The equation d= -6t + 10 represents the distance d, in miles, Ralph walks from the library to his house in t hours. His sister, Joan, leaves the library right after Ralph. She rides her bicycle from the library to their house at a constant rate. The equation d = 14t represents Joan's bicycle ride where d, is the distance, in miles, and t is the time, in hours.After how many miles will Joan meet Ralph walking to their house?
A. 2.5 miles
B. 7 miles
C. 18 miles
D. 28 miles
Answers
Answer:
B. 7 miles
General Formulas and Concepts:
Algebra I
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Terms/Coefficients
Functions
- Function Notation
Systems of Linear Equations
- Solving methods: Substitution/Elimination
Step-by-step explanation:
Step 1: Define
Identify given.
[Ralph's Walking Distance Function]: d = -6t + 10
[Joan's Bicycle Distance Function]: d = 14t
Step 2: Find Meeting Point
To find where Joan and Ralph will meet, we need to find where they intersect. Therefore, we need to find the time which they both meet up at. To do this, we can use the process of substitution to find our value of t:
- [Equation 1] Substitute in d:
From here, we can simply use techniques listed under "Algebra I" to solve for t:
∴ both Joan and Ralph will meet up in half an hour, or 0.5 hours.
Step 3: Find Mileage
To find how many miles they will meet up at, we substitute the number of hours elapsed (found in Step 2) and substitute it into any of the equations given:
∴ Joan will meet Ralph after 7 miles.
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Topic: Algebra I
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of the same object in millimeters. Which
is a smaller number, x or y?
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Answer:
y
Step-by-step explanation:
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Answers
The solution to the equation 9s + 3 = 57 is s = 6.
What is the solution to the given equation?
Given the equation in the question:
9s + 3 = 57
To solve the equation 9s + 3 = 57, first, isolate the variable "s" on one side of the equation.
9s + 3 = 57
Move the constant term (3) to the other side of the equation by subtracting 3 from both sides:
9s + 3 - 3 = 57 - 3
9s = 57 - 3
9s = 54
Now, solve for "s" by dividing both sides by 9:
9s / 9 = 54 / 9
s = 54 / 9
s = 6
Therefore, the value of 's' is 6.
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Answer: 6
Step-by-step explanation:
9s+3+57
57-3=54
Divide it by 9
54 divided by 9=6
Answers
47 minus 3 times the difference of 15 and 2
47-3(15-2)
Now we have to take the order of operations into consideration.
Parenthesis
Exponents
Multiplication/Division
Addition/Subtraction
Lets clear out the parenthesis.
47-3(15-2)
47-3(13)=47-39=8
Therefore, the final answer is 8
Answer:
Step-by-step explanation:
47 minus 3 times the difference of 15 and 2:
47 - 3(15-2) = 47 - 3(13) =47 - 39 = 8
VS
47 minus 3, times the difference of 15 and 2:
(47-3) (15-2) = (44)(13) = 572
Answers
Answer: B
Answer:
The answer is B
Step-by-step explanation:
First, subtract 13 from both sides to get m≤10. As long as the variable is on the left side then the arrow points in the same direction as the answer so it should be pointing to the left.
Answers
The total balance in Kimmy account in December is $468.98
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In June, Kimmys savings account has a balance of $76.23.
And, By September, her balance is 5 times as much as her June balance.
Between September and December, Kimmy deposits a total of $87.83 into her account.
Now,
Since, In June, Kimmys savings account has a balance of $76.23.
And, By September, her balance is 5 times as much as her June balance.
So, The account balance in September = 5 x $76.23
= $381.15
And, Between September and December, Kimmy deposits a total of $87.83 into her account.
So, The account balance in December = $381.15 + $87.83
= $468.98
Thus, The total balance in Kimmy account in December is $468.98
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The correct answer is:
$468.98.
Explanation:
The account balance in June is 76.23. Since the value in September is 5 times that, the September balance is 5(76.23) = 381.15.
She deposits 87.83 between September and December; this makes the total 381.15+87.83 = $468.98.
Answers
The simplest method to know how 7/10 is greater than 1/2 is to familiarize yourself with the division operation. For example:
If we have the following rational number: 8/4, the division tells us how many 4s are needed to make 8. In this case, there are 2 fours needed to make 8.
Likewise:
7/10: There are 0.7 tens needed to make 7 as 0.7*10 = 7.
1/2: There are 0.5 twos needed to make 1 as 0.5*2 = 1.
It means that 0.7 > 0.5; therefore, 7/10 > 1/2.
Method 2:
1/2 can be represented as 5/10.
Now if we compare 5/10 with 7/10, we can see that 0.5 is less than 0.7. Hence 7/10 is greater than 1/2.
Answer:
Multiply 1/2 by 5 to get the same denominator, which would equal 5/10
Step-by-step explanation: