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Alexandra [31]
3 years ago
12

What should you do if you are surrounded by 20 lions and 15 tigers and 10 leopards

Mathematics
1 answer:
emmainna [20.7K]3 years ago
3 0
You should run away from them
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Mark has 5 more pencils than Bill. If Mark has m amount of pencils, which expression gives the number of pencils Bill has?
mars1129 [50]

Answer:

m-5 Tray would be Bill's amount of pencils

5 0
2 years ago
If (2i/2+i)-(3i/3+i)=a+bi, then a=<br>A. 1/10<br>B. -10<br>C. 1/50<br>D. -1/10​
Verizon [17]

Answer:

Option A is correct.

Step-by-step explanation:

We are given:

\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi

We need to find the value of a.

The LCM of (2+i) and (3+i)  is (2+i)(3+i)

=\frac{2i(3+i)}{(2+i)(3+i)}-\frac{3i(2+i)}{(2+i)(3+i)}\\=\frac{6i+2i^2}{(2+i)(3+i)}-\frac{6i+3i^2}{(2+i)(3+i)}\\=\frac{6i+2i^2-(6i+3i^2)}{(2+i)(3+i)}\\=\frac{6i+2i^2-6i-3i^2)}{5+5i}\\=\frac{-i^2}{5+5i}\\i^2=-1\\=\frac{-(-1)}{5+5i}\\=\frac{1}{5+5i}

Now rationalize the denominator by multiplying by 5-5i/5-5i

=\frac{1}{5+5i}*\frac{5-5i}{5-5i} \\=\frac{5-5i}{(5+5i)(5-5i)}\\=\frac{5-5i}{(5+5i)(5-5i)}\\(a+b)(a-b)= a^2-b^2\\=\frac{5(1-i)}{(5)^2-(5i)^2}\\=\frac{5(1-i)}{25+25}\\=\frac{5(1-i)}{50}\\=\frac{1-i}{10}\\=\frac{1}{10}-\frac{i}{10}

We are given

\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi

Now after solving we have:

\frac{1}{10}-\frac{i}{10}=a+bi

So value of a = 1/10 and value of b = -1/10

So, Option A is correct.

8 0
3 years ago
State the common factor of the terms in the polynomial 5x^2 + 30x^2 - 10x. Then factor the polynomial
tatuchka [14]

Answer:

The common factor is 5x.

The factored polynomial is: 5x(7x - 2)

Step-by-step explanation:

Factor of the numbers:

The common factor of the numbers 5, 30 and 10 is 5, as it is the greater common divisor of them, as found below:

5 - 30 - 10|5

1 - 6 - 2

Factor of the exponents:

Between x^2, x^2 and x, the common factor is the x with the lowest exponent. So x

Common factor

Number multiplied by exponents, so 5x.

Factoring the polynomial:

5x^2 + 30x^2 - 10x = 5x(\frac{5x^2}{5x} + \frac{30x^2}{5x} - \frac{10x}{5x}) = 5x(x + 6x - 2) = 5x(7x - 2)

The factored polynomial is: 5x(7x - 2)

6 0
2 years ago
Draw the two-dimensional shape<br> that makes up the faces of this<br> solid shape.
Art [367]

Answer:

like this?

Step-by-step explanation:

5 0
2 years ago
Need help with this question.
Vaselesa [24]

Answer:

4:1 (I think)

Step-by-step explanation:

Let's write some equations first:

For both prices increasing by 20:

\frac{x+20}{y+20} =\frac{5}{2}

then we can use cross multiplication

2x+40=5y+100

For both prices decreasing by 5:

\frac{x-5}{y-5} =\frac{5}{1}

same here:

5y-25=x-5

Using substitution for 5y, we get: 5y=x+20

2x+40=5y+100

2x+40=x+20+100

x=80

plugging this in to the second equation:

5y-25=x-5

5y-25=80-5

5y-25=75

5y=100

y=20

therefore we get x:y=80:20

4:1

4 0
2 years ago
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