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intersection of x + 3y and y = -1, linear equations










































1. The lines x + 3y and y = -1 intersect at x =

2. The vertical intercept of the line 5 - 4x is y =

3. The solution of 5x - 3 = 2x - 9
is x =

4. Simplified the following expression:
a) p + 4q + 5p + q^2
b) p - 4q + 5p + q^2
C) q - 4q + 5p + q^2
D) q + 4q + 5p + q^2

6.Find the horizontal intercept/s of x^2 - 2x - 3

7.Find the vertical intercep of y = x^2 + 16

8.Find the solution of 10q = 2q + 100
is q =

9.If PV = 100,r=0.03 and n = 5 evaluate to 2 decimal places
FV = PV (1+r)^n

10. If q = 1000 evaluate
p = 100 - 0.1q

11. Evaluate 10 + (-3.3)

12. Evaluate (-3) X (-2.5)

13. Cakculate 215% of 150

14. Solve for t
2e^t = 26.927 Give answer to one decimal place.

15. Express 375/300 as percentage.




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May 29, 2012
Algebra Problems
by: Staff


Part I

Question:

1. The lines x + 3y and y = -1 intersect at x =

2. The vertical intercept of the line 5 - 4x is y =

3. The solution of 5x - 3 = 2x - 9
is x =

4. Simplified the following expression:
a) p + 4q + 5p + q^2
b) p - 4q + 5p + q^2
C) q - 4q + 5p + q^2
D) q + 4q + 5p + q^2

6.Find the horizontal intercept/s of x^2 - 2x - 3

7.Find the vertical intercept of y = x^2 + 16

8.Find the solution of 10q = 2q + 100
is q =

9.If PV = 100,r=0.03 and n = 5 evaluate to 2 decimal places
FV = PV (1+r)^n

10. If q = 1000 evaluate
p = 100 - 0.1q

11. Evaluate 10 + (-3.3)

12. Evaluate (-3) X (-2.5)

13. Calculate 215% of 150

14. Solve for t
2e^t = 26.927 Give answer to one decimal place.

15. Express 375/300 as percentage.

Answer:

1. The lines x + 3y and y = -1 intersect at x =

There is information missing from the problem statement.

y = -1 is valid. This is a horizontal line at y = -1


x + 3y is not a line. It is an expression.

To be a valid equation there must be an EQUAL SIGN, such as:

x + 3y = 0


Assuming the two equations are:

x + 3y = 0
y = -1

The answer is:

x + 3y = 0

x + 3*(-1) = 0

x - 3 = 0

x - 3 + 3 = 0 + 3

x + 0 = 0 + 3

>>> x = 3




2. The vertical intercept of the line 5 - 4x is y =


There is also information missing from this problem statement.

5 - 4x is an expression, not an equation.

To be an equation there must be an EQUAL sign, such as:

5 - 4x = y

Assuming the equation is:

5 - 4x = y

The answer is:

5 - 4x = y

y = 5 - 4x

y = 5 - 4*0

y = 5 - 0

>>> y = 5




3. The solution of 5x - 3 = 2x - 9
is x =


5x - 3 = 2x - 9

5x - 3 - 2x = 2x - 9 - 2x

5x - 2x - 3 = 2x - 2x - 9

(5x - 2x) - 3 = (2x - 2x) - 9

3x - 3 = 0 - 9

3x - 3 = - 9

3x - 3 + 3 = - 9 + 3

3x + 0 = - 6

3x = - 6

3x / 3 = - 6 / 3

x * (3 / 3) = (- 6 / 3)

x * (1) = (- 6 / 3)

x = (- 6 / 3)

>>> x = -2


----------------------------------------------------

May 29, 2012
Algebra Problems
by: Staff


----------------------------------------------------

Part II



4. Simplify the following expression:
a) p + 4q + 5p + q²

p + 4q + 5p + q²

= q² + p + 5p + 4q

>>> q² + 6p + 4q


b) p - 4q + 5p + q²

= q² + p + 5p - 4q

>>> q² + 6p - 4q


C) q - 4q + 5p + q²

= q² + 5p + q - 4q

>>> q² + 5p - 3q


D) q + 4q + 5p + q²

= q² + 5p + q + 4q

>>> q² + 5p + 5q



6.Find the horizontal intercept/s of x^2 - 2x - 3


There is information missing from the problem statement.


x² - 2x - 3 is not an equation, and does not have horizontal intercepts. It is an expression.

To be a valid equation there must be an EQUAL SIGN, such as:

x² - 2x - 3 = f(x)

Assuming the equation is:

x² - 2x - 3 = f(x)

The answer is the answer can be computed using the quadratic equation:

ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/(2a)


Or, you can just factor it:

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0

x₁ - 3 = 0

x₁ - 3 + 3 = 0 + 3

x₁ = 3

x₂ + 1 = 0

x₂ + 1 - 1 = 0 - 1

x₂ = - 1

>>> the final answer is:


x ∈{-1, 3}



7.Find the vertical intercept of y = x^2 + 16

The vertical intercept will occur when x = 0

y = x² + 16

y = 0² + 16

y = 16


>>> the vertical intercept occurs at the point (0,16)





8.Find the solution of 10q = 2q + 100
is q =

10q = 2q + 100

10q - 2q = 2q + 100 - 2q

10q - 2q = 2q - 2q + 100

8q = 0 + 100

8q = 100

8q / 8 = 100 / 8

q * (8 / 8) = 100 / 8

q * (1) = 100 / 8

q = 100 / 8

>>> q = 12.5




9.If PV = 100,r=0.03 and n = 5 evaluate to 2 decimal places
FV = PV (1+r)^n

FV = 100 * (1 + .03)⁵

FV = 100 * (1.03)⁵

FV = 100 * 1.1592740743

>>> FV = 115.93



10. If q = 1000 evaluate
p = 100 - 0.1q

p = 100 - 0.1 * 1000

p = 100 - 100


>>> p = 0



11. Evaluate 10 + (-3.3)

10 + (-3.3)

= 10 - 3.3

>>> = 6.7



12. Evaluate (-3) X (-2.5)

(-3) * (-2.5)

>>> +7.5



13. Calculate 215% of 150

215% of 150

= 215% * 150

= (215 / 100) * 150

= 2.15 * 150

>>> 322.5



14. Solve for t
2e^t = 26.927 Give answer to one decimal place.

2e^t = 26.927

2e^t / 2= 26.927 / 2

e^t = 26.927 / 2

log_base e_(e^t) = log_base e_(13.4635)

t = log_base e_(13.4635)

t = ln(13.4635)

t ≈ 2.5999823201324

>>> t ≈ 2.6



15. Express 375/300 as percentage.


(%) / 100 = 375/300

(%) = (375/300)*100

(%) = 125

>>> 125 %







Thanks for writing.

Staff
www.solving-math-problems.com


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