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Angelina_Jolie [31]
3 years ago
15

If the sum of five consecutive even integers is 90, what is the smallest of the five integers?

Mathematics
1 answer:
ruslelena [56]3 years ago
5 0

So the pattern of even integers is: 2, 4, 6, 8, etc. They are always 2 more than the prior even integer. Using this knowledge, our 5 consecutive even numbers are (let x = smallest even number): x, x + 2, x + 4, x + 6, and x + 8.

Now that we have the numbers, we can form our equation as such: x+x+2+x+4+x+6+x+8=90 . From here we can solve for x.

Firstly, combine like terms: 5x+20=90

Next, subtract 20 onto both sides of the equation: 5x=70

Lastly, divide both sides by 5 and <u>your smallest integer is x=14</u>

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2 years ago
If (x + 1)(x-3) = 5, then which of the following statements is true?
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x=−2 or x=4

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3 years ago
How many 4 digit codes are possible if the first digit cannot be 0 and digits can be repeated?
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What’s the vertex form of F(x)=x^2+2x-3
kupik [55]

Answer:

\large\boxed{f(x)=(x+1)^2-4}

Step-by-step explanation:

\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================

\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================

\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4

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