Answer:
Symbols (or letters) in an equation can be important.
Step-by-Step Explanation:
The symbol [or letter (x, m, n, etc.)] is usually not important because the symbol represents a number. Sometimes it is important because each symbol (or letter) can represent another number.
for example: n+3 = 4-m (the symbol/ letters are different because they represent a different number).
for another example: n+3 = 4 (the symbol/ letter is only one letter).
The choice of letter or symbol to represent an unknown number in mathematics is arbitrary. It doesn't impact the mathematical operation or relationships, as the fundamental principles of algebra apply universally to any symbol.
It doesn't matter what letter or symbol is used to represent an unknown number because the essence of algebra and mathematical expressions is based on abstraction and generality. Mathematical symbols are placeholders for values and can be interchanged without changing the underlying mathematical relationships. Here's why it doesn't matter:
1. Universality of Symbols: Mathematical symbols and variables are universally understood and follow consistent rules. Whether you use "x," "y," "a," "b," or any other symbol, the principles of mathematics remain the same.
2. Abstraction: Algebra allows us to work with general concepts rather than specific numbers. The choice of symbols is arbitrary and doesn't affect the mathematical operations. The symbols represent placeholders for any number that satisfies the given conditions.
3. Flexibility: Different symbols can be used for different contexts or problems. For example, "x" is often used for unknowns in equations, "a" for constants, and "y" for dependent variables in functions. However, this is a convention, and other symbols can be used interchangeably.
4. Consistency: The rules of algebra, such as the commutative, associative, and distributive properties, hold true regardless of the symbols used. Algebraic manipulations and equations remain valid irrespective of the choice of symbols.
In summary, mathematical symbols are versatile and interchangeable because they serve as placeholders for values. The principles of algebra and mathematics are symbol-independent, allowing for flexibility in representation while maintaining the same underlying mathematical relationships.
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How do i graph the equation -x + 2y = 2
Step-by-step explanation:
Firstly, set the x value as 0:
-0 + 2y = 2
2y = 2
y = 1
So when x = 0, y = 1
Now set y to 0:
-x + 2(0) = 2
-x = 2
x = -2
So when y = 0, x = -2
Simply plot the two following points:
(0 , 1) and (-2 , 0)
And don't forget to join these two points up!
Attatched is an image of this graph.
Thank you so much
I need the help
Answer:
g(x) is translated 6 units down from f(x)
Step-by-step explanation:
given a function f(x) then f(x) + c represents a vertical translation
• If c > 0 then vertical translation up ↑
• If c < 0 then vertical translation down ↓
5 days 6 hours 20 minutes minus 3 days 8 hours 40 minutes plz help will make brainliest
Answer:
1 day 21 hours 40 minutes
Step-by-step explanation:
5 days 6 hours 20 minutes
- 3 days 8 hours 40 minutes
============================
We will need to borrow minutes from the hours because we don't have enough.
1 hour = 60 minutes
6-1 = 5 hours
20 +60 = 80 minutes
5 days 5 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
We will need to borrow hours from the days because we don't have enough.
1 day = 24 hours
5 -1 =4 days
5 + 24 = 29 hours
4 days 29 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
1 day 21 hours 40 minutes
Answer:
1 day 21 hours 40 minutes
Step-by-step explanation:
you have to convert the days to hours, then convert the hours to minutes then subtract
4 days 29 hours 80 minutes - 3 days 8 hours 40 minutes = 1 day 21 hours 40 minutes
PLZ MARK BRAINIEST
If you are 14 years old now, which equation could be used to solve for your age, Y, 22 years from now?
14*Y=22
14+22=Y
14-22=Y
14+Y=22
Answer:
14+22=Y
Step-by-step explanation:
Since it is 22 years from now, you would add 22 to your current age, 14, to get Y, the age.
The correct equation to find your age 22 years from now, if you are currently 14, is 14 + 22 = Y. Solving the equation gives Y equals to 36.
Explanation:The correct equation that can be used to solve for your age, Y, in 22 years if you are currently 14 years old then the second option i.e., equation 14 + 22 = Y is the correct answer.
This equation represents an addition where you add the number of future years (22 years) to your current age (14 years old). When you solve this equation, Y equals to 36, which would be your age 22 years from now, assuming you're currently 14 years old.
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Annette has 5more dimes than quarters, the total amount is $3.30. How many of each coin does she have?
A
Step-by-step explanation:the answer is you have 8 quarter and 13 dimes .
Because you have 5 more dimes than quarters which will equal 3 dollars and 30 cents
Annette has a total of 5 coins according to the total money she has.
Given that,
Annette has 5more dimes than quarters, the total amount is $3.30. How many of each coin does she have is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
let the number of dimes be x
Now a number of quarters is x - 5
Accoding to the question,
x + x - 5 = 3.30
2x = 3.30 + 5
2x = 8.30
x = 4.15
Now,
here
number of dimes has approximately = 4
number of quarters = x - 5 = 4 - 5 = -1 (value is negative which is not possible). = 0
Thus, Annette has a total of 5 coins according to the total money she has.
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Triangle ABC was dilated to triangle A'B'C'. What was the magnitude of the dilation?
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2
Step-by-step explanation:
If you start from the origin and go to point B, you went up 2, and to the left 1. Now if you go from the origin to B', you went up 4, and to the left 4. Lets compare the ratios.
2/1 and 4/2
You had to multiply the first ration by 2 to get to the second ratio.
a store has some sale on let supplies the price of each item is marked down 25% the store also offers a coupon for 5 off for when you check out write an expression that represents the final price after a customer uses the coupon
what kind of decimal is an irrational number give an example
Answer:
An irrational decimal is a decimal that cannot be written in fraction form
Ex: Pi or any decimal that keeps going and doesn't repeat
Step-by-step explanation:
I would give you more examples but they are all really long numbers and go on forever.
Answer:
Pi!
Step-by-step explanation:
I know it might sound silly but Pi and it's digits are part of the irrational decimal family! It's irrational because the digits of Pi seem like they never end, right? Hope this helped!
This week, Jamyra spent a total of 100 minutes studying. This total was 8 more than four times the amount of minutes she studied last week. How many minutes did Jamyra spend studying last week?
Answer: 23 minutes
Step-by-step explanation:
4x + 8 = 100
100 is 8 more than 4 times of minutes than last week.
X = minuted she studied last week.
Find x
4x = 100 - 8
4x = 92
x = 92/4
x = 23 minutes
Based on the problem, we form an equation 4x + 8 = 100 to represent the given situation. After solving this equation, we find that Jamyra spent 23 minutes studying last week.
Explanation:The question is asking about the amount of time that Jamyra spent studying last week based on the information provided about this week. It's given that Jamyra spent 100 minutes studying this week and that this total was 8 more than four times the amount of minutes she studied last week.
We can form an equation from this information: 4x + 8 = 100, where 'x' is the time Jamyra spent studying last week. Subtract 8 from both sides to get 4x = 92.
Then, divide both sides of the equation by 4 to isolate 'x', and we get x = 23.
So, Jamyra spent 23 minutes studying last week.
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Two cars leave towns
950
kilometers apart at the same time and travel toward each other. One car's rate is
16
kilometers per hour less than the other's. If they meet in
5
hours, what is the rate of the slower car?
Final answer:
The speed of the slower car is 87 km/h. This was calculated by setting up an equation with the sum of the distances traveled by both cars after 5 hours, which is 950 km, and solving for the speed of the faster car first, then finding the speed of the slower car.
Explanation:
To determine the rate of the slower car in a scenario where two cars travel toward each other from 950 kilometers apart and meet in 5 hours, we set up an equation based on the relative speeds and distances covered. Let the speed of the faster car = v km/h; therefore, the speed of the slower car would be (v - 16) km/h, since it's given that the slower car travels 16 km/h less than the faster one.
The sum of the distances traveled by both cars when they meet after 5 hours is 950 km. We can express this with the equation: 5v + 5(v - 16) = 950.
Solving for v:
Subtracting 16 km/h from the faster car's speed gives us the slower car's speed:
v - 16 km/h = 103 km/h - 16 km/h = 87 km/h.
Therefore, the rate of the slower car is 87 km/h.
A line has a slope of -1/2 and a y-intercept of –2.
What is the x-intercept of the line?
a.–4
b.–1
c.1
d.4
Answer:
a.-4
Step-by-step explanation:
I pictured it as a graph and since the slope is negative, the line goes down and to the right. Since the slope is -1/2, for every 2 you move horizontally, you move one vertically. You have to move two up and unless the y intercept is 0, when the line intercepts y, you have 0 as x. You move two up and 4 backwards so the x intercept is -4
The point (2,-2) and (-4,13) on the graph of a linear function of x. Which point also lies on the graph of this function?
A. (-6,18)
B. (-1,5)
C. (7,14.5)
D. (13, -4)
Answer:
A. (-6,18)
Step-by-step explanation:
The point (2,-2) and (-4,13) on the graph
First we frame an equation of the line using two points
y = mx + b where m is the slope and b is y intercept
slope = [tex]\frac{y_2-y_2}{x_2-x_1} =\frac{13+2}{-4-2} = \frac{15}{-6} = -2.5[/tex]
m = -2.5
Lets find out b
y = mx+b
y= -2.5x + b
Plug in (2,-2) and find out b
-2 = -2.5(2) + b
-2 = -5 + b (add 5 on both sides)
b = 3
so equation of line is y = -2.5 x + 3
Now we check with each option
(-6,18)
Plug in the x and y in our equation and check it
y = -2.5 x + 3
18 = -2.5(-6) + 3
18 = 15+3
18=18 true
So (-6,18) lies on the graph
William is 1/6 as old as his father but 5 years older than his sister Mary. If the sum of all their ages is 51, how old is William?
Answer: William is 7 years old
Hope this helps, I can take the time to explain if needed:)
By creating a system of equations from the information given and solving for William's age, we determine that William is 7 years old.
The question presents a typical age-related algebra problem. We have three unknowns: William's age, his father's age, and his sister Mary's age. To solve this problem, we need to set up a system of equations based on the information provided.
Let's let W stand for William's age, F for his father's age, and M for Mary's age.
The first piece of information tells us that William is 1/6 as old as his father, so F = 6W.
The second piece says that William is 5 years older than his sister Mary, so W = M + 5.
Lastly, we know that the sum of all their ages is 51, so W + F + M = 51.
Now, we'll substitute F and M from the first two equations into the third equation:
W + 6W + (W - 5) = 51
This simplifies to:
8W - 5 = 51
Adding 5 to both sides gives us:
8W = 56
Dividing both sides by 8, we find:
W = 7
Therefore, William is 7 years old.
I spent 3/4 of my money and then I spent 1/5 of what was left.
a) What part of all my money did I spend?
b) What part of all my money do I have left?
Answers:
a) 4/5
b) 1/5
================================================
Let's say you start off with $100. If you spend 3/4 of that, then you spend 75 dollars (because 75/100 = 3/4). Think of it like 75 cents = 3 quarters. If you spend 75 dollars out of 100 total, then you have 100-75 = 25 dollars left after the first round of spending.
If you spend 1/5th of what is left, then you spend $5 on the second round leaving 25-5 = 20 dollars left at the end of the day.
Total up what you spend for both rounds: 75+5 = 80, which divides over the original amount 100 to get 80/100 = 8/10 = 4/5
If you had 20 dollars at he end of the day, out of 100 initially, then 20/100 = 2/10 = 1/5 is the fraction of what you have left.
note how 4/5 and 1/5 add to 5/5 = 1.00 = 100%. This is because the amount you spend and the amount you have left over must add to 100% of all the money you started with
What is the range of AB?
a, b, c - sides of a triangle
Therefore:
a + b > c
a + c > b
b + c > a
---------------------------------
We have a = AB, b = 140mi, c = 100mi.
(1) a + b > c
AB + 140 > 100 subtract 140 from both sides
AB > -40 → AB > 0
----------
(2) a + c > b
AB + 100 > 140 subtract 100 from both sides
AB > 40
-----------
(3) b + c > a → a < b + c
AB < 140 + 100
AB < 240
Answer: 40 < AB < 240write a story problem that represents 528 divided by 24
Answer:
Micheal owns a farm. On that farm he plants 528 oranges. After harvest, he decides to pack all of his oranges into crates to sell. If he has 24 crates, how many oranges should he pack into each crate? Will there be too many oranges in which there will be some left over?
Step-by-step explanation:
PLEASE HELP ME
And show work
Answer:
The snow cone in a cup will hold more.
Step-by-step explanation:
Traditional snow cone:Firstly, to find the area of the cone you need to know the formula:
[tex]\frac{1}{3}\pi r^{2} h[/tex]
So simply plug the values in:
[tex]\frac{1}{3}\pi 4^{2} 13[/tex]
= 217.81 = 218cm³
Snow cone in a cup:To find the area of a cylinder, you need to remember the formula:
The radius is half the diameter so:
Radius = 8 ÷ 2 = 4
[tex]\pi r^{2} h[/tex]
So simply plug these values in:
[tex]\pi 4^{2} 5[/tex]
= 251.33 = 251cm³
So this means that because the snow cone in a cup is 251cm³ whereas the traditional snow cone is only 218cm³, the snow cone in a cup will hold more.
Which of the following does not represent a function? graph of a sine wave function graph of a line with a negative slope and a y intercept of negative 5 graph of a positive parabola oriented about the y axis with y intercept negative 6 graph of an absolute value function oriented about the x-axis
How do I solve this math problem?
Answer: 4x² + 4x - 2 - [tex]\frac{3}{2x+3}[/tex]
Step-by-step explanation:
You can use either synthetic or long division. I am using synthetic division:
2x + 3 = 0 ⇒ x = [tex]-\frac{3}{2}[/tex]
[tex]-\frac{3}{2}[/tex] | 4 10 4 -6
| ↓ -6 -6 3
4 4 -2 -3 ← -3 is the remainder
↓ ↓ ↓
4x² +4x -2 ← factored polynomial
Which graph shows the solution set for 4x+3>-9
[tex]4x+3>-9\qquad\text{subtract 3 from both sides}\\\\4x>-12\qquad\text{divide both sides by 4}\\\\\boxed{x>-3}[/tex]
Year 1 number sold 725
Year 2 number sold 579
Year 3 number sold in year 4 the store sold 112% of the total number of scooters sold during the previous three years combined determine the number of scooter sold in year 4
Answer:
2, 240
Step-by-step explanation:
In the table, the values should be
Year 1 725
Year 2 579
Year 3 696
Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.
[tex]\frac{112}{100} =\frac{x}{2000}[/tex]
We solve through cross multiplication of numerator and denominator of the opposite fraction.
[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]
Lucy made a pumpkin pie to sell at a bake sale. She cut it into 6 slices and sold each slice for $1.25. How much money will she make if she sells the entire pie
Answer: $7.50
Step-by-step explanation: 1.25(6)
Suppose that y varies directly with x, and y = 10 when x = 5. What direct variation equation relates x and y? What is the value of y when x = 2?
The constant of variation is usually given using the letter k.
To find K you would divide Y by x, so the equation becomes k = Y/x.
First find k using the first y and x values provided:
k = 10/5 = 2
Now you know k, you can solve for y when x = 2:
using the equation k =y/x, replace k and x with the known values and solve for y:
2 = y/2
y = 2*2
y = 4
Answer: Linear equation y=2x
Step-by-step explanation:
If x=2
Then y=2(2)
y=4
What is the solution of 14=y-10
Answer:
24
Step-by-step explanation:
Just Add 10 to both sides (The rule is that in equations, what you do to one side, must be done to the other
[tex]14=y-10\\14+10=y-10+10\\24=y[/tex]
Answer:
24
Step-by-step explanation:
14 = y - 10
Addition property of equality: You can add the same value to both sides.
14 + 10 = y - 10 + 10
Add: 24 = y
y = 24
Solution means the value of the variable.
Tom, Sally, Bob, and Jill ran a race. Toms time was 12.03 seconds, Sally's was 12.284 seconds, Bobs was 12.62 seconds, and Jills was 12.9 seconds. In what order did they finish? who won?
Answer:
1.Tom
2.Sally
3.Bob
4.Jills
The U.S. produces about 5.5 million tons of apples each year. Of the total, $20\%$ is mixed with other products, with $50\%$ of the remainder used for apple juice and the other $50\%$ sold fresh. How many million tons of apples are used for apple juice? Express your answer as a decimal to the nearest tenth.
Answer:
2.2 million tons
Step-by-step explanation:
20% of 5.5 million tons is 1.1 million tons. That is how many are mixed with other products. So that would leave you 4.4 million tons of apples.
50% of 4.4 is 2.2 so 2.2 million tons are used for apple juice.
Answer:
2.2 Million
Step-by-step explanation:
First, we wish to determine what percentage of the tons of apples are used for apple juice. After 20% is mixed with other products, 80% remains. Half of this is used for apple juice; therefore, 40% of the tons of apples is used for apple juice. To calculate 40% of 5.5 million tons, we find 10% and then multiply by four. 10% = 0.55, and 0.55* 4 = 2.2. Thus, 2.2 million tons are used for apple juice.
Addison plays 1/2 of a song in 1/4 of a minute. How minutes will she need to play a full song?
Answer:
30 minutes
Step-by-step explanation:
She plays 1/2 of a song in 1/4 of a minute so that would be 15 minutes because if you divide 60 by 4 you would get 15. You would multiply 15 by 2 because if she plays a full song you multiply 1/2 by 2 to get a whole. So she will need 30 minutes to play a full song
Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?
graph of line going through 1, 2 and 3, 4
graph of line going through 1, 1 and 3, 3
graph of line going through 1, 4 and 3, 10
graph of line going through 1, 2 and 2, 5
The graph that represents Margo's coin collection is:
Graph of line going through (1, 4) and (3, 10).
Step-by-step explanation:It is given that:
She was given 1 coin as a gift, and she adds 3 coins per year.
Let a_n denote the amount of Money Margo had in the end of the "nth" year.
According to the given information we have:
[tex]a_1=1+3=4[/tex]
[tex]a_2=4+3=7\\\\a_2=a_1+3[/tex]
[tex]a_3=10\\\\a_3=a_2+3\\\\\\a_3=a_1+3\times 2[/tex]
and so on.
Hence, we get:
[tex]a_n=a_1+3(n-1)[/tex]
Hence, we get a Arithmetic progression.
with first term as 4 and common difference as 3.
Hence, the graph is:
Graph of line going through (1, 4) and (3, 10).
( Since at n=1 we have: [tex]a_n=4[/tex]
and at n=3 we have: [tex]a_3=10[/tex] )
select the angle that correctly completes the law of cosines for this triangle 24^2+25^2-2(24)(25)cos ____=7^2
a) 180 degrees
b) 90 degrees
c) 74 degrees
d) 16 degrees
The value of angle θ will be 16 degrees. Then the correct option is D.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
24² + 25² – 2(24)(25) cos θ = 7²
Then the value of angle θ will be
24² + 25² – 2(24)(25) cos θ = 7²
576 + 625 – 1200 cos θ = 49
1200 cos θ = 1152
cos θ = 1152 / 1200
θ = cos⁻¹ (1152 / 1200)
θ = 16°
Then the correct option is D.
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in my house, the ratio of dogs to fish is 1:10. the ratio of fish to cats is 6:1. What is the ratio of dogs to cats?
Answer:
The ratio of dogs to cats is 3 dogs to 5 cats
Step-by-step explanation:
dogs to fish: 1:10
fish to cats : 6:1
dogs to cats: 3:5
FISH:
llllllllll (10) llllllllll (10) llllllllll(10) (30 fish)
DOGS: 1 dog per 10 fish
D D D 3 dogs
CATS: 1 cat per 6 fish
C C C C C
Ratio represents partial data as some multiplies from numerator and denominator are lost due to simplification. You can assume them to be variables.
The ratio of dogs to cats is 3:5
How to get real quantity of ratio of first quantity to second quantity = a:b?We actually cannot get real quantities but we can use variables to partially get the information of how much their quantities were.
I said 'partially' since we don't get real values but with variables only.
Since the ratio is a:b, thus let the cancelled multiple during simplification was x.
Then we have:
First quantity = ax
Second quantity = bx
How to calculate the ratio of dogs to cats?It is given that:
Ratio of dogs to fish = 1:10
Then let number of dogs = 1x = x and number of fishes = 10x
Similarly,
Ratio of fish to cats = 6:1
Then let the multiple was y, then
Number of fishes = 6y,
Number of cats = 1y = y
But we have number of fishes = 10x and 6y both
Since number of fishes is constant, thus, they are equal. Or
[tex]10x = 6y\\\dfrac{x}{y} = \dfrac{6}{10} = \dfrac{3}{5}\\[/tex]
The ratio of dogs to cats = [tex]\dfrac{\text{Numbers of dogs}}{\text{Number of cats}} = \dfrac{x}{y} = \dfrac{3}{5}[/tex]
Thus, the ratio of dogs to cats is 3:5
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