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Alchen [17]
2 years ago
7

a sports team has b teams. each team has 7 players. using b, write an expression for the total number of players in the tourname

nt
Mathematics
1 answer:
Rufina [12.5K]2 years ago
6 0
The amount of players can be represented with the expression 7b.
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Given: PRST is a square
xxTIMURxx [149]

Answer:

(1-\sqrt{2})a^2

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a

Thus,

MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a

Consider isosceles triangle MSC. In this triangle

MS=MC=(\sqrt{2}-1)a.

The area of this triangle is

A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}

Consider right triangle PTS. The area of this triangle is

A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2

5 0
3 years ago
How do you know if something is congruent? (scale Factors)
igomit [66]

example: Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal.

7 0
3 years ago
Read 2 more answers
I added a screeshot thank you
atroni [7]

Answer:

w

Step-by-step explanation:

4 0
3 years ago
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A baker sells cookies for $1.50 each. If a minimum of two dozen cookies is ordered, the baker gives a 40% discount for each cook
pychu [463]
The answer will be 0.4(c - 24). Hope it help!
8 0
3 years ago
Four feet less than twice its width? What does this mean? can I get the formula and steps?
spin [16.1K]

Let's get a feel for what information we need for this problem. We ultimately want to <em>find </em>the dimensions of the mural. What we <em>know </em>are

  • The area of the mural (70 ft²)
  • The relationship between length and width (the length is four less than twice the width)

Let's see how this information can help us through the different parts of the problem.

<h3>"Write the length in terms of width."</h3>

A good place to start is with naming our variables so we can start to put together equations. Let's call our length l and our width w. We're told that l is "four feet less than twice" w, or symbolically:

l = 2w - 4

Any time we have to use an l, we're now able to substitute the expression 2w - 4 instead.

<h3>"Write a function that represents the area in terms of width."</h3>

Again, let's start with giving our function a name. If we call the area of the mural A, we use the abbreviation A(w) to mean "A as a function of w," or "A of w" for short.

We know that the area A of a rectangle is normally just its length times its width - A = lw - but sense we want this function as a function of w alone, we can replace l with the expression 2w - 4 from earlier to give us

A(w) = (2w - 4)w = 2w² - 4w

<h3>"Find the dimensions."</h3>

We're finally ready to tackle this problem's main question. Our function from the last section tells us what the area of the mural is entirely in terms of w, and the first section tells us how to find l if we already know w. Going back to one of the first bullet points, we also know that <em>the area of the mural is 70 ft²</em>, so we can say that we want to know what w is when A(w) = 70, or equivalently, when

2w² - 4w = 70

To solve for w, we can first divide away a 2 on either side, leaving us with

w² - 2w = 35

or equivalently,

w(w - 2) = 35

The only value w can be to make this true is 7, since 7(7 - 2) = 7(5) = 35, so we know that the width must be 7 ft. The area is 70 ft², so the length of the mural must be 10 ft., since 7 x 10 = 70.

4 0
2 years ago
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