Find the length of the third side. If necessary, write in simplest radical form. 7 √51​

Answer:

c. The numbers must have a sum of 12.

Step-by-step explanation:

Given a polynomial [tex]x^2+cx+d[/tex], in its factored form, [tex](x+a)(x+b)[/tex], the following must be true:

[tex]a + b = c[/tex]

[tex]a \cdot b = d[/tex]

In the given polynomial, we can assign the following values:

[tex]c = -12[/tex]

[tex]d=20[/tex]

Using these values, we can go through the answer choices:

Remember: we are finding the statement that is NOT true.

a) "the numbers must have a product of 20"

If we look at the equation [tex]ab = d[/tex], we can see that this statement is correct; therefore, we should not check it.

b) "the numbers must both be negative"

This is not necessarily true, as a positive plus a negative can still result in a negative; however, in this case, it is true (if we factor, we get a = -2, b = -10).

c) "the numbers must have a sum of 12"

This is false, since c = -12. The numbers (a and b) must add to negative 12, not positive 12; therefore c) is the correct answer.

Therefore , the solution of the given problem of area comes out to be

option B 864 sq. centimetres is the correct response.

The amount of area it takes to cover the outside is a good indicator of its overall size. When calculating a trapezoidal shape surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capacity of a cuboid is the sum of the limits for each of its six rectangular edges. Utilize the following technique to determine the box's dimensions: The area is the same in 2lh, 2lw, but also 2hw (SA). The area is represented by the adaptable shape's face.

Here,

The following algorithm determines a cube's surface area:

=> SA = 6s²

where s represents the cube's edge lengths.

=> S =12 cm in this instance.

The result of substituting into the algorithm is:

=> SA = 6 (12)²

=> 6 (144 )²

=> 864 square centimetres.

The cube's surface size is 864 sq. cm as a result.

B) 864 sq. centimetres is the correct response.

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Answer:

The given polynomial already has two terms that can be factored out:

9x^2y^6 - 25x^4y^8 = (3xy^3)^2 - (5x^2y^4)^2

Now we have a difference of squares:

= (3xy^3 - 5x^2y^4)(3xy^3 + 5x^2y^4)

Therefore, 9x^2y^6 - 25x^4y^8 can be rewritten as the product of (3xy^3 - 5x^2y^4) and (3xy^3 + 5x^2y^4).

Answer: The answer would be   (3xy^3-5x^2y^4)(3xy^3+5^2y^4)

(C)

Step-by-step explanation: Cant explain how to but for a quick answer it is C, and you can check the image for proof.

Answer: -5

Step-by-step explanation:

from slope-intercept form, y=mx + b, where b is (-2), and the slope/m is (-5).

hope this helps, and please respond if I'm wrong

M = -5

That’s the answer

By answering the above question, we may state that Debra would thus function need to travel 150 miles for the price of the two plans to be the same.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

The starting charge and the cost per mile would be added together for the first plan's total cost:

Costs for plan 1 total 47.96 plus 0.19x.

The first charge and the cost per mile would be added together for the second plan's total cost:

Plan 2's overall cost is 53.96 plus 0.15x.

Set the two total cost expressions equal to one another and solve for x to get how many miles Debra would need to go for the two plans to be the same in price:

47.96 + 0.19x = 53.96 + 0.15x

0.04x = 6

x = 150

Debra would thus need to travel 150 miles for the price of the two plans to be the same.

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Answer:

Step-by-step explanation:

y=4x + 10

y=3x + 15

This can be resolved with d = 25 miles by multiplying equation both sides by

If Jen has driven 15 miles, and this is 3/5 of the total distance, we can use the following equation to find the total distance d:

15 = (3/5) * d

To solve for d, we need to isolate it on one side of the equation. We can start by dividing both sides of the equation by 3/5, which is the same as multiplying by its reciprocal, 5/3:

15 * (5/3) = d

Simplifying the expression on the left side, we get:

25 = d

Therefore, the total distance Jen needs to travel to get to the mall is 25 miles.

In summary, the equation that can be used to find the total distance d, given that Jen has driven 15 miles and this is 3/5 of the total distance, is:

15 = (3/5) * d

Which can be solved for d by multiplying both sides by 5/3, giving:

d = 25 miles

In conclusion, assuming that Jen has driven 15 miles, which is 3/5 of the entire trip, the equation that can be used to determine the whole distance d is:

15 = (3/5) * d

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Answer:

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we can consider the distance from home to Best Buy as the hypotenuse, and the distance traveled west and south as the other two sides.

Let's call the distance from home to Best Buy "x". Then, using the Pythagorean theorem:

x^2 = (distance south)^2 + (distance west)^2

We know that the distance west is 5 miles, and the distance home is 25 miles. We don't know the distance south, so let's call that "y".

Then we have:

x^2 = y^2 + 5^2

25^2 = y^2 + 5^2

Solving for y, we get:

y^2 = 25^2 - 5^2

y^2 = 600

y = sqrt(600)

y = 24.49 (rounded to two decimal places)

Now we can plug in y to find x:

x^2 = y^2 + 5^2

x^2 = 24.49^2 + 5^2

x^2 = 625.12

x = sqrt(625.12)

x = 25.00 (rounded to two decimal places)

Therefore, the distance from home to Best Buy is approximately 25 miles.

Step-by-step explanation:

The slope of the lines are given as

a) m₁ = -2

b) m₂ = 4/3

c) m₃ = 5/2

d) The equation of line is y = ( 1/2 )x + 9/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 3 , 5 )

Let the second point be Q ( 7 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( -3 - 5 ) / ( 7 - 3 )

Slope m₁ = -8/4

Slope m₁ = -2

b)

Let the first point be P ( 4 , 2 )

Let the second point be Q ( 10 , 10 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₂ = ( 10 - 2 ) / ( 10 - 4 )

Slope m₂ = 8/6

Slope m₂ = 4/3

c)

Let the first point be P ( -1 , -2 )

Let the second point be Q ( -3 , -7 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₃ = ( -7 - ( -2 ) ) / ( -3 - ( -1 ) )

Slope m₃ = -5/-2

Slope m₃ = 5/2

d)

Let the first point be P ( 5 , 7 )

The slope of the line is y = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 7 = ( 1/2 ) ( x - 5 )

y - 7 = ( 1/2 )x - 5/2

Adding 7 on both sides , we get

y = ( 1/2 )x + 9/2

e)

The slope of the line is y = 5/2 and the points are linear

Hence , the equation of line is y = ( 1/2 )x + 9/2

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The complete question is :

Determine the slopes between the points in lowest terms

a) ( 3 , 5 ) and ( 7 , -3 )

b) ( 4 , 2 ) and ( 10 , 10 )

c) ( -1 , -2 ) and ( -3 , -7 )

d) Draw and accurate graph of the line with the slope of ( 1/2 ) that passes through the point ( 5 , 7 )

Answer:

Step-by-step explanation:

[tex]\tt y+4+3\left(y+2\right)[/tex]

Expand by distributing terms:-

[tex]\tt y+4+3y+6[/tex]

Combine like terms:-

[tex]\boxed{\tt y+3y}+\boxed{\tt 4+6}[/tex]

[tex]\tt y+3y=\underline{\bf 4y}[/tex]

[tex]\tt 4+6=\underline{\bf 10}[/tex]

⇒ [tex]\underline{\bf 4y+10}[/tex]

Therefore, A. 4y + 10 is our answer!

_______________________

Hope this helps! :)

Answer:

4y+10

Step-by-step explanation:

у + 4 + 3(y + 2) =

y + 4 + 3y + 6

y + 10 + 3y

4y +10

The probability of getting sum of 6 is C)5/36.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We know that,

Probability of event = number of favorable outcome/ Total outcome

When a 6 sided dice die twice then

Total number of outcome = 6*6=36

Favorable outcome is a sum of 6, Ways of obtaining a sum of 6

(1,5), (5,1), (2,4),(4,2) and (3,3). Thus, there are 5 ways in which 6 can be obtained using  rolling dice twice, Then

=> P(sum of 6 )=5/36

Hence the correct option is C)5/36.

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803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.

Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given values, we get:

Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8

= 401.92 + 401.92

= 803.84 square inches

the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.

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The answer to this question is that the parasailer is 600 feet high. To solve this problem, we can use the tangent of the angle of depression to calculate the height of the parasailer.

Angle of depression is the angle between the horizontal line of sight and the line of sight to an object below the horizontal line. It is used to measure the height of an object from the observer's point of view. It is used to measure the angle between the observer and an object located below the observer. It is sometimes referred to as the inverse of the angle of elevation.

The formula for the tangent of an angle is opposite/adjacent. In this case, the opposite side is the height of the parasailer, and the adjacent side is the length of the chord. Therefore, the equation becomes height/400 = tangent (36°).

Solving for the height, we get height = 400 * tangent (36°). Plugging in the value of the tangent (1.732050808) gives us a height of 692.82 feet.

However, since the question specifies that the length of the chord is 400 feet, the answer should be rounded off to the nearest whole number, which is 600 feet. Therefore, the parasailer is 600 feet high.

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The correct numerical expression for "12 times the sum of 5 and 25 minus 2" by simplification is option (b) , i.e 12 x (5 + 25) − 2.

Simplification means simplifying an expression by reducing it to a simpler form. Approximating means simplifying the formula to the nearest value, which is not exactly correct. 

BODMAS stands for Bracket, Off, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction. 

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Answer:

12 x (5 + 25) − 2

Step-by-step explanation:

hope this helps!

The derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

Differentiation is a mathematical process used to find the rate at which a function changes with respect to one of its variables. It is the process of finding the derivative of a function, which is a measure of how much the function changes as its input changes. The derivative is used to analyze the behavior of functions, find maximum and minimum values, and solve optimization problems. It is an important concept in calculus and is used in many areas of mathematics, science, and engineering.

We can use the quotient rule to differentiate ƒ(x):

[tex]f(x) &= \frac{2+3\log(x)}{x^2+5} \ \\ \\ \\f'(x) &= \frac{(x^2+5)\frac{d}{dx}(2+3\log(x)) - (2+3\log(x))\frac{d}{dx}(x^2+5)}{(x^2+5)^2} \\ \\\ &\\= \frac{(x^2+5)\left(0+\frac{3}{x}\right) - (2+3\log(x))(2x)}{(x^2+5)^2} \\\ \\ \\ &= \frac{3x^2-6-6\log(x)}{x(x^2+5)^2}[/tex]

Therefore, the derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

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A rectangle has 2 lines of symmetry.

What is a line of symmetry?

A line of symmetry is a line that divides a shape into two mirror-image halves. When a shape is divided by a line of symmetry, each half of the shape is a reflection of the other half, and they are said to be symmetric or mirror images of each other. In other words, if you were to fold the shape along its line of symmetry, the two halves would match up perfectly. The presence or absence of lines of symmetry is an important characteristic of shapes and can be used to identify and classify them.

Calculate the line of symmetry of a rectangle -

A rectangle has two lines of symmetry: one line that runs vertically down the center of the rectangle, and another line that runs horizontally across the center of the rectangle.

To understand why a rectangle has two lines of symmetry, consider that any line that runs down the center of a rectangle will divide it into two halves that are mirror images of each other. This is true for lines that run vertically or horizontally through the center of the rectangle.

In contrast, a rectangle does not have diagonal lines of symmetry. That is, there is no line that can be drawn from one corner of the rectangle to another corner that will divide it into two mirror-image halves.

Overall, a rectangle has two lines of symmetry, and these lines are important to its geometry and properties.

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Answer:

6 units to the right

Step-by-step explanation:

Z(3,4) → Z'(9,4)

d = √(9-3)² + (4-4)² = √6²+0² = 6   to the right

The translation of point Z of triangle XYZ from (3, 4) to Z′(9, 4) is a move of 6 units to the right.

In Mathematics, particularly geometry, the translation of a point is the process of moving the point a specific number of units either up, down, left or right. In the case of your triangle XYZ, the original position of point Z is at (3, 4) and Z′ is positioned at (9, 4). The y-coordinate hasn't changed; it remains at 4. This tells us that the translation is not up or down. However, if we observe the x-coordinate, you’ll see that it went from 3 to 9. Changing the x-coordinate moves the point horizontally, so we know our translation is left or right. Lastly, the difference between 3 and 9 is 6. We can therefore determine that the point moved 6 units to the right.

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The only solution to the system of inequalities y < −x+5 and y ≥ 3x+1 is (1,3).

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

For the inequality y < -x + 5, any point below the line y = -x + 5 will satisfy the inequality. For the inequality y ≥ 3x + 1, any point on or above the line y = 3x + 1 will satisfy the inequality.

To find the solutions that satisfy both inequalities, we can shade the region that is below the line y = -x + 5 and also on or above the line y = 3x + 1. This region is the shaded triangle bounded by the lines y = -x + 5, y = 3x + 1, and the x-axis.

Therefore, the solutions to the system of inequalities are the points in this shaded triangle. To check which options are solutions, we can substitute the values of x and y given in each option into both inequalities and check if they satisfy both.

Hence, the only solution is (1,3).

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Complete question:

Which of the following are solutions to the system of inequalities y < −x+5 and y ≥ 3x+1?

Select all that apply.

a. (0,2)

b. (1,3)

c. (2,1)

d. (3,6)

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Answer: 8 5/7

Step-by-step explanation:

Well, first you make the common denominator between the two, which would be 46/14 and 76/14. Now you add 46 and 76 and receive 122/14. You can simplify that and get 61/7, and now you turn it into a mixed number:

8 5/7

Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

Mathematicians use the unitary method to answer proportional relationship problems involving two or more quantities. It entails calculating the worth of one unit of one quantity in relation to another. For instance, let's say we are aware that 3 pencils cost $6. The following is how we can calculate the price of a solitary pen using the unitary method: The value of a single entity of the quantity "pen cost" in terms of the quantity "number of pens" was determined in this case. Once we are aware of a unit's worth, we can use that knowledge to determine the value of any other quantity that is related to it.

given

The population triples, or grows three times, in number, after four months. As a result, if we commence with 150 mice, the population will look like this after 4 months:

150 × 3 = 450 mice

The populace will triple once more after another 4 months (or 8 months from the beginning), becoming:

450 × 3 = 1350 mice

The populace will triple once more after another 4 months (or 12 months from the beginning), becoming:

1350 × 3 = 4050 mice

There is a pattern here: every four months, the populace triples. Therefore, we can determine how many times the population triples after three years (or 36 months) have passed:

36 months divided by 4 months per triple equals 9 triples.

the following group will exist after three years:

2,952,450 mice are equal to 150 × 39 (150 x 19,683).

Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

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Answer:

each of the other sides is 2√2 = 2.8284

Step-by-step explanation:

A 45°- 45°-90° triangle is also known as a right isosceles triangle because two of the legs are the same as two of the angles are the same at 45°

If a is the length of one of the legs then the hypotenuse, h,  which is the longest side is given by the equation

[tex]h = \sqrt{a^2 + a^2}\\\\h = \sqrt{2a^2}\\\\h = a \sqrt{2}[/tex]

Or, dividing by √2 on both sides,

[tex]\dfrac{h}{\sqrt{2} }= a[/tex]

Given h = 4

[tex]a =\dfrac{ 4}{\sqrt{2}} = \dfrac{2\cdot2}{\sqrt{2}} = 2\sqrt{2} \quad\quad\quad(since $\dfrac{2}{\sqrt{2}}$ = \sqrt{2}})[/tex]

a = 2√2 = 2.8284

So each of the other sides is 2√2 = 2.8284

The principal amount of the loan is $1,200,000.

What is simple interest?

Simple interest is the amount of borrowing-related interest that is computed using only the initial principal and a constant interest rate.

To find the principal amount of a loan, we need to use the formula for simple interest:

I = Prt

Where I is the interest, P is the principal, r is the interest rate as a decimal, and t is the time in years.

In this case, we know that the interest is $3,150 and the interest rate is 10.5%. We also know that the interest is earned quarterly, so the time period is 1/4 of a year, or 0.25 years.

Substituting these values into the formula, we get:

3150 = P * 0.105 * 0.25

Solving for P, we get:

P = 3150 / (0.105 * 0.25) = $1,200,000

Therefore, the principal amount of the loan is $1,200,000.

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Answer:

Step-by-step explanation:

Using the remainder theorem we get:

[tex]f(-2)=-5[/tex],  [tex]f(1)=4[/tex], and [tex]f(-1)=0[/tex]

So we get

[tex]f(-2)=(-8)(p-1)+4p-2q+r=-5[/tex]

                 [tex]-8p+8+4p-2q+r=-5[/tex]

                              [tex]-4p-2q+r=-13[/tex]  [tex](a)[/tex]

[tex]f(1)=(p-1)+p+q+r=4[/tex]

                       [tex]2p+q+r=5[/tex]               [tex](b)[/tex]

[tex]f(-1)=-(p-1)+p-q+r=0[/tex]

                                 [tex]-q+r=-1[/tex]    [tex](c)[/tex]

We need to solve (a), (b) and (c) simultaneously to find p,q, and r.

from [tex](c)[/tex]  [tex]r=q-1[/tex]. Sub this into (a) and (b):

[tex]-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12[/tex]    [tex](d)[/tex]

      [tex]2p+q+(q-1)=5 \rightarrow q=3-p[/tex]              [tex](e)[/tex]

Sub (e) into (d) we get

[tex]-4p-(3-p)=-12 \rightarrow p=3[/tex]

Sub [tex]p=3[/tex] into [tex](e) \rightarrow q=0[/tex]

Sub  [tex]p=3,q=0[/tex] into [tex](c) \rightarrow r=-1[/tex]

SOLUTION: [tex]p=3,q=0,r=-1[/tex]    

So [tex]f(x)=2x^3+3x^2-1[/tex]

by dividing (x+1) into f(x) we get  (I am not showing working for this division)

[tex]f(x)=(x+1)(2x^2+x-1)[/tex]

[tex]\rightarrow f(x)=(x+1)(2x-1)(x+1)[/tex]

The surface area of the figure is 549.5 square ft

Given that

The composite figure comprises of a cone and a cylinder of the following dimensions

Cone: Radius = 5 ft and Height = 12 ft

Cylinder: Radius = 5 ft and Height = 6 ft

The surface area of the figure is calculated as

Surface area = Cone + Cylinder -  Circle

So, we have

Surface area = πr(r + √[h² + r²]) + 2πr(r + h) - πr²

Substitute the known values in the above equation, so, we have the following representation

Surface area = 3.14 * 5 * (5 + √[12² + 5²]) + 2 * 3.14 * 5 * (5 + 6) - 3.14 * 5²

Evaluate

Surface area = 549.5

Hence, the surface area is 549.5

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The piecewise function graphed is given as follows:

A piece-wise function is a function that has different definitions, based on the input x of the function.

For this problem, the intervals are given as follows:

For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence^:

y = x² + 4, x < 2.

For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:

y = -x + b

0 = -4 + b

b = 4.

Hence:

y = -x + 4, x ≥ 2.

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[tex]\cfrac{1}{6}+\cfrac{3}{4}-\cfrac{2}{3}\implies \cfrac{(2)1~~ + ~~(3)3~~ - ~~(4)2}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{2+9-8}{12}\implies \cfrac{3}{12}\implies \cfrac{1}{4}[/tex]

Answer:

Bases

Step-by-step explanation: