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Nezavi [6.7K]
3 years ago
10

AB=A, B, equals Round your answer to the nearest hundredth.

Mathematics
1 answer:
suter [353]3 years ago
7 0

Step-by-step explanation:

\sin(20 \degree)  =  \frac{3}{AB}  \\ AB =  \frac{3}{ \sin(20 \degree) }  \\ AB =  \frac{3}{0.342}  \\ AB = 8.77

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The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions
Mariulka [41]

Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}

The quadratic equation can now be solve using factorization method:

\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\  \\ Width=x=5\text{ }ft \end{gathered}

7 0
1 year ago
Algebra 2 Please Help
hammer [34]
No sé lo que quieres decir
5 0
3 years ago
Hamid's soccer game will start at 11:00 A.M., but the players must arrive at the field three-quarters of an hour early to warm u
Minchanka [31]
If the game will start at 11:00 A.M., but the players must arrive at the field three-quarters of an hour early to warm up, it refers to 8:45 a.m. Why? If we start to count in 11 backward and start to trace the three-quarters, it shows that 10:45, 9:45, and 8:45 are the three-quarters. So Hamid statement that he has to be at the field at 9:45 A.M is not correct.  
4 0
3 years ago
Point B has coordinates ​(4,1). The​ x-coordinate of point A is -4. The distance between point A and point B is 10 units. What a
klasskru [66]

Given:

Point B has coordinates ​(4,1).

The​ x-coordinate of point A is -4.

The distance between point A and point B is 10 units.

To find:

The possible coordinates of point​ A.

Solution:

Let the y-coordinate of point A be y. Then the two points are A(-4,y) and B(4,1).

Distance formula:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The distance between point A and point B is 10 units.

\sqrt{(4-(-4))^2+(1-y)^2}=10

Taking square on both sides, we get

(8)^2+(1-y)^2=100

(1-y)^2=100-64

(1-y)^2=36

Taking square root on both sides, we get

(1-y)=\pm \sqrt{36}

-y=\pm 6-1

y=1\mp 6

y=1-6 and y=1+6

y=-5 and y=7

Therefore, the possible coordinates of point​ A are either (-4,-5) or (-4,7).

7 0
2 years ago
Use a proof by contradiction to show that the square root of 3 is national You may use the following fact: For any integer kirke
Ierofanga [76]

Answer:

1. Let us proof that √3 is an irrational number, using <em>reductio ad absurdum</em>. Assume that \sqrt{3}=\frac{m}{n} where  m and n are non negative integers, and the fraction \frac{m}{n} is irreducible, i.e., the numbers m and n have no common factors.

Now, squaring the equality at the beginning we get that

3=\frac{m^2}{n^2} (1)

which is equivalent to 3n^2=m^2. From this we can deduce that 3 divides the number m^2, and necessarily 3 must divide m. Thus, m=3p, where p is a non negative integer.

Substituting m=3p into (1), we get

3= \frac{9p^2}{n^2}

which is equivalent to

n^2=3p^2.

Thus, 3 divides n^2 and necessarily 3 must divide n. Hence, n=3q where q is a non negative integer.

Notice that

\frac{m}{n} = \frac{3p}{3q} = \frac{p}{q}.

The above equality means that the fraction \frac{m}{n} is reducible, what contradicts our initial assumption. So, \sqrt{3} is irrational.

2. Let us prove now that the multiplication of an integer and a rational number is a rational number. So, r\in\mathbb{Q}, which is equivalent to say that r=\frac{m}{n} where  m and n are non negative integers. Also, assume that k\in\mathbb{Z}. So, we want to prove that k\cdot r\in\mathbb{Z}. Recall that an integer k can be written as

k=\frac{k}{1}.

Then,

k\cdot r = \frac{k}{1}\frac{m}{n} = \frac{mk}{n}.

Notice that the product mk is an integer. Thus, the fraction \frac{mk}{n} is a rational number. Therefore, k\cdot r\in\mathbb{Q}.

3. Let us prove by <em>reductio ad absurdum</em> that the sum of a rational number and an irrational number is an irrational number. So, we have x is irrational and p\in\mathbb{Q}.

Write q=x+p and let us suppose that q is a rational number. So, we get that

x=q-p.

But the subtraction or addition of two rational numbers is rational too. Then, the number x must be rational too, which is a clear contradiction with our hypothesis. Therefore, x+p is irrational.

7 0
3 years ago
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