Where must the fulcrum be located if a 300-pound weight and a 450-pound
weight balance when placed on each end of a 15-foot bar
Answers
Answer:
9 foot.
Step-by-step explanation:
From the question given, we were told that a 300-pound weight and a 450-pound weight are placed on each end of a 15-foot bar.
The diagram illustrating the question can be seen on the attached photo.
Weight 1 (W1) = 300 pound
Weight 2 (W2) = 450 pound.
Distance to which the fulcrum must be placed in order to balance (d1) = x
Distance from the other side of the bar (d2) = 15 – x
W1d1 = W2d2
300 × x = 450 (15 – x)
Clear bracket
300x = 6750 – 450x
Collect like terms
300x + 450x = 6750
750x = 6750
Divide both side by the coefficient of x i.e 750
x = 6750/750
x = 9 foot.
Therefore, the fulcrum must be placed at 9 foot in order to balance the bar.
Related Questions
How many different "words" can be made from the given word by re-arranging the letters in DIGIT
Answers
Answer:
I, It, Dig, Digit,
Id, Ti (the seventh note of a major scale), Git, Dit (another word for dot)
hope i got them all, and this is what you need.
Please help ASAP
These box plots show the number of electoral votes won by the democratic and republican candidates for the elections 1984 through 2012
Answers
Answer:
A.
Step-by-step explanation:
The interquartile range for republicans is 185.5. The interquartile range for democrats is 186.5.
367.5 - 181 = 186.5
356 - 170.5 = 185.5
Answer:
A
Step-by-step explanation:
a/-6 + 8 = 12. a =
Please help!!! Thanks so much!
~kweenie~
Answers
Answer:
a = -24
Step-by-step explanation:
-a/6 +8 = 12
Subtract 8 from each side
-a/6 +8-8 = 12 -8
-a/6 = 4
Multiply by -6 on each side
-a/6 * -6 = 4*-6
a = -24
What is the value of xx) = 9^x when x= -2?
A. 1/81
B. 81
C. 1/81
D. 18
Answers
Answer:
C. [tex]9^{-2} = \frac{1}{81}[/tex]
Step-by-step explanation:
Given
[tex]9^{x}[/tex]
Required
Find the expression where x - 2
[tex]9^{x}[/tex]
Substitute 2 for x
[tex]9^{-2}[/tex]
From law of indices which states
[tex]a^{-b} = \frac{1}{a^b}[/tex]
So, the expression becomes
[tex]9^{-2} = \frac{1}{9^2}[/tex]
Expand the denominator
[tex]9^{-2} = \frac{1}{9 * 9}[/tex]
[tex]9^{-2} = \frac{1}{81}[/tex]
Hence, [tex]9^{x}[/tex] is [tex]\frac{1}{81}[/tex] when x = 2
Whích quadratic inequality does the graph below represent?
у
5
4
3
2
1
→
wa-
5-32
12
3
5
2
Answers
Answer:
The third option
Step-by-step explanation:
first, you can eliminate the 2nd and the 4th option because the vertex of the graph is located at -3, and not 3. The reason it is not the 1st option is, because of the greater than or equal to sign, this inequality actually shows the white area.
Therefore, leaving the 3rd option. The y-intercept is correct, it is -3. The sign is also correct, because on the axis of the quadratic, -3 is the highest possible y-intercept. So y has to be less than or equal to -3.
Hope this helps! :D
what is the value of the expression 11 + 1/2 to the fourth * 48
Answers
Answer:
839523
Step-by-step explanation:
Use BPEMDAS
Step 1: Parenthesis
(11.5)^4(48)
Step 2: Exponents
(17490.1)(48)
Step 3: Multiply
839523
This set of 3 numbers are measurements of a right triangle. 10,8,6
True
False
Answers
Answer:
True
Step-by-step explanation:
**plug it in using the Pythagorean Theorem**
6^2+8^2= 10^2
36+64=100
100=100 (true)
Answer:
True
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We can prove that it is a right triangle by using the Pythagorean Theorem. We have the hypotenuse as 10 and our legs as 8 and 6:
8² + 6² = 10²
64 + 36 = 100
100 = 100
So, 6-8-10 is a Pythagorean Triple.
which phrase describes an unknown or changeable quantity?
Answers
Answer:2 o’clock in the afternoon
Step-by-step explanation:
The time is constantly changing where as 4 quarts will always be a gallon, 3 feet and 7 inches will always be the same length, and the height of that buildingx1/2 will come to the same number.
Answer: The height of the building times 1/2
Step-by-step explanation:
Just did this
how many tiles 4 inches on a side should be used to cover a portion of a wall 56 in Long by 32 in high
Answers
80g of a 35% salt solution
Answers
Answer:
The total weight is 80g, this is equal to the weight of the salt in the mixture plus the weight of the water in the mixture.
Ws = Weight of the salt
Ww = Weight of the water.
Then:
Ww + Ws = 80g
and the solution is 35% salt, so we have:
Ws/80g = 0.35
We must solve the system of equations, we can write the second equation as:
Ws = 80g*0.35 = 28g
Then we have 28 grams of salt, and the other 62g must be of water.
Step-by-step explanation:
Let x represent the weight of the salt
Let y represent the weight of the water
We know x + y = 80g total
If the salt solution is 35%, we can write the following equation:
x/80g = 0.35
x = 80g x 0.35 = 28
28 grams
PLS HELP ME!!!!! Find the sum of the first 100 terms of the arithmetic sequence with the first term 2 and the common difference 5.
Answers
Answer:
24,950.
Step-by-step explanation:
You can use the arithmetic series formula (a sequence is the list of numbers; a series is the summation of the list).
To find the sum...
(100 / 2) (2 * 2 + (100 - 1)5) = 50 * (4 + 99 * 5) = 50 * (4 + 495) = 50 * 499 = 24950.
Hope this helps!
Answer:
The sum of the first 100 terms of the arithmetic sequence is 24,950.
Step-by-step explanation:
Sn (sum of the first n terms of an AP) is given by n/2(2a + (n-1)d)
Where
n is the number of terms
a is the first term
d is the common difference
S100 = 100/2(2×2 + (100-1)5) = 50(4 + 99×5) = 50(4 + 495) = 50(499) = 24,950
Find The Area of the shape below
Answers
Explanation:
Formula for area of trapezoid:
A=a+b/2 * h
A=7.5+2.5/2 * 2.5
A=10/2 * 2.5
A=5 * 2.5
A=12.5
Find the area of the triangle. a) 225 units2 b) 75√3 units2 c) 150√3 units2 d) 27.5√3 units2
Answers
Answer:
Thus, area of triangle is [tex]225/\sqrt{3}[/tex]
Step-by-step explanation:
Area if triangle is given by 1/2( base*height)
Given
Height = 15 units
also one angle is given as 30 degrees
we know Tan of any angle is ratio of perpendicular and base
[tex]tan\alpha = perpendicular /base[/tex]
lets calculate tan 30 in the given triangle
we will take the smaller triangle containing angle 30 degrees and right angle
perpendicular will be half of base of triangle
base will be side with length 15 units
tan30 = perpendicular/15
[tex]1/\sqrt{3} = perpendicular/15\\=> perpendicular = 15/\sqrt{3}[/tex]
Thus, half of base of full triangle is [tex]15/\sqrt{3}[/tex]
so full base will be [tex]15*2/\sqrt{3} = 30/\sqrt{3}[/tex]
Full full triangle
height = 15 units
base = [tex]15*2/\sqrt{3} = 30/\sqrt{3}[/tex]
Thus, area of triangle is [tex]1/2* 30/\sqrt{3}*15= 225/\sqrt{3}[/tex]
PLEASE HELP ME!!! :'(
1. Create a data set with at least 5 values.
2. Write instructions that tell a friend how to find the mean absolute deviation of your data set.
Answers
Answer: KINDLY CHECK EXPLANATION
Step-by-step explanation:
Given the data:
1) dataset:
My data(x) : 2, 4, 6, 8, 10
2) to calculate the mean absolute deviation of the data above :
Step 1: Find the mean (m) of the dataset (my data)
Mean(m) = sum of values in my data / number of observations in my data (n)
m = (2+4+6+8+10) / 5
m = 30 / 5 = 6
The mean absolute deviation(MAD) :
Sum of The absolute value of the difference between values in my data and the mean value (m) Divided by the number of observations.
MAD = (Sum of |x - m|) / n
MAD = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|) / 5
MAD = (4 + 2 + 0 + 2 + 4) / 5
MAD = 12 / 5
MAD = 2.4
Massachusetts has a population of over 6,550,000 people. The maximum number of hairs that can grow on a human head is 500,000. Prove that there are at least 14 residents of Massachusetts who have the same number of hairs on their heads.
Answers
Answer:
So, basically, you can do this:
500,001*14<6,550,000.
This works because there is one person that can have 0 hairs, 1 hair, 2 hair and so on until we reach 500,000 hairs. Then, there has to be a repeat. So, we can do this fourteen times. Then, we can see that there are at least 14 people with a certain amount of hairs.
Choose the number sentence that illustrates the distributive property of multiplication over addition.A. 3 × (4 + 7) = (3 × 4) + (3 × 7)B. 3 × (4 + 7) = (3 × 4) + 7C. 3 × (4 + 7) = (3 + 4) × (3 + 7) brainly
Answers
Answer:
Option A is the answer.
The answer of term 3 x (4 + 7) after applying distributive property of multiplication over addition is 3 x 4 + 3 x 7.
Hence, option (A) is correct.
What is distributive property?Distributive property explains to us how to solve expressions in the form of a(b + c).
After apply distributive property, this term converts as ab+ac.
The given term is,
3 x (4 + 7)
To find the answer, using distributive property of multiplication over addition,
Use distributive property,
According to property, expression a(b + c) changes as ab + ac after applying distributive property,
The term can be solved as,
3 x (4 + 7) = 3 x 4 + 3 x 7
Therefore, option (A) is correct option.
To know more about Distributive property on:
https://brainly.com/question/5637942
#SPJ3
HELP!
After a rotation, A(-3, 4) maps to A'(4, 3), B(4, -5) maps to B'(-5, -4), and C(1,6) maps to C'(6, -1). Which rule
describes the rotation?
R0, 90°
R0, 180°
Ro, 270°
RO, 360°
Answers
270 degree counterclockwise rotation around the origin
=============================================================
Check out the diagram below. In the diagram, I only focus on points A and A'.
We have A = (-3,4) move to A ' = (4, 3). We see the x and y coordinates swap places. Then the new second coordinate -3 becomes positive, or it has flipped sign. So the rule applied here is [tex](x,y) \to (y,-x)[/tex] which describes a 90 degree clockwise rotation; which is equivalent to a 270 degree counterclockwise rotation
The other points follow the same idea.
Answer:
c
Step-by-step explanation:
9. If the velocity of a car is 45 km/h west, how far can it travel in 0.5 hours?
Answers
Answer:
22.5 km
Step-by-step explanation:
hello,
the car travels 45 km in 1 hour
so in 1/2=0.5 hour it travels 45/2=22.5 km
hope this helps
Answer:
22.5km
Step-by-step explanation:
speed=distance/time taken
distance=45*0.5
=22.5km
what is y=2/3x-4 graphed
Answers
Answer:
Please see attached
Step-by-step explanation:
Which is an equation of a direct proportion?
A.y=1/3x−2
B.y=3/x
C.y=−3x+4
D.y=−3x
Answers
Step-by-step explanation:
As someone has thankfully answered your question. I'll just try to explain that concept to you.
In direct proportion, as the first variable increases or decreases, the second variable also increases or decreases. In mathematical statements, it can be expressed as y = kx. This reads as “y varies directly as x” or “y is directly proportional as x” where k is constant in the equation.
So yes the answer is D
y = -3x
Answer:
D
Step-by-step explanation:
y = -3x
maths question pls answer
Answers
Answer:
72
Length=12
Width=6
Answer:
72cm²
Step-by-step explanation:
perimeter= 2(l+w)
36 = 2(l+w)
36/2 = l+w
18 = l+w
since, l is twice as w
18= 2w + w
18 = 3w (we can add since all the variables, and exponents are same)
18/3 = w
6= w
NOW,
w=6 and l is equal to twice as 6
so l=12
area= l×b
= 12×6 = 72cm²
hope this helps. It was toooo long
Which best describes the relationship between the line that passes through the points
Answers
Answer:
Neither perpendicular nor parallel.
Step-by-step explanation:
To find the answer, you just need to find the slopes of each line.
The slope of the line with points at (-6, 5) and (-2, 7) would be (7 - 5) / (-2 + 6) = 2 / 4 = 1/2.
The slope of the line with points at (4, 2) and (6, 6) would be (6 - 2) / (6 - 4) = 4 / 2 = 2.
They are most definitely not the same line.
They are not perpendicular, either, since although they are [eek I forgot the term for it] opposites, they are both positive. To be perpendicular, one slope must be negative and the other positive.
They are not parallel, since the slopes are not the same.
So, the relationship between the lines are that they are neither parallel nor perpendicular.
Hope this helps!
In two or more complete sentences describe the process in writing the equation of a line given two points?
Answers
Answer:
First, we have to find slope. We do that by using slope formula. Once we have found slope, we have start to write our equation in slope-intercept form. To get the complete equation, we need to find the y-intercept. To do so, we simply plug in one of the coordinates given to us into our half-formed equation. We should be able to find the y-intercept and then have our complete linear equation once we write it all out.
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope Formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
I need helpppppppppppp
Answers
Answer:
1/4 I'm pretty sure
Step-by-step explanation:
because half of the class already went to the afternoon session and 3/4 went to see the movie
Answer:1/4 I think
Step-by-step explanation:3/4-1/2=1/4
simplify the following equation 4-11/3 divided by 4-2/3
Answers
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]4-\frac{11}{3}=\frac{4*3}{1*3}-\frac{11}{3}\\\\=\frac{12}{3}-\frac{11}{3}\\\\=\frac{12-11}{3}\\\\=\frac{1}{3}\\\\\\4-\frac{2}{3}=\frac{4*3}{1*3}-\frac{2}{3}\\\\=\frac{12}{3}-\frac{2}{3}\\\\=\frac{12-2}{3}\\\\=\frac{10}{3}[/tex]
[4 - 11/3] ÷ (4 - 2/3) = [1/3] ÷ (10/3)
[tex]=\frac{1}{3}*\frac{3}{10}\\\\=\frac{1}{10}[/tex]
Janet correctly answers 45 questions on her science test. There are 50 questions on the test. What percentage did she answer correctly?
Answers
Answer:
90%
Step-by-step explanation:
45*2=90
50*2=100
90/100=90%
Hope this helped! brainliest would be great and good luck! :)
A flat surface that extends without end in all directions and is named by three points that are not on the same line is known as which geometric term? A. point B. ray C. line D. plane
Answers
which of the following is the correct graph of the compound inequality 4p+1>-7 or 6p+3<33
( the answers^)
Answers
Answer:
Step-by-step explanation:
4p+1>-7 , p>-2
6p+3<33 , p<5
-2<p<5
What is the recursive formula for the geometric sequence ? 6,-24,96,-384,...
Answers
Answer:
[tex]the \: recursive \: formula \: is \\ tn = 6( {4}^{n - 1} )[/tex]
Answer is given below with explanations.
Step-by-step explanation:
[tex]the \: given \: geometric \: sequence \: is \\ 6, \: - 24, \: 96, \: - 384 \\ the \: first \: term \: is \: 6 \: and \: the \: common \: ratio \: is \: - 4 \\ the \: {n}^{th} term \: of \: the \: geometric \: sequence \: is \\ tn = a {r}^{n - 1} \\ here \: first \: term \:( a) = 6 \\ common \: ratio \: (r) = - 4 \\ on \: substituting \: the \: values \: in \: formula \\ tn = 6( { - 4}^{n - 1} ) \\ the \: above \: mentioned \: formula \: is \: \\ the \: recursive \: formula \: \\ for \: geometric \: sequence.[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
I’m not sure if this is right I need help
Answers
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Odd and Even Functions.
Basically an Even Function is such that,
If there is a function f(x) is positive, then if we replace x as -x, then also it should give a positive function such as,
f(x) = f(-x)
thus, square of any function is always positive, so the answer is, option 2)
===> g(x) = 2x^2 + 1