Adam is 4 years old. This conclusion is reached by setting up a system of equations based on the information that Mark and Adam's ages add up to 28 years and Mark is 20 years older than Adam.
The student is asking how old Adam is, given that the total age of Mark and Adam is 28 years, and Mark is 20 years older than Adam. To solve this, we can set up a system of equations. Let Mark's age be represented by M and Adam's age be represented by A. The two equations based on the given information would be:
M + A = 28 (The sum of their ages is 28)M = A + 20 (Mark is 20 years older than Adam)Now, substituting the second equation into the first one, we get:
A + 20 + A = 28
This simplifies to:
2A + 20 = 28
Subtracting 20 from both sides, we have:
2A = 8
Dividing both sides by 2, we find:
A = 4
So, Adam is 4 years old.
The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hour while hiking. Write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.
Answer:d
Step-by-step explanation:
Rivka and Sara are sisters and contestants on a survival reality tv show. They must each build a raft that will ultimately carry them off the island. Rivka can build her raft in 5 days. Sara can build her raft in 6 days. Though, as sisters, they sometimes fight, they decided to work together to build their rafts. How many days will it take Rivka and Sara to build their two rafts? (Round your answer to one decimal.)
Final answer:
Rivka and Sara can build their two rafts together in approximately 5.5 days, as they have a combined work rate of 11/30 rafts per day when they work together.
Explanation:
Rivka and Sara, working together to build their rafts, would combine their work rates to find out how many days it will take to build two rafts. Rivka can build a raft in 5 days, which means her work rate is 1 raft per 5 days or 1/5 raft per day. Sara can build a raft in 6 days, equating to a work rate of 1/6 raft per day.
When they work together, their combined work rate is 1/5 + 1/6 rafts per day. To combine these, we find a common denominator:
1/5 + 1/6 = (6 + 5) / 30 = 11/30 rafts per day
The question asks how long it takes to build two rafts. Therefore, we divide the total number of rafts by their combined work rate:
2 rafts / (11/30 rafts per day) = (2 * 30) / 11 days = 60/11 days ≈ 5.5 days
Hence, Rivka and Sara will take approximately 5.5 days, or 5.5 days rounded to one decimal, to build two rafts if they work together without stopping.
Which property justifies the following equation 7 [6+5+(-6)=7 [6+(-6)+5]
Round 894-352 to the nearest ten
is 5.75 greater than 5 8/12
Yes, 5.75 is greater than 5 8/12 because 5 8/12 is equal to 5.67 which is less than 5.75.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
We have been given two numbers as
5.75 and 5 8/12
To determine the value 5.75 is greater than or less than 5 8/12
We have to convert the fraction 5 8/12 into the decimal,
⇒ 5 8/12
⇒ (60 + 8)/12
⇒ (68)/12
Apply the division operation,
⇒ 5.67
Therefore, 5.75 is greater than 5 8/12 because 5 8/12 is equal to 5.67 which is less than 5.75.
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Evaluate [(21 + 6) − 3squared] ÷ 9 ⋅ 2.
choices are
4
4.6
1
52
The sum of 16 and a number x is equal to 20
Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the graph of the first function. y=-2(x) and y=-2(x)-3
The graph of the function y = -2 - 3 is shifted down 3 units from the graph of the function y = -2x.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The equations of the functions are:
y -2x
y = -2x - 3
The graph of the function y = -2x will be a straight line that is passing through origin (0, 0).
Applying transformation to the graph of the function y = -2x
y = -2x - 3
As we can see in the graph:
The graph y=-2x - 3 is shifted down 3 units from y = -2x
Thus, the graph of the function y = -2 - 3 is shifted down 3 units from the graph of the function y = -2x.
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A rectangle is twice twice as long as it is wide and has the same perimeter as a square whose area is 9 square feet feet larger than that of the rectangle. what are the dimensions of both the rectangle and the square?
The dimension of rectangle : 6 and 12 units
square= 9 units
What is Perimeter ?Perimeter is the distance around the edge of a shape.
Given:
let the width of rectangle be x.
length= 2x
let the side of square is y units.
Perimeter of rectangle = Perimeter of square
and, Area of square= Area of rectangle + 9
First, Perimeter of square= 4* side
= 4y units
Perimeter of rectangle,
=2(l+b)
=2(2x+x)
=6x units
Since, Perimeter of rectangle = Perimeter of square
6x=4y
3x=2y
Now, Area of square= Area of rectangle +9
y²= x*2x+9
y²= 2x²+9
y²= 2(2y/3)²+9
y²= 8y²/9+9
1/9 y²= 9
y²=81
y=±9
So, x=2y/3= 2*9/3
x= 6
Hence, dimension of rectangle is 6 and 12.
dimension of square is 9 units.
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How to you solve this problem
Raylene bought a roll of tape with a length of 18.9 feet. if she has used 6.3 feet, how much tape is left?
A = Pe^rt
Can you please help me solve for t?
I've tried using logs to isolate it, but I'm not good with logs and I couldn't figure it out.
Simplify
4.4² + 5 =
5.10÷15−3=
6.2 ⋅ 72−10(9+1)3=2 · 72−10(9+1)3=
Which expression represents the distance the two points, X and Y, on the number line?
|-4-7| is the expression represents the distance the two points, X and Y, on the number line
What is Number system?A number system is defined as a system of writing to express numbers.
Number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
The x point is at minus four and y is at point three.
The distance will be always positive
As we count the units from -4 to 3 we get seven humps.
So the distance will be 7 units.
This we can get by taking |-4-3| which is |-7|=7 units.
Hence, |-4-7| is the expression represents the distance the two points, X and Y, on the number line
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The population of a city increases by 4000 people each year. In 2025, the population is projected to be 450,000 people. What is an equation that gives the city’s population p (in thousands of people) x years after 2010?
What is the answer to question 3. Letter A?
put in least to highest order 6.86,6.8,7,6.9,6.827 and 12.03,1.2,12.3,1.203,12.301
Answer:
6.8,6.827,6.86,6.9
Step-by-step explanation:I hope it helps
Name the property shown by the statement.
2 + 5 = 7
solve for y, 3xy+x=9 Then find f(x) when x=2
If JK LM , which statement is true ?
what seperates the places larger than 1 from those that are fractions of 1 such as tenths,hundreths
I need help with this
Ryan works at the car wash making $5.30 per hour plus tips. Last week Ryan worked 32 hours and earned $403. How much in tips did Ryan make last week?
a. $86.40
b. $148.00
c. $169.60
d. $233.40
Answer:
Option d.
Step-by-step explanation:
Ryan works at the car wash and earns = $5.30 per hour plus tips.
His earning from 32 hours of work = 32 × 5.30 = $169.60
He total earned = $403.00
Therefore, he earned from tips = $403 - $169.60
= $233.40
Ryan earned in tips $233.40.
The measure of one of the acute angles in a right triangle is 59°. what is the measure of the other acute angle?
the expression 2x+50 represents the elevation above sea level, in meters, of a rock climber after x minutes of climbing.
Which is the rock climbers initial height above sea level?
Enter your answer in the box.
The rock climbers initial height above sea level is:
50 meters.
Step-by-step explanation:The expression which is used to represent the elevation above sea level, in meters, of a rock climber after x minutes of climbing is given by:
2x+50
Now, we are asked to find the rock climbers initial height above sea level i.e. we are asked to find the value of the expression when x=0.
Hence, when x=0 we have:
2x+50=2×0+50
= 50
Hence, the answer is: 50 meters.
Is (1,-4) a solution to the equation y=-2x?
Yes or no? Please help /:
The width of a rectangle is 3 inches shorter than the length. the perimeter of the rectangle is 18 inches. what is the length of the rectangle
22>= 5(2y+3)-3y how do I solve this
Final answer:
To solve the inequality 22 >= 5(2y+3)-3y, we distribute the 5, combine like terms, then isolate and solve for y, showing that y must be less than or equal to 1.
Explanation:
To solve the inequality 22 >= 5(2y+3)-3y, follow these steps:
Distribute the 5 into the parentheses: 22 >= 10y + 15 - 3y.Combine like terms on the right side: 22 >= 7y + 15.Subtract 15 from both sides to isolate the term with y: 7 >= 7y.Divide both sides by 7 to solve for y: y <= 1The final answer is that y must be less than or equal to 1.
If two cards are drawn without replacement, what is the probability of drawing at least one ace
Given that (-4,5) is on the graph of f(x), find the corresponding point for the function f(2x)
Answer:
the correct answer is (-2,5)
Step-by-step explanation:
you multiply 1/2 by -4 to get the x value
To find the corresponding point on the function f(2x) given a point on the original function f(x), simply multiply the x-coordinate by 2. In this case, the corresponding point is (-8,5).
Given: Point (-4,5) is on the graph of f(x).
To find: Corresponding point for the function f(2x).
Solution:
When x = -4, 2x = 2*(-4) = -8.So, the corresponding point for f(2x) would be (-8,5).