Hello!
Using Hooke's law, F spring=k delta x, find the distance a spring with an elastic constant of 4 N/cm will stretch if a 2 newton force is applied to it.
Data:
Hooke represented mathematically his theory with the equation:
F = K * Δx
On what:
F (elastic force) = 2 N
K (elastic constant) = 4 N/cm
Δx (deformation or elongation of the elastic medium or distance from a spring) = ?
Solving:
[tex]F = K * \Delta{x}[/tex]
[tex]2\:N = 4\:N/cm*\Delta{x}[/tex]
[tex]4\:N/cm*\Delta{x} = 2\:N[/tex]
[tex]\Delta{x} = \dfrac{2\:\diagup\!\!\!\!\!N}{4\:\diagup\!\!\!\!\!N/cm}[/tex]
simplify by 2
[tex]\Delta{x} = \dfrac{2}{4}\frac{\div2}{\div2}[/tex]
[tex]\boxed{\boxed{\Delta{x} = \dfrac{1}{2}\:cm}}\Longleftarrow(distance)\end{array}}\qquad\checkmark[/tex]
Answer:
B.) 1/2 cm
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A pair of in-line skates is on sale for $90 iF this price represents 9% discount form the original price,what is the original price to the nearest cent
The required original cost of the in-line skates is given as $100.00.
Given that,
A pair of in-line skates are on sale for $90, this price represents a 9% discount from the original price, and the original price to the nearest cent is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Let the original price of the in-line skates be x,
according to the question,
0.9 [x] = 90
x = 90 / 0.9
x = $100
Thus, The required original cost of the in-line skates is given as $100.00.
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Solve for M
6M=2
Simplify your answer as much as possible. 20 Points
Mary can paint a house 12 hours. if Nancy helps, it takes them 2 hours. without help, how long would it take Nancy to complete the same job?
Final answer:
To find out how long it will take Nancy to paint the house alone, we calculate her work rate by subtracting Mary's rate from their combined rate. This gives us Nancy's work rate as 5/12 of a house per hour, which means Nancy would take 2.4 hours to paint the house by herself.
Explanation:
To determine how long it would take Nancy to paint the house by herself, we can set up an equation based on the rates of work done by Mary and Nancy together, and by Mary alone. We know that Mary can paint a house in 12 hours, so her work rate is 1/12 of a house per hour. When Nancy helps, together they can paint the house in 2 hours, so their combined work rate is 1/2 of a house per hour.
To find Nancy's work rate, we set up the equation:
1/12 + 1/N = 1/2
Now, we solve for N (Nancy's time to paint the house alone):
1/N = 1/2 - 1/12
1/N = 6/12 - 1/12
1/N = 5/12
N = 12/5
N = 2.4 hours
Therefore, it would take Nancy 2.4 hours to complete the same job by herself.
A chef had to fill up 4/5 of a container with mash potatoes. He ended up using 2 4/6 pounds of mashed potatoes. How many pounds would he need to fill the container all the way
Answer: He would need [tex]3\dfrac{1}{3}[/tex] pounds to fill the container all the way.
Step-by-step explanation:
Since we have given that
Fraction of mashed potatoes he had to fill up a container = [tex]\dfrac{4}{5}[/tex]
Fraction of mashed potatoes he ended up using = [tex]2\dfrac{4}{6}=2\dfrac{2}{3}=\dfrac{8}{3}[/tex]
So, we need to find the number of pounds that he would need to fill the container all the way.
So, number of pounds would be
[tex]\dfrac{8}{3}\div \dfrac{4}{5}\\\\=\dfrac{8}{3}\times \dfrac{5}{4}\\\\=\dfrac{10}{3}\\\\=3\dfrac{1}{3}[/tex]
Hence, he would need [tex]3\dfrac{1}{3}[/tex] pounds to fill the container all the way.
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The table below shows some properties of regular polygons.
When compared with the independent variable, how many of the remaining three columns represent a linear relationship?
A. 0
B. 1
C. 2
D. 3
Answer: C.2
Step-by-step explanation:
Given: Independent variable= Number of sides
To check how many of the remaining three columns represent a linear relationship, we need to check the rate of change of the three columns with respect to dependent variable.
For number of diagonals
The rate of change of diagonals w.r.t number of sides is constant and that is 1.
For Sum of all interior angles (degrees)
The rate of change of Sum of all interior angles w.r.t number of sides is constant and that is 180°.
For measure of each angle (degrees)
The rate of change of measure of each angle w.r.t number of sides is not constant and that is 180°.
Since for vertices 3 , measure of angle=60
vertices 4 , measure of angle=90
From vertices 3 to 4 change in measure of angle is 30
vertices 5 , measure of angle=108
From vertices 4 to 5 change in measure of angle is 18
Thus number of diagonals and Sum of all interior angles are the columns represent a linear relationship when compared with the independent variable.
Therefore there are 2 columns represent a linear relationship when compared with the independent variable.
Solution:
The equation of linear relationship is , y= k x
That is, [tex]\frac{y-value}{x-value}=k({\text{a constant})[/tex]
As, you can see that , ratio of
1.
[tex]\frac{\text{Sum of interior angles of a regular polygon}}{\text{number of sides of that polygon}}={\text{Measure of each interior angle of regular polygon}}[/tex]
2. Also, as number of sides increases, the smallest regular polygon is equilateral triangle(3 sides) , having 0, diagonal, the number of diagonal increases by 1.
→→Regular polygon having sides , n≥3=k, where k is number of diagonals=0,1,2,3,4,[ For example, for, n=3,k=1,n=4, k=2,...]
Column (2)
[tex]C_{4}-C_{3}=C_{3}-C_{2}=C_{2}-C_{1}=1[/tex]
Column (4)
[tex]C_{2}-C_{1}=90-60=30\\\\ C_{3}-C_{2}=108-90=18\\\\ C_{4}-C_{3}=120-108=12[/tex]
Column (3)
[tex]C_{4}-C_{3}=720-540=180\\\\ C_{3}-C_{2}=540-360=180\\\\ C_{2}-C_{1}=360-180=180[/tex]
In, Column (2) and Column(3) the difference between two consecutive values is same, while in column (4) difference between two consecutive values is not same.So, C(2) and C(3) shows linear relationship, column (4) do not.
Option (C) 2 is Right choice.
PLEASE HELP
1.A store increases the price of a sweater from $20 to $22.
What is the percent of increase?
2.Kevin buys 4 folding chairs. Each chair costs $13.50. The sales tax is 6.5%.
What is the amount of sales tax for Kevin's purchases?
3.Harriet's haircut costs $36.
As a tip, she gives the hairdresser 15% of this amount.
What is the total amount Harriet pays for her haircut, including tip?
4.At an appliance store, the price of a refrigerator is marked up 25% to $406.25.
What was the price of the refrigerator before the markup?
5.Clea estimates that a glass contains 250 mL of water. The actual amount of water in the glass is 279 mL.
To the nearest tenth of a percent, what is the percent error in Clea's estimate?
6.The price of a wallet is $32.95 and the sales tax is 7.5%.
What is the total cost of the wallet?
7.A car salesman had $65,100 in total monthly sales last month. He made $1,953 in commission from those sales.
What is the salesman's commission as a percent of his total monthly sales?
Convert 125 yards into inches ?
URGENT!
How do I work out the gradient of lines on a graph in the simplest way possible? BBC Bitesize just confused me even more XD
Samantha and her friends are going on a trip that is 254 7/50 miles long they already went 128 53/100 how much farther DO they need to drove
Bradley’s T.V. screen is 15 feet by 20 feet. He wants to put new cover on the T.V. screen that costs $25 per square foot. How much will it cost Bradley to cover his T.V. screen?
Answer:
$7500
Step-by-step explanation:
What is the slope of the line?
27y = 3x - 54
round 1050 to one hundred
What is the equation in point slope form of a line that passes through the points (5,-3)
Write an algebraic expression with the variable x that has a value of 3 when evaluated
The required expression is x + 2y = 2 (3/2 + y) that gives the value 3.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
To write the algebraic expression with variable x that has a value of 3.
Let x is a variable and y is another variable,
The expression for the x equal to 3 can be written as,
x + 2y = 2 (3/2 + y)
The expression x + 2y = 2 (3/2 + y) gives the value 3.
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Which rational numbers is not equivalent to the others. 75%,3/4,0.75,7/50
The rational number 7/50 is not equivalent to the other numbers listed (75%, 3/4, 0.75) as it converts to a decimal value of 0.14, which is distinct from 0.75.
Explanation:The question asks which rational number is not equivalent to the others: 75%, 3/4, 0.75, or 7/50. To determine this, we can convert all the numbers to a common format, such as decimals or fractions, and compare their values.
First, 75% is equivalent to 0.75, as percent means "per hundred," so 75% is 75 per 100, which can be written as 75/100 and simplified to 3/4 or 0.75. Next, 3/4 is exactly 0.75 when converted to a decimal. This means that these three are equivalent to each other.
However, 7/50 is a different case. When we convert 7/50 to a decimal, we get 0.14, which is evidently different from 0.75. Therefore, 7/50 is not equivalent to the other rational numbers listed.
what is 3r+n^(2)-r+5-2n+2 simplified
A function is represented by the values in the table.
x y
2 4
4 8
5 10
7 14
8 16
Choose from the drop-down menu to complete the statement.
The function represented in the table ? linear
A) Is
B) Is not
For the question mark at last sentence replace it with A or B
The function represented in the table is linear, so option A is correct.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given :
For x = 2, y = 4,
x = 4, y = 8...
As you can that the y is double of x,
So the equation of this condition is,
y = 2x
Hence, the function is dependent on x, and it is linearly dependent.
Therefore, The function represented in the table is linear.
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The table represents a function.
x y
0 6
2 8
4 10
6 12
Complete the statement by selecting from the drop-down menu. greater or less than
The rate of change in the function y=x+4 is____ the rate of change of the function represented in the table.
Answer:
The rate of change in the function y=x+4 is _Equal_ the rate of change of the function represented in the table.
How to solve 37=-3+5(x+6)
what is half of 2.9 leave at least some evidence
Identify the linear function graph.
A)
B)
C)
D)
A student earns a 98 on a test for answering one question incorrectly and earns a 90 for answering five questions incorrectly. Is the slope of the line that models the linear relationship a positive negative zero or undefined slope?
Answer:
Negative Slope
Step-by-step explanation:
The slope is the ratio of Change in height to the change in horizontal distance. It can also be define as tangent of angle made by that line and it is find by formula, [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
The slope is said to be a positive slope when a line is moving from left to right, the line rises.
The slope is said to be a negative slope when a line is moving from left to right, the line falls.
Here, Let the student earns be y marks in test
and let incorrect question be x
then y₁ = 98 , y₂ = 90 and x₁ = 1 , x₂ = 5
then [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
[tex]slope (m)= \frac{90 - 98}{5 - 1} [/tex]
⇒ m = -2
Hence, it has negative slope.
58% of what number is 29
Answer:
50
Step-by-step explanation:
Jack has 4/8 of a pizza left from a party. If he eats another 1/8, how much is left?
A) 3/8
B) 2/3
C) 5/8
D)1/2
Lars bought 3 jars of marbles. Each jar has 42 marbles, of which 13 are red. Lars can use the calculation below to find the total number of red marbles. 3×(13×42)
Answer: (3x1/3) x 42
Step-by-step explanation: trust me I took the test.
There are total 1638 marbles.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Number of jars = 3
Each bar contain = 42 marbles
Red marbles = 13
So, total number of marbles
= 3 x 13 x 42
= 1638.
Hence, there are total 1638 marbles.
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Expand and simplify (x-6)(x+2)
combine like terms to simplify the expression 2/5k-3/5k+1/10k
Answer:
k/2 − 3/5
Step-by-step explanation:
To simplify the expression 2/5k - 3/5k + 1/10k, we combine the like terms and simplify the fractions. The simplified expression is -1/10k.
Explanation:To simplify the expression 2/5k - 3/5k + 1/10k, we can combine like terms. Like terms have the same variable raised to the same power. In this case, the variable is 'k'. So, combining the fractions, we get:
(2/5 - 3/5 + 1/10)k
Now, let's simplify the fractions:
Therefore, the simplified expression is -1/10k.
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Expand and simplify (x+2)(x+1)
A bank charges you $3 each time you use an out of network Atm. At the beginning of the month you have $1500 in your bank account. You withdraw $60 from your bank account each time you use an out of network ATM. Write and graph a linear equation that represents the balance in your account after you use an out of network Atm x times.
a student received a coupon for 17% off the total purchase price at a clothing store. let b be the original price of the purchase. use the expression b - 0.17b for the new price of the purchase. write an equivalent expression by combining like terms.
An equivalent expression for the given expression by combining like terms is 0.83b.
Given that, a student received a coupon for 17% off the total purchase price at a clothing store.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let b be the original price of the purchase.
So, new price =original price-17% of original price
⇒ new price =b - 17% of b
⇒ new price =b - 0.17b
= 0.83b
Therefore, an equivalent expression for the given expression by combining like terms is 0.83b.
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