Answer Math Problems

All grade answer math problems are solved here from different topics. A large number of objective answer math problems are solved here to help the students quickly to test their knowledge and skills on different topics.

1. Simplify: (4x² - 2x) - (-5x² - 8x).

Solution:

(4x² - 2x) - (-5x² - 8x)

= 4x² - 2x + 5x² + 8x.

= 4x² + 5x² - 2x + 8x.

= 9x² + 6x.

= 3x(3x + 2).

Answer: 3x(3x + 2)



2. Simplify: (-7x² - 3x) - (4x² - x)

Solution:

(-7x² - 3x) - (4x² - x)

= -7x² - 3x - 4x² + x

= -7x² - 4x² - 3x + x

= -11x² – 2x

= -x(11x + 2)

Answer: -x(11x + 2)



3. Simplify: (-5x² - 8x + 7) - (5x² - 4)

Solution:

(-5x² - 8x + 7) - (5x² - 4)

= -5x² - 8x + 7 - 5x² + 4

= -5x² - 5x² - 8x + 7 + 4

= -10x² – 8x + 11

Answer: -10x² – 8x + 11



4. Simplify: (4x² + 5x) + (x² - 5x + 1)

Solution:

(4x² + 5x) + (x² - 5x + 1)

= 4x² + 5x + x² - 5x + 1

= 4x² + x²+ 5x - 5x + 1

= 5x² + 0 + 1

= 5x² + 1

Answer: 5x² + 1



5. Simplify: (-6x + 3) - (-x² + 5x)

Solution:

(-6x + 3) - (-x² + 5x)

= -6x + 3 + x² - 5x

= -6x - 5x + x² + 3

= x² – 11x + 3

Answer: x² – 11x + 3



6. Simplify: (-9x - 5) - (-9x² + x - 5)

Solution:

(-9x - 5) - (-9x² + x - 5)

= -9x - 5 + 9x² - x + 5

= 9x² - 9x – x – 5 + 5

= 9x² – 10x

= x(9x – 10)

Answer: x(9x – 10)

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7. Simplify: (2x - 4) - (6x + 6)

Solution:

(2x - 4) - (6x + 6)

= 2x - 4 - 6x – 6

= 2x – 6x – 4 – 6

= -4x – 10

= -2(2x + 5)

Answer: -2(2x + 5)


8. Simplify:(8+4x)/4x

Solution:

(8+4x)/4x

= 4(2 + x)/4x

[Cancel 4 from the numerator and denominator]

= (2 + x)/x

Answer: (2 + x)/x


9. Decide whether the lines are parallel, perpendicular or neither.

x + 4y = 7 and 4x – y = 3

Solution:

x + 4y = 7

4y = -x + 7

y = (-1/4) x + 7

Slope of the equation x + 4y = 7 is -1/4.

Again, 4x – y = 3

y = 4x – 3

Slope of the equation 4x – y = 3 is 4.

Since multiplying both the slope of the equation = -1/4 × 4 = -1

Therefore, the given two equations are perpendicular to each other.

Answer: Perpendicular


10. Simplify: 3x – 5 + 23x – 9

Solution:

3x – 5 + 23x – 9

= 3x + 23x – 5 – 9

= 26x – 14

= 2(13x – 7)

Answer: 2(13x – 7)

11. Use the discriminant to determine the number of real roots the equation has. 3x² – 5x + 1 =0

(a) One real root (a double root),

(b) Two distinct real roots,

(c) Three real roots,

(d) None (two imaginary roots)

Solution:

Discriminant = bx² – 4ac

Compare the above equation 3x² – 5x + 1 =0 with ax² + bx + c = 0

We get, a = 3, b = -5, c = 1

Put the value of a, b and c;

Discriminant = bx² – 4ac

Discriminant = (-5)² - 4 × 3 × 1

= 25 – 12

= 13 [13 > 0]

Therefore, discriminant is positive.

So the given equation has two distinct real roots.

Answer: (b)



12. Use the discriminant to determine the number of real roots the equation has. 7x² + 3x + 1 =0.

(a) One real root (a double root),

(b) Two distinct real roots,

(c) Three real roots,

(d) None (two imaginary roots)

Solution:

Discriminant = b² – 4ac

Compare the above equation 7x² + 3x + 1 =0 with ax² + bx + c = 0

We get, a = 7, b = 3, c = 1

Put the value of a, b and c;

Discriminant = b² – 4ac

Discriminant = (3)² - 4 × 7 × 1

= 9 – 28

= -19 [13 < 0]

Therefore, discriminant is negative.

So the given equation has none (two imaginary roots).

Answer: (d)

13. Fill in the blank:

(a) The point with coordinates (0,0) is called ........of a rectangular coordinate system.

(b) To find the x-intercept of a line, we let....equal 0 and solve for ......; to find y-intercept, we let ......equal 0 and solve for.......

Solution:

(a) The point with coordinates (0,0) is called origin of a rectangular coordinate system.

(b) To find the x-intercept of a line, we let y equal 0 and solve for x ; to find y-intercept, we let x equal 0 and solve for y .

14. Name the quadrant, if any, in which each point is located.

(a) (1, 6)

(b) (-4, -2)

Solution:

(a) (1, 6) --------- I Quadrant.

(b) (-4, -2) --------- III Quadrant.


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