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Black_prince [1.1K]
3 years ago
5

George is twice as old as Edward, and Edward's age exceeds Robert's age by 4 years. If the sum of the three ages is at least 56

years, what is Robert's minimum age?
Mathematics
1 answer:
marshall27 [118]3 years ago
8 0

Answer:Robert's minimum age is 11 years.

Step-by-step explanation:

Let x represent George's age.

Let y represent Edward's age.

Let z represent Robert's age.

George is twice as old as Edward. It means that

x = 2y

Edward's age exceeds Robert's age by 4 years. It means that

z = y - 4

If the sum of the three ages is at least 56 years, it means that

x + y + z ≥ 56 - - - - - - - - - - 1

Substituting x = 2y and z = y - 4 into equation 1, it becomes

2y + y + y - 4 ≥ 56

4y - 4 ≥ 56

4y ≥ 56 + 4

y ≥ 60/4

y ≥ 15

z = y - 4 = 15 - 4

z ≥ 11

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Answer:

No, it is not tangent

Step-by-step explanation:

XY can only be tangent to the circle if it forms a right angle to the diameter. To test this, you need to figure out whether the three parts of the triangle make a Pythagorean triple. 8.5×2=17, and 17^2+5^2 is 314, which is not equal to 20 squared. Therefore, it is not tangent. Hope this helps!

3 0
4 years ago
X=7w^+4w-6 and y=w^-11w+13
aleksandr82 [10.1K]
Although the terms might seem intimidating, this is a simple substitution problem.

X + Y = _______
Substitute the values of X and Y in terms of w
(7w^2 + 4w - 6) + (w^2 - 11w + 13) = ______
Now all you need to do is combine like terms (terms that have the same variables raised to the same power)
8w^2 - 7w + 7

Final Answer: 8w^2 - 7w + 7
3 0
4 years ago
20. Determine the rate of change for the following equation on the given interval.
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-2<x<3   | *2
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3< 2x+7< 13


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4 0
3 years ago
Read 2 more answers
A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as ch
Troyanec [42]

The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

<h3>What is probability?</h3>

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

  • A locker combination consists of two nonzero digits, and each combination consists of different digits. Event A is defined as choosing an odd number as the first digit, and event B is defined as choosing an odd number as the second digit.

The total sample will have 9 numbers

S = { 1,2,3,4,5,6,7,8,9} = 9

Even Number = { 2,4,6,8} = 4

Odd Number  = { 1,3,5,7,9} = 5

P ( A ) = ( 4 / 9 )

P ( B ) = ( 5 / 9 )

The probability will be calculated as:-

P( A:B ) = \dfrac{P(A)\times P(B)}{P(B)}

P( A:B ) =\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }

P( A:B ) = 4 / 9

Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

To know more about probability follow

brainly.com/question/24756209

#SPJ1

4 0
2 years ago
4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.
nikitadnepr [17]

Answer:

\sum_{n=0}^9cos(\frac{\pi n}{2})=1

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0

\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}

Step-by-step explanation:

\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))

=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})

=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1

2nd

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}

=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0

3th

\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))

=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}

What we use?

We use that

e^{i\pi n}=cos(\pi n)+i sin(\pi n)

and

\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}

6 0
3 years ago
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