Maths-
General
Easy
Question
A system of two linear equations has no solutions. The graph of one of the equations in the system is shown in the xy - plane.
The second equation in the system is , where a is a constant. What is the value of a ?
The correct answer is: 1.25
Step 1 :- find the slope of line passing through points (0,4) and (-4,-1)
Slope m for the line passing through (x1 ,y1) and (x2 ,y2) is
m =
Step 2 : finding slope of equation
it is in the form of slope-intercept form of line
So, slope = a and y intercept = -1( which is different from shown line)
The two lines are not overlapping .so, the infinite no.of solutions condition is avoided.
Both slopes are equal so a = (or) 1.25
Related Questions to study
Maths-
If a is the mean and b is the median of nine consecutive integers, what is the value of |a - b|?
If a is the mean and b is the median of nine consecutive integers, what is the value of |a - b|?
Maths-General
Maths-
y = -16t2 + 64t +80
The equation above gives the height of an object above the ground, y, in feet, t seconds after it is launched from a platform. How many seconds after it is launched does the object reach the ground?
y = -16t2 + 64t +80
The equation above gives the height of an object above the ground, y, in feet, t seconds after it is launched from a platform. How many seconds after it is launched does the object reach the ground?
Maths-General
Maths-
In the figure, triangles ABC and DBE are right triangles. What is ?
In the figure, triangles ABC and DBE are right triangles. What is ?
Maths-General
Maths-
I =
The formula above is Ohm's law for an electric circuit with current I, in amperes, potential difference V, in volts, and resistance R, in Ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by n six-volt batteries that produce a total potential difference of 6n volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, n, of six-volt batteries that can be used?
I =
The formula above is Ohm's law for an electric circuit with current I, in amperes, potential difference V, in volts, and resistance R, in Ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by n six-volt batteries that produce a total potential difference of 6n volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, n, of six-volt batteries that can be used?
Maths-General
Maths-
The histogram summarizes the distribution of a data set composed of 50 integers. The first bar represents the number of integers that are at least 0 but less than 5. The second bar represents the number of integers that are at least 5 but less than 10 , and so on. What is a possible value of the median of the data set?
The histogram summarizes the distribution of a data set composed of 50 integers. The first bar represents the number of integers that are at least 0 but less than 5. The second bar represents the number of integers that are at least 5 but less than 10 , and so on. What is a possible value of the median of the data set?
Maths-General
Maths-
If what is the value of x ?
If what is the value of x ?
Maths-General
Maths-
In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the point (2, 2). If the point (20, w) lies on line k, what is the value of w?
In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the point (2, 2). If the point (20, w) lies on line k, what is the value of w?
Maths-General
Maths-
Number of Contestants by Score and Day
The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above.
What was the mean score of the contestants on Day 1 ?
Number of Contestants by Score and Day
The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above.
What was the mean score of the contestants on Day 1 ?
Maths-General
Maths-
In the figure above, tan B = . If BC = 15 and DA = 4, what is the length of DE ?
In the figure above, tan B = . If BC = 15 and DA = 4, what is the length of DE ?
Maths-General
Maths-
Several values of x and their corresponding values of y are shown in the table. A linear equation that represents the relationship shown in the table x = k, where k is a constant. What is the value of k ?
Several values of x and their corresponding values of y are shown in the table. A linear equation that represents the relationship shown in the table x = k, where k is a constant. What is the value of k ?
Maths-General
Maths-
The equation (x + 6)2 + (y + 3)2 = 121 defines a circle in the xy-plane. What is the radius of the circle?
The equation (x + 6)2 + (y + 3)2 = 121 defines a circle in the xy-plane. What is the radius of the circle?
Maths-General
Maths-
2 , 10 , 3 , 7 , 6
The mean of the list of numbers above is what fraction of the sum of the five numbers?
2 , 10 , 3 , 7 , 6
The mean of the list of numbers above is what fraction of the sum of the five numbers?
Maths-General
Maths-
y = x2 – 4x + 4
y = 4 – x
If the ordered pair (x, y) satisfies the system of equations above, what is one possible value of x ?
y = x2 – 4x + 4
y = 4 – x
If the ordered pair (x, y) satisfies the system of equations above, what is one possible value of x ?
Maths-General
Maths-
In a science classroom, when labs are performed, students are seated at lab tables. If the teacher assigns 2 students to each lab table, 4 additional lab tables will be needed to seat all of the students. If the teacher assigns 4 students to each lab table, 4 lab tables will not be used. How many students are there in the science class?
In a science classroom, when labs are performed, students are seated at lab tables. If the teacher assigns 2 students to each lab table, 4 additional lab tables will be needed to seat all of the students. If the teacher assigns 4 students to each lab table, 4 lab tables will not be used. How many students are there in the science class?
Maths-General
Maths-
Point C is the centre of the circle above. What fraction of the area of the circle is the area of the shaded region?
Point C is the centre of the circle above. What fraction of the area of the circle is the area of the shaded region?
Maths-General