A solid is made by a hemisphere and cylinder having equal radii. The volume of the solid is 2707 cm'. If the height of the cylinder is 80 cm, find the total surface area of the solid
Answers
The total surface area of the solid is approximately 1818 \(cm^{2}\). Let's call the radius of the hemisphere and cylinder "r".
The volume of the solid is the sum of the volumes of the hemisphere and cylinder: V = (2/3)π\(r^{3}\) + π\(r^{2}\)h. Substituting in the given values, we get: 2707 = (2/3)π \(r^{3}\) + π\(r^{2}\)(80)
To solve for r, we can rearrange the equation and use a numerical method or calculator. We get: r ≈ 11.6 cm
Now, we can use the radius to find the surface area of the solid. The surface area is the sum of the curved surface areas of the hemisphere and cylinder, plus the area of the circular base of the cylinder: A = 2π\(r^{2}\) + 2πrh + π\(r^{2}\).
Substituting in the given values and solving for A, we get: A ≈ 1818 \(cm^{2}\). Therefore, the total surface area of the solid is approximately 1818 \(cm^{2}\).
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Related Questions
50 POINTS
19. Ift(x) = 7 - 2x and t(x) = 0, then find x.
20. If h(x) = 4x + 2, then h(x + 3) =
Answers
Answer:
see below
Step-by-step explanation:
(x) = 7 - 2x
Let t(x) =0
0 = 7-2x
Subtract 7 from each side
-7 = -2x
Divide by -2
-7/-2 =-2x/-2
7/2 =x
h(x) = 4x + 2
Replace x with x+3
h(x+3) = 4(x+3) + 2
Distribute
= 4x+12 +2
=4x+14
Answer:
19) \(x=\frac{7}{2}\)
20) \(h(x+3)=4x+14\)
Step-by-step explanation:
19)
We have the function:
\(t(x)=7-2x\)
And we want to find x such that t(x)=0.
So, substitute 0 for t(x):
\(0=7-2x\)
Solve for x. Subtract 7 from both sides:
\(-7=-2x\)
Divide both sides by -2:
\(\frac{7}{2}=x\)
Flip:
\(x=\frac{7}{2}\)
20)
We have:
\(h(x)=4x+2\)
To find h(x+3), substitute (x+3) for x. This yields:
\(h(x+3)=4(x+3)+2\)
Multiply:
\(h(x+3)=4x+12+2\)
Add:
\(h(x+3)=4x+14\)
And we're done!
A rectangle is drawn in the first quadrant so that the base lies on the x -axis, bottom left corner on the origin, top right comer is on the line 2y+4x=40. Draw a diagram. Find the maximum area of such a rectangle. 11. A rectangle is drawn in the first and second quadrants so that the base lies on the x -axis, upper left comer on the line y=2x+6, top right corner is on the line y=−2x+6. Draw a diagram. Find the maximum area of such a rectangle.
Answers
a) The maximum area of such a rectangle is 50 square units. b) The maximum area of such a rectangle is 36.
What is Quadratic and Linear equation ?When graphed, a linear equation results in a straight line. Since each value of x results in just one value of y, this relationship is referred to as being one-to-one. When a quadratic equation is graphed, the result is a parabola that extends uphill or downward in the y direction, starting at a single point known as the vertex. Because there are two values for x for every value of y (aside from the y-value at the vertex point), the relationship between x and y is not one-to-one.
a) The given equation is 2y + 4x =40
Let the coordinates of the top right corner be (x,y).
Then, y = (40 -4x)/2
The area of the rectangle is given by A =xy
A= x x (40 -4x)/2
A = 20x-2x²
We have to find the maximum area of the rectangle.
Differentiate the expression for Area A with respect to x to get the slope of the curve
A’ = 20-4x
At the maximum area, A’=0
Therefore, 20 -4x =0
4x =20
X=5
Substituting x=5 in the equation of the line 2y + 4x =40
2y +20 =40
2y = 20
Y =20
Therefore, the coordinates of the top right corner of the rectangle are (5,10).
The maximum area of the rectangle is given by A = xy = 5 x 10 =50 sq.units
b) The maximum area of such a rectangle can be found by using the formula: A = lw,
where l is the length of the rectangle
w is the width of the rectangle
Since the base of the rectangle is on the x-axis and the upper left corner is on the line y=2x+6, the length of the rectangle is equal to the distance between y=2x+6 and the x-axis, which is 6. The width of the rectangle is equal to the distance between y=-2x+6 and the x-axis, which is also 6. Thus, the maximum area of such a rectangle is 36 square units.
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Which of the following motion rules represents a transformation that preserves orientation, but not congruence?
Answers
Hey can someone help me with this?
Answers
Answer:
Step-by-step explanation:
A. a = $1350 b. b= 89%
B. 1350(.89)^t = 675
t = 5.9 years
More info a. Theoretical capacity-based on three shifts, completion of five motorcycles per shift, and a 360 -day year-3 −3×360=5,400. b. Practical capacity-theoretical capacity adjusted for unavoidable interruptions, breakdowns, and so forth-3 −4×320=3,840. c. Normal capacity utilization-estimated at 3,240 units. d. Master-budget capacity utilization-the strengthening stock market and the growing popularity of motorcycles have prompted the marketing department to issue an estimate for 2020 of 3,600 units. Requirement 2. What are the benefits to Zippy, Inc., of using either theoretical capacity or practical capacity? to managers. As a general rule, however, it is important on the production-volume variance as a measure of the economic costs of unused capacity. Requirement 3. Under a cost-based pricing system, what are the negative aspects of a master-budget denominator level? What are the positive aspects? What are the negative aspects of a master-budget denominator level? referred to as the demand spiral. What are the positive aspects? The positive aspects of the master-budget denominator level are that is based on for the product and indicates the price at which would be recovered to enable the company to make a profit.
Answers
The benefits of using the theoretical capacity for Zippy, Inc. include providing a maximum production potential based on ideal conditions, aiding in long-term planning, and setting performance benchmarks. Practical capacity considers unavoidable interruptions and breakdowns, providing a more realistic estimate. The negative aspect of a master-budget denominator level is the potential for unused capacity costs, while the positive aspect is using a predetermined cost base for pricing decisions.
Theoretical capacity, based on three shifts and completion of five motorcycles per shift, gives Zippy, Inc. a maximum production potential of 5,400 units per year. This capacity measure helps in long-term planning, resource allocation, and setting performance benchmarks. On the other hand, practical capacity takes into account unavoidable interruptions, breakdowns, and other factors that can impact production. It provides a more realistic estimate of 3,840 units.
Regarding cost-based pricing, the negative aspect of a master-budget denominator level is that it may lead to unused capacity costs. If the estimated demand falls below the master-budget level, there could be underutilized resources, resulting in economic costs for the company. However, the positive aspect of using a master-budget denominator level is that it provides a predetermined cost base for pricing decisions. It helps in setting prices that ensure the company's costs are covered and profitability is achieved.
In summary, theoretical capacity aids in long-term planning and setting benchmarks, while practical capacity considers interruptions. The negative aspect of a master-budget denominator level is unused capacity costs, but it provides a predetermined cost base for pricing decisions, ensuring cost recovery and profitability.
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which graph best represents the following inequality y<_ -5/6 +2/3
Answers
The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ y ≤ - 5/6x + 2/3
Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.
Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.
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(1.3) Let f be a function defined by f(x,y)= 2xy^2 /3x^2 +y^4 for (x,y)=/=(0,0). Show that f has no limit at (x,y)→(0,0).
Answers
The function f(x, y) has no limit at (x, y) → (0, 0).
How did we arrive at this assertion?To show that the function f(x, y) does not have a limit as (x, y) approaches (0, 0), we need to demonstrate that the limit of f(x, y) does not exist. This can be done by finding two different paths along which the function approaches different values or by showing that the limit along any path is not consistent.
Let's consider two paths:
Path 1: Let y = mx, where m is a non-zero constant.
Path 2: Let y = x².
For Path 1, substitute y = mx into the function f(x, y):
\(f(x, mx) = (2x(mx)^2) / (3x^2 + (mx)^4) \\
= (2x(m^2)x^2) / (3x^2 + (m^4)(x^4)) \\
= (2m^2x^3) / (3 + m^4x^2)\)
As x approaches 0, the numerator approaches 0, but the denominator remains nonzero since m⁴x² will still have a positive value. Therefore, the limit of f(x, mx) as x approaches 0 is 0.
Now let's consider Path 2:
\(f(x, x^2) = (2x(x^2)^2) / (3x^2 + (x^2)^4) \\
= (2x^5) / (3x^2 + x^8) \\
= (2x^5) / (x^2(3 + x^6))\)
As x approaches 0, the numerator approaches 0, but the denominator becomes nonzero since x²(3 + x⁶) will still have a positive value. Therefore, the limit of f(x, x²) as x approaches 0 is 0.
Since the limits along Path 1 and Path 2 are both 0, but they approach 0 through different values (m² and 0), we conclude that the limit of f(x, y) as (x, y) approaches (0, 0) does not exist. Thus, the function f(x, y) has no limit at (x, y) → (0, 0).
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An infinite geometric series has S=\(\frac{64}{3}\) and \(S_{3}\)=21. Find \(S_{5}\).
Answers
Since 64/3 = 21 + 1/3 > 21, I assume S is supposed to be the value of the infinite sum. So we have for some constants a and r (where |r | < 1),
\(S = \displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac{64}3 \\\\ S_3 = \sum_{n=1}^3 ar^{n-1} = 21\)
Consider the k-th partial sum of the series,
\(S_k = \displaystyle \sum_{n=1}^k ar^{n-1} = a \left(1 + r + r^2 + \cdots + r^{k-1}\right)\)
Multiply both sides by r :
\(rS_k = a\left(r + r^2 + r^3 + \cdots + r^k\right)\)
Subtract this from \(S_k\):
\((1 - r)S_k = a\left(1 - r^k\right) \implies S_k = a\dfrac{1-r^k}{1-r}\)
Now as k goes to ∞, the r ᵏ term converges to 0, which leaves us with
\(S = \displaystyle \lim_{k\to\infty}S_k = \frac a{1-r} = \frac{64}3\)
which we can solve for a :
\(\dfrac a{1-r} = \dfrac{64}3 \implies a = \dfrac{64(1-r)}3\)
Meanwhile, the 3rd partial sum is given to be
\(\displaystyle S_3 = \sum_{k=1}^3 ar^{n-1} = a\left(1+r+r^2\right) = 21\)
Substitute a into this equation and solve for r :
\(\dfrac{64(1-r)}3 \left(1+r+r^2\right) = 21 \\\\ \dfrac{64}3 (1 - r^3) = 21 \implies r^3 = \dfrac1{64} \implies r = \dfrac14\)
Now solve for a :
\(a\left(1 + \dfrac14 + \dfrac1{4^2}\right) = 21 \implies a = 16\)
It follows that
\(S_5 = a\left(1 + r + r^2 + r^3 + r^4\right) \\\\ S_5 = 16\left(1 + \dfrac14 + \dfrac1{16} + \dfrac1{64} + \dfrac1{256}\right) = \boxed{\frac{341}{16}} = 21 + \dfrac5{16} = 21.3125\)
Question 4. A mathematical sentence whose truth depends on the value of a variable is called an open sentence. For example, P(x):x
2
=4 cannot be determined to be true or false until we assign a value to x. If x∈{−2,2} then P(x) will evaluate to "True," Otherwise, P(x) will evaluate to "False." Many of the mathematical proofs we will be working with later on will be attempting to prove that some open sentence is true for every value of x in some large (often infinite) set. Let P(x) and Q(x) be the following open sentences: P(x):x
2
−5x+6=0,Q(x):x−3<0 Determine if the following statements are true or false. For each answer, you should first explain why each open sentence is true/false, then use properties of the logical operators to explain why the entire statement is true or false. a) P(1) b) P(2)∪Q(2) c) P(3)∧Q(3) d) P(4)⟹Q(4)
Answers
a) False. The open sentence P(x): x^2 - 5x + 6 = 0 is false when x = 1. Substituting x = 1 into P(x) gives 1^2 - 5(1) + 6 = 2 ≠ 0.
b) True. P(2) is true because substituting x = 2 into P(x) gives 2^2 - 5(2) + 6 = 0. Q(2) is false because substituting x = 2 into Q(x) gives 2 - 3 < 0, which is false. The union (∪) of true and false is true.
c) False. P(3) is false because substituting x = 3 into P(x) gives 3^2 - 5(3) + 6 = 0, which is false. Q(3) is true because substituting x = 3 into Q(x) gives 3 - 3 < 0, which is true. The conjunction (∧) of false and true is false.
d) True. P(4) is true because substituting x = 4 into P(x) gives 4^2 - 5(4) + 6 = 0. Q(4) is true because substituting x = 4 into Q(x) gives 4 - 3 < 0, which is true. The implication (⟹) "P(4) implies Q(4)" is true when both P(4) and Q(4) are true.
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In AEFG, the measure of ZG=90°, FG = 21 feet, and EF = 63 feet. Find the measure
of ZE to the nearest degree.
Answers
Answer:
44
Step-by-step explanation:
1/3b+2/3b-5/6(b+1)
A. 1/6b+5/6
B. 1/6b-5/6
C. 11/6b-5/6
D. 1/6b+1
Answers
Answer:
Answer is B.1/6b-5/6
Step-by-step explanation:
I hope it's helpful!
The index of refraction of the core of a typical fiber optic is ncore = 1.46; the cladding has nclad = 1.4. calculate the critical angles for the total internal reflection icrit and crit .
Answers
Critical angle for the total internal reflection icrit, β = 78.28⁰
Critical angle for the total internal reflection crit, α = 17,22⁰
We have the refractive index of core, \(n_c_o_r_e\) = 1.46
We have the refractive index of clad , \(n_c_l_a_d\) = 1.4
Critical angle can be defined as the incidence angle which results in the refraction angle being equal to at that angle of incidence.
For Total Internal Reflection to occur, the incidence angle must be greater than the critical angle.
We know that the critical angle, θ is given by:
sinθ = \(\frac{n_c_l_a_d}{n_c_o_r_e}\)
sinθ = \(\frac{1.4}{1.46}\)
sinθ = 0.959 = sin⁻¹(0.979) = 78.28⁰
β = θ = 78.28⁰
Now, for α:
\(\frac{sin(90-\alpha )}{sin\alpha } = \frac{1}{n_c_o_r_e}\)
sinα = sin(90⁰-78.28⁰) × 1.46
sinα = sin(11.72⁰) × 1.46
α = sin⁻¹(0.296)
α = 17,22⁰
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Critical angle for total internal reflection icrit β = 78.28⁰
Critical angle for total internal reflection crit, α = 17.22⁰
The critical angle can be defined as the angle of incidence at which the angles of refraction are equal to angle of incidence.
The angle of incidence must be greater than the critical angle for total internal reflection to occur.
The refractive index of the core is ncore = 1.46.
The refractive index of clad is nclad = 1.4.
We know that the critical angle, θ is given by:
sinθ = nclad/ ncore
sinθ = 1.4/1.46
sinθ = 0.959
sin⁻¹(0.979) = 78.28⁰
β = θ = 78.28⁰
Now, for α:
sin(90- α) / sin α = 1 / ncore
sinα = sin(90⁰-78.28⁰) × 1.46
sinα = sin(11.72⁰) × 1.46
α = sin⁻¹(0.296)
α = 17.22⁰
Critical angle for icrit β = 78.28⁰
Critical angle for crit α = 17.22⁰
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of the respondents, 519 replied that america is doing about the right amount. what is the 95 % confidence interval for the proportion of all american adults who feel that america is doing about the right amount to protect the environment.
Answers
The number of intervals that feel that America is doing about the right amount to protect the environment is 0.487, and 0.551 intervals
To find the number of adults who feel that America is doing about the right amount to protect the environment, we need to use the confidence interval proportion formula
CI = p ± Zα/2 * √(p * (1-p)/n
where:
p = sample proportion = 519/1000 = 0.519
n = sample size = 1000
Zα/2 = the critical value for the desired confidence level = 1.96
By substuting the values, we get:
CI = 0.519 ± 1.96 * √(0.519 * (1-0.519) / 1000)
= 0.519 ± 0.032
= (0.487, 0.551)
Therefore, (0.487, 0.551) interval feel that America is doing about the right amount to protect the environment.
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please help me with this problem
Answers
Answer:
Step-by-step explanation:
The answer is (56+232)w_sd
your welcome
Answer:
as below
Step-by-step explanation:
use the table to put a number into f(x)
f(-3) = -3+4 = 1
f(-1) = -1+4= 3
f(2) = 2+4=6
f(11) = 2+11=13
Calculate the distance traveled when moving at a rate
of 60mph for 3.5hrs.
Sentence Answer
Answers
Answer:
The distance traveled when moving at a rate of 60mph for 3.5 hours is 210 miles.
Hope this helped!
the pencil factory wraps pencils in packages of 6. Today there are 5,750 pencils to be packaged How many packages will there be? How many pencils will be leftover
Answers
Answer: 958 packages, 2 leftover
Step-by-step explanation:
divide 5,750 by 6 to get the number of packages that will be made:
5750/6 = 958 R2
There will be 958 packages, with 2 pencils leftover
Hare Krishna! :)
use the number line to represent the solution 5 x < 20
Answers
x<4 is the solution of the inequality 5 x < 20
What is Number system?A number system is defined as a system of writing to express numbers.
The given inequality is 5 x < 20
We have to solve for x
Divide both sides by 5
x<20/5
Divide numerator and denominator by 5
x<4
The graph of x<4 is given in the attachment.
Hence, x<4 is the solution of the inequality 5 x < 20
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Step 3: Multiply by the scalar (1 over the determinant): Aâ’1 = a11 a12 a21 a22 a11 = a12 = a21 = a22 =
Answers
Answer:
a11 = 1
a12 = -1
a21 = -1.5
a13 = 2
What is 6 divided by 9.51
Answers
Answer:
The result of 6 divided by 9.51 is approximately 0.63.
Answer:
0.63091482649
Step-by-step explanation:
A person must pay $ 6 to play a certain game at the casino. Each player has a probability of 0.16 of winning $ 12 , for a net gain of $ 6 (the net gain is the amount won 12 m
Answers
Given that a person must pay $ 6 to play a certain game at the casino. Each player has a probability of 0.16 of winning $ 12 , for a net gain of $ 6 (the net gain is the amount won 12 minus the amount paid 6 which is equal to $ 6). Let us find out the expected value of the game. The game's anticipated or expected value is $6.96.
The expected value of the game is the sum of the product of each outcome with its respective probability.The amount paid = $6The probability of winning $12 = 0.16
The net gain from winning $12 (12 - 6) = $6 The expected value of the game can be calculated as shown below:Expected value = ($6 x 0.84) + ($12 x 0.16)= $5.04 + $1.92= $6.96 Thus, the expected value of the game is $6.96.
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Form an expression for the area of a composite rectilinear shape.
Answers
The expression for the area of composite rectilinear shape is, Area = L1W1 + L2W2 + L3W3 + ... + LnWn
To find the area of a composite rectilinear shape, you need to break it down into smaller rectangles and add up the areas of those rectangles.
Let's say you have a composite rectilinear shape that can be divided into n smaller rectangles. Each rectangle has a length and width, which we'll call L1, W1, L2, W2, L3, W3, and so on, up to Ln, Wn.
The total area of the composite rectilinear shape can be expressed as
Area = L1W1 + L2W2 + L3W3 + ... + LnWn
In other words, you find the area of each rectangle by multiplying its length by its width, and then add up all those areas to get the total area of the composite rectilinear shape
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q. a rectangular garden measures 60 feet by 25 feet. a fence completely encloses the garden. what is the length, in feet, of the fence?
Answers
The length of fence is 170feet if a rectangular garden measures 60 feet by 25 feet. Fencing is used to cover the garden from any unwanted animals.
A fence is defined as the structure that encloses an area, typically outdoors, and is usually constructed from the posts that are connected by boards, wire, rails or netting.
We know very well that the length of the fencing can be found by the perimeter of rectangle.
Perimeter of rectangle is given by =2×(length + breadth) or
=>P=2L +2W
if L is the length of rectangle and W is the width of rectnagle
Now, here we have length of rectangular garden as 60 feet and width as 25 feet
=>P=2×60+2×25
=>P=120+50
=>P=170feet
Hence, required length of fence is 170 feet.
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A spherical container has a diameter of 100 centimeters. It is filled with a liquid that costs $80 per cubic centimeter. What is the total value of the liquid in the container?
Use 3.14 for π.
Enter your answer in the box to the nearest penny. will mark brainliest
Answers
Answer:
The total value of the liquid in the container is about $41,866,666.67.
Step-by-step explanation:
A spherical container has a diameter of 100 centimeters.
It is filled with a liquid that costs $80 per cubic centimeter.
And we want to determine the total value of the liquid in the container.
We can start by finding the volume of the container.
Since the container has a diameter of 100 centimeters, its radius if 50 centimeters.
The volume of a sphere is given by:
\(\displaystyle V=\frac{4}{3}\pi r^3\)
Substitute. We will also use 3.14 for π. So:
\(\displaystyle =\frac{4}{3}(3.14)(50)^3=523333.33...\text{ cm}^3\)
(Try not to round intermediate values.)
Since each cubic centimeter costs $80, we will multiply the total volume by the cost per cubic centimeter to find the total value. Thus, the total value is:
\((523333.\overline{3})(80)\approx \$41, 866, 666.67\)
The total value of the liquid in the container is about $41,866,666.67.
PLEASE HELP ME OUT :)))
Answers
Answer:
Step-by-step explanation:
sorry not gonna do full proof for this but ill give you the general idea
goal: trying to prove <HGJ congruent <KLJ
usually for these problems you have to prove the two triangles and derive the angles from the congruent triangles.
pretend < is the angle symbol its close enough
so try to get triangle GHJ congruent to triangle LKJ
remember order is important !!
-mark up the givens on the triangle, HJ congruent to JK (given)
-J is midpt of GL. (given)
-midpoint divides a segment into 2 congruent parts. therefore GJ congruent to JL (by def midpt, ref line with given)
-can get <GHJ congruent to <LKJ because they are vertical angles (by VAT)
when you draw it, you will see that we have a side, an angle, then another side ! with congruent side, angle, side, you can use SAS congruence postulate to get triangles congruent
-ref all lines with the side angle side, and figure depending on your teacher to get triangles congruent
-derive angle <HGJ congruent <KLJ from congruent triangles
hope this helps
The population of your town is about 30,000. This is about 1/10 the population of your friend’s town about what is the population of your friend’s town?
Answers
The population of your friend's town is 300,000 if the population of your town is about 30,000.
To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.
If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.
So, the population of your friend's town is
30,000 x 10 = 300,000
Therefore, your friend's town has a population of about 300,000.
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What is the cube root?
Answers
Answer:
its 4/5
Step-by-step explanation:
cube of four is 64 and cube of 5 is 125
Answer:
4 / 5
Step-by-step explanation:
∛( 64 / 125 )
= ∛64 / ∛125
64 can be simplified as 4 x 4 x 4.
∛64
= ∛ ( 4 x 4 x 4 )
= 4
125 can be written as 5 x 5 x 5.
∛125
= ∛ ( 5 x 5 x 5 )
= 5
∛ ( 64 / 125 ) = 4 / 5
Three less than a number x is more than 15. an inequality that represents this word sentence is
Answers
Answer:
x - 3 > 15
Step-by-step explanation:
Answer both questions please
Answers
Answer:
I cannot see the x values so I cannot help with part D, but part C is y=3.50x+9.50
Step-by-step explanation:
the question states there is a fee of 9.50 for shipping costs, which is constant. this means it will be the y intercept in addition, since each shirt costs 3.50 each, the equation is y=3.50x+9.50
Proposed solutions for which any denominator equals ____ are excluded from the solution set of a rational equation.
Answers
The proposed solutions for which any denominator equals zero are excluded from the solution set of a rational equation.
To solve a rational equation, multiply each side by the equation's terms' least common denominator (L C D), then solve the resultant equation. Because a rational expression does not exist when its denominator is 0, suggested solutions with any denominator equal to 0 are eliminated from the solution set.
Extraneous solutions in rational equations are numbers that make any denominator in the original problem to be 0. Of course, when we have 0 in the denominator, we get an undefined expression. As a result, we would have to exclude any numbers that would result in the denominator being 0.
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what is the value of x in the equation 1/4x-1/8=7/8+1/2x?
A. x=-5
B. x=-4
C. x=4
D.x=5
Answers
Answer:
B) x = -4
Step-by-step explanation:
\(\frac{1}{4}x-\frac{1}{8}=\frac{7}{8}+\frac{1}{2}x\\\\\frac{1}{4}x-\frac{1}{2}x-\frac{1}{8}=\frac{7}{8}\\\\\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8}+\frac{1}{8}\\\\\frac{1}{4}x-\frac{1*2}{2*2}=\frac{7+1}{8}\\\\\frac{1}{4}x-\frac{2}{4}x=1\\\\\frac{1-2}{4}x=1\\\\\frac{-1}{4}x=1\\\\x=1*\frac{-4}{1}\\\\x=-4\)