The statement "If A is non-diagonalizable, then A has a square root" is false. This can be disproved by considering a non-diagonalizable matrix with a single linearly independent eigenvector. Such a matrix does not have a square root.
The statement "If A is non-diagonalizable, then A has a square root" is false. There exist non-diagonalizable matrices that do not have a square root.
To disprove the statement, we can provide a counterexample. Consider the following 2x2 matrix:
A = [[0, 1], [0, 0]]
To determine if A is diagonalizable, we need to find its eigenvalues and corresponding eigenvectors. The eigenvalues can be obtained by solving the characteristic equation:
det(A - λI) = 0,
where λ is the eigenvalue and I is the identity matrix. For matrix A, the characteristic equation becomes:
det([[0-λ, 1], [0, 0-λ]]) = 0
-λ * (-λ) - (1 * 0) = 0
λ^2 = 0
This shows that the only eigenvalue of A is λ = 0. To find the eigenvectors, we solve the homogeneous system of equations:
(A - λI) * v = 0,
where v is the eigenvector corresponding to eigenvalue λ. For A = [[0, 1], [0, 0]] and λ = 0, the homogeneous system becomes:
[[0, 1], [0, 0]] * [x, y] = [0, 0]
0 * x + 1 * y = 0
y = 0
From the second equation, we can see that the eigenvector [x, y] can have any value for x. Therefore, there is only one linearly independent eigenvector [1, 0].
Since there is only one linearly independent eigenvector, the matrix A is non-diagonalizable. However, A does not have a square root.
To see this, assume that A has a square root B such that B² = A. Let's consider B as:
B = [[a, b], [c, d]]
Then, we have:
B² = [[a, b], [c, d]] * [[a, b], [c, d]]
= [[a² + bc, ab + bd], [ac + cd, bc + d²]]
For B² to equal A, we must have:
a² + bc = 0 (Equation 1)
ab + bd = 1 (Equation 2)
ac + cd = 0 (Equation 3)
bc + d² = 0 (Equation 4)
From Equation 3, we have:
c(a + d) = 0
Since A is positive definite, its eigenvalues must be positive. This implies that the eigenvalues of B are also positive. Hence, neither a nor d can be zero. Therefore, c must be zero. However, this leads to a contradiction because Equation 4 requires bc + d² = 0, but since c = 0, this implies that d² = 0, which means d must be zero. But this contradicts our assumption that d cannot be zero.
Hence, there does not exist a matrix B that satisfies B² = A, and therefore A does not have a square root.
Therefore, the statement "If A is non-diagonalizable, then A has a square root" is false.
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what is the solution of x equals 2 + sqrt x - 2
a.) x=2
b.)x=3
c.)x=2 or x=3
d.) no solution
Answer:
x = 2 or x = 3
Step-by-step explanation:
x = 2 + sqrt(x - 2)
x - 2 = sqrt(x - 2) You could divide both sides by sqrt(x - 2)
sqrt(x - 2) = 1 Square both sides
x - 2 = 1 Add 2 to both sides
x = 3
There is a second way.
x - 2 = sqrt(x - 2) Square
x^2 - 4x + 4 = x - 2 Transfer x - 2 to the left
x^2 - 5x + 6 = 0 Factor
(x - 2)(x-3) = 0 Find the roots.
x - 2 = 0
x = 2
x - 3 = 0
x = 3
We have to check both results.
x = 2 + sqrt(x - 2)
2 = 2 + sqrt(2 -2)
2 = 2 + 0
2 = 2 This seems to work.
x = 2 + sqrt(x - 2)
3 = 2 + sqrt(3 - 2)
3 = 2 + sqrt(1)
3 = 2 + 1
3 = 3 And this works.
Help is much needed pls. I can only put 15 points.
Answer:
9.2
Step-by-step explanation:
first i added 5 + 3 = 8
then i did 1 1/5 + 8=9 1/5
Denira needs to run 9 4/10 miles this week to meet her goal for her training plan. So far this week she has run 3 1/2 miles on Monday and 2 1/2 miles on Tuesday. How many more miles does she need to run this week in order to meet her goal
Answer:
3 2/5
Step-by-step explanation:
Add the distance she already ran, and subtract the sum from the total she needs to run.
Add two distances she ran:
3 1/2 + 2 1/2 = 3 + 2 + 1/2 + 1/2 = 5 + 1 = 6
Subtract sum from total:
9 4/10 - 6 = 3 4/10 = 3 2/5
Answer:
She needs to run 3 4/10 more miles
Step-by-step explanation:
If you add the amount she ran on Monday and the amount she ran on Tuesday you get 6 miles then subtract the 6 miles minus 9 4/10 you will get 3 4/10.
Eleven increased by three times a number equals 68) Write an equation for this situation and then find the
number
Answer:
11+3x=68
x=19
Step-by-step explanation:
11+3x=68 is your equation.
subtract 11 from both side to get 3x alone
3x=68-11
3x=57
divide 3 from both sides to get x alone
x=57/3
x=19
19 is your number.
f(1) = -6
f(2) = -4
f(n) = f(n − 2) + f(n − 1)
f(3) =
Answer:
-10
Step-by-step explanation:
f(n)= f(n-2)+f(n-1)
• Put n = 3
=> f(3) = f(3-2) + f(3-2)
=> f(3) = f(1) + f(2)
=> f(3) = -6 + -4
=> f(3) = -10
Answer:
it in a file here
Step-by-step explanation:
xycba.com/file
How many edges does the complete bipartite graph K_(4, 9) have? Your answer
The number of edges in the complete bipartite graph is 36
How to determine the number of edges in the complete bipartite graphFrom the question, we have the following parameters that can be used in our computation:
K = (4, 9)
The above means that
The vertices in the sets of the bipartite graph are
Set 1 = 4
Set 2 = 9
The number of edges in the complete bipartite graph is then calculated as
Vertices = Set 1 * Set 2
So, we have
Vertices = 4 * 9
Evaluate
Vertices = 36
Hence, there are 36 edges in the bipartite graph
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PLS HELP ME ASAP PLS PLS PSL
Answer:
25
Step-by-step explanation:
Finding slope..
Photo included^
Answer:
slope=2/3
y intercept=4
Step-by-step explanation:
Solve the triangle using the law of cosines
edg2021
How to write the equation for ¨The quotient of x and three increased by 12 is 20. What is x?
Answer:
x/3 + 12 = 20
Step-by-step explanation:
Alright here is a repost
Answer:
50 degrees
Step-by-step explanation:
180-130=50
Answer:
The answer was already given(50°), but I can explain it further.
Step-by-step explanation:
These are supplementary angles, two angles that, together, make 180 degrees.
We know the angle of one of them, 130°, and in order to find the other one, x, we have to subtract what the entire this equals, 180°:
180° - 130° = x
50° = x
x = 50°
I hope this helped you, even if this was two hours ago.
Viking Voyager specializes in the design and production of replica Viking boats. On January 1, 2021, the company issues $2,900,000 of 9% bonds, due in 20 years, with interest payable semiannually on June 30 and December 31 each year.
Required:
1. If the market interest rate is 9%, the bonds will issue at $2,900,000. Record the bond issue on January 1, 2021, and the first two semiannual interest payments on June 30, 2021, and December 31, 2021. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field.)
2. If the market interest rate is 10%, the bonds will issue at $2,651,193. Record the bond issue on January 1, 2021, and the first two semiannual interest payments on June 30, 2021, and December 31, 2021. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field. Round your answers to the nearest dollar amount.)
3. If the market interest rate is 8%, the bonds will issue at $3,186,995. Record the bond issue on January 1, 2021, and the first two semiannual interest payments on June 30, 2021, and December 31, 2021. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field. Round your answers to the nearest dollar amount.)
The bond issue and interest payments are recorded differently based on the market interest rate.
How to find the bond issue and interest payments recorded based on the market interest rate?The recording of bond issue and interest payments depends on the market interest rate. When the market interest rate is equal to the stated rate of 9%, the bonds will issue at their face value of $2,900,000.
On January 1, 2021, the company would debit Cash for $2,900,000 and credit Bonds Payable for $2,900,000 to record the bond issue.
The interest payments on June 30, 2021, and December 31, 2021, would be recorded by debiting Interest Expense for $130,500 ([$2,900,000 * 9%]/2) and crediting Cash for $130,500.
However, when the market interest rate is 10% or 8%, the bonds will issue at a discount or premium, respectively. If the market interest rate is 10%, the bonds will issue at $2,651,193 (rounded).
In this case, the bond issue on January 1, 2021, would be recorded by debiting Cash for $2,651,193 and crediting Discount on Bonds Payable for $248,807 ($2,900,000 - $2,651,193).
The interest payments on June 30, 2021, and December 31, 2021, would be recorded as mentioned earlier.
Conversely, if the market interest rate is 8%, the bonds will issue at $3,186,995 (rounded).
The bond issue on January 1, 2021, would be recorded by debiting Cash for $3,186,995 and crediting Premium on Bonds Payable for $286,995 ($3,186,995 - $2,900,000).
The interest payments on June 30, 2021, and December 31, 2021, would be recorded accordingly.
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Determine the are length on a circle of radius 7 and an included angle of 4.5 radians.
Answer:
The arc length of a circle is 31.5.
Step-by-step explanation:
The arc length can be found as follows:
[tex] arc = r\theta [/tex]
Where:
arc: is the length of the arc of the circle
r: is the radius = 7
θ: is the angle = 4.5 rad
[tex] arc = r\theta = 7*4.5 = 31.5 [/tex]
Therefore, the arc length of a circle is 31.5.
I hope it helps you!
PLEASE HELP FAST WILL GIVE BRAINLIEST
Answer:
QT=8 VQ=17 this is what i came up with because i myself have ur question and i don't know what it is?
If 23 cubic meters of water are poured into a conical vessel, it reaches a depth of 12 cm. how much water must be added so that the length reaches 18 cm.?
Let V be the volume of the conical vessel and r and h be the radius and height of the vessel respectively. Given that: V = (1/3)πr²hLet V' be the volume of the water that is added to the vessel. The volume of the water in the vessel with a depth of 12 cm is given by: V₁ = (1/3)πr₁²h₁where h₁ = 12 cm. We know that 23 cubic meters of water are poured into the vessel, which is equivalent to 23,000 liters or 23,000,000 cubic centimeters.
Thus:23,000,000 = (1/3)πr₁²(12)Simplifying and solving for r₁, we get: r₁ = 210.05 cm Using similar triangles, we know that :r/h = r₁/h₁ where r is the radius of the water surface when the depth is 18 cm. Thus: r/h = 210.05/12Therefore:r = (210.05/12)·18 = 3,152.5/6 ≈ 525.4 cm The new volume of the water with a depth of 18 cm is given by: V₂ = (1/3)πr²h₂where h₂ = 18 cm.
Therefore: V₂ = (1/3)π(525.4)²(18) ≈ 21,154,116.9 cubic centimeters The additional volume of water needed is therefore: V' = V₂ - V₁ = 21,154,116.9 - 23,000,000 ≈ -1,845,883.1 cubic centimeters.
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What is the range and domain of y = (x - 4)(x - 6)? I have already sketched out the graph and parabola.
Answer: The domain of the function y = (x - 4)(x - 6) is all real numbers, since there are no restrictions on the values that x can take. The range of the function is also all real numbers.
To see why this is the case, we can rewrite the function in standard form by expanding the product: y = (x - 4)(x - 6) = x^2 - 10x + 24. This is a quadratic function with a positive leading coefficient, so its graph is a parabola that opens upwards. The vertex of the parabola is at x = -b/2a = 10/2 = 5, and y = (5 - 4)(5 - 6) = -1. Since the parabola opens upwards, it extends infinitely upwards from its minimum value at the vertex. Therefore, the range of the function is all real numbers greater than or equal to -1.
So, the domain of y = (x - 4)(x - 6) is all real numbers and its range is all real numbers greater than or equal to -1.
Step-by-step explanation:
Answer:
[tex]y = {x}^{2} - 10x + 24[/tex]
Domain: all real numbers
Range: all real numbers > -1
Determine L {f(t)} for f (t) = sin (V24) + te- T sin (T) dr. S Ts +1 Fully explain your reasoning to receive full credit. Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f (t)?
The Laplace transform of [tex][f(t) = \sin{\sqrt{24}} + te^{-t}\sin{t} \implies L{f(t)} = \frac{\sqrt{24}}{s^2 + 24} + \frac{1}{(s + 1)^2 + 1}][/tex] . However, F(s) = 1 + 1 cannot be the Laplace transform of any valid function f(t) because it does not satisfy the properties and rules of Laplace transforms.
To determine the Laplace transform of the function [tex]\[f(t) = \sin{\sqrt{24}} + te^{-t}\sin{t}\][/tex], we need to apply the properties and formulas of Laplace transforms.
1. Laplace Transform of sin(√24):
The Laplace transform of sin(at) is given by [tex]\[F(s) = \frac{a}{s^2 + a^2}\][/tex]. In this case, a = √24.
So, the Laplace transform of [tex]\[\sin{\sqrt{24}} \implies F(s) = \frac{\sqrt{24}}{s^2 + 24}\][/tex].
2. Laplace Transform of [tex]\[te^{-t}\sin{t}\][/tex]:
To find the Laplace transform of this term, we can use the product rule and the Laplace transform of each component.
The Laplace transform of t is given by [tex]\[F(s) = \frac{1}{s^2}\][/tex], and the Laplace transform of e^(-t)sin(t) can be found using the table of Laplace transforms.
Using the table, the Laplace transform of [tex]\begin{equation}\mathcal{L}(e^{-t}\sin(t)) = \frac{1}{(s + 1)^2 + 1}[/tex].
3. Adding the Laplace transforms:
Since the Laplace transform is a linear operator, we can add the individual Laplace transforms of [tex]sin(\sqrt{24})[/tex] and [tex]te^{-t}\sin(t)[/tex] to obtain the Laplace transform of the whole function f(t).
Therefore, [tex]L\{f(t)\} = \frac{\sqrt{24}}{s^2 + 24} + \frac{1}{(s + 1)^2} + 1[/tex]
Now, to address the second part of the question:
Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f(t)?
No, it is not possible for F(s) = 1 + 1 to be the Laplace transform of a valid function f(t). The Laplace transform is a mathematical operation that converts a function of time (f(t)) into a function of the complex variable s (F(s)). The Laplace transform must follow specific properties and rules, and it is not possible for F(s) = 1 + 1 to satisfy these properties and correspond to a valid function f(t).
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The Laplace transform of
L {f(t)} for f (t) = sin (V24) + te- T sin (T) => Lf(t) = √24/s²+24 + 1/(s+1)²+1 .
However, F(s) = 1 + 1 cannot be the Laplace transform of any valid function f(t) because it does not satisfy the properties and rules of Laplace transforms.
Here, we have,
To determine the Laplace transform of the function
f (t) = sin (V24) + te- T sin (T) , we need to apply the properties and formulas of Laplace transforms.
1. Laplace Transform of sin(√24):
The Laplace transform of sin(at) is given by F(s)= a/s²+a².
In this case, a = √24.
So, the Laplace transform of sin(√24) => F(s)= √24/s²+24 .
2. Laplace Transform of te- T sin (T):
To find the Laplace transform of this term, we can use the product rule and the Laplace transform of each component.
The Laplace transform of t is given by F(s)=1/s², and the Laplace transform of e^(-t)sin(t) can be found using the table of Laplace transforms.
Using the table, the Laplace transform of L(e^(-t)sin(t)) = 1/(s+1)²+1.
3. Adding the Laplace transforms:
Since the Laplace transform is a linear operator, we can add the individual Laplace transforms ofsin(√24) and e^(-t)sin(t) to obtain the Laplace transform of the whole function f(t).
Therefore,
Lf(t) = √24/s²+24 + 1/(s+1)²+1
Now, to address the second part of the question:
Is it possible for F(s) = 1 + 1 to be the Laplace transform of some function f(t)?
No, it is not possible for F(s) = 1 + 1 to be the Laplace transform of a valid function f(t). The Laplace transform is a mathematical operation that converts a function of time (f(t)) into a function of the complex variable s (F(s)). The Laplace transform must follow specific properties and rules, and it is not possible for F(s) = 1 + 1 to satisfy these properties and correspond to a valid function f(t).
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Maria is decorating her school's cafeteria for the end- of- year dance. The dimensions of the room are labelled below. What is the smallest length of streamer that will go around the entire perimeter of the room? Round your answer to the nearest foot.
Answer:
59 feets
Step-by-step explanation:
The length of bottom base = (8 + 2 + 2) = 12
Circumference of semicircle : 2πr/2 ; r = 4/2 = 2
Circumference of semicircle = π * 2 = 6.28
Length of streamer that will go around the entire perimeter :
From the figure attached :
Circumference of semicircle = 6.28
6.28 + 6 + 2(down) + 2(right) + 8(down) + 2(left) + 2(up) + 2(left) + 2(down) + 8(left) + 10
6.28 + 6 + 2 + 2 + 8 + 2 + 2 + 2 + 2 + 8 + 10 = 50.28 feets = 50 ft (nearest whole number)
HELP HELP PLS I NEED TO DO THIS BY TONIGHT PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Question:What percent of the time did Trent spend at least 80 minutes on homework?
Answer:
25%
Step-by-step explanation:
If You Have NO EXPLANATION Don't ANSWER
Answer:
C
Step-by-step explanation:
y=5x reads "y equals (5 times x)", which we can rephrase to "the value of y is 5 times the value of x"
y=x+5 reads "y equals (x plus 5)", which we can rephrase to "the value of y is 5 more than the value of x".
Ergo, answer C is what we're looking for.
Answer: C
Step-by-step explanation:
in y=5x, we can see a 5 placed in front of x. If there is no addition, subtraction, or division sign between a number and a variable, it always means it's multiplication.
We know now that this is 5 times x.
In y=x+5, we see that 5 is being added to x. Therefore, y is 5 more than x.
So there you have it.
Someone help me out plzz
Answer:
with what? You forget to attach the problem lol
Step-by-step explanation:
Answer: What is the question you need help with??
Step-by-step explanation:
what is the measure of ∠x?
Answer:
83°
Step-by-step explanation:
WZ is a straight line. Angles at a straight line add up to 180°.
180 - 97 =83°
help pleaseee, no links!
Which choice does not represent a set of endpoints that create a horizontal line segment? A (1, 13) and (14, 13) B (-10, 0) and (-10, 1) C (3, -20) and (-11, -20) D (16, 2) and (-2, 2)
Answer:
Step-by-step explanation:
horizontal line segment: B (-10, 0) and (-10, 1)
What is the equation, in slope-intercept form, of the line that contains the points (3, -4) and (5, -6)? A. y = -x - 1 B. y = -x + 1 C. y = x - 1 D. y = x + 1
Answer:
Hi! The answer to your question is A. [tex]y=-x-1[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☁Brainliest is greatly appreciated!☁
Hope this helps!!
- Brooklynn Deka
Answer:
a
Step-by-step explanation:
A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3 Find P81, which separates the bottom 81% from the top 19%.
Value of x corresponding to P81 is 59.06.
A normal distribution has a mean u = 67.3 and a standard deviation of o=9.3.
The task is to find P81, which separates the bottom 81% from the top 19%.
For any normally distributed variable z with mean u and standard deviation o, the cumulative distribution function is defined as the probability of a standard normal variable being less than or equal to z.
A standard normal distribution has a mean of 0 and a standard deviation of 1.
That is, the variable z can be calculated as: z = (x - u) / o
The value P(z < z0) can be read off a standard normal table for any value z0.
As the normal distribution is symmetric, we can use the fact that P(z < -z0) = 1 - P(z < z0).
We now calculate z as follows: z0 = (P81 + 1) / 2 = 0.9051
From a standard normal table, we can see that P(z < 0.9051) = 0.8186.
Therefore, P(z < -0.9051) = 1 - P(z < 0.9051) = 0.1814.
Now we calculate the corresponding value of x:
z = (x - u) / o-0.9051 = (x - 67.3) / 9.3x = 59.06
Therefore, P81 corresponds to the value x = 59.06.
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Malik and Nora are playing a video game.
Malik starts with m points and Nora starts n points.
Then Malik gets 150 more points, while Nora loses 50 points.
Finally, Nora gets a bonus and her score is doubled.
Nora now has 50 more points than Malik.
Enter an equation that represents the relationship between m and n
given the information above.
Answer:
Equation below
Step-by-step explanation:
An equation that represents the relationship between m and n is 2(n - 150) - (m + 150) = 50 .
The expression that represents Malik's score after he gets 150 points = m + 150
The expression that represents Nora's score after she loses 50 points = n - 150
Nora's score after her score is doubled = 2(n - 150)
The difference between Nora and Malik's score is 50. This can be represented as: 2(n - 150) - (m + 150) = 50
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Find the lengths of the curves in y = tan x, -7/3 = x < 0
The length of the curve y = tan x, -7/3 ≤ x < 0 is approximately 4.481 units.
To calculate the length of the curve, we can use the arc length formula. For a function y = f(x) on the interval [a, b], the arc length is given by the integral:
L = ∫[a,b] √(1 + (f'(x))²) dx,
where f'(x) represents the derivative of f(x) with respect to x.
In this case, the function is y = tan x and the interval is -7/3 ≤ x < 0. To find the derivative, we differentiate y = tan x with respect to x, which gives:
y' = sec² x.
Now we can substitute these values into the arc length formula:
L = ∫[-7/3,0] √(1 + (sec² x)²) dx.
Simplifying the expression under the square root gives:
L = ∫[-7/3,0] √(1 + tan⁴ x) dx.
To evaluate this integral, we can make a substitution. Let u = tan x. Then du = sec² x dx. Using this substitution, the integral becomes:
L = ∫[tan(-7/3),tan(0)] √(1 + u⁴) du.
Now we need to find the limits of integration. Since -7/3 ≤ x < 0, we can evaluate the tangent function at these values to get:
L = ∫[tan(-7/3),0] √(1 + u⁴) du.
Finally, we can use numerical methods or a calculator to evaluate this integral. The result is approximately 4.481 units.
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Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found. Type of Crust Number Sold Thin crust 312 Thick crust 245 Stuffed crust 179 Pan style 304
Question:
Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.
Type of Crust Number Sold
Thin crust 312
Thick crust 245
Stuffed crust 179
Pan style 304
Based on this information, of the next 4500 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Answer:
1060 thick crusts
Step-by-step explanation:
Given
The above table
Required
Expected number of thick crust for the next 4500
For last week data, calculate the proportion of thick crust sold
[tex]\hat p = \frac{Thick\ crust}{Total}[/tex]
[tex]\hat p = \frac{245}{312+245+179+304}[/tex]
[tex]\hat p = \frac{245}{1040}[/tex]
[tex]\hat p = 0.235577[/tex]
For the next 4500;
[tex]n = 4500[/tex]
The expected number of thick crust is (E(x)):
[tex]E(x) = \hat p * n[/tex]
[tex]E(x) = 0.235577 * 4500[/tex]
[tex]E(x) = 1060.0965[/tex]
[tex]E(x) \approx 1060[/tex]
8/6 + (3/8 + x)(2) =
Answer:
2x+25/12
Step-by-step explanation:
Hope this helps and have a great day!!!!!