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3 years ago

A pair of shoes cost $120 but they are 25% Off;

Mathematics

1 answer:

Sever21 [200]3 years ago

3 0

Answer:

Discount = $30, Final price = $90

Step-by-step explanation:

25% is one quarter. 120/4=30

One quarter of 120 is 30, so - 30 would give discounted price of $90.

Similarly you could think of it like the discounted price is 75% of the original one and do 120x0.75=90 to find 75% of 120.

Hope this helped!

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Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?

garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is $z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$ .

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be $z (x) = \cos x$ the base formula, where $x$ is measured in sexagesimal degrees. This expression must be transformed by using the following data:

$T = 180^{\circ}$ (Period)

$z_{min} = -4$ (Minimum)

$z_{max} = 5$ (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of $2\pi$ radians. In addition, the following considerations must be taken into account for transformations:

1) $x$ must be replaced by $\frac{2\pi\cdot x}{180^{\circ}}$ . (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

$\Delta z = \frac{z_{max}-z_{min}}{2}$

$\Delta z = \frac{5+4}{2}$

$\Delta z = \frac{9}{2}$

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

$z_{m} = \frac{z_{min}+z_{max}}{2}$

$z_{m} = \frac{1}{2}$

The new function is:

$z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)$

Given that $z_{m} = \frac{1}{2}$ , $\Delta z = \frac{9}{2}$ and $T = 180^{\circ}$ , the outcome is:

$z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)$

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0

3 years ago

1. You are going to make one of these bags from a roll of cloth 1 meter wide. What

maks197457 [2]

Answer:

1 cm

You are going to make one of these bags from a roll of cloth 1 meter wide. What

is the shortest length that you need to cut from the roll for the bag?

Step-by-step explanation:

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2 years ago

Will mark you as brainliest. If your good with polynomials.

kobusy [5.1K]

To solve/simplify this all you have to do is group like terms (the x^2's with each other, the x's with each other, and the normal numbers, -8)

14x^2-8+5x-6x^2+2x

group the x^2 (add 14x^2 to -6x^2)

8x^2-8+5x+2x

group the x's together (add 5x and 2x together)

8x^2+7x-8

Your answer will be d) 8x^2+7x-8

4 0

3 years ago

A town's population has been growing linearly. In 2003, the population was 59.000 and the population has been growing by 1,700 p

Rudiy27

Answer:

In 2003, the population was 59000 and the population has been growing by 1,700 people each year.

The equation will be:

59000+1700x = (population 'x' years after 2003)

For x, you plug in the amount of years after 2003.

Like if it is the year 2003, the population is $59000+1700(0)$