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3 years ago

A department store buys 500 shirts at a cost of $3,500 and sells them at a selling price of $10 each. Find the percent markup.

Mathematics

1 answer:

Ratling [72]3 years ago

5 0

Answer: 30 percent.

Step-by-step explanation: First do 3,500 divided by 10 to find the cost of each shirt. Second subtract 7 from 10 which is 3. Then divide 3 by ten because you always divide by the amount being paid for. So 3 divided by 10 is .3 then multiply .3 by 100 which is 30 and that is your percent markup

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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

Now let's calculate the area

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;

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

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.

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

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3 years ago

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Varvara68 [4.7K]

−a4−4 a2 is the answer for your question.

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3 years ago

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den301095 [7]

Answer:

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Step-by-step explanation:

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3 years ago

F(x) = x^2. What is g(x)

Alexeev081 [22]

Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)

If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)

If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k

If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k

f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

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→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

∴ Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

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3 years ago

What is the value of a for the equation below?

Mice21 [21]

Steps to solve:

15 + 2a = 35

~Subtract 15 to both sides

2a = 20

~Divide 2 to both sides

a = 10

Best of Luck!

7 0

3 years ago

A department store buys 500 shirts at a cost of $3,500 and sells them at a selling price of $10 each. Find the percent markup.​

A department store buys 500 shirts at a cost of $3,500 and sells them at a selling price of $10 each. Find the percent markup.