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ryzh [129]
3 years ago
7

find three consecutive even integers such that the sum of the smallest integer and twice the second is 12 more than the third (o

nly an algebraic solution will be accepted )
Mathematics
1 answer:
Helga [31]3 years ago
3 0
Let us call them a, b and c
we know that
a+1=b
a+2=c
a+2b=12+c
we can deduce the following:
a+2(a+1)=12+(a+2)
3a+2=a+14
2a=12
a=6

so b would be 7 and c would be 8
Makes sense ?
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If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her a
RSB [31]

Answer:

14 years old

Step-by-step explanation:

<u>Define the variable</u>

Let x be the actual age of Zeba (in years).

<u>Create an equation</u> using the give information and the variable x:

(x - 5)^2=5x+11

To find Zeba's age now, <u>solve the equation for x</u>.

Expand the brackets:

\implies x^2-10x+25=5x+11

Subtract 5x from both sides:

\implies x^2-10x+25-5x=5x+11-5x

\implies x^2-15x+25=11

Subtract 11 from both sides:

\implies x^2-15x+25-11=11-11

\implies x^2-15x+14=0

<u>Factor the found quadratic</u>

To factor a quadratic in the form ax^2+bx+c<em>, </em>find two numbers that multiply to ac and sum to b, then rewrite b as the sum of these two numbers:

\implies x^2-14x-x+14=0

Factor the first two terms and the last two terms separately:

\implies x(x-14)-1(x-14)=0

Factor out the common term (x - 14):

\implies (x-1)(x-14)=0

Apply the <u>zero product property</u>:

\implies (x-1)=0 \implies x=1

\implies (x-14)=0 \implies x=14

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an <u>extraneous solution</u> since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

<u>Check</u>

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as:  14 - 5 = 9

The square of 9 is:  9² = 81.

5 times her actual age:  5 × 14 = 70

81 is 11 more than 70, hence verifying that her <u>actual age is 14 years old</u>.

Learn more about quadratic equations here:

brainly.com/question/27956741

brainly.com/question/27947331

5 0
1 year ago
Read 2 more answers
Help me please , I’ll mark brainliest
dexar [7]

Answer:

42 feet squared

Step-by-step explanation:

6 0
3 years ago
Elijah buys a jersey that costs $56.00. His bank account balance is now -$6.50. Which math sentence describes how much he owes?
soldier1979 [14.2K]
It would be (B) > $6.00 since he owes $6.50, which is a larger value than $6.00.
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3 years ago
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a bicycle tire is 28 inches in diameter. approximately how far does the bicycle move forward each time the wheel goes around? (u
belka [17]

ANSWER

88 \: inches

EXPLANATION

The given bicycle has a tyre that is 28 inches in diameter.

How far the bicycle moves forward each time the wheel goes around is the circumference of the bicycle tyre.

This is calculated using the formula:

C =\pi \: d

We substitute the diameter and

\pi =  \frac{22}{7}

C =  \frac{22}{7}  \times 28

This simplifies to

C =22 \times 4

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8 0
3 years ago
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PLEASE HELP
Veseljchak [2.6K]

Answer:

Step-by-step explanation:

intersection = { } no common elements.

union = { b,d,f,a,c,k}

6 0
2 years ago
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