When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.
In simpler terms, that means if A is always twice as much as B, then they directly vary. If a gallon of milk costs $3, and I buy 1 gallon, the total cost is $3. If I buy 10 gallons, the price is $30. In this example the total cost of milk and the number of gallons purchased are subject to direct variation -- the ratio of the cost to the number of gallons is always 3.
To be more "geometrical" about it, if y varies directly as x, then the graph of all points that describe this relationship is a line going through the origin (0, 0) whose slope is called the constant of variation. That's because each of the variables is a constant multiple of the other.Hope I helped
An equation in the slope-intercept form represents a direct variation only when the y-intercept is zero. For instance, y=3x is a direct variation while y=3x+9 isn't due to having y-intercept 9. The differentiation between a direct variation and a simple linear equation helps understand the relationship in algebra.
Explanation:In mathematics, the slope-intercept form of an equation can represent a direct variation, but it's only sometimes true. An equation in the slope-intercept form represents a direct variation only when the y-intercept (the 'b' in the equation y=mx+b) is zero.
For example, the equation y = 3x represents a direct variation because the y-intercept is 0. Here, the value of y changes proportionately with x, which denotes a direct variation. However, in the equation y=3x+9 (represented in Figure A1), it does not represent a direct variation since the y-intercept is 9 (b ≠0).
Therefore, the direct variation depends on whether the y-intercept is zero or not in a slope-intercept equation. This relationship between the x and y variables in algebra helps scholars understand the difference between a direct variation and a simple linear equation.
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a certain truck carry 3450 pounds each bible weighs 3 fourths how many bibles can be carried
Use doubles minus one to solve 8 + 7
I have 4 times as many hats as my brother. Together we have 50 hats. How many hats do we each have?
4p+8=12p-16????????????
is y=2x+5 a propotional relationship? explain your answer
Answer: YES
Step-by-step explanation: yes it is proportional because ut is a linear equation and you know where to set the y and the x
Divide decimals 1.52 / 1.9
a sum of money is divided in the ratio 4:3 if the smaller share is ,€45 what is the sum of money
50-10x=20 what is the value of x in this problem
To find the value of x in the equation 50 - 10x = 20, we subtract 50 from both sides and then divide by -10, leading to x = 3.
To solve the equation 50 - 10x = 20 for the value of x, we need to isolate x on one side of the equation. First, we subtract 50 from both sides, which gives us -10x = -30. Next, we divide both sides by -10 to solve for x, resulting in x = 3. This process demonstrates the systematic approach to solving linear equations, ensuring accurate determination of unknown variables and facilitating problem-solving in various mathematical contexts. Once simplified, the equation x=3 represents the solution where the given expression is true, providing clarity on the value of x that satisfies the equation.
Multiplying a number by 4/5 then dividing by 2/5 is the same as multiplying by what number?
Use properties of addition to find 37 + 58 mentally.
if the body makes 100 billion new blood cells each day,approximately how many blood cells can it make each hour
Jade used Fraction 3 over 4 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 4 over 5 yards of fabric, and why?
A. No, because the quotient of Fraction 3 over 4division signFraction 1 and 4 over 5 is 1 and 7 over 20
B.No, because the quotient of Fraction 1 and 4 over 5Division signFraction 3 over 4 is 1 and 7 over 20
C.Yes, because the quotient of Fraction 3 over 4division signFraction 1 and 4 over 5 is 2 and 2 over 5
D.Yes, because the quotient of Fraction 1 and 4 over 5Division signFraction 3 over 4 is 2 and 2 over 5
Answer:
The answer is D:)
Step-by-step explanation:
a triangle has base 7m and area 17.5 m^2 . what is the height?
A box of cereal advertised that the new box contained 30% more cereal than the previous box. If the new box contains 26 ounces of cereal, how many ounces of cereal were in the previous box?
a skateboard has probability of a 0.015 defective wheel. what is the probability of it not having a defective wheel
Jonah and his friends go apple picking.Jonah fill 5 baskets. Each basket holds 15 apples. If 4 of Jonah's friends pick the same amount as Jonah, how many apples do Jonah and his friends pick in all? Draw a diagram to solve the problem.
1) make a trail mix with 5 ingredients. they should make exactly 10 cups but the
ALL THE INGREDIENTS SHOULD BE DIFFERENT MIXED NUMBERS
Given ΔRST : ΔLMN, which of the following is true
1.
The answerto you question is the third one
Rachel finished 3/4 of the race in 6 hours. How long was the entire race?
Bill and,Alyssa helped pack books to donate to a charity. Bill packed 28 boxes with 30 books in each box. Alyssa packed 31 boxes with 25 books in each box. How many more books did Bill pack? show your work.
16x+5=-11 what is the solution?
Find the sum of 136 + 212. Explain why you did or did not regroup.
Find 3 multiple 1,789 how is multiplying a 3 digit number like multiplying a 4 digit number
Multiplication is a method of finding the product of two or more numbers5367 is the 3 multiple 1,789
What is Multiplication?
Multiplication is a method of finding the product of two or more numbers
We need to find 3 multiple 1,789
Three times of one thousand seven hundred eighty nine.
1789 has four digits and 3 has only one digit.
We have to multiply one digit number with all the four digits
1789
× 3
_________
5367
Hence 5367 is the 3 multiple 1,789.
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At your construction job, you're standing on a ladder at ground level. First, you climb down 7 feet to see the basement. Then you climb up 22 feet to see the second floor. Later, you climb down 9 feet. How high above or below the ground are you?
if there are 1200 calories in 8 ounces of hot fudge how many calories are in 3 ounces of hot fudge??
A pencil Company used 60 grams of rubber to make 10 pencils how many pencils can be made with 50 grams of rubber
with 50 grams of rubber, you can make approximately 8 pencils.
To solve this problem, we need to set up a proportion to find out how many pencils can be made with 50 grams of rubber.
Let's set up the proportion using the given information:
[tex]\[\frac{\text{Grams of rubber}}{\text{Number of pencils}} = \frac{60}{10} = \frac{50}{x}\][/tex]
Where:
- 60 grams of rubber is used to make 10 pencils.
- 50 grams of rubber is the amount we have.
- x is the number of pencils we want to find.
Now, let's solve for x:
[tex]\[\frac{60}{10} = \frac{50}{x}\][/tex]
Cross multiplying:
60x = 500
Dividing both sides by 60:
[tex]\[ x = \frac{500}{60} \][/tex]
x = 8.333
Since you can't make a fraction of a pencil, we need to round down to the nearest whole number because you can't make a fraction of a pencil. Therefore, with 50 grams of rubber, you can make approximately 8 pencils.
The probable question maybe:
A pencil Company used 60 grams of rubber to make 10 pencils how many pencils can be made with 50 grams of rubber?
A football team receives the ball on their own 10 yard line. They make a gain of 15 yards in the first play. What yard line is the ball on?
Final answer:
The football team starts at their own 10 yard line, and after a gain of 15 yards, the ball is on the 25 yard line.
Explanation:
The question is about calculating the new position of a football on the field after a team makes a gain. Initially, the football team starts with the ball on their own 10 yard line. After making a gain of 15 yards in the first play, we can determine the new yard line position by simply adding the gain to the starting position.
Step-by-Step Calculation:
Starting yard line: 10 yards.
Gain made: 15 yards.
Calculate the new yard line position: Starting yard line + Gain made = 10 yards + 15 yards = 25 yards.
Therefore, after the gain, the ball is on the 25-yard line.
Sandy works at a clothing store. She makes $7 per hour plus earns 15% commission on her sales. She worked 74 hours over the last two weeks and had a total of $1,678 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
Sandy's total earnings before taxes for the two weeks will be $769.70, which includes $518 from her hourly wages and $251.70 from her sales commission.
To solve how much Sandy will earn in hourly wages and commission over two weeks of work at a clothing store, where she makes $7 per hour and earns a 15% commission on her sales of $1,678, we first calculate her hourly wages: Sandy worked 74 hours, and at $7 per hour, her earnings from hours worked are 74 hours x $7/hour = $518.
Next, we calculate her commission earnings: 15% of $1,678 in sales is 0.15 x $1,678 = $251.70.
Adding both earnings gives us Sandy's total earnings before taxes, which is $518 + $251.70 = $769.70.
What is the pattern for this numbers 1/1000, 1/100, 1/10
The previous number is multiplied by 10 to get the next number.
We have numbers [tex]\frac{1}{1000} ,\frac{1}{100},\frac{1}{10}[/tex]
Here first number is [tex]\frac{1}{1000}[/tex]
Second number is [tex]\frac{1}{100}[/tex]
Third number is [tex]\frac{1}{10}[/tex]
So ratio is [tex]\frac{ \frac{1}{100}}{ \frac{1}{1000}}=10[/tex]
And [tex]\frac{ \frac{1}{10}}{ \frac{1}{100}}=10[/tex]
As the ratio between each number is 10.
Therefore the previous number is multiplied by 10 to get the next number.
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A school bought 32 new desks. Each desk cost $24. Estimate how much the school spent on the new desk?