Answer:
3x+12 is the sum
9x-2 is differences
Step-by-step explanation: Combine like terms
A chain lying on the ground is 19 meters long and its mass is 84 kilograms. The chain is threaded through a pulley, which is fixed to the ground, and pulled directly up so that it forms the shape of an L. How much work is required to raise one end of the chain to a height of 7 meters? Use that the acceleration due to gravity is 9.8 m/s^2. You may assume that the chain slides effortlessly and without friction along the ground as its end is lifted.
Answer:
Step-by-step explanation:
Given that, the length of the chain is
L= 19m
And the mass of the chain is
M= 84kg
Work to raise the chains to a height of
H = 7m
Acceleration due to gravity
g = 9.8m/s²
Since the chain is 19m long and it has a mass of 84kg
Then, it mass/ length is 84/19
M/L = 4.42kg/m
So, it weight / length is mass / length × gravity
W/L = M/L × g
W/L = 4.42 × 9.8
W/L = 43.33 N/m
So, workdone can be calculated using
Work = ∫F∆x
Work = ∫(W/L)•xdx.
Work = ∫43.33x dx. From x = 0 to 7
Work = 43.33 ∫x dx.
Work = 43.33 x²/2. From x = 0 to 7
Work = 21.66 [x²] from x = 0 to 7
Work = 21.66 ( 7²-0²)
Work = 21.66 × 49
Work = 1061.5 Joule
The workdone to lift the chain to 7m is 1061.5 J
"When work is done to lift the chain to 7m is 1061.5 J. To understand the calculations, check below".
Calculation of Acceleration due to GravityGiven that, the length of the chain as per the question is:
L= 19m
And also the mass of the chain is
Then M= 84kg
Now Work to raise the chains to a height of
After that H = 7m
Acceleration due to gravity
Then g = 9.8m/s²
Since When the chain is 19m long and it has a mass of 84kg
Then, it mass/ length is 84/19
M/L = [tex]4.42kg/m[/tex]
After that, it weight / length is mass / length × gravity
W/L = M/L × g
W/L = 4.42 × 9.8
W/L = 43.33 N/m
Then, work done can be calculated using
Work is = ∫F∆x
Work is = ∫(W/L)•xdx.
Then Work = ∫43.33x dx. From x = 0 to 7
After that Work = 43.33 ∫x dx.
Now Work = 43.33 x²/2. From x = 0 to 7
Work is = 21.66 [x²] from x = 0 to 7
Work is = 21.66 ( 7²-0²)
Then Work = 21.66 × 49
Hence Work = 1061.5 Joule
Therefore, The work done to lift the chain to 7m is 1061.5 J
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Which could be the dimensions of a rectangular prism whose surface area is less than 160 square feet? Select two options.
8 feet by 4 feet by 3 feet
7 feet by 6 feet by 4 feet
3 feet by 7 feet by 8 feet
3 feet by 6 feet by 7 feet
3 feet by 5 feet by 7 feet
Answer:
First answer and last
Step-by-step explanation:
Explanation on paper
I got the first and last right
hi:) I’m so sorry , i uploaded this question earlier but I think the picture couldn’t load. Yea I need help with this question, the last 2 parts. Thank you very much!:)
Answer:
(ii) [tex] \frac{1}{2} - \frac{1}{3} [/tex]
(iii) [tex] \frac{25}{51} [/tex]
Step-by-step explanation:
Please see the attached picture for full solution.
Second last question what is the area of this compound shape?
Answer:
43.13 yd squared
Step-by-step explanation:
This is a figure composed of a semicircle and a right triangle.
Triangle:
The area of a triangle is denoted by A = (1/2) * B * h, where b is the base and h is the height. Here, the base is actually also the radius of the semicircle, which is 4. The height is 9. Plug these in: A = (1/2) * 4 * 9 = 36/2 = 18 yd squared.
Semicircle:
The area of a semicircle is denoted by A = [tex](1/2)\pi r^{2}[/tex], where r is the radius. Here the radius is 4. So: A = [tex](1/2)\pi *4^{2}=8\pi[/tex] ≈ 25.13 yd squared.
Adding these up: 18 + 25.13 = 43.13 yd squared
Hope this helps!
Answer:
43.12 yd²
Step-by-step explanation:
Semicircle + triangle
½×pi×r² + ½×b×h
½(3.14)(4²) + ½(4)(9)
43.12 yd²
y = 2x + 1
y = 4x - 1
Answer:
y = 2x + 1
y = 4x - 1
Step-by-step explanation:
You haven't mentioned the question so, unfortunately I can't give you the answer.
The correct answer is that the system of equations has no solution.
To determine the solution to the system of equations, we need to compare the two equations
1. [tex]\( y = 2x + 1 \)[/tex]
2. [tex]\( y = 4x - 1 \)[/tex]
For a system of equations to have a solution, both equations must be satisfied simultaneously. This means that the values of [tex]\( x \) and \( y \)[/tex] that satisfy one equation must also satisfy the other equation.
Let's analyze the equations. Both equations are in slope-intercept form, [tex]\( y = mx + b \)[/tex], where m is the slope and b is the y-intercept.
For the first equation, the slope is 2 and the y-intercept is 1. For the second equation, the slope is 4 and the y-intercept is -1 .
Since the slopes of the two lines are different (2 for the first line and 4 for the second line), the lines are not parallel. However, the y-intercepts are different as well (1 for the first line and -1 for the second line). This means that the lines are not the same line and they will never intersect because two lines with different slopes and different y-intercepts cannot meet.
Therefore, there is no point [tex]\( (x, y) \)[/tex] that satisfies both equations simultaneously, and the system of equations has no solution. This is an example of a system of linear equations that is inconsistent.
In conclusion, the system of equations given by [tex]\( y = 2x + 1 \)[/tex] and [tex]\( y = 4x - 1 \)[/tex] has no solution because the lines represented by these equations are neither parallel nor do they intersect.
Katie has to drive 15 miles east and 36 miles north to get to her aunt's house. What is the direct distance to her aunt's house?
Answer: 39 miles
Step-by-step explanation:
Hi, since the travelling forms a right triangle, (see attachment) we have to apply the Pythagorean Theorem formula.
a^2 +b ^2 =c ^2
Assuming a and b are the distances driven, and c the direct direction formed (hypotenuse)
15^2 +36 ^2 =c ^2
225+1,296 =c ^2
1,521 =c ^2
√1,521= c
c= 39 miles
Feel free to ask for more if needed or if you did not understand something.
Answer:
39 miles
Step-by-step explanation:
Riley is going snowboarding over the holiday break. To go snowboarding you have a one time fee of $75 to rent the snowboard equipment, plus a fee of $5 per ride on the ski lift to get up and down the mountain. Write an equation that could be used to find the total amount it would cost to go snowboarding.
Answer:
y = 5x + 75
Step-by-step explanation:
"One time" = no change = constant
"per" = varies per person = variable
It is 5 dollars per ride, 5 dollars per x, 5x.
y = 5x + 75
Can anyone help with this(Also have another question that is posted if you would like to answer that as well!)
Answer:
From the info you give us it should be around 8.57 in. per book.
Step-by-step explanation:
5x12=60/7=8.57
Which of the following rotations around the origin of the triangle with
vertices H(2,-6), 1 (1,5), J(-3,4) produces an image with vertices
H'(-6,-2), I' (5,-1), J'(4,3)
8G
a) 180°
c) 360°
b) 90°
d) 270°
Answer:
Step-by-step explanation:
270 degrees
What is the surface area of the present?
Answer:
1,350
Step-by-step explanation:
To find Surface Area you need to area of all the sides and add them
So to find one side of the cube you do L x H
So 15 x 15 = 225
Since all the sides of the cube are the same, you don't need to figure out the area of the other sides.
225 x 6 sides = 1,350
Hope this helped
Please help! 20 points
Answer:
A
Step-by-step explanation:
It has the least amount of area cut out of it.
Answer:
The answer would be A
Select the expression that is equivalent to: 3 root 1089
Answer:
[tex]3\sqrt{1089}=3\sqrt{3^2(11)^2}[/tex]
Step-by-step explanation:
Given : Expression [tex]3\sqrt{1089}[/tex]
To find : Select the expression that is equivalent to expression ?
Solution :
Re-write the expression as,
[tex]3\sqrt{1089}=3\sqrt{3\times 3\times 11\times 11}[/tex]
[tex]3\sqrt{1089}=3\sqrt{3^2\times 11^2}[/tex]
[tex]3\sqrt{1089}=3\sqrt{(3\times 11)^2}[/tex]
[tex]3\sqrt{1089}=3\sqrt{(33)^2}[/tex]
[tex]3\sqrt{1089}=3\times 33[/tex]
[tex]3\sqrt{1089}=99[/tex]
The above are the possible equivalent expressions.
Answer:
A
Step-by-step explanation:
Which of these myths do you think is probably believed by more people?
SELECT AN ANSWER
Europeans "discovered" new parts of the world during the Age of Discovery.
European explorers, like Christopher Columbus, were the first to cross the great oceans of the world.
Answer:
European explorers, like Christopher Columbus, were the first to cross the great oceans of the world.
Make 24 using the numbers 1,6,8,8
Answer:
((1 - 6) + 8) * 8
(1 - (6 - 8)) * 8
((1 + 8) - 6) * 8
(1 + (8 - 6)) * 8
8 * ((1 - 6) + 8)
((8 + 1) - 6) * 8
(8 + (1 - 6)) * 8
8 * ((1 + 8) - 6)
((8 - 6) + 1) * 8
(8 - (6 - 1)) * 8
8 * ((8 + 1) - 6)
8 * ((8 - 6) + 1)
There are 12 solutions above
HOPE I HELPED!!!
<3
Answer:
(8-6+1)8=24
Step-by-step explanation:
Use order of operations to solve
The wind speed s (in miles per hour) is related to the distance (in miles) the tornado travels by the equation s = 93log d + 65. On March 18, 1925, a tornado whose wind speed was about 280 miles per hour struck the Midwest. How far did the tornado travel?
Answer:
The distance the tornado traveled was approximately 205 miles.
Step-by-step explanation:
The equation representing the relationship between the wind speed (in miles per hour) and the distance the tornado travels (in miles) is:
[tex]s=93\log d+65[/tex]
Compute the value of d for s = 280 as follows:
[tex]s=93\log d+65[/tex]
[tex]280=93\log d+65[/tex]
[tex]93\log d=280-65\\93\log d=215[/tex]
[tex]\log d=2.312\\[/tex]
[tex]d=10^{2.312}\\d=205.035\\d\approx 205[/tex]
Thus, the distance the tornado traveled was approximately 205 miles.
Complete the steps to find the area of the trapezoid.
Area of rectangle = _ square units
Area of triangle 1 = square units
Area of triangle 2 = _ square units
Area of triangle 3 = _ square units
Area of trapezoid = _ square units
Given:
In the given diagram
Each small box along X axis = 2 unit
Each small Box along Y axis = 2 unit
For rectangle:
Length = 16 unit
Width = 16 unit
For triangle 1
Base = 8 unit
Height = 6 unit
For triangle 2
Base = 8 unit
Height = 4 unit
For triangle 3
Base = 16 unit
Height = 12 unit
Formula
Area of the trapezoid is
[tex]A = R -T_{1} -T_{2} -T_{3}[/tex]
Where, [tex]A[/tex] be the area of the trapezoid
[tex]R[/tex] be the area of the rectangle
[tex]T_{1} ,T_{2} ,T_{3}[/tex] be the area of the triangle 1, 2 and 3 respectively.
[tex]R = lb[/tex] where, l be length and b the width
[tex]T_{1} = \frac{1}{2} bh[/tex], where, b be the base and h be the height
Now,
Taking, l = 16 and b = 16 we get,
[tex]R = (16)(16)[/tex] = 256 sq unit
For Triangle 1
Taking, b = 8 and h = 6 we get,
[tex]T_{1} = \frac{1}{2}(8)(6)[/tex] sq unit
[tex]T_{1} = 24[/tex] sq unit
For Triangle 2
Taking, b = 8 and h = 4 we get,
[tex]T_{2} = \frac{1}{2}(8)(4)[/tex] sq unit
[tex]T_{2} = 16[/tex] sq unit
For Triangle 3
Taking, b = 16 and h = 12 we get,
[tex]T_{3} = \frac{1}{2}(16)(12)[/tex] sq unit
[tex]T_{3} = 96[/tex] sq unit
Therefore,
The area of the trapezoid is = 256-24-16-96 sq unit = 120 sq unit
Hence,
Area of rectangle =256 square units
Area of triangle 1 = 24 square units
Area of triangle 2 = 16 square units
Area of triangle 3 = 96 square units
Area of trapezoid = 120 square units
Answer:
Area of rectangle =256 square units
Area of triangle 1 = 24 square units
Area of triangle 2 = 16 square units
Area of triangle 3 = 96 square units
Area of trapezoid = 120 square units
Step-by-step explanation:
If the legs of the triangle are doubled in length what is the length of the hypotenuse
7
10
14
48
None of the above
Which system of linear equations appears to have a solution of (3, 0)?
The solution of a system of equations is (3,0).
What is a system of linear equations?A system of linear equations is a collection of one or more linear equations involving the same variables in mathematics. The system of linear equations appears to have a solution of (3, 0).
A linear equation is one in which the variable's maximum power is always 1. The degree of the linear equation is always equal to one.
If a system of linear equations has two equations and a graph of these two equations intersect each other at (a,b), then the point (a,b) is the solution of that system of equations.
Since, the solution of a system of equations is (3,0), therefore on a coordinate plane, 2 lines intersect at (3, 0).
Therefore, the solution of a system of equations is (3,0).
To know more about the system of equations follow
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Final answer:
The system of linear equations with a solution of (3, 0) is the one where two lines intersect at the point (3, 0) on a coordinate plane.
Explanation:
The student is asking which system of linear equations appears to have a solution of (3, 0). In the context of a coordinate plane, the solution to a system of linear equations is the point where the equations' graphs intersect. The given options describe where two lines intersect on different coordinate planes. Only the option stating 'On a coordinate plane, 2 lines intersect at (3, 0)' would represent a system where the solution is (3, 0). Therefore, the correct answer is the one where two lines intersect at the point (3, 0) on a coordinate plane.
A cone has a lateral surface area of 62.8 square yards. If the slant height is 2 yards, what is the total surface area of the cone?
The total surface area of the cone is 7π square yards.
Explanation:To find the total surface area of the cone, we need to find the lateral surface area and add it to the base area.
The lateral surface area of a cone is given by the formula πrℓ, where r is the radius and ℓ is the slant height.
In this case, the lateral surface area is 62.8 square yards and the slant height is 2 yards.
So, the lateral surface area of the cone is π(2)(2) = 4π square yards.
The base area of a cone is given by the formula πr^2, where r is the radius.
Since the slant height is given, we can use the Pythagorean theorem to find the radius. The radius is the hypotenuse of a right triangle with the slant height as one of the legs and the height of the cone as the other leg.
Using the Pythagorean theorem, we have r^2 = (2)^2 - (1)^2 = 4 - 1 = 3.
Therefore, the radius is √3 yards.
The base area of the cone is then π(√3)^2 = 3π square yards.
The total surface area of the cone is the sum of the lateral surface area and the base area, 4π + 3π = 7π square yards.
Could you help me solve this problem ASAP :D
Answer:
B) 1/4x+1/2=1/3x
Hope this helps!
What is the mean of these numbers? 2,2,8
Answer:
4
Step-by-step explanation:
(2+2+8)/3
brainliest please
If you are given the two sides that are not the hypotenuse, which trig function should
you use?
A) tangent
B) sine
C) cosine
D) cotangent
Answer:
A
Step-by-step explanation:
Tangent = opposite/adjacent
The trigonometric function that can be used when given 2 sides that are not the hypotenuse is tangent.
The sides of a right angle triangle are as follows:
HypotenuseAdjacent sideOpposite sideThe simplest trigonometric ratio we can use to solve for the angles of a right angle triangle are as follows:
sin∅ = opposite / hypotenusecos∅ = adjacent / hypotenusetan∅ = opposite / adjacentTherefore, the trigonometric function one can use to find the angle of a right angle triangle when given 2 sides apart from hypotenuse is tangent
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Plot the location of -9 and -3 on the number line. Use mathematical symbols to write an inequality that compares -9 and -3. Explain how the number line can be used to show that your inequality is correct.
Answer:
-9<-3
Step-by-step explanation:
Since -3 is closer to 0 than -9, then -3 is the greater number.
How is the process of finding the surface area of a rectangular prism the same as finding the surface area of a triangular prism? How is it different?
ANSWER:
For both prisms, you can draw a net to help you find the areas of the faces. Add the areas together to find the surface area. A rectangular prism has only rectangular faces, and you use the formula bh to find area. A triangular prism has triangular and rectangular faces, and you use the area formula bh for rectangular faces and the area formula 1/2bh for triangular faces.
Final answer:
The process of finding the surface area of a rectangular prism is similar to finding the surface area of a triangular prism. Both involve drawing a net and adding the areas of the faces. However, the formulas used are different because the shapes have different types of faces.
Explanation:
For both prisms, you can draw a net to help you find the areas of the faces. Add the areas together to find the surface area. A rectangular prism has only rectangular faces, and you use the formula bh to find area. A triangular prism has triangular and rectangular faces, and you use the area formula bh for rectangular faces and the area formula 1/2bh for triangular faces.
You earn $42 for washing 7 cars. How much do you earn for washing 3 cars?
Answer:
42/7 = x/3
7x = 126
x = $18 for washing 3 cars
Step-by-step explanation:
what is the coordinate if (2,2) is reflected over x=2
Answer:
2,-2
Step-by-step explanation:
Its pretty simple, all you have to do is find opposite of y and put it.
You need to buy enough sand to fill a sandbox to the top. The sandbox is modeled by the right rectangular prism in the diagram. How much sand do you need to buy?
Which equation is equivalent to 8x + 3(x + 5) - 5(x - 4) = 2? A. 6x + 35 = 2 B. 6x + 1 = 2 C. 6x – 5 = 2 D. 43x = 2
[tex]8x + 3(x + 5) - 5(x - 4) = 2 \\ 8x + 3x + 15 - 5x + 20 = 2 \\ 6x + 35 = 2[/tex]
Answer: A.
[tex]6x + 35 = 2[/tex]
Answer:
A
Step-by-step explanation:
8x + 3(x + 5) - 5(x - 4) = 2
Distribute the 3
8x + 3*x +3*5 -5(x-4)=2
8x+3x+15 -5(x-4)=2
Distribute the -5
8x+3x+15 -5*x +-5*-4=2
8x+3x+15-5x+20=2
Combine like terms
8x+3x-5x+20+15=2
6x+35=2
So, A is the correct choice
Do either of these display exponential behavior? Please help!
Answer:
no. 7 does
Step-by-step explanation:
brainlest please
x increases by three each time but y decreases less each time
Which answer includes the intervals that contain the solution to the inequality?
The correct option is D (-∞,-3)∪(-1,1)
Step-by-step explanation:
Given,
[tex]\frac{x^{2}-1 }{3x+9}[/tex] ≤ 0
To find the solution.
The solution could be found if
[tex]x^{2} -1[/tex] ≤ 0 and
3x+9 ≠ 0 [if the denominator is 0, it gives ∞ as solution]
Now,
[tex]x^{2} -1[/tex] ≤ 0
or, (x+1)(x-1) ≤0
or, x ≤1 and x≤-1
Both of the above condition holds is x≤1
Again,
3x+9≠0
or, x≠-3
All the conditions gold for the values (-∞,-3)∪(-1,1)
Hence the correct option is D.