Two consecutive even integers have the following property. When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer. Find the two consecutive even integers
Final answer:
The problem is solved by creating an equation based on the given properties and solving for x, which represents the smaller even integer. After solving, we find that the two consecutive even integers in question are 8 and 10.
Explanation:
Let the smaller even integer be denoted as x. Consequently, the larger consecutive even integer will be x + 2, since even integers are two units apart.
The problem states that when we add the smaller integer to three times the larger integer (x + 3(x + 2)), the result is two less than five times the smaller integer (5x - 2). This gives us an equation to solve:
x + 3(x + 2) = 5x - 2
Expanding the left side of the equation:
x + 3x + 6 = 5x - 2
Combining like terms:
4x + 6 = 5x - 2
Now, subtract 4x from both sides:
6 = x - 2
Finally, add 2 to both sides to find the value of x:
x = 8
Therefore, the smaller integer is 8, and the larger consecutive even integer is 10.
So, the two consecutive even integers are 8 and 10.
Final answer:
To find the two consecutive even integers, assign variables x and x + 2. Set up and solve the equation x + 3(x + 2) = 5x - 2 to find x = 8. The consecutive even integers are 8 and 10.
Explanation:
To find the two consecutive even integers, let's assign variables to represent the integers. Let the smaller integer be x and the larger integer be x + 2 (since they are consecutive even integers). The problem states that when the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer.
So, we can set up the equation: x + 3(x + 2) = 5x - 2. Simplify and solve for x:
x + 3x + 6 = 5x - 24x + 6 = 5x - 24x - 5x = -2 - 6-x = -8x = 8Therefore, the smaller integer is 8 and the larger integer is 8 + 2 = 10. The two consecutive even integers are 8 and 10.
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50 POINTS!!!!!!!!!
Using the figure below to answer the questions.
(a) Describe in words a sequence of transformations that maps triangle JKL to triangle J’K’L’.
(b) Write an ordered-pair rule for each transformation in the sequence.
what is 0.4% of $100
0.4% = 0.004
100 * 0.004 = 0.4
There are 7 days in 1 week. How many days are there in 4 weeks?
A glass pitcher holds 6 1/3 cups of pineapple juice. Tracy transfers the juice in equal amounts into 3 bottles. How many cups of juice will each bottle contain? (Show ur work plz)
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If the original quantity is 15 and the new quantity is 18, what is the percent increase?
The percent increase is 20%.
What is Percent increase?The ratio of the increased value to the original value, multiplied by 100, is the percentage increase formula. It is outlined as a percentage. Anything's value will increase if it is valued more, so will its proportion.
Given:
original quantity = 15 and the new quantity =18
so, Change in amount = 18- 15= 3
So, the percent increase
= Change in amount / original amount x 100
= 3/ 15 x /100
= 100/5
= 20 %
Hence, the percent increase is 20%.
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Which number is a perfect cube A 3 B 15 C 64 D567
of all the whole numbers that divide evenly into two or more numbers the one with the highest value is called the _____________.
What is the slope of the graph for the equation y = -5x + 8? A. 0 B. -5 C. 8
Hans rented a truck for one day. There was a base fee of $19.99 , and there was an additional charge of 85 cents for each mile driven. Hans had to pay $205.29 when he returned the truck. For how many miles did he drive the truck?
Jenny's frog made one jump of 2.34 meters. Christina's frog made jumps of 1.22 meters and 0.89 meters. How much further did Jenny's frog jump in one jump than Christina's frog in two jumps combined? 0.23 m 0.33 m 1.12 m 1.45 m
took the k12 test it 0.23
Choose the answer based on the most efficient method as presented in the lesson. If the first step in the solution of the equation - X + 6 = 5 - 3x is " subtract 5," then what should the next step be?
You would add x to -3x
In the diagram AB is parallel to CD. What is the term for the line that intersects the two parallel lines?
Answer:
its been 3 years but the answer is b
Step-by-step explanation:
how many time more respondents chose silver than red round to the nearest tenth if necessary red is .2 and .09 is silver
Jack and Jessica and the same amount last week.Jack earned $18 per hour and had $41 taken away from his check for Taxes. Jessica earned $15 an hour and had to $17 deducted from her pay. how many hours did they each work in order to get paid the same amount
terrell runs 15 sprints. each is 65 meters. how many does terrell run
where would 2015 be on a mod 7 clock
ANSWER A B C AND D DOWN BELOW
Uptown Photography charges $15 per portrait sheet, plus $19 for a session fee. Downtown Photography charges $29 for a session fee and $10 per portrait sheet. Find the number of portrait sheets for which the total price is equal for the companies with the solution stated as an ordered pair. A) (5, 79) B) (4, 69) C) (3, 59) D) (2, 49)
The answer is (2,49).
The odometer on your family car reads 20,186.7 after going
62.3 miles. How many miles were on the odometer before
going 62.3 miles?
What is the cost of 2 kilograms of flour if 3 Kg cost $4.86 and the unit price for each packet of flower is the same? A. $0.81 B. $2.86 c. $3.24 d. $9.72
f y = 16x, which table shows the values of y for different values of x?
x 0 2 4
y 0 18 20
x 0 2 4
y 0 8 4
x 0 2 4
y 0 32 64
x 0 2 4
y 0 16 32
Answer:
D
Step-by-step explanation:
Christopher recorded the low temperature each day for 1 week and recorded his results in this table. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Low −5 °F −8 °F −6 °F −8 °F −3 °F 2° F 7° F What is the average low temperature for the week? Enter your answer in the box.
You are working as an assistant to a chef.the chef has 6 cups of berries and will use 2/3 cup of berries for each dessert he makes.how many desserts can he make?
Find the value of x. (5x+15) (6x-10)
Answer:
We get x = -5/3 and x = -3
Step-by-step explanation:
[tex](5x+15) (6x-10)[/tex]
Multiplying this and equating to zero, to find x.
[tex]30x^{2} -50x+90x-150=0[/tex]
[tex]30x^{2} +40x-150=0[/tex]
Factoring out 10.
[tex]3x^{2} +4x-15=0[/tex]
[tex]3x^{2} +9x-5x-15=0[/tex]
3x(x+3)-5(x+3)=0[tex]
[tex](3x-5)(x+3)=0[/tex][/tex]
We get x = -5/3 and x = -3
Write a decimal that is greater than 3.4 but less than 3.5
The graph shows the distances traveled by two hikers over several hours.
A graph measuring distance and time. Two lines, labeled Hiker A and Hiker B, exit the origin to show that distance increases as time increases
Which hiker is moving at a faster rate?
Select from the drop-down menu to correctly complete the statement.
Hiker is moving at a faster rate.
Answer:
Hiker A is moving at a faster rate.
Step-by-step explanation:
When two lines are being compared, the one that moves faster is the one with the higher slope. Looking at these two graphs, we see that the graph of Hiker A has a higher slope; therefore Hiker A is moving faster.
Using the information depicted on the graph, the speed of the hikers is given by the slope of the graph. Hence, Hiker A is moving at a faster rate.
The steepness of the slope of a linear graph can be used to measure the rate of change.
Steeper slope means a higher rate of change. Since, Hiker A has a steeper slope, then he is moving at a faster rate.
Therefore, the hiker moving at a faster rate is hiker A.
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What’s 8,450 divided by 125