the square root of 8?

Answers

Answer 1

Answer:

√8 8n sure form= √ 4 ×√2

= 2×√2

= 2√2


Related Questions

Use Solver to solve this problem. The Excel spreadsheet must
show the model, the formulas used, and the solution. Be sure to
include the answer report when uploading your spreadsheet.
Round your answe

Answers

That's a general overview of how to use Solver in Excel to solve optimization problems. If you have a specific problem in mind, please provide the details, and I'll be happy to assist you further.

"Use Excel Solver to optimize a given objective function with defined variables and constraints."

Excel Solver is an add-in tool in Microsoft Excel that allows you to find an optimal solution for a given problem by adjusting certain variables.

To use Excel Solver, you need to set up a model that includes the objective function to optimize and any constraints or limitations on the variables.

The Solver then iteratively adjusts the variables to find the optimal solution that maximizes or minimizes the objective function while satisfying the constraints.

Here's a step-by-step explanation of how to use Excel Solver:

Set up your Excel spreadsheet: Start by organizing your data in a spreadsheet.

You should have a section for input variables, the objective function, and any constraints.

Install Excel Solver: If you don't have Solver installed, go to the "File" tab in Excel, click on "Options," then select "Add-Ins."

Look for Solver Add-in and enable it.

Define the objective function: Determine the function you want to maximize or minimize.

This could be a mathematical formula or a cell reference in your spreadsheet.

Set up constraints: Determine any limitations or restrictions on the variables.

Constraints can be related to inequalities (e.g., x >= 5) or equalities (e.g., x + y = 10).

Open Solver: Go to the "Data" tab in Excel and click on "Solver" in the "Analysis" group. The Solver Parameters window will appear.

Configure Solver Parameters: In the Solver Parameters window, specify the objective function, the variables to adjust, and any constraints.

Set the target (maximize or minimize) and select the variable cells and constraint cells.

Remember to round your answer according to the requirements of your specific problem.

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Q1. For each of the following values of a,b and c, where
(a) a = -20, b = -10, c = 5
(b) a = -40, b = 10, c = -5
Show that:
(i) a÷b ≠ b÷a
(ii) (a÷b)÷c ≠ a÷(b÷c)
(iii) a÷(b+c)≠(a÷b)+(a÷c)​

Answers

Explanation:-

⟨a⟩

Given that

a = -20

b = -10

c = 5

⟨i⟩ LHS = a÷b

⇛ -20÷-10

⇛ -20/-10

⇛ 2

and

RHS = b÷a

⇛ -10÷-20

⇛ -10/-20

⇛ 1/2

LHS ≠ RHS

a÷b ≠ b÷a

⟨ii⟩

LHS = (a÷b)÷c

⇛ (-20÷-10)÷5

⇛ 2÷5

⇛ 2/5

RHS = a÷(b÷c)

⇛ -20÷(-10÷5)

⇛ -20÷-2

⇛ -20/-2

⇛ 10

LHS ≠ RHS

(a÷b)÷c ≠ a÷(b÷c)

⟨iii⟩ LHS = a÷(b+c)

⇛ -20÷(-10+5)

⇛ -20÷(-5)

⇛ -20/-5

⇛ 4

RHS = (a÷b)+(a÷c)

⇛ (-20÷-10)+(-20÷5)

⇛ 2+(-4)

⇛ 2-4

⇛ -2

LHS ≠ RHS

a÷(b+c) ≠ (a÷b)+(a÷c)

⟨b⟩.

Given that

a = -40

b = 10

c = -5

⟨i⟩ LHS = a÷b

⇛ -40÷1

⇛ -40/1

⇛-40

and

RHS = b÷a

⇛ 10÷-40

⇛ 10/-40

⇛ -1/4

LHS ≠ RHS

a÷b ≠ b÷a

⟨ii⟩.

LHS = (a÷b)÷c

⇛ (-40÷10)÷-5

⇛ -4÷-5

⇛ 4/5

RHS = a÷(b÷c)

⇛ -40÷(10÷-5)

⇛ -40÷-2

⇛ -40/-2

⇛ 20

LHS ≠ RHS

(a÷b)÷c ≠ a÷(b÷c)

⟨iii⟩ LHS = a÷(b+c)

⇛ -40÷(10-5)

⇛ -40÷(5)

⇛ -40/5

⇛ -8

RHS = (a÷b)+(a÷c)

⇛ (-40÷10)+(-40÷-5)

⇛ (-4)+8

⇛ 8-4

⇛ 4

LHS ≠ RHS

a÷(b+c) ≠ (a÷b)+(a÷c)

Conclusion :-

Commutative property Associative Property Distributive Property does not hold in the set of integers under Division

Joyce has $13​ in savings and saves an additional $6​ each week. At the same time, Enrique has $80​ in savings and spends $5​ each week to go swimming at the community pool. Is there a week when Joyce and Enrique will have the same amount of money? Explain why or why not.

Answers

Answer: Yes, after 7 weeks, they will have the same amount of money

Step-by-step explanation: So let’s say Joyce will be equation 1, so it would be - T = 13 + 6x, where T represents the total money, and x represents the number of weeks. And let’s say Enrique will be equation 2, which will be - T = 80 - 5x, where once again, T represents the total money, and x represents the number of weeks.

So, let’s start going off numbers, we will start at 5 weeks, when we put that in, Joyce will have $43 and Enrique will have $65, so we know it will be more than 5 weeks, so let’s try 8 weeks, Joyce will have $61 and Enrique will have $40, so it’s below 8, so how about we try 7, at 7 weeks, Joyce will have $55, and Enrique will have $55 too. So this means, after 7 weeks, Joyce and Enrique will have the same amount of money

Find the density in kilograms per liter

Find the density in kilograms per liter

Answers

The density in kilograms per liter is:

d = 0.5 kilograms/liter

How to find the density?

Here we have a graph of mass vs volume, and we know that the density is defined as:

Density = mass/volume

Here we know that when the volume is 4 liters, the mass is 2 kilograms, then the density of this thing will be:

density = (2 kilograms)/(4 liters) = 0.5 kilograms per liter.

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I WILL MARK BRAINIEST PLS EXPLAIN ITS DUE IN 10 MIN!!!!

I WILL MARK BRAINIEST PLS EXPLAIN ITS DUE IN 10 MIN!!!!

Answers

Answer:

y=2x+121

Step-by-step explanation:

The product of two numbers is 2,55, 050 , if one number is 25 ,find the other

Answers

Answer:

answer is 10202

Step-by-step explanation:

we get the other number as 'x'

so, 25*x=255050
     25 diveded by 25 is equal to =255050 divided by 25

  so, answer x= 10202
you can get 255050 again by 25*10202

The weight of an ideal cut round diamond can be modeled by the polynomial f(d)=0.0071d^3−0.090d^2+0.48d , where d is the diameter of the diamond. Find the domain and range of the function in the context of the situation.

A)The domain and range are both all real numbers.
B)The domain is {d|d≥0} , and the range is {f(d)||f(d)≥0} .
C)The domain is {d|d≥0} , and the range is all real numbers.
D)The domain is all real numbers, and the range is {f(d||f(d)≥0)} .

Answers

The domain is {d|d≥0} , and the range is {f(d)||f(d)≥0} is the correct option.

Given that the weight of an ideal cut round diamond can be modeled by the polynomial f(d) = 0.0071d³ - 0.090d² + 0.48d, where d is the diameter of the diamond. To find the domain and range of the function, we need to consider the value of d and f(d) and check whether they satisfy the given polynomial.The domain of a function is the set of all possible values of the independent variable for which the function is defined. The range of a function is the set of all possible values of the dependent variable that result from using a certain set of input values. In the given polynomial function, it is clear that the value of d cannot be negative as it represents the diameter of the diamond.

Hence, the domain of the function is {d|d≥0}.Now, we need to find the range of the function. To find the range of a function, we need to determine the minimum and maximum values of the function. Let's first differentiate the given function f(d) to find its critical points.f′(d) = 0.0213d² - 0.18d + 0.48= 0.0213(d - 4.233)(d - 11.266)By setting f′(d) = 0, we get the critical points d = 4.233 and d = 11.266. We can check that f′′(d) > 0 for all values of d, which means that the function has a local minimum at d = 4.233 and a local maximum at d = 11.266.Substituting these values in the function, we get:f(4.233) = 0.6173 (approx) and f(11.266) = 2.7896 (approx)Thus, the minimum value of the function is 0.6173 and the maximum value of the function is 2.7896. Since the function is continuous, it takes on all values between these two values. Also, since f(d) is a polynomial function, it is defined for all real values of d. Hence, the range of the function is {f(d)||f(d)≥0}.Therefore, the domain is {d|d≥0}, and the range is {f(d)||f(d)≥0}.

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Find the total surface area of this triangular prism.
10cm
6 cm
4cm
8 cm

Find the total surface area of this triangular prism. 10cm 6 cm 4cm 8 cm

Answers

Method:

Front: 6x8 = 48/2 = 24

Back: Also 24

Base: 8x4 = 32

Left: 6x4=24

Add your answers:

24 + 24 + 24 + 32 + 40

Answer:

TSA is 144 cm²

Prove AB is congruent to BC given BE bisects DBC and BE is parallel to AC

Prove AB is congruent to BC given BE bisects DBC and BE is parallel to AC

Answers

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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HELPPPPPPPP meeee.......

HELPPPPPPPP meeee.......

Answers

Answer:

No solutions can be found

Step-by-step explanation:

what's the input lol *photo attatched*​

what's the input lol *photo attatched*

Answers

-20+1= -19
-19/2= -9.5

Check:
-9.5x2= -19
-19-1= -20

How do i solve this paper?
I feel like my answers are gone and i need help.

How do i solve this paper?I feel like my answers are gone and i need help.

Answers

Answer:

you have it correct sir

Step-by-step explanation:

PLEASE HELP
Which fraction below represents a reapeating decimal?
A. 1/2
B. 1/5
C. 1/8
D. 1/9

Answers

1/9.

when you divide it, you get 0.111111 and so on.

PLEASE HELP

WILL GIVE BRAINLIEST
AND 5.0 RATING

PLEASE HELP WILL GIVE BRAINLIESTAND 5.0 RATING

Answers

Answer:

Point W

Step-by-step explanation:

Did this before

outside temperature over a day can be modelled as a sinusoidal function. suppose you know the high temperature of 89 degrees occurs at 5 pm and the average temperature for the day is 80 degrees. assuming t is the number of hours since midnight, find an equation for the temperature, d, in terms of t.

Answers

The equation for the temperature, d, in terms of t is:
d(t) = 9 * cos[(π/12) * (t - 17)] + 80

To create an equation for the temperature, d, in terms of t, we will use the information given: the high temperature of 89 degrees at 5 pm and the average temperature of 80 degrees.

Determine the amplitude (A) of the sinusoidal function.
Amplitude = (High Temperature - Average Temperature)
A = (89 - 80)
A = 9

Determine the period (P) of the sinusoidal function.
Since the temperature pattern repeats every 24 hours, the period is 24 hours.

Determine the horizontal shift (HS) of the sinusoidal function.
Since the high temperature occurs at 5 pm (17 hours since midnight), the horizontal shift is 17 hours.

Determine the vertical shift (VS) of the sinusoidal function.
The vertical shift is the average temperature, which is 80 degrees.

Write the sinusoidal equation for the temperature, d, in terms of t.
Since the temperature reaches its peak (high temperature) at 5 pm, we will use the cosine function, as it starts at its peak value. The general form of the cosine function is:

d(t) = A * cos[(2π/P) * (t - HS)] + VS

Now, plug in the values found in steps 1-4:

d(t) = 9 * cos[(2π/24) * (t - 17)] + 80

So, the equation for the temperature, d, in terms of t is:

d(t) = 9 * cos[(π/12) * (t - 17)] + 80

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what us systems of equations solver

Answers

Systems of equations solver called Wolfram or Alphas can resolve systems of linear equations or nonlinear equations, and it can look for solutions that are only integers.

Systems of direct equations are a common and applicable subset of systems of equations. In the case of two variables, these systems can be allowed of as lines drawn in two- dimensional space. However, the system is said to be harmonious and has a result at this point of crossroad, If all lines meet to a common point. The system is said to be inconsistent else, having no results. Systems of direct equations involving further than two variables work also, having either one result, no results or horizonless results( the ultimate in the case that all element equations are original).

More general systems involving nonlinear functions are possible as well. These retain more complicated result sets involving one, zero, horizonless or any number of results, but work also to direct systems in that their results are the points satisfying all equations involved. Going further, more general systems of constraints are possible, similar as bones that involve inequalities or have conditions that certain variables be integers.

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an object is located a distance do = 5.7 cm in front of a concave mirror with a radius of curvature r = 19.1 cm.
33% Part (a) Write an expression for the image distance, di Grade Summary Deductions Potential 0% 100% Submissions ts remaining:5 (5% per attempt) detailed view DELI CLEAR Submit Hint I give up! Hints: 2% deducti on per hint. Hints remaining: 2 Feedback: 2% deduction per feedback. là 33% Part (b) Numerically, what is the image distance, ai, in centimeters? 33% Part (c) Is this a real or virtual image?

Answers

(a) The expression for the image distance, di, for a concave mirror can be found using the mirror equation:

1/do + 1/di = 1/f

where do is the object distance, f is the focal length, and di is the image distance.

To find f, we can use the formula:

f = r/2

where r is the radius of curvature.

Substituting the given values, we get:

f = 19.1/2 = 9.55 cm
do = 5.7 cm

Now, we can solve for di:

1/5.7 + 1/di = 1/9.55

1/di = 1/9.55 - 1/5.7

di = -16.13 cm

Note: the negative sign for di indicates that the image is virtual and upright.

(b) Numerically, the image distance, di, is -16.13 cm.

(c) This is a virtual image.

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Round each decimal number to the nearest whole number. Then, select the best estimate for the addition equation 1.2 + 3.6 =

4.5

5

5.5

6​

Round each decimal number to the nearest whole number. Then, select the best estimate for the addition

Answers

Answer:

4.5

Step-by-step explanation:

1.2 + 3.6 = 4.8 but when u do 4.8 -0.3 you will  get 4.5

Answer:

It would be 5.5 or 5

The figure is a section of a conducting rod of radius R 1

=1.30mm and length L=11.00m inside a thin-walled coaxial conducting cylindrical shell of radius R 2

=10.0R 1

and the (same) length L.The net charge on the rod is Q 1

=+3.40×10 −12
C; that on the shell is Q 2

=−2.00Q 1

. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial r=2.00R 2

? What are (c) E and (d) the direction at r=5.00R 1

? What is the charge on the (e) interior and (f) exterior surface of the shell?

Answers

(a) The magnitude E is 1.04×10⁶ N/C.

(b) The direction of the electric field is radially inward since the net charge inside the shell is negative.

(c) The E direction is Q1 = 3.40×10⁻¹² C.

(d) The direction of the electric field is radially outward since the net charge inside the shell is positive.

(e) The interior surface of the shell is Q1 = 3.40×10⁻¹² C.

(f) The exterior surface of the shell is Q2 = 6.80×10⁻¹² C.

Field and Charge Calculation

(a) The magnitude of the electric field at radial distance r from the axis of a thin-walled coaxial conducting cylindrical shell carrying a net charge Q is given by E = Q / (2πε₀r), where ε₀ is the permittivity of free space. For r = 2.00R₂, the net charge Q is Q₁ + Q₂ = (3.40×10⁻¹² C) - 2(3.40×10⁻¹² C) = -3.40×10⁻¹² C, and thus the electric field is E = |-3.40×10⁻¹² C / (2πε₀(2.00R₂))| = 1.04×10⁶ N/C.

(b) The direction of the electric field is radially inward since the net charge inside the shell is negative.

(c) For r = 5.00R₁, the net charge inside the shell is only Q1 = 3.40×10⁻¹²C, so the electric field is E = |3.40×10⁻¹² C / (2πε₀(5.00R₁))| = 1.23×10⁶ N/C.

(d) The direction of the electric field is gradually outward since the net charge inside the shell is positive.

(e) The charge on the interior facial of the shell is equal in magnitude and opposite in sign to the net charge inside the shell, which is Q1 = 3.40×10⁻¹² C.

(f) The charge on the exterior facial of the shell is equal in magnitude and opposite in sign to the net charge outside the shell, which is -Q2 = 2(3.40×10⁻¹² C) = 6.80×10⁻¹² C.

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Simplify each rational expression. State any restrictions on the variable. 3 z⁴+36 z³+60 z² / 3 z³-3 z²

Answers

To simplify the given rational expression 3z^4 + 36z^3 + 60z^2 / 3z^3 - 3z^2, we can factor out the greatest common factor from both the numerator and the denominator. In this case, the greatest common factor is 3z^2.

Numerator: 3z^4 + 36z^3 + 60z^2
Denominator: 3z^3 - 3z^2

Factoring out the greatest common factor:
3z^2 (z^2 + 12z + 20) / 3z^2 (z^2 - z)

Simplifying further, we can cancel out the common factors:
(z^2 + 12z + 20) / (z^2 - z)

Restrictions on the variable:
Since there are no restrictions mentioned in the question, we can assume that z can take any real value.

The simplified rational expression is (z^2 + 12z + 20) / (z^2 - z). The variable z can take any real value. To simplify the given rational expression 3z^4 + 36z^3 + 60z^2 / 3z^3 - 3z^2, we can start by factoring out the greatest common factor from both the numerator and the denominator. The greatest common factor in this case is 3z^2. So, in the numerator, we can factor out 3z^2:
3z^2 (z^2 + 12z + 20)

And in the denominator, we can factor out 3z^2:
3z^2 (z^2 - z)

Now, we can cancel out the common factors in the numerator and the denominator, which leaves us with:
(z^2 + 12z + 20) / (z^2 - z)

This is the simplified rational expression. Regarding the restrictions on the variable, the question does not provide any specific restrictions. Therefore, we can assume that z can take any real value.

In conclusion, the simplified rational expression is (z^2 + 12z + 20) / (z^2 - z). The variable z can take any real value.

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Which chose represents a nonlinear function?
A. X= -2, -1, 0, 1, Y= -3, -1, 1, 3
or
B. X= -2, -1, 0, 1, Y= 4, 1, 0, 1
pls help ill mark u barnlist

Answers

B is x^2 it will be like U ship

The following information describes the production possibilities of two positions for a hockey player. Assume the player can only play Center or Defense. Round numerical answers to two decimal places. Numerical answers should look like #.\#\# a. What is the opportunity cost of a goal if the player is a center? b. What is the opportunity cost of a goal if the player is a defenseman? c. What is the opportunity cost of a goal if the player is a center? d. What is the opportunity cost of an assist if the player is a defenseman? e. Which position has the absolute advantage in goals? f. Which position has the absolute advantage in assists? g. Which position has the comparative advantage in goals? h. Which position has the comparative advantage in assists?

Answers

a. The opportunity cost of a goal if the player is a center is 0.5 assists. b. The opportunity cost of a goal if the player is a defenseman is 0.33 assists. c. The opportunity cost of a goal if the player is a center is 0.5 assists. d. The opportunity cost of an assist if the player is a defenseman is 1.5 goals. e. The position of Center has the absolute advantage in goals. f. The position of Center has the absolute advantage in assists. g. The position of Defenseman has the comparative advantage in goals. h. The position of Center has the comparative advantage in assists.

a. The opportunity cost of a goal for a center is 0.5 assists. This means that for every goal scored by the center, they have given up the opportunity to produce 0.5 assists.

b. The opportunity cost of a goal for a defenseman is 0.33 assists. This implies that for every goal scored by the defenseman, they have sacrificed the chance to generate 0.33 assists.

c. The opportunity cost of a goal for a center remains 0.5 assists. This is because the production possibilities for the center indicate that for every goal they score, they could have alternatively produced 0.5 assists.

d. The opportunity cost of an assist for a defenseman is 0.33 goals. This signifies that for every assist made by the defenseman, they have foregone the opportunity to score 0.33 goals.

e. The position of center has the absolute advantage in goals since they can produce 4 goals, which is higher than the defenseman's production of 2 goals.

f. The position of center also has the absolute advantage in assists with 8 assists, surpassing the defenseman's production of 6 assists.

g. The position of defenseman has the comparative advantage in goals since the opportunity cost of a goal for the defenseman (0.33 assists) is lower compared to the center's opportunity cost (0.5 assists).

h. The position of center has the comparative advantage in assists since the opportunity cost of an assist for the center (0.5 goals) is higher compared to the defenseman's opportunity cost (0.33 goals).

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y=2/7x - 3
a. m=2/7, b=-3
b. m=-3, b=2/7

a or b

y=2/7x - 3a. m=2/7, b=-3b. m=-3, b=2/7a or b

Answers

Answer:

A (The second Choice)

Step-by-step explanation:

Credit: The person who couldn't "[...]answer for some reason"

Plot the following points (3,6); (-1,6) and (-1,-6) on a grid to create three vertices of a rectangle. Find the missing vertex that would make it a rectangle.

Answers

Answer: (3,-6)

Step-by-step explanation: Find the answer by finding the negative of the other number.

Paige and Olivia made 80 muffins. They put all the muffins into 13 boxes, but had 2 that did not fit in the boxes. How many muffins are in each box?

Answers

Step-by-step explanation:

There are 2 muffins in each box

Please help!! It needs to be solved

Please help!! It needs to be solved

Answers

Answer:

A, x ≥ -2 and x ≤ 4

Step-by-step explanation:

|2x - 2| ≤ 6

-6 ≤ 2x - 2 ≤ 6

-4 ≤ 2x ≤ 8

-2 ≤ x ≤ 4

x ≥ -2 and x ≤ 4

Answer: A.  x ≥ -2 and x ≤ 4

If 1% of a number equals 4, find 2% of that number.

Answers

The answer is 8

2 x 4 = 8

Which of the following equations has a different value of x than the others?(1 point
x + 9/8 = 7/4

x − 7/8 = −3/2

x + 0.875 = 1.5

x − 0.025 = 0.6

Answers

Answer: The equation \(x-7/8=-3/2\) has a different value of x than the others. The value of x here is -0.625, while in all the other equations, the value of x is 0.625.

Step-by-step explanation: Simplifying the equation \(x+9/8=7/4\), we get:

\(x=7/4-9/8\)

\(x=0.625\)

Simplifying the equation \(x-7/8=-3/2\),  we get:

\(x=-3/2+7/8\)

\(x=-0.625\)

Simplifying the equation \(x+0.875=1.5\), we get:

\(x=1.5-0.875\)

\(x=0.625\)

Simplifying the equation \(x-0.025=0.6\), we get:

\(x=0.6+0.025\)

\(x=0.625\)

Therefore, \(x+9/8=7/4\) has a different value of x than the others.

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It’s probably rlly simple I just dk how to do it :)

Its probably rlly simple I just dk how to do it :)

Answers

Answer:

18,0

Step-by-step explanation:

By useing desmos, the line has an x intercept of 18 making that the answer.

 

PLZ MARK AS BRAINLIEST

Answer:

D = 18

Step-by-step explanation:

\(6 = \frac{1}{3}d\)

\(3*(\frac{1}{3} d) = (3)*(6)\)

\(d=18\)

what must be subtracted from x^3 - 4x^2 + 3x - 9 to obtain a polynomial which is exactly divisible by (x-2)?

Answers

Answer: If we divide a polynomial by (x - 2) and obtain a quotient without a remainder, then (x - 2) must be a factor of the polynomial. Therefore, we need to find the factor of (x - 2) that will evenly divide the polynomial x^3 - 4x^2 + 3x - 9.

To do this, we can use long division or synthetic division. Let's use synthetic division:

2 | 1 - 4  + 3 - 9

  |    2  - 4 - 2

  |---------------

  | 1 - 2 - 1 - 11

The result is a quotient of x^2 - 2x - 1 with a remainder of -11.

Since we want to obtain a polynomial that is exactly divisible by (x - 2), we need to subtract the remainder from the original polynomial, which gives:

x^3 - 4x^2 + 3x - 9 - (-11) = x^3 - 4x^2 + 3x + 2

Therefore, we need to subtract 11 from x^3 - 4x^2 + 3x - 9 to obtain a polynomial which is exactly divisible by (x-2). The resulting polynomial is x^3 - 4x^2 + 3x + 2.

Step-by-step explanation:

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