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3 years ago

The price of a sweater was reduced from $20 to $12.By what percentage was the price of the sweater reduced?

Mathematics

1 answer:

Katen [24]3 years ago

3 0

The price of the sweater was reduced by 40%

Step-by-step explanation:

Step 1; Cost before reduction was $20. The cost after reduction was 12$. Cost reduced= cost before reduction - cost after reduction

Cost reduced= $20 - $12 = $8

Step 2; We must find how much of the cost was reduced from the initial cost i.e. how much $8 is to $20. To do this we must convert it into a percentage. We divide the $8 with the $20 to get a value. This value must be multiplied with a 100 to be converted into a percentage.

Cost by which sweater was reduced= $\frac{8}{20}$ * 100 = 0.4 * 100 = 40

So the price of the sweater was reduced from $20 to $8 which equates to a reduction in 40%.

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A vegetable garden is 12 meters long by 7 meters wide. In one square meter, you count two toads. Estimate the population of toad

zavuch27 [327]

Answer: 168 toads

Step-by-step explanation:

First we need to find the area of the garden. Area = length x width

Area = 12m x 7m = 84 m²

2 toads/ 1 sq m

84(2) = 168

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3 years ago

Shawndra said that it is not possible to draw a trapezoid that is a rectangle, but it is possible to draw a square that is a rec

ICE Princess25 [194]

Shawndra is correct

She made two statements, and both are true:

1. It is not possible to draw a trapezoid that is a rectangle.

This is true because a trapezoid<span> is a quadrilateral that has exactly one pair of parallel sides, whereas a rectangle is a parallelogram (i.e. it has two pairs of parallel sides)</span>

2. It is possible to draw a square that is a rectangle.

This is true because a rectangle refers to any parallelogram with right angles. A square is also a parallelogram (has two pairs of opposite sides) with right angles. In fact, all squares are rectangles; only that they are a special kind of rectangle, where all the sides are equal in length.

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4 years ago

Read 2 more answers

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

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3 years ago

Writing an equation and drawing its graph to model a real-world situation

Mariana [72]

Answer:

A = B + 15

Step-by-step explanation:

Let Diane sold B books in one hour,

Additional earning by selling 1 book = 1$

Additional earning by selling B books = Number of books sold × Additional earning by selling one book

= B × ($1.00)

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Total earnings = B + 15

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3 years ago

A scale model of a building is 3 inches tall. If the building is 90 feet tall, find the scale of the model.

olganol [36]

The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

<h3>Scaling of measurement</h3>

Scaling is the way of enlarging or reducing the image of an object.

Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;

Convert both measures to same units

Since 1 feet. = 12 in

90 feet = 90/12 in = 7.5 in

Take the ratio

3 : 7.5 = 30: 75

Reduce to lowest term

30: 75 = 2 : 5

Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

Learn more on scale model here: brainly.com/question/261465

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