The value of the triple integral z dV is 256π/35.
How to evaluate the triple integral z dV?To evaluate the triple integral z dV, we need to set up the integral using the given bounds for E.
We can use cylindrical coordinates to represent the bounds of E. In cylindrical coordinates, the paraboloid \(z = x^2 + y^2\) is represented as \(z = r^2\), and the plane z = 4 is still z = 4. Thus, we have:
0 ≤ θ ≤ 2π (since we're integrating over the full circle)
0 ≤ r ≤ 2 (since the paraboloid intersects the plane z = 4 at z = \(2^2 = 4\))
\(r^2\) ≤ z ≤ 4 (since \(z = r^2\) for the paraboloid)
Using this, we can set up the integral:
∫∫∫ z dV = ∫\(0^2\) ∫\(0^{2\pi}\) ∫\(r^{2^{4}}\) zr dz dθ dr
Evaluating the innermost integral first, we get:
∫\(r^{2^{4}} zr dz\) = [1/2 \(z^2\)]\(r^{2^{4}}\) =\(8r^6/2 - r^4/2 = 4r^6 - r^4/2\)
Substituting this back into the integral and evaluating the next integral:
∫∫∫ z dV = ∫\(0^2 \int 0^2\pi (4r^6 - r^4/2)\)dθ dr ∫∫∫ z dV
= ∫\(0^2 (4r^6 - r^4/2)(2\pi) dr\)
\(= 2\pi [(4/7)r^7 - (1/10)r^5]\)from 0 to 2
\(= 2\pi [(4/7)(2^7) - (1/10)(2^5)] = 256\pi/35\)
Thus, the value of the triple integral z dV is 256π/35.
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Complete the square for the following equations:
1)6x^2+3x+9
2)x^2+5x+26
3)-x^2+6x+9
The complete square of the given numbers are-
Part a: 6(x + 1/4)^2 + 69/8
Part b: (x + 5/2)^2 + 27/2
Part c: -(x + 3)^2 + 18
What is meant by completing the square?A quadratic equation is represented as a mixture of quadrilaterals was using to form a square by the method of completing the square.The idea behind this method is to find a special value that, when added both to sides of a quadratic, produces a perfect square trinomial.For the given question
Part a: 6x^2+3x+9
Tale 6 commom;
6(x^2 + x/2 + 3/2)
Add and subtract 1/16 to the equation;
6(x^2 + x/2 + 1/16 - 1/16 + 3/2)
6((x^2 + x/2 + 1/16) - 1/16 + 3/2)
6((x + 1/4)^2 + 23/16)
6(x + 1/4)^2 + 69/8
Part b: x^2+5x+26
Add and subtract 25/4 to the equation;
x^2 + 5x + 25/4 - 25/4 + 26
(x^2 + 5x + 25/4) - 25/4 + 26
(x + 5/2)^2 + 27/2
Part c: -x^2+6x+9
Taking - 1 common.
-(x^2 - 6x - 9)
Add and subtract 9 in the equation;
-(x^2 - 6x + 9 ) - 9 - 9)
-((x^2 - 6x + 9 ) - 9 - 9)
-((x + 3)^2 -18)
-(x + 3)^2 + 18
Thus, the complete square of the umber are found.
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Answer: 123
Step-by-step explanation:
what you mean bae
This histogram shows the number of peanuts per bag of trail mix. Choose ALL statements about the data that are true? A) The most common range of peanuts per bag is 30-39. B) There are more bags with 10-19 peanuts than 40-49. C) The least common range of peanuts per bag is 10-19. D) The ranges with the same number of bags are 10-19 and 40-49. E) The ranges with the same number of bags are 20-29 and 50-59.
Answer:
A), C), E)
Step-by-step explanation:
a cylindrical tank standing upright has a radius of 20cm. how fast does the water level in the tank drain
A cylindrical tank standing upright has radius 20cm. If the water is being drained at rate 25 cm³/s the tank level drops at rate 0.02 cm/s.
Recall the formula for the volume of a cylinder:
V = πr². h
Where:
r = radius of the base
h = height of the cylinder
Take the derivative with respect to t
dV/dt = πr². dh/dt
Substitute dV/dt = 25 cm³/s and r = 20 cm:
25 = π x 20² x dh/dt
dh/dt = 25 / (400π) = 0.02 cm/s
Therefore, the level of the cylindrical tank drops at rate 0.02 cm/s
Complete question:
A cylindrical tank standing upright has radius 20cm. How fast does the water level in the tank drop when the water is being drained at 25 cm³/s?
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The following two triangles are similar. Solve for x, please show all your work!!
Answer:
Step-by-step explanation:
Since 2 triangle are similar
So sides of both triangle are equal
So 72/X=12/10
X= 72x10/12
=60
X=60 is the answer
what is the slope of the line that goes through points (2, -4) and (-1, 8)
Answer:
Slope = -4
Step-by-step explanation:
Given coordinates,
→ x1 = 2, y1 = -4
→ x2 = -1, y2 = 8
Now we have to,
→ Find the required slope of the line.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Then the required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (8 - (-4))/(-1 - 2)
→ m = (8 + 4)/-3
→ m = 12/(-3)
→ m = -12/3
→ [ m = -4 ]
Therefore, the value of m is -4.
Hello !
Answer:
\(\Large \boxed{\sf Slope =-4}\)
Step-by-step explanation:
The slope of a line is given by the following formula : \(\sf m=\dfrac{y_B-y_A}{x_B-x_A}\) where \(\sf x_A\) and \(\sf y_A\) are the coordinates of A (same for B).
Given :
\(\sf A(2,-4)\)\(\sf B(-1,8)\)Let's calculate the slope with the previous formula :
\(\sf m=\frac{8-(-4)}{-1-2} \\\sf m=\frac{8+4}{-3}\\ \sf m=-\frac{12}{3} \\\boxed{\sf m=-4}\)
Have a nice day ;)
devide 240g in to the ratio 5:3:4
How many metres are there in two and three-quarter kilometres?
Answer:
2 3/4 kilometers is equal to 2,750 meters
Step-by-step explanation:
Answer:
2 3/4 kilometers is equal to 2,750 meters
Step-by-step explanation:
Alice and Bob have just met, and wonder whether they have a mutual friend. Each has 50 friends, out of 1000 other people who live in their town. They think that its unlikely that they have a friend in common, saying each of us is only friends with 5% of the people here, so it would be very unlikely that our two 5%s overlap. Assume that Alices 50 friends are a random sample of the 1000 people (equally likely to be any 50 of the 1000), and similarly for Bob. Also assume that knowing who Alices friends are gives no information about who Bobs friends are.
(a) Compute the expected number of mutual friends Alice and Bob have.
(b) Let X be the number of mutual friends they have. Find the PMF of X.
(c) Is the distribution of X one of the important distributions we have looked at? If so, which?
The expected number of mutual friends Alice and Bob have is 2.5.
In the scenario described, Alice and Bob each have 50 friends out of 1000 people in their town. They believe that the probability of having a mutual friend is low since each of them is only friends with 5% of the population. To calculate the expected number of mutual friends, we can consider it as a matching problem.
Alice's 50 friends can be thought of as a set of 50 randomly selected people out of the 1000, and similarly for Bob's friends. The probability of any given person being a mutual friend of Alice and Bob is the probability that the person is in both Alice's and Bob's set of friends.
Since the selection of friends for Alice and Bob is independent, the probability of a person being a mutual friend is the product of the probability that the person is in Alice's set (5%) and the probability that the person is in Bob's set (5%). Therefore, the expected number of mutual friends is \(0.05 * 0.05 * 1000 = 2.5\).
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Gloria had a rectangular garden plot last year with an area of 60 square feet. This year, Gloria's plot is 1 foot wider and 3 feet shorter than last year's garden, but it has the same area. What were the dimensions of the garden last year?
The dimensions of the garden last year were 15 feet by 4 feet.
How to solve for the dimensionLet the length of the garden last year be L feet, and the width be W feet. We are given that the area of the garden last year was 60 square feet:
L * W = 60
This year, the garden is 1 foot wider and 3 feet shorter than last year's garden:
Length: L - 3
Width: W + 1
The area of the garden remains the same:
(L - 3) * (W + 1) = 60
Now we have two equations with two variables:
L * W = 60
(L - 3) * (W + 1) = 60
We can solve this system of equations using substitution or elimination. Let's use substitution. From equation 1, we can write L as:
L = 60 / W
Now substitute this expression for L in equation 2:
(60 / W - 3) * (W + 1) = 60
Simplify and solve for W:
60 + 60 / W - 3W - 3 = 60
Combine like terms:
60 / W - 3W = 3
Multiply both sides by W to eliminate the fraction:
60 - 3W² = 3W
Move all terms to one side:
3W² + 3W - 60 = 0
Divide the equation by 3:
W² + W - 20 = 0
Factor the quadratic equation:
(W + 5)(W - 4) = 0
The possible values for W are -5 and 4. However, since width cannot be negative, W must be 4 feet. Now, use the expression for L to find the length:
L = 60 / W = 60 / 4 = 15 feet
So, the dimensions of the garden last year were 15 feet by 4 feet.
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what is the value of 130 kph in mph
To convert kilometers per hour (kph) to miles per hour (mph), we use the following formula: mph = kph x 0.621371. This is because there are 0.621371 miles in a kilometer.
To calculate the value of 130 kph in mph, we can simply plug the value into the formula: mph = 130 x 0.621371 = 80.78 mph. Therefore, the value of 130 kph in mph is 80.78 mph. To further understand how this conversion works, we can break down the calculation into its basic components. First, we divide 130 by 1. That gives us 130. Then, we multiply 130 by 0.621371, which gives us the result of 80.78. Therefore, the value of 130 kph in mph is 80.78 mph. The above formula and calculation can be used to convert any value from kph to mph. All we need to do is plug the kph value into the formula and we will get the equivalent mph value. It is important to note that the conversion from kph to mph is not exact, as there are slight variations in the exact value of a kilometer. However, this formula provides a good approximation and is accurate enough for most purposes.
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Straight leg jeans are 20% off at Kohls this week. How much will you pay for 4 pairs if the regular price is $59.99?
A cellphone company charges you $17 a month plus $0.25 for each text message you send. The total bill last month was $45.50. Which of the following equations could you use to figure out how many text messages you sent?
17x - 0.25 = 45.50
17x + 0.25 = 45.50
17 - 0.25x = 45.50
17 + 0.25x = 45.50
HURRRYYY PLZZZZ
Answer:
last one
Step-by-step explanation:
Please Answer!!!
Answer is 2,4, and 6
Solve for x, Round to the nearest tenth.
Answer:
2= 18.88 4=24.752 . 6=13.74713
Step-by-step explanation:
Solve 3^x + 6 = 3^4.
−2
4
6
10
Answer:
The answer is 4
Step-by-step explanation:
x
=
ln
(
75
)
ln
(
3
)
Decimal Form:
x
=
3.92994704
…
Answer: Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
x
=
ln
(
75
)
ln
(
3
)
Decimal Form:
x
=
3.92994704
…
Step-by-step explanation:
1^2/10 as a negative power of 10
Tony is solving the equation 4x = 12x + 20 for x. Tony uses the multiplicative property of equality to rewrite the equation as x = 3x + 20. Which statement correctly explains whether
A Tony used the property correctly? Tony used the property correctly because he multiplied one term on each side of the equals sign by 1/4
B Tony did not use the property correctly because he should have multiplied both sides of the equals sign by 1/12 not 1/4
C Tony did not use the property correctly because he did not multiply every term on both sides of the equals sign by 1/4
D Tony used the property correctly because he multiplied every term containing x by 1/4
Answer:
C)
Step-by-step explanation:
The correct answer is C: Tony did not use the property correctly because he did not multiply every term on both sides of the equals sign by 1/4.
To solve the equation 4x = 12x + 20, Tony used the multiplicative property of equality but made an error in the application. The correct approach would be to multiply every term on both sides of the equals sign by the reciprocal of the coefficient of x, which is 1/4 in this case.
However, Tony only multiplied one term on each side by 1/4, resulting in equation x = 3x + 20. This action is incorrect because it does not apply the property to every term containing x. To solve the equation correctly, Tony should have multiplied both sides by 1/4, resulting in x/4 = (3x + 20)/4.
The ________reauthoization of the Elementary and Secondary Act, that included a Title 1, the government's flagship aid program for disadvantage students.
The reauthorization of the Elementary and Secondary Act, that included a Title 1, the government's flagship aid program for disadvantage students.
The Every Student Succeeds Act (ESSA) is the reauthorization of the Elementary and Secondary Education Act (ESEA) that included Title I, the government's flagship aid program for disadvantaged students.
ESSA was signed into law by President Barack Obama in 2015, replacing the previous iteration of the law known as the No Child Left Behind Act (NCLB). It aimed to provide more flexibility to states in setting education policies while still ensuring accountability and support for students, particularly those from low-income backgrounds.
Title I of ESSA focuses on providing financial assistance to schools with high percentages of students from low-income families. The program aims to bridge the achievement gap by offering additional resources and services to disadvantaged students to enhance their educational opportunities. Title I funds can be used for various purposes, such as hiring highly qualified teachers, providing tutoring or intervention programs, and implementing instructional strategies to improve student achievement.
By including Title I in ESSA, the federal government reaffirmed its commitment to addressing educational inequities and supporting disadvantaged students. The reauthorization of the Elementary and Secondary Education Act through ESSA ensured that funding and resources continued to be allocated to schools and districts serving students with the greatest needs.
Correct Question :
The ________ of the Elementary and Secondary Act, that included a Title 1, the government's flagship aid program for disadvantage students.
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Find the average rate of change of f(x) = x^2–5x+1 from x = 2 to x= 5.
Simplify your answer as much as possible.
Answer:
12
Step-by-step explanation:
it should be the answer if not messge me so we can work it out
What is the period of the function given?
pls
Answer:
2. ☑ A \(\displaystyle f(x) = tan\:\frac{1}{2}x\)
☐ B \(\displaystyle f(x) = tan\:2x\)
☐ C x = \(\displaystyle 2tan\:x\)
1. ☐ A \(\displaystyle \frac{\pi}{2}\)
☐ B \(\displaystyle \pi\)
☑ C \(\displaystyle 2\pi\)
Explanation:
\(\displaystyle \boxed{f(x) = -cot\:(\frac{1}{2}x - \frac{\pi}{2})} \\ \\ y = Acot(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pi} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{1}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A\)
OR
\(\displaystyle y = Atan(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{\pi}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\pi}{\frac{1}{2}} \\ Amplitude \hookrightarrow N/A\)
Here is all the information you will need. Now, what you need to know is that ALL tangent, secant, cosecant, and cotangent functions have NO amplitudes. Also, keep in mind that although this IS the tangent graph, if you plan on writing your equation as a function of cotangent, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = cot\:\frac{1}{2}x,\) in which you need to replase "tangent" with "cotangent", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the tangent graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cotangent graph [photograph on the right] is shifted \(\displaystyle \pi\:units\) to the left, which means that in order to match the tangent graph [photograph on the left], we need to shift the graph FORWARD \(\displaystyle \pi\:units,\) which means the C-term will be positive, and perfourming your calculations, you will arrive at \(\displaystyle \boxed{\pi} = \frac{\frac{\pi}{2}}{\frac{1}{2}},\) but we are NOT YET DONE. Although we shifted the graph back into position, remember, cotangent is graphed in REVERCE, so we need to insert a negative in front of the amplitude term, and with that, the cotangent graph of the tangent graph, accourding to the horisontal shift, is \(\displaystyle y = -cot\:(\frac{1}{2}x - \frac{\pi}{2}).\) Now, with all that being said, we can move forward. To find the period in this case, you need to take a look at the distanse between each vertical asymptote. Now, accourding to this graph, the vertical asymptotes are \(\displaystyle -\pi = x\:and\:\pi = x.\) From here, you will then find the distanse between these asymptotes by simply perfourming the operation of Deduction, and doing that will give you \(\displaystyle \boxed{2\pi} = \pi + \pi.\) So, the period of this function is \(\displaystyle 2\pi.\) Now, you will instantly get the jist of the horisontal shift by looking at the above formula. Just keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to what is given to you inside those parentheses. Finally, the midline is the centre of your graph, also known as the vertical shift, which in this case is at \(\displaystyle y = 0.\)
Well, that just about wraps it up. Now that everything has been explained, you should understand it better. If you still have questions, do not hesitate to comment any you have.
I am delighted to assist you at any time.
function or not a function
Answer:
non functional
Step-by-step explanation:
since the line that is graphed goes straight up and down it doesn’t pass the function test because multiple points are plotted on the same line
what is the radius of a right circular cylinder with a volume of 12 in3 if it has a minimum surface area?
The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.
Define right circular cylinder?A cylinder with two circular bases and a line connecting their centers that is perpendicular to both bases.Volume of the right circular cylinder be;
v(c) = 12 in³ = π*r²*h
In which, h is the height of the cylinder,
Then , h = 12 / π*r²
Surface area of a right circular cylinder is:
S = area of base and top + lateral area
S(A) = 2*π*r² + 2*π*r*h ....eq 1
Put value of 'h' in equation (1)
S(r) = 2*π*r² + 2*π*r* ( 12 / π*r²)
S(r) = 2*π*r² + 24 /r
Differentiate both sides,
S´(r) = 4*π*r - 24 /r²
Put , S´(r) = 0 to get the critical points.
4*π*r - 24 /r² = 0
π*r - 6/r² = 0
π*r³ - 6 = 0
r³ = 1,91
r = 1,248 in
Check for the minimum surface area for r = 1,248 in.
Find the second derivative,
S´´(r) = 4*π + 48/r³
S´´(r) will always be positive.
Thus, the minimum surface area S is for r = 1,248 in.
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if 11600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
The compound interest after 5 years is $7,081.916.
Compound interest:
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Here we have to find the interest earned after 5 years.
Data given:
Principle (P) = $11600
rate(r) = 10%
time(t) = 5 years.
Formula to find compound interest:
CI = P( 1 + r/100\()^{t}\) - P
Now put the values in the formula.
CI = 11600 ( 1 + 10/100\()^{5}\) - 11600
= 18681.916 - 11600
= 7081.916
Therefore the compound interest is $7081.916.
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Form and solve an equation for x.
6x +40
Х
3x + 100
Answer:
x = 22
Step-by-step explanation:
The sum of the angles round a point is 360°
Sum the given angles and equate to 360
x + 6x + 40 + 3x + 100 = 360
10x + 140 = 360 ( subtract 140 from both sides )
10x = 220 ( divide both sides by 10 )
x = 22
For the linear model, y = -67.9x +679, the distance, in miles y, is a function of time, x, in hours. Use the model to calculate the total distance, in miles, at x = 2 hours.
Answer:
543.2 miles
Step-by-step explanation:
Input the given value of x into the equation and solve for y:
y = -67.9x + 679
y = -67.9(2) + 679
y = -135.8 + 679
y = 543.2
The total distance in miles after 2 hours is 543.2 miles.
An object with a mass of 5.0kg accelerates 8.0m/s2 when an unknown force is applied to what is the force?
Answer:
The correct amount of force i believe is
f= 40 newton
i got the answer by using the formula below
force = mass x acceleration
f=5kg *8.0 m/s^2
Step-by-step explanation:
Each segment of an oil pipeline is 30 feet long. If a segment of the pipeline leaks, repair workers reach the leak by opening the pipeline at the nearest end of the segment. The probability of a leak is distributed continuously and uniformly through each segment.
Required:
a. How far can repair workers expect to travel to reach a leak?
b. There is a 0.30 probability repair workers will travel between three feet and how many feet to reach a leak?
a) There is a 0.30 probability repair workers will travel between three feet and twelve feet to reach a leak.
b) The repair workers can expect to travel 15 feet to reach a leak because the leak can occur anywhere on the 30 feet long segment.
(a) Since each segment of an oil pipeline is 30 feet long. Hence, repair workers can expect to travel 15 feet to reach a leak because the leak can occur anywhere on the 30 feet long segment.
(b) Let X be the distance from one end of the pipe segment to the leak, then X follows a uniform distribution from 0 to 30.
Therefore, the PDF of X is given by `f(x) = 1/30` for `0 ≤ x ≤ 30`Now, P(3 ≤ X ≤ x) = 0.3
Since the distribution is uniform, the area of the shaded region is `0.3 × 30 = 9` square feet.
So, we have: `∫[3, x] f(t)
dt = 9/30` or `∫[3, x] 1/30
dt = 9/30`
Now, `∫[3, x] 1/30 dt = [t/30]_3^x = (x - 3)/30`
Hence, we can write as:`(x - 3)/30 = 0.3`
Solving for x, we get:x - 3 = 9 => x = 12 feet
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What is the approximate total percent off when you buy something at "An extra 20% off of 40% off"?
Please help me
Answer:
48%
Step-by-step explanation:
let's say the initial price of an item is $100
if you take 40% off then you pay only $60
now if you take 20% off 60 you pay $48
$48 is 48% of 100
Cameron challenges you to race on the first turn you run off the Course and your car strikes a large bale of hay. your car still produces 5000 Newtons of force but now it accelerates at 2 m\s2. what is the mass of your car now that the bail of hay is stuck to it?
F= ?
M= ?
A = 2m /s2
Help asap please I’ll give brainlyest A set of equations is given below:
Equation C: y = 4x + 8
Equation D: y = 4x + 2
Which of the following best describes the solution to the given set of equations?
O No solution
One solution
OTwo solutions
O Infinitely many solutions
Answer:
No solutions.
Step-by-step explanation:
Easy way to spot is to take the 4x term to the LHS.
\(y-4x = 8\\y-4x = 2\)
You're required to find a quantity that is at the same time equal to both 8 and 2, which is obviously impossible.
There are two ways to figure this equation out.
Answer: O No solution
Way One - Graphing
We can graph the two equations. Points of intersection represent a solution to the set.
-> See attached.
Since there are no points of intersection, the answer is "O No solution"
Way Two - Analyzing the Equations
We can see that both of these equations have a slope of 4. We then can set them both equal to the y-intercept to see if they will have solutions.
y = 4x + 8
-> y - 4x = 8
y = 4x + 2
-> y - 4x = 2
Because 8 ≠ 2, but y - 4x = y - 4x, the answer is "O No solution"
3½ • 1⅘
You get points for answering this
Answer:
6 3/10
Step-by-step explanation:
3 1/2 = 7/2
1 4/5 = 9/5
7/2 x 9/5 = 7x9/2x5 = 63/10 = 6 3/10