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Algebra
(a) Solve the following linear systems by the
process of elimination : 3
x + 2y + 5z = 9
x — y + $z = 2
3x — 6y z = 26
(b) Give an example, with justification, of each of
the following : 2
(i) An element of (C x Q) \(Q x C);
(ii) An infinite set whose complement in R
is infinite.
2. (a) Find the roots of the polynomial equation
x4— 9x3+ 17x2+ 33x — 90 = 0,
given that two of its roots are equal to 3. 2
(b) Use the principle of mathematical induction
to show that for any positive integer n,
(311— 2n) > O.
3. (a) A coach buys 3 cricket bats and 6 balls for
3,900. Later, he buys 1 bat and 3 balls for
another team for 1,450. Write two linear
equations to represent the purchases. Why
can the linear system so obtained be solved
by Cramer's rule ? Also, use the rule to
solve the system, and interpret the solution
in the given context. 4
(b) Give an example of a 4 x 1 matrix with
entries from Z \ N. 1
process of elimination : 3
x + 2y + 5z = 9
x — y + $z = 2
3x — 6y z = 26
(b) Give an example, with justification, of each of
the following : 2
(i) An element of (C x Q) \(Q x C);
(ii) An infinite set whose complement in R
is infinite.
2. (a) Find the roots of the polynomial equation
x4— 9x3+ 17x2+ 33x — 90 = 0,
given that two of its roots are equal to 3. 2
(b) Use the principle of mathematical induction
to show that for any positive integer n,
(311— 2n) > O.
3. (a) A coach buys 3 cricket bats and 6 balls for
3,900. Later, he buys 1 bat and 3 balls for
another team for 1,450. Write two linear
equations to represent the purchases. Why
can the linear system so obtained be solved
by Cramer's rule ? Also, use the rule to
solve the system, and interpret the solution
in the given context. 4
(b) Give an example of a 4 x 1 matrix with
entries from Z \ N. 1
Algebra
Consider the expression LaTeX: \frac{\sqrt{x-4}}{x-7} x − 4 x − 7 . What is the domain of the numerator? Explain how you know. What is the domain of the denominator? Explain how you know.
Put both parts together to define the domain for the entire expression. Enter your response in the submission window.
Put both parts together to define the domain for the entire expression. Enter your response in the submission window.
Algebra
Catch the mistake.
Morgan is working on her last Algebra II homework problem but realizes that her answer is incorrect. Help Morgan understand her mistake by writing a paragraph explaining the error as well how it may be corrected.
The problem:
The resistance, R, measured in ohms, of an electrical circuit in a given length of wire is inversely proportional to the square of the diameter of the wire, d, measured in centimeters. If the resistance is 0.60 ohms when the diameter is 0.45 cm, what is the resistance of the same length of wire when the diameter is 0.54 cm? Round the solution to the nearest hundredth.
Morgan’s solution:
First, Morgan wrote the inverse variation formula, . Next she plugged in the known values for resistance and diameter and found the k value.
0.27 = k
Now Morgan substituted in the value for the diameter of the wire, .54, the k-value and solved for R.
R = 0.5 ohms
BUT…this is not the answer in the back of the book!
Morgan is working on her last Algebra II homework problem but realizes that her answer is incorrect. Help Morgan understand her mistake by writing a paragraph explaining the error as well how it may be corrected.
The problem:
The resistance, R, measured in ohms, of an electrical circuit in a given length of wire is inversely proportional to the square of the diameter of the wire, d, measured in centimeters. If the resistance is 0.60 ohms when the diameter is 0.45 cm, what is the resistance of the same length of wire when the diameter is 0.54 cm? Round the solution to the nearest hundredth.
Morgan’s solution:
First, Morgan wrote the inverse variation formula, . Next she plugged in the known values for resistance and diameter and found the k value.
0.27 = k
Now Morgan substituted in the value for the diameter of the wire, .54, the k-value and solved for R.
R = 0.5 ohms
BUT…this is not the answer in the back of the book!
Algebra
5 servers recieve 436 dollars in tips. How much do they get each using compatible numbers?
Algebra
How do we determine when a polynomial cannot be factored any further?
Algebra
Directions: Find the equation of the line that passes through each of the following pairs of points.
1) (1,7) and (4,22) 2) (-2,13) and (2,3) 3) (0,-10) and (16,2)
PS: These next problems are fractions and I am going to use a "/" to seperate them. The first one is 3 and negative one and a half. The last set is one comma one and three secondths.
4) (3, -1/2) and (1, 1 3/2)
Thank you! I have math soon!
1) (1,7) and (4,22) 2) (-2,13) and (2,3) 3) (0,-10) and (16,2)
PS: These next problems are fractions and I am going to use a "/" to seperate them. The first one is 3 and negative one and a half. The last set is one comma one and three secondths.
4) (3, -1/2) and (1, 1 3/2)
Thank you! I have math soon!
Algebra
Harmony is going to divide a 4 digit number by 10 and then divide the same 4 digit number by 100. Which sentence is true?
A. The first quotient will be 10 times less than the second quotient.
B. The 1st quotient will be 100 times as many as the 2nd quotient.
C. The 1st quotient will be 10 times less than the 2nd quotient.
D. The 1st quotient will be 10 times as many as the 2nd quotient.
A. The first quotient will be 10 times less than the second quotient.
B. The 1st quotient will be 100 times as many as the 2nd quotient.
C. The 1st quotient will be 10 times less than the 2nd quotient.
D. The 1st quotient will be 10 times as many as the 2nd quotient.
Algebra
4. Which of the following statements are true and
which are false ? Justify your answers with a
short proof or counter-example. 5x2=10
(a) If A and B are two subsets of a universal set
U, then Ac \B = A\ Bc.
(b) The roots of a quadratic equation are always
real numbers.
(c) lx+yl = lx1 + ly1 for all x,yE R.
(d) The contrapositive of 'If two triangles have
the same area, then they are congruent' is 'If
two triangles are congruent, then they have
the same area'.
(e) If A is a square matrix with I A l = 0, then
two of its rows or two of its columns must be
the same.
5. (a) If x, y and z are positive real numbers,
show that
(x2y + y2z + z2x) (xy2+ yz2+ zx2) > 9x2y2z2.
(b) Use Cardano's method to obtain the roots of
x3— 3x + 2 = 0.
which are false ? Justify your answers with a
short proof or counter-example. 5x2=10
(a) If A and B are two subsets of a universal set
U, then Ac \B = A\ Bc.
(b) The roots of a quadratic equation are always
real numbers.
(c) lx+yl = lx1 + ly1 for all x,yE R.
(d) The contrapositive of 'If two triangles have
the same area, then they are congruent' is 'If
two triangles are congruent, then they have
the same area'.
(e) If A is a square matrix with I A l = 0, then
two of its rows or two of its columns must be
the same.
5. (a) If x, y and z are positive real numbers,
show that
(x2y + y2z + z2x) (xy2+ yz2+ zx2) > 9x2y2z2.
(b) Use Cardano's method to obtain the roots of
x3— 3x + 2 = 0.
Algebra
Solve the following linear systems by the
process of elimination : 3
x + 2y + 5z = 9
x — y + $z = 2
3x — 6y z = 26
process of elimination : 3
x + 2y + 5z = 9
x — y + $z = 2
3x — 6y z = 26
Algebra
Hi,i can’t upload attachment but the question says the graph of f(x)=square root -x+2 and h(x)= 2 to the power of x then -1.The graph of f(x) has a restricted domain.Then they drew a graph of these functions,now they ask:
1)For what values of x is h(x)=f(x)+3?
2)For what values of x is h(x) . f prime x smaller than and equal to 0?
How do I do these questions,do I have to calculate or where do I start?Please help me,I’m very confused.Thanks
1)For what values of x is h(x)=f(x)+3?
2)For what values of x is h(x) . f prime x smaller than and equal to 0?
How do I do these questions,do I have to calculate or where do I start?Please help me,I’m very confused.Thanks
