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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QUESTION WORTH 20 POINTS, ANSWER A.S.A.P.!!!!!!!!!!!!!
The charges for two shuttle services are shown in the table. Find the number of miles for which the cost of both shuttles is the same.
Pickup Charge ($) Charge per Mile ($)
-----------------------------------------l--------------------------------------------
Easy Ride: $10 l $0.10
-----------------------------------------l--------------------------------------------
Best: $0 l $0.35
-----------------------------------------l--------------------------------------------
The number of miles for which the cost of both shuttles is the same is 40.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The charges for two shuttle services are shown in the table.
m=0-10/0.35-0.10
=10/0.25
Ten divided by zero point two five is 10 by one divided by 4.
=40 miles
Hence, the number of miles for which the cost of both shuttles is the same is 40.
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140 ft is 97 percent of what
The number is 144.32 whose 97% is 140 ft .
Given,
140 ft is 97 percent of what number .
Here,
Let the number be x .
Forming the equation,
97% of x = 140
97/100 of x = 140
x = 140 * 100/97
x = 140000/97
x = 144.32
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Order from least to greatest 0.5 0.41 3/5
What does y equal ?
4y^2= 5.76
y =
How do you solve for B?
Equation is T = hP + 2B.
To solve for B in the given equation, subtract hP from both sides and then divide both sides by 2. This results in B = (T - hP) / 2.
Explanation:To solve for B in the equation T = hP + 2B, you need to isolate B. Here's a step-by-step process to do that:
Subtract hP from both sides of the equation to get: T - hP = 2B.Then divide both sides of the equation by 2 to isolate B. The equation becomes B = (T - hP)/2.So, the solution for B in the equation is B = (T - hP)/2.
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Addition with unequal denominators 1/3+1/6=
What is the function rule for the line?
A. f(x) = 3/2x - 2
B. f(x) = -2/3x - 2
C. f(x) = -3/2x - 2
D. f(x) = -3/2x + 2
How many more equal angles does a square have than a rectangle?
what is the answer to this
3b+8= -10
a bank gives you a simple interest loan at a rate of 5.5% after 3 years, you have paid the entire principal + 41.91 dollars in interest what was the original principal amount of your loan
Use known facts to find the product 9x5
simplify the expression by combining like terms.
7b + 4 - 3b - 2
what the number that goes n the box ?
( ? ) b + ( ? )
Final answer:
Combine like terms by adding or subtracting the coefficients of terms with the same variable and combining constants. The simplified expression is 4b + 2, so the coefficients that go in the boxes are 4 and 2.
Explanation:
To simplify the expression by combining like terms, follow the process of identifying and adding/subtracting like terms. The expression 7b + 4 - 3b - 2 contains both variable terms (containing 'b') and constant terms (just numbers).
Combine like terms:
Combine variable terms: 7b - 3b = 4b.
Combine constant terms: 4 - 2 = 2.
After combining like terms, the simplified expression is 4b + 2.
Therefore, the numbers that go in the boxes are 4 for the coefficient of 'b' and 2 for the constant term.
Relationship A has a greater rate than Relationship B. This table represents Relationship B. Hours worked 2 4 5 8 Amount paid 30.40 60.80 76 121.60 Which equation could represent Relationship A? Hours worked is represented by x and Amount paid is represented by y. Select each correct answer. y = 15.4x y = 15.2x y = 16.4x y = 14.9x
Answer:
The answers are y=15.4x and y=16.4x.
Step-by-step explanation:
I took the test just 3 minutes ago
Two or more expressions with an equal sign is called as Equation. y = 15.2x is the equation which could represent Relationship A.
What is Equation?Two or more expressions with an equal sign is called as Equation.
Given that,
Relationship A has a greater rate than Relationship B
Hours Worked Amount Paid
2 30.4
4 60.8
5 76
8 121.60
Let us take hours worked as x and Amount paid as y.
In the given functions
y = 15.4x ...(1)
y = 15.2x ...(2)
y = 16.4x ...(3)
y = 14.9x....(4)
We need to check which satisfies the relationship between x and y.
If x=2 then we need to get 30.4
So let us put x=2 in equation 1.
y=15.4×2
=30.8
Which does not matches.
Now let us check with second function.
y=15.2×2
y=30.4
It matches.
So let us check for other values.
x=4
y=15.2×4
y=60.8
x=5
y=15.2×5=76
if x=8, y=15.2×8=121.6
Hence y = 15.2x is the equation which could represent Relationship A.
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Nelson opened a savings account 11 years ago with a deposit of $3,115.89. The account has an interest rate of 5.3% compounded monthly. How much interest has Nelson earned?
Answer:
2458.77
Step-by-step explanation:
3115.89*(1+0.053/12)^(11*12) - 3115.89 = 2458.77
Jake, Becky, and Max are meeting at Charley's Pizza for dinner and then plan to go to a movie. When they arrive at the pizza place, each one of them has a different coupon. They decide to use the coupon that will give them the best deal. Jake's coupon is $19.99 for a pizza and pasta meal deal; Becky's coupon is for two large one-topping pizzas--each at 2/3 of the menu price; and Max's coupon is for three medium one-topping pizzas -- each at 1/4 off the menu price. According to the menu, a medium one-topping pizza is $8.99, and a large one-topping pizza is $14.89. They also spend $1.25 each for sodas and $5.00 on the tip. At the movie theater, Max has a coupon that's good for 1/2 off a third movie ticket when you purchase two other movie tickets at the regular price. The regular price of each movie ticket is $9.80. Although Jake, Becky, and Max plan to split the cost of the pizza and movie, they decide that with the coupons, it's just easier if one of them pays at each place. So, the friends agree that Jake will pay for the pizza and Becky will pay for the movies. At the end of the night, they'll figure out how much Max owes both Jake and Becky. At charleys pizza Whos coupon should they use?
the answer is Becky,s hope this helped
A business owner pays $1,200 per month in rent and a total of $120 per hour in employee salary for each hour the store is open. On average, the store brings in $200 in net sales per hour. Which equation can be solved to determine the break-even point if x represents the number of hours per month the store is open?
The break-even point can be determined by setting the net sales per hour equal to the total cost per hour. The equation to solve for the break-even point is $200x = $1,320x. By dividing both sides of the equation by $1,320, we can find the value of x, which represents the number of hours per month the store needs to be open to break even.
Explanation:To determine the break-even point, we need to find the number of hours per month the store needs to be open in order to cover all its costs. The total cost for each hour the store is open is the sum of the rent and the employee salary. So, the total cost per hour is $1,200 + $120 = $1,320. The break-even point is reached when the net sales per hour equals the total cost per hour:
Net sales per hour = Total cost per hour
In this case, the net sales per hour is $200, so we can set up the equation:
$200x = $1,320x
where x represents the number of hours per month the store is open. By dividing both sides of the equation by $1,320, we can solve for x:
$200 = $1,320x / $1,320
$200 / $1,320 = x
x = 0.1515...
So, the break-even point is approximately 0.1515... hours per month, or about 9.09 minutes per month.
the walls of a square room need painting.Each of the four walls is 12 ft wide by 8.5 feet tall.One gallon of paint covers 75 ft.How many gallons will you need?
The walls of a room need painting. Each of the four walls is 12 ft wide by 8.5 feet tall.
We know that, Area = length [tex]\times[/tex] width.
So, the area of one wall = 8.5 ft [tex]\times[/tex] 12 ft = 102 square feet
Thus, the area of 4 walls = 4 [tex]\times[/tex] 102 = 408 square feet
One gallon of paint covers 75 square feet. We need to find how many gallons of paint will cover 408 square feet.
So, the amount of gallons of paint needed = 408[tex]\div[/tex]75
= 5.44 gallons
So, 5.44 gallons are needed to cover 408 square feet.
To find the number of gallons of paint needed to paint the walls of a square room, calculate the total area of all four walls and divide it by the coverage of one gallon of paint.
Explanation:To find the total area of all four walls, we need to calculate the area of one wall and then multiply it by four. The area of one wall is the product of its width and height, which is 12 ft x 8.5 ft = 102 ft².
So, the total area of all four walls is 102 ft² x 4 = 408 ft².
Since one gallon of paint covers 75 ft², we divide the total area of all four walls (408 ft²) by the coverage of one gallon of paint (75 ft²) to find the number of gallons needed: 408 ft² ÷ 75 ft² = 5.44 gallons.
Therefore, you will need approximately 5.44 gallons of paint to paint the walls of the square room.
What number is 1/10 as great as 7962
Answer:
796.2
Step-by-step explanation:
a number 1/10 as great as 7962 can be found in two ways the first way is
1) Divide 7962 by 10 we get 796.2
there fore 7962/10= 796.2
second way to get
2) multiply 7962 by 1/10 we again get 796.2
therefore from both the calculation a number 1/10 as great as 796.2
hope you got the point, feel free to ask doubt in comments
If a photo measuring 4 inches by 6 inches is placed in a photo frame that is 2 inches wide all around, what percent of the framed photo is the photo itself?
Answer:
Percentage of the photo = 50%
Step-by-step explanation:
Given that the measurement of the photo is 4 inches by 6 inches and the measurement of the photo frame is 2 inches wide all around, it simply implies that is measurement of the photo frame is (4inches + 2inches) by (6 inches + 2inches). I.e 6inches by 8inches
To find the percentage of the photo itself, let find the area of the photo and that of the frame
Area of photo = 4 inches x 6 inches = 24inches²
Area of photo = 6 inches x 8 inches = 48inches²
Percentage of the photo = area covered by the photo / area covered by the frame x100
Percentage of the photo = 24/48 * 100
Percentage of the photo = 50%
Violet is watching the sand in a hourglass drain from the upper portion to the lower portion of the glass. She wonders how fast the sand is draining.
Which unit rates would be reasonable for Violet to use to describe how fast the sand is draining from the upper portion to the lower portion of the glass?
Select EACH correct answer.
gallons per hour
liters per hour
cubic centimeters per minute
cubic inches per second
The unit rates which will be reasonable for Violet to use to describe how fast the sand is draining from the upper portion to the lower portion of the glass is cubic centimeters per minute.
Explanation:
As the first 2 options gallons per hour and liters per hour, these denote liquid forms. But sand is not liquid that is why it cannot be the answer.
Cubic inches per second is very fast as compared to the small hourglass and the amount of sand that could be present in it. Moreover one side of the hourglass needs to be emptied in 24 hours, so this option is also not possible.
Paul's car will go 49 kilometers on 7 tanks. Paul wants to know how fuel efficient the car is.
Please help by computing the ratio.
Can a brick of 9cm by 12 cm by 25 cm can pass through a pipe of diameter 14 cm?
Write an expression for the perimeter of the triangle shown below: (4 points)
A triangle is shown with side lengths labeled 0.5x plus 9, 3x, and negative 3.4x minus 25.
6.9x − 16
6.9x + 16
0.1x − 16
0.1x + 16
Answer:
The correct option is 3.
Step-by-step explanation:
It is given that the length of sides of a triangle are 0.5x+9, 3x, and -3.4x-25.
Let a=0.5x+9, b=3x, and c=-3.4x-25.
Perimeter of a triangle is the sum of length of all three sides.
[tex]Perimeter=a+b+c[/tex]
Substitute a=0.5x+9, b=3x, and c=-3.4x-25 in the above equation.
[tex]Perimeter=(0.5x+9)+(3x)+(-3.4x-25)[/tex]
On simplification, we get
[tex]Perimeter=0.5x+9+3x-3.4x-25[/tex]
Combine like terms.
[tex]Perimeter=(0.5x+3x-3.4x)+(9-25)[/tex]
[tex]Perimeter=(0.1x)+(-16)[/tex]
[tex]Perimeter=0.1x-16[/tex]
Perimeter of the triangle is 0.1x-16. Therefore the correct option is 3.
three times a number increased by 5 is less than 17
I need help on this problem
How you write 5×923 in expanded form
At 9:00 am linda leave work on a trip, sets her cruise control at 60mph. At 9:30 am, Bruce notices she left her briefcase and gets on the free way driving 90mph. At what time will Bruce catch up with Linda?
Bruce will catch up with Linda at 9:48 am.
Explanation:To find the time at which Bruce catches up with Linda, we need to determine the time it takes for Bruce to cover the same distance that Linda has already covered.
Since Linda starts her trip at 9:00 am and Bruce starts 30 minutes later at 9:30 am, Linda has a head start of 30 minutes or 0.5 hours.
In that 0.5 hours, Linda travels a distance of:
Distance traveled by Linda = Speed * Time
Distance traveled by Linda = 60 mph * 0.5 hours
Distance traveled by Linda = 30 miles
Now, Bruce needs to catch up with that distance of 30 miles. Let's find the time it takes for Bruce to cover that distance at his speed of 90 mph:
Time taken by Bruce = Distance / Speed
Time taken by Bruce = 30 miles / 90 mph
Time taken by Bruce = 0.33 hours
Since Bruce started at 9:30 am, he will catch up with Linda at:
Catch up time = Start time + Time taken by Bruce
Catch up time = 9:30 am + 0.33 hours
Catch up time = 9:48 am
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what is the distributive property for 8 times 19
The distributive property: a(b + c) = ab + ac
8 × 19 = 8 × (20 - 1) = 8 × 20 - 8 × 1 = 160 - 8 = 152
on a blueprint of a house, 25 millimeters represents 4 meters. the actual length of the living room is 5 meters. what is its length on the blueprint?
Answer:
31.25 mm
Step-by-step explanation:
Use a proportion.
25 mm is to 4 m as x mm is to 5 m
25/4 = x/5
4x = 125
x = 125/4
x = 31.25
Answer: 31.25 mm
The graph below represents the function f(x), and the table below represents the function g(x).
Which statement is true?
The maximum value of g(x) is greater than the minimum value of f(x).
The minimum value of g(x) is less than the maximum value of f(x).
The minimum value of g(x) is greater than the maximum value of f(x).
The maximum value of g(x) is less than the minimum value of f(x).
Thank you! :)
The statement that is true about the graph is The maximum value of g(x) is greater than the minimum value of f(x).
1. "The maximum value of g(x) is greater than the minimum value of f(x)": This is true because the maximum value of g(x) is -10, which is greater than the minimum value of f(x) (which we don't know, but it cannot be lower than -10 based on the given data).
2. "The minimum value of g(x) is less than the maximum value of f(x)": This is true based on the given data, as the minimum value of g(x) is -1, which is less than the maximum value of f(x) (which we don't know, but it cannot be higher than -1 based on the given data).
3. "The minimum value of g(x) is greater than the maximum value of f(x)": This is false based on the given data. The minimum value of g(x) is -1, which is less than the maximum value of f(x) (which we don't know).
4. "The maximum value of g(x) is less than the minimum value of f(x)": This is false based on the given data. The maximum value of g(x) is -10, which is less than the minimum value of f(x) (which we don't know, but it cannot be lower than -10 based on the given data).
The greatest value of g(x) is -1 (the higher number for the g(x) entry in the table), and the minimum value of f(x) is -3 (the lower y/f(x) you may point on the graph). As a result, the maximum value of g(x) exceeds the minimum value of f(x).