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steposvetlana [31]
3 years ago
6

Simplify the expression

Mathematics
1 answer:
Grace [21]3 years ago
6 0
(-5+8*i)+(-9+5*i) evaluates to <span>-14+13i</span>
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Solve the system of equations using the substitution method. Show your work and be sure to include the solution to the system y=
Sliva [168]

Answer:

Is that simultaneous equation

6 0
2 years ago
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I need help. I’ll seriously make you brainly
ser-zykov [4K]

Answer:

a = 12

Step-by-step explanation:

add 2 to each side

5a/3 = a/4 + 17

distribute 12 to remove fractions

20a = 3a + 204

17a = 204

a = 12

7 0
3 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
A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters. Which expression represe
mash [69]
Recall that the volume of a regular prism is given by the area of the base times the height.

Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.
The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.

Recall that the are of a triangle is given by 1/2 base times height.

Thus the area of of the pentagon base of the prism is given by
Area= \frac{5}{2} x\times2.8=7x

Therefore, the volume of the prism is given by
Volume=7x(2x+1)=14x^2+7x
5 0
3 years ago
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Write a problem that can be solved by comparing feet and inches using a model. Include a solution. Explain why you are changing
agasfer [191]
Example Problem:
Billy goes to the nurse and she says Billy is 4 Feet 6 Inches. Billy's mom wants to know how many inches tall Billy is. How tall is Billy on Inches?

Solution:
Billy is 54 Inches tall.
=(4 × 12) + 6
=48 + 6
=54 Inches

Explanation:
You are converting the larger unit to the smaller one because you are trying to find how tall Billy is in inches and you know Billy is 4 feet 6 inches, so you need to convert 4 feet to inches.
Please Vote Me The Brainliest!
6 0
3 years ago
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