Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If the sum of three consecutive even integers is 78 , what is the first of the three even integers? (Hint: If
x and
x+2 represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)
ion 5
The first of the three even integers is
◻

If the sum of three consecutive even integers is $78$ , what is the first of the three even integers? (Hint: If $x$ and $x+2$ represent the first two consecutive even integers, then how would the third consecutive even integer be represented?) $\newline$ ion $5$ $\newline$ The first of the three even integers is $\square$

View step-by-step help

View step-by-step help

Powers with negative bases

Full solution

Q. If the sum of three consecutive even integers is

78

, what is the first of the three even integers? (Hint: If

x

and

x+2

represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)

\newline

ion

5

\newline

The first of the three even integers is

\square

Define Even Integers: Let $x$ be the first even integer, then the second and third even integers are $x+2$ and $x+4$ respectively
Calculate Sum: The sum of these three consecutive even integers is $x + (x + 2) + (x + 4)$
Set Up Equation: We know the sum is $78$ , so we set up the equation: $x + (x + 2) + (x + 4) = 78$
Combine Like Terms: Combine like terms: $3x + 6 = 78$
Subtract $6$ : Subtract $6$ from both sides: $3x = 78 - 6$
Simplify Equation: Simplify the right side: $3x = 72$
Divide by $3$ : Divide both sides by $3$ to solve for $x$ : $x = \frac{72}{3}$
Calculate x: Calculate the value of x: $x = 24$
Find First Integer: The first even integer is $24$ , so the answer is $24$

More problems from Powers with negative bases

Question

Write the expression using an exponent.

\newline

2 \times 2

\newline

Posted 3 months ago

Question

Evaluate the expression.

4 - 4^2

Posted 3 months ago

Question

x^2 = 4

Posted 2 months ago

Question

x^2 = 9

Posted 4 months ago

Question

\newline

x^2 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

Posted 4 months ago

Question

x

\newline

8 = 2^x

\newline

x =

Posted 4 months ago

Question

x

\newline

6 = 7^x

\newline

x =

Posted 4 months ago

Question

Select the equivalent expression.

\newline

((8^{-5})/(2^{-2}))^{-4}=?

\newline

1

\newline

\newline

(8^{20})/(2^{8})

\newline

\newline

(2^{6})/(8^{9})

\newline

\newline

(1)/(8\cdot 2^{2})

Posted 16 days ago

Question

Select the equivalent expression.

\newline

\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?

\newline

1

\newline

\frac{b^{21}}{4^{15}}

\newline

\frac{4^{15}}{b^{21}}

\newline

b^{-21}\cdot 4^{-15}

Posted 2 months ago

Question

Select the equivalent expression.

\newline

(3^{3}\cdot6^{6})^{-3}=

\newline

1

\newline

\frac{1}{3^{9}\cdot6^{18}}

\newline

\frac{6^{18}}{3^{9}}

\newline

\frac{3^{9}}{6^{18}}

Posted 2 months ago