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Naddika [18.5K]
2 years ago
9

A sporting goods store purchased a snowboard and marked it up 25% from the original cost of $120. Then, wanting to make room for

summer inventory, the store placed the snowboard on sale for 70% off. What was the price after the discount? $
Mathematics
1 answer:
Margaret [11]2 years ago
3 0

The price after the discount was $45.

When the sporting goods store bought the snowboard and marked it up by 25%, the price became:

<em>= Original cost x ( 1 + markup percentage)</em>

= 120 x ( 1 + 25%)

= 120 x 1.25

= $150

The snowboard was then discounted by 70%, the new price becomes:

<em>= Current price x ( 1 - discount rate)</em>

= 150 x ( 1 - 70%)

= 150 x 30%

= $45

In conclusion, the price after the discount was $45.

<em>Find out more at brainly.com/question/1472521.</em>

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a picture 10 1/4 feet long is to be centered on a wall that is 14 1/2 feet long. How much more space is there from the edge of t
Zarrin [17]

Answer:

Length from the edge will be =2{\frac{1}{8}} feet

Step-by-step explanation:

To find length we have to conver mixed fraction to improper fraction


The length of the wall = \frac{29}{2}


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First we find the total length of wall remain after picture was hung to the wall.


Length of wall remain vacant =\frac{29}{2}-\frac{41}{4}


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Total length of wall remain vacant =\frac{17}{4}


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Space from one edge =\frac{17}{4} \times \frac{1}{2}


= \frac{17}{8}

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2. Find the lateral area of the pyramid to the nearest whole number.
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What is the height of each triangle side?

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Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
3 years ago
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