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Factorize completely: (h -k - p(h+k)

Mathematics

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Answer

B

Step-by-step solution

12 steps

Part 1· 3 steps

Factorize completely (h2−k2)−p(h+k)(h^2 - k^2) - p(h+k).

  1. Factor the difference of squares h2−k2h^2 - k^2.

    h2−k2=(h−k)(h+k)h^2 - k^2 = (h-k)(h+k)

  2. Substitute this into the original expression.

    (h−k)(h+k)−p(h+k)(h-k)(h+k) - p(h+k)

  3. Factor out the common term (h+k)(h+k).

    (h+k)((h−k)−p)(h+k)((h-k) - p) (h+k)(h−k−p)(h+k)(h-k-p)

    The correct option is B.
    The final answer is B. (h+k)(h−k−p)\boxed{\text{B. } (h+k)(h-k-p)}.

Part 2· 2 steps

A pilot flies from Lisbon to Kuala Lumpur on a bearing of 163∘163^\circ. If the pilot flew from Kuala Lumpur to Lisbon on the same route, find the bearing.

  1. Identify the given bearing.

    The bearing from Lisbon to Kuala Lumpur is 163∘163^\circ.

  2. Calculate the back bearing.

    To find the back bearing (from Kuala Lumpur to Lisbon), we add 180∘180^\circ if the original bearing is less than 180∘180^\circ, or subtract 180∘180^\circ if it's greater than 180∘180^\circ. Since 163∘<180∘163^\circ < 180^\circ, we add 180∘180^\circ.

    Back bearing=163∘+180∘=343∘\text{Back bearing} = 163^\circ + 180^\circ = 343^\circ

    The correct option is D.
    The final answer is D. 343∘\boxed{\text{D. } 343^\circ}.

Part 3· 3 steps

Given that (x−2)(x-2) is a factor of 8−2qx−x28 - 2qx - x^2, find the value of qq.

  1. Apply the Factor Theorem.

    If (x−2)(x-2) is a factor of the polynomial P(x)=8−2qx−x2P(x) = 8 - 2qx - x^2, then P(2)P(2) must be equal to 0.

  2. Substitute x=2x=2 into the polynomial.

    P(2)=8−2q(2)−(2)2P(2) = 8 - 2q(2) - (2)^2 P(2)=8−4q−4P(2) = 8 - 4q - 4 P(2)=4−4qP(2) = 4 - 4q

  3. Set P(2)=0P(2) = 0 and solve for qq.

    4−4q=04 - 4q = 0 4=4q4 = 4q q=44q = \frac{4}{4} q=1q = 1

    The correct option is B.
    The final answer is B. 1\boxed{\text{B. } 1}.

Part 4· 4 steps

Given that x:34=12:98x : \frac{3}{4} = \frac{1}{2} : \frac{9}{8}, find the value of xx.

  1. Write the proportion as an equation of fractions.

    x34=1298\frac{x}{\frac{3}{4}} = \frac{\frac{1}{2}}{\frac{9}{8}}

  2. Simplify both sides of the equation.

    For the left side:

    x34=x×43=4x3\frac{x}{\frac{3}{4}} = x \times \frac{4}{3} = \frac{4x}{3}

    For the right side:

    1298=12×89=818=49\frac{\frac{1}{2}}{\frac{9}{8}} = \frac{1}{2} \times \frac{8}{9} = \frac{8}{18} = \frac{4}{9}

  3. Set the simplified expressions equal to each other.

    4x3=49\frac{4x}{3} = \frac{4}{9}

  4. Solve for xx.

    Multiply both sides by 3:

    4x=49×34x = \frac{4}{9} \times 3 4x=1294x = \frac{12}{9} 4x=434x = \frac{4}{3}

    Divide both sides by 4:

    x=43×14x = \frac{4}{3} \times \frac{1}{4} x=13x = \frac{1}{3}

    The correct option is B.
    The final answer is B. 13\boxed{\text{B. } \frac{1}{3}}.

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