In this fulcrum, the weights are perfectly balanced. How far must the fulcrum be located from the 60 pound weight if the bar is 24 feet long?
A) 9
B) 15
C) 12
Answer:
15 feet
Step-by-step explanation:
Given : In this fulcrum, the weights are perfectly balanced.
To Find: How far must the fulcrum be located from the 60 pound weight if the bar is 24 feet long?
Solution:
To make the weights perfectly balanced torque must be equal
[tex]Torque = Force \times d[/tex]
Where [tex]Force = Mass \times Acceleration[/tex]
Let a be the acceleration
d= Distance between the pivot and the acting point.
Let x be the distance from 60 pound weight where fulcrum is located
Since we are given that Length of bar = 24 feet.
So,Distance of fulcrum from 100 pound weight = 24-x
Now torque for 60 pound weight :
[tex]Torque = 60a \times x[/tex]
Now torque for 100 pound weight.
[tex]Torque =100a \times (24-x)[/tex]
Now to maintain the equilibrium i.e. To make the weights perfectly balanced
[tex]60a \times x =100a \times (24-x)[/tex]
[tex]60x = 2400-100x[/tex]
[tex]160x = 2400[/tex]
[tex]x = \frac{2400}{160}[/tex]
[tex]x = 15[/tex]
Hence The fulcrum must be located 15 feet from the 60 pound weight if the bar is 24 feet long.
Answer:
15
Step-by-step explanation:
Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
these equations must be for pre-algerbra
Answer:
One step equations
3 + x = 5 ___x = 2
Y + 14 = 20____x = 6
Equations with Fractions
4/5q = 32___q = 40
3/4x = 6___x = 8
Equation with decimals
3.2x – 2.7 = 1.2x___x = 1.35
Equation with distributive Property
7x + 3 (x + 1) = 10x + 3
Infinitely Many solutions
Real World Problem
Monica knows that she should spend no more than 1/3 of her income on her rent. She really wants to move into a cool condo downtown and has found a great place where the rent is $2,300 per month. Based on that, how much should Monica earn each month to afford the rent on her cool new place?
Hope This Helps!
Given the equation 2(3x − 4) = 5x + 6, solve for the variable. Explain each step and justify your process. Charlie solved a similar equation below. Is Charlie's solution correct? Explain why or why not.
Multiple Choice
For questions 1–7, choose the word or phrase that best defines the italicized word.
1. "Only reapers reaping early/In among the bearded barley…" (1 point)
people who toil
people who obey
people who
Answer:
people who toil
Step-by-step explanation:
The above lines have been taken from the poem "The Lady of Shalott" written by Alfred, Lord Tennyson. The poem is about the mysterious Lady of Shalott who lives on the Island of Shalott. People who wanted to see her have never got the opportunity to see her. On the other hand, the people who work in the fields have listened to her singing an eerie song. The song which the lady sings echoes all over the river Camelot.
PLEASE HELP !!! 15 POINTS !! PLUS BRAINLIEST !!
The graph shows the shape of an arched bridge cable. What does the y-intercept represent?
The total length of the cable is 15 m.
The left end of the cable is 15 m above the roadway.
The minimum distance between the cable and roadway is 15 m.
The total length of the road is 15 m.
Answer:
The left end of the cable is 15 m above the roadway
Step-by-step explanation:
Let
x----> the horizontal distance from left end of cable (m)
y----> the height above roadway (m)
we know that
The y-intercept is the value of y when the value of x is equal to zero
In this problem
The y-intercept is the height above roadway (m) when the distance from end of cable is equal to zero
so
The y-intercept is the point (0,15)
so
The left end of the cable is 15 m above the roadway
The left end of the cable is 15 m above the roadway]
Step-by-step explanation:
A small company has 20,000 shares. Anastasia owns 400 of these shares. The company decides to split its shares. What is Anastasia's ownership percentage after the split?
Answer:
2%
Step-by-step explanation:
A P E X
At the Roadside Restaurant, each milkshake comes with 2 straws.
Which equation shows the number of straws the restaurant will use if they serve m milkshakes?
Use t to represent the total number of straws used and m to represent the number of milkshakes served.
A.
t = 2m
B.
t = 2 + m
C.
t = 2 – m
D.
t =
A city was founded at the beginning of 1990 with a population of 55,000, and since then, the growth in its population has been exponential, increasing at x percent per year. If the city's population at the beginning of 2000 was 108,193, at what percent per year to the nearest percent is the city's population increasing?
What's the recursive formula?? help!
Solve for x 16 = -2 -1
Factor completely 3x(x + 2) + 4(x + 2). (1 point)
(x + 2)(7x)ANSWER
[tex](x + 2)(3x + 4)[/tex]
EXPLANATION
The given expression is
[tex]3x(x + 2) + 4(x + 2)[/tex]
We can see that (x+2) is the greatest common factor.
We factor to obtain;
[tex](x + 2)( 3x + 4)[/tex]
The correct choice is C.
Answer:
(x + 2) (3x + 4)
Step-by-step explanation:
I got it correct on my test
Which transformations are rotations?
Choose all answers that are correct.
^ please help me____________
what does a^2+b^2=C^2 mean
The equation a² + b² = c² represents the Pythagorean theorem, which describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. For example, in a triangle with legs of 3 and 4 units, the hypotenuse would be 5 units.
The equation a² + b² = c² represents the Pythagorean theorem in mathematics. This theorem is used to describe the relationship between the lengths of the sides of a right triangle.
Pythagorean Theorem
In a right triangle:
a and b are the lengths of the legs (the two sides that form the right angle).
c is the length of the hypotenuse (the side opposite the right angle).
The theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides:
a² + b² = c²
This can also be expressed as c = √(a² + b²).
For example, if one leg of the triangle is 3 units and the other leg is 4 units, you can find the hypotenuse as follows:
3² + 4² = c²9 + 16 = 25c = √25 = 5Question:
what does a^2+b^2=C^2 formula mean ?
How do I find x in this triangle?
What is the value of n?
Enter your answer in the box.
n =
Answer:
The value of n is 4.
Step-by-step explanation:
Theorem of intersection of two cords : If two cords AB and CD intersecting at point P, then
[tex]|AP|\times |PB|=|CP|\times |PD|[/tex]
Using the theorem of intersection of two cords, we get
[tex](n-2)\times 16=8\times (n+8)[/tex]
Use distribution property,
[tex]16n+32=8n+64[/tex]
[tex]16n-8n=64-32[/tex]
[tex]8n=32[/tex]
Divide both sides by 8.
[tex]n=\frac{32}{8}[/tex]
[tex]n=4[/tex]
Therefore the value of n is 4.
You are an accountant doing an audit for a law firm. A paralegal worked for a client for 5 hours per day for 3 days. The client was billed $50 per hour, and the paralegal was paid $30 per hour. After the paralegal’s wages were paid, what was the amount made by the law firm?
Carl borroowed $2,500 for six months at an annual interest rate
of 11%. How much must he repay at the end of six months?
a. $275
b. $2,637.50
c. $87.50
d. $2,762.50
Please help! Picture included!!!
In the figure below, triangle ABC is similar to triangle PQR.
What is the length of PQ?
A)18
B)4
C)32
D)6
Sean Wrona is the fastest typist in the world and can type an average of about 500 words in three minutes. What is Sean’s average typing speed in words per minute, WPM, to the nearest whole number? *** Answer with number only***'
Logan can paint a room in 12 hours. Marcus can paint the same room in 16 hours. How long does it take for both Logan and Marcus to paint the room if they are working together?
The graph of a linear function has a slope of 5, and it passes through the point (–7, 5). What is the value of the dependent variable when the independent variable is equal to 2?
Final answer:
To find the value of the dependent variable, we use the point-slope form of the linear equation. Using the given slope of 5 and point (-7, 5), we first find the y-intercept to be 40. We then calculate the dependent variable's value to be 50 when the independent variable is 2.
Explanation:
The student has asked about the value of the dependent variable when the independent variable is 2 for a given linear function that has a slope of 5, and passes through the point (–7, 5). To find this value, one should use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, using the given point (–7, 5), we can find the y-intercept by substituting the slope and point into the equation:
y = 5x + b
5 = 5(-7) + b
b = 5 + 35
b = 40
So the equation of the line is y = 5x + 40. Now, to find the value of y when x is 2:
y = 5(2) + 40
y = 10 + 40
y = 50
Therefore, the value of the dependent variable when the independent variable is 2 is 50.
solve - 2 x 3 + 22 - 8 - 2 =
in a exponent 3 + 3 + 3 + 3 + 3
Select the scenarios that correctly represent the given graph.
Answer:
The correct options are 1 and 2.
Step-by-step explanation:
From the given graph it is clear that it is a graph of an exponential function and the graph passes through the points (0,100) and (1,150).
The general form of an exponential function is
[tex]y=ab^x[/tex] .... (1)
Where, a is the initial value and b is growth rate.
The initial value is 100 because the y-intercept of the graph is 100.
The graph passes through (1,150). Put y=150, a=100 and x=1 in the above formula to find the value of b.
[tex]150=100b^1[/tex]
Divide both the sides by 100.
[tex]1.5=b[/tex]
The value of b is 1.5.
Substitute a=100 and b=1.5 in equation (1).
[tex]y=100(1.5)^x[/tex]
It means the value is 1.5 times larger in every unit of time.
It can be written as
[tex]y=100(1+0.5)^x[/tex]
It means the initial value increased by 50% per unit of time.
So, the required scenarios are
1. The amount of money in a bank account increased by 505 per year.
2. The amount of a substance is one and a half times larger after every minute.
Therefore the correct options are 1 and 2.
Mrs. Cho has 24 students in her class. Some of her students are also in the play. Explain why it is not possible for exactly 24% of the students in Mrs. Cho’s class to be in the play.
A ladder reaches a window 20 feet above the ground. The foot of the ladder is 4 feet from the wall. Which of the following measures correspond to the length to the laddder? Round to the nearest hundredth
Answer:
20.40
Step-by-step explanation:
Test Yourself
[tex]y = - x + 10 \\ y = x + 2[/tex]
Calculate the averages for each category for the three-month period. category jan. feb. mar. average wages $2,100.00 $2,300.00 $2,000.00 $ donations $210.00 $230.00 $200.00 $ mortgage $590.50 $590.50 $590.50 $ electricity $101.25 $89.75 $80.00 $ water $20.10 $22.30 $24.55 $ car loan $172.54 $172.54 $172.54 $ food $200.25 $220.70 $205.50 $ insurance $310.50 $0.00 $0.00 $ clothes $0.00 $0.00 $75.00 $ car license fee $0.00 $120.90 $0.00 $ newspaper $0.00 $0.00 $45.00 $ movies $18.00 $0.00 $36.00 $ new car $100.00 $100.00 $100.00 $ gasoline $80.00 $70.00 $75.00 $ car repairs $0.00 $119.00 $0.00 $ miscellaneous $64.50 $59.25 $72.50 $ savings $140.00 $140.00 $140.00 $
what is x in the equation
4(x+6)= 5(x+9)+4x?
The temperature of a cup of coffee t minutes after it has been poured is described by the function
C(t) = 20 + 60(0.95)^t .
a. How many minutes does it take for the coffee to cool to a temperature of d degrees?
b. About how fast is the temperature dropping when t = 1?