial fractions are used to simplify complex fractions in control system design, particularly in Laplace Transform. Moreover, it's also used in calculus to integrate rational functions.
In the realm of computer science, partial fractions can assist with algorithm efficiency when dealing with fractions or rational numbers. They are also used in signal processing and electrical circuits, which are a major part of our daily life as most electronics operate on these principles.
In everyday life, the use of partial fractions might not be directly observed but their applications in various fields make many of our daily life operations and technologies possible.
Learn more about Uses of Partial Fractions here:
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Answers
Answer:
The inverse is g(x)=-x+5.
Both f and g have domain and range all real numbers.
In interval notation that is
Step-by-step explanation:
f(x)=-x+5 is a linear function.
Since isn't f(x)=constant then it is diagonal so this means the range is all real numbers.
For any linear function, the domain will be all real numbers.
So to find the inverse of y=-x+5, you interchange x and y and resolve for y.
y=-x+5
(interchange)
x=-y+5
(solve for y)
Subtract 5 on both sides:
x-5=-y
Multiplying both sides by -1:
-x+5=y
So the inverse is g(x)=-x+5. To find find the domain and range of the inverse function given you already did it for the original function, the sets are swapped. The sets were the same here because they were both all real numbers.
Answer:
Domain of this function become R
Step-by-step explanation: