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Factorise: -2xy - 6x

Mathematics

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Part 8· 2 steps

Factorise: −2xy−6x-2xy - 6x

  1. Identify the common factors in both terms.

    The terms are −2xy-2xy and −6x-6x.
    The common factors are −2-2 and xx.

  2. Factor out the common factors.

    −2xy−6x=−2x(y)+(−2x)(3)=−2x(y+3)-2xy - 6x = -2x(y) + (-2x)(3) = -2x(y+3)

    The correct option is A.

    A\boxed{\text{A}}

Part 9· 1 step

Which of the following is an empty set?

  1. Evaluate each option.

    • A. {Triangle with 4 sides}: A triangle, by definition, has 3 sides. A figure with 4 sides is a quadrilateral, not a triangle. Therefore, there are no triangles with 4 sides. This set is empty.
    • B. {Multiples of 3}: This set includes numbers like 3, 6, 9, ... It is not empty.
    • C. {Days of the week}: This set includes Monday, Tuesday, etc. It is not empty.
    • D. {Months of the year}: This set includes January, February, etc. It is not empty.

    The correct option is A.

    A\boxed{\text{A}}

Part 10· 2 steps

A boy bought a book for D50.00 and sold it at a profit of 10%. What was his selling price?

  1. Calculate the profit amount.

    Profit = 10% of D50.00

    Profit=0.10×D50.00=D5.00\text{Profit} = 0.10 \times \text{D}50.00 = \text{D}5.00

  2. Calculate the selling price.

    Selling Price = Cost Price + Profit

    Selling Price=D50.00+D5.00=D55.00\text{Selling Price} = \text{D}50.00 + \text{D}5.00 = \text{D}55.00

    The correct option is C.

    C\boxed{\text{C}}

Part 11· 2 steps

Convert 0.25 to a fraction.

  1. Write the decimal as a fraction with a denominator of 100.

    0.25=251000.25 = \frac{25}{100}

  2. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 25.

    25÷25100÷25=14\frac{25 \div 25}{100 \div 25} = \frac{1}{4}

    The correct option is D.

    D\boxed{\text{D}}

Part 12· 2 steps

Which of the following options is the greatest?

  1. Convert all fractions to decimals for easy comparison.

    • A. 14=0.25\frac{1}{4} = 0.25
    • B. 25=0.4\frac{2}{5} = 0.4
    • C. 35=0.6\frac{3}{5} = 0.6
    • D. 34=0.75\frac{3}{4} = 0.75

  2. Compare the decimal values.

    0.25<0.4<0.6<0.750.25 < 0.4 < 0.6 < 0.75
    The greatest value is 0.75, which corresponds to 34\frac{3}{4}.
    The correct option is D.

    D\boxed{\text{D}}

Part 13· 4 steps

If a die is tossed once, what is the probability of getting an even number?

  1. List all possible outcomes when tossing a standard six-sided die.

    The possible outcomes are {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}.
    Total number of outcomes = 6.

  2. List the even numbers among the possible outcomes.

    The even numbers are {2,4,6}\{2, 4, 6\}.
    Number of favorable outcomes (even numbers) = 3.

  3. Calculate the probability.

    Probability=Number of favorable outcomesTotal number of outcomes=36\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{6}

  4. Simplify the fraction.

    36=12\frac{3}{6} = \frac{1}{2}

    The correct option is not visible in the provided image, but the probability is 12\frac{1}{2}.

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