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sergeinik [125]
2 years ago
15

Twice the sum of a number and 3 times a second number is 4. The difference of ten times the seco

Mathematics
1 answer:
34kurt2 years ago
4 0

Two numbers that gives twice the sum of a number and 3 times a second number is 4. The difference of ten times the second number and five times the first is 90 are -10  and 4

Given :

Twice the sum of a number and 3 times a second number is 4. The difference of ten times the second number and five times the first is 90.

Let a  and b be the two  unknown numbers

Lets frame equation using the given statements

Twice the sum of a number and 3 times a second number is 4.

2(a+3b)=4\\a+3b=2

the difference of ten times the second number and five times the first is 90

10b -5a=90\\Divide \; by \;5 \\2b-a=18

Now use these two equations to solve a  and b

a+3b=2\\-a+2b=18

Add both the equations

a+3b=2\\-a+2b=18\\--------------------------\\5b=20\\b=4

Now find out 'a'

a+3b=2\\a+3(4)=2\\a+12=2\\a=2-12\\a=-10

The two numbers are -10  and 4

Learn more :  brainly.com/question/13856304

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Point.

<h3>Further explanation</h3>
  • This is one of the classic problems of Euclidean geometry.
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  • We express an angle with three points and a symbol ∠. The middle point represents constantly vertex. We can, besides, give angle names only with vertices. For example, based on the accompanying image, the angle can be symbolized as ∠BAC, or ∠CAB, or ∠A.  

Types of Angles  

  • The acute angle represents an angle whose measure is greater than 0° and less than 90°.
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  • The obtuse angle represents an angle whose measures greater than 90° and less than 180°.  
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<u>Note:</u>

Undefined terms are the basic figure that is undefined in terms of other figures. The undefined terms (or primitive terms) in geometry are a point, line, and plane.

These key terms cannot be mathematically defined using other known words.

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<h3>Learn more   </h3>
  1. Undefined terms are implemented to define a ray brainly.com/question/1087090
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Keywords: the definition of an angle, the undefined term, line, point, line, plane, ray, endpoint, acute, obtuse, right, straight, Euclidean geometry

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Please help with imaginary numbers worksheet!
mihalych1998 [28]

Problem 5

<h3>Answer:   6i</h3>

------------------

Explanation:

We have these four identities

  • i^0 = 1
  • i^1 = i
  • i^2 = -1
  • i^3 = -i

Notice how computing i^4 leads us back to 1. So i^4 = i^0. The pattern repeats every 4 terms. So we divide the exponent by 4 and look at the remainder. We ignore the quotient entirely. We can see that 28/4 = 7 remainder 0. Meaning that i^28 = i^0 = 1.

We can think of it like this if you wanted

i^28 = (i^4)^7 = 1^7 = 1

Then the sqrt(-36) becomes 6i

So overall, we end up with the final answer of 6i

=============================================

Problem 6

<h3>Answer:  -3i</h3>

------------------

Explanation:

We'll use the ideas mentioned in problem 5

46/4 = 11 remainder 2

i^46 = i^2 = -1

sqrt(-9) = 3i

The two outside negative signs cancel out, but there's still a negative from -1 we found earlier. So we end up with -3i

In other words, here is one way you could write out the steps

-i^{46}*-\sqrt{-9}\\\\-i^{2}*-3i\\\\i^{2}*3i\\\\-1*3i\\\\-3i\\\\

=============================================

Problem 7

<h3>Answer:   -1</h3>

------------------

Work Shown:

i^10 = i^2 because 10/4 = 2 remainder 2

i^19 = i^3 because 19/4 = 4 remainder 3

i^7 = i^3 because 7/4 = 1 remainder 3

Again, all we care about are the remainders.

i^{10}+i^{19} - i^{7}\\\\i^{2}+i^{3} - i^{3}\\\\i^{2}\\\\-1

=============================================

Problem 8

<h3>Answer:    -1 + i</h3>

------------------

Work Shown:

i^22*i^6 = i^(22+6) = i^28

Earlier in problem 5, we found that i^28 = i^0 = 1

So,

i^1 - \left(i^{22}*i^{6}\right)\\\\i^1 - i^{28}\\\\i^1 - i^{0}\\\\i - 1\\\\-1+i

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