Question
In the equation above, if a is negative and b is positive, which of the following must be true?
- C > 1
- C = 1
- c = -1
- c < -1
The correct answer is: C > 1
- We have given the equation
- The equation can be rewritten as
,
or .
- Since
and 
, it follows that 
- And as b/a < 0
-
- 1-c < 0, or equivalent to c > 1.
- Option B is incorrect. If c = 1, then a – b = a, or b = 0. But it is given that b > 0, so c = 1 cannot be true.
- Option C is incorrect. If c = -1, then a - b = -a, or 2a = b. But this equation contradicts the premise that a < 0 and b > 0, so c = -1 cannot be true.
- Option D is incorrect. For example, if c = -2, then a - b = -2a, or 3a = b. But this contradicts the fact that and have opposite signs, so c < -1 cannot be true.
,or .
and , it follows that - 1-c < 0, or equivalent to c > 1.
- Option B is incorrect. If c = 1, then a – b = a, or b = 0. But it is given that b > 0, so c = 1 cannot be true.
- Option C is incorrect. If c = -1, then a - b = -a, or 2a = b. But this equation contradicts the premise that a < 0 and b > 0, so c = -1 cannot be true.
- Option D is incorrect. For example, if c = -2, then a - b = -2a, or 3a = b. But this contradicts the fact that and have opposite signs, so c < -1 cannot be true.
Related Questions to study
In the equation above, k is a constant. If x = 9, what is the value of K ?
In the equation above, k is a constant. If x = 9, what is the value of K ?
What value of x satisfies the equation above?
Note:
Whenever we encounter a square root while solving an equation, our first attempt should be to somehow remove the square root by squaring both sides and get a simpler equation to solve. Another way to find the value of x which satisfies the equation would be to simply put the values in the options in the equation and check if it is satisfied
What value of x satisfies the equation above?
Note:
Whenever we encounter a square root while solving an equation, our first attempt should be to somehow remove the square root by squaring both sides and get a simpler equation to solve. Another way to find the value of x which satisfies the equation would be to simply put the values in the options in the equation and check if it is satisfied
y ≤3x +1
x – y >1
Which of the following ordered pairs ( x, y)satisfies the system of inequalities above?
y ≤3x +1
x – y >1
Which of the following ordered pairs ( x, y)satisfies the system of inequalities above?
The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is 
the corresponding original dimension, what is the height of the reproduction, in inches ?
The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width 36.25 inches. If a reproduction was made where each dimension is the corresponding original dimension, what is the height of the reproduction, in inches ?
Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?
Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?
Maria plans to rent a boat. The boat rental costs $60 per hour, and she will also have to pay for a water safety course that costs $10. Maria wants to spend no more than $280 for the rental and the course. If the boat rental is available only for a whole number of hours, what is the maximum number of hours for which Maria can rent the boat?
Maria plans to rent a boat. The boat rental costs $60 per hour, and she will also have to pay for a water safety course that costs $10. Maria wants to spend no more than $280 for the rental and the course. If the boat rental is available only for a whole number of hours, what is the maximum number of hours for which Maria can rent the boat?
What are the solutions of the quadratic equation 
?
What are the solutions of the quadratic equation ?
In the xy-plane, the point (2, 5) lies on the graph of the function f. If f(x)= k - x2 , where k is a constant, what is the value of k ?
In the xy-plane, the point (2, 5) lies on the graph of the function f. If f(x)= k - x2 , where k is a constant, what is the value of k ?
(½)y = 4
x – (½)y= 2
The system of equations above has solution (x, y). What is the value of x ?
(½)y = 4
x – (½)y= 2
The system of equations above has solution (x, y). What is the value of x ?
A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?
A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?
In the xy-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?
The slope-intercept form is one of the most common ways to represent a line's equation. For example, the slope of a straight line, slope-intercept, and y-intercept formula determine the equation of a line (where the line intersects the y-axis at the point of the y-coordinate). An equation must be satisfied by each point on a line. For example, the graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.
¶A line's slope, m, represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.
In the xy-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?
The slope-intercept form is one of the most common ways to represent a line's equation. For example, the slope of a straight line, slope-intercept, and y-intercept formula determine the equation of a line (where the line intersects the y-axis at the point of the y-coordinate). An equation must be satisfied by each point on a line. For example, the graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.
¶A line's slope, m, represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?
To calculate average miles, divide the total distance traveled by the time spent traveling. This will provides us with your average speed.
So, for example, if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in an hour, his average speed was about 57 miles per hour. In this case, Alan can travel a hundred miles per week at 25 miles per gallon of gasoline to save $5 per week on gas, assuming gasoline costs $4 per gallon.
Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week?
To calculate average miles, divide the total distance traveled by the time spent traveling. This will provides us with your average speed.
So, for example, if Ben traveled 150 miles in 3 hours, 120 miles in 2 hours, and 70 miles in an hour, his average speed was about 57 miles per hour. In this case, Alan can travel a hundred miles per week at 25 miles per gallon of gasoline to save $5 per week on gas, assuming gasoline costs $4 per gallon.
Point P is the center of the circle in the figure above. What is the value of x ?
Point P is the center of the circle in the figure above. What is the value of x ?
The circle above with center O has a circumference of 36. What is the length of minor arc 
?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
The circle above with center O has a circumference of 36. What is the length of minor arc ?
The diameter of a circle is also known as its measurement of the circle's edge, circumference, or perimeter.
As opposed to this, a circle's area indicates the space it occupies.
The circle circumference is the length when we cut it, open and draw a straight line from it.
Units like centimeters or meters are typically used to measure it.
The circle's radius is considered when applying the formula to determine the circumference of the circle.
Therefore, to calculate a circle's circumference, we must know its radius or diameter.
Therefore, the circumference of a circle formula is the circle perimeter or circumference is 2πR.
where,
R is the circle's radius.
π is a mathematical constant with an estimated value of 3.14 (to the nearest two decimal places).
