Is the point (5, –9) a solution in the equation y < -x -3

\( \Large{\boxed{\sf r = 10.2 \: m \: \: (Rounded \: to \: the \: nearest \: tenth.) }} \)

\( \\ \)

To find the radius of the circle, we will use the given formula:

\( \Large{\sf r = \left( \dfrac{A}{4 \pi } \right)^{\dfrac{1}{2}} } \)

Where:

\( \\ \)

\( \Large{\boxed{\sf Given \text{:} } \begin{cases} \sf A &=\sf 1493 \: m^3 \\ \sf \pi &=\sf 3.14 \: (Approximately) \end{cases} } \)

\( \\ \)

Substitute these values into our formula:

\( \sf r = \left( \dfrac{1493 \: m^3}{4 \times 3.14} \right)^{\dfrac{1}{2} } = \sqrt{ \dfrac{1493 \: m^3 }{12.56} } \approx 10.90272 \: m \)

\( \\ \)

Rounding our answer to the nearest tenth, we get:

\( \boxed{\boxed{\sf r = 10.9 \: m }} \)

Answer:

Solve the following pair of equations for x and y :

\(\rm :\longmapsto\:\dfrac{ {a}^{2} }{x} - \dfrac{ {b}^{2} }{y} = 0, \: \: \dfrac{ {a}^{2}b}{x} + \dfrac{ {b}^{2} a}{y} = a + b\)

\( \red{\large\underline{\sf{Solution-}}}\)

Given pair of equations are

\(\rm :\longmapsto\:\dfrac{ {a}^{2} }{x} - \dfrac{ {b}^{2} }{y} = 0 - - - - (1)\)

and

\(\rm :\longmapsto\:\dfrac{ {a}^{2} b}{x} + \dfrac{ {b}^{2}a }{y} = a + b - - - - (2)\)

On multiply equation (1) by a, we get

\(\rm :\longmapsto\:\dfrac{ {a}^{3} }{x} - \dfrac{ {b}^{2} a}{y} = 0 - - - (3)\)

On adding equation (3) and (2), we get

\(\rm :\longmapsto\:\dfrac{ {a}^{3} }{x} + \dfrac{ {a}^{2} b}{x} = a + b \)

\(\rm :\longmapsto\:\dfrac{ {a}^{3} + {a}^{2} b}{x} = a + b \)

\(\rm :\longmapsto\:\dfrac{{a}^{2}(a + b)}{x} = a + b \)

\( \\ \rm\implies \:\boxed{\tt{ \: \: x \: \: = \: \: {a}^{2} \: \: }} \\ \)

On substituting the value of x in equation (1), we get

\(\rm :\longmapsto\:\dfrac{ {a}^{2} }{ {a}^{2} } - \dfrac{ {b}^{2} }{y} = 0\)

\(\rm :\longmapsto\:1 - \dfrac{ {b}^{2} }{y} = 0\)

\(\rm :\longmapsto\: - \dfrac{ {b}^{2} }{y} = - 1\)

\(\rm :\longmapsto\: \dfrac{ {b}^{2} }{y} = 1\)

\( \\ \rm\implies \:\boxed{\tt{ \: \: y \: \: = \: \: {b}^{2} \: \: }} \\ \)

Consider the first equation

\(\rm :\longmapsto\:\dfrac{ {a}^{2} }{x} - \dfrac{ {b}^{2} }{y} = 0\)

On substituting the values of x and y, we get

\(\rm :\longmapsto\:\dfrac{ {a}^{2} }{ {a}^{2} } - \dfrac{ {b}^{2} }{ {b}^{2} } = 0\)

\(\rm :\longmapsto\: 1 - 1 = 0\)

\(\rm\implies \:0 = 0\)

Hence, Verified

So, Solution of pair of equations is

\( \purple{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\bf{x \: = \: {a}^{2} } \\ \\ &\bf{y \: = \: {b}^{2} } \end{cases}\end{gathered}\end{gathered}}\)

Depending on the type of triangle, the value or angle WXY can be determined.

Angle is a figure formed by two lines or rays diverging from a common point. It is usually measured in degrees, or in radians. Angles are used to measure the size of angles and can be classified as acute, right, obtuse, straight, reflex, or full.

Angles can be used to describe the direction of a line or the relationship between two lines. They are also used in geometry and trigonometry to calculate distances and determine the size of shapes.

In order to determine the value or angle WXY, we need to first identify the type of triangle. If the triangle is an isosceles triangle, then the angle WXY is equal to the other two angles of the triangle. If the triangle is a right triangle, then the angle WXY is 90 degrees. If the triangle is an equilateral triangle, then all three angles are equal and the angle WXY is equal to 60 degrees.

If the triangle is an isosceles triangle, then the angle WXY can be determined by measuring the other two angles. The two angles will be equal, so if one is 65 degrees, then angle WXY will also be 65 degrees. If the other angle is 115 degrees, then angle WXY will also be 115 degrees.

If the triangle is a right triangle, then the angle WXY will be 90 degrees.

If the triangle is an equilateral triangle, then the angle WXY will be equal to 60 degrees.

Therefore, depending on the type of triangle, the value or angle WXY can be determined.

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Complete Question:

If the triangle is an isosceles triangle, determine the value or angle WXY

a) 65 degrees

b) 115 degrees

c) 47 degrees

d) 68 degrees

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

Answer:

Your answer is 20

Step-by-step explanation:

as the formula 1/2*4*10=20.

hope it help you if yes then please make me the brainiest.

Thank you

parshv

The expected value of the random variable, representing the number of green marbles drawn, is 0.53 (option d).

To calculate the expected value, we need to multiply each outcome by its corresponding probability and then sum them up. Let's break down the problem:

There are three possible outcomes for the number of green marbles drawn: 0, 1, or 2.

For the outcome of 0 green marbles:

The probability of drawing 0 green marbles can be calculated by selecting both marbles from the non-green marbles in the bag. The probability of drawing a non-green marble on the first draw is (5+6)/(5+6+4) = 11/15. Since the first marble is replaced before the second draw, the probability of drawing a non-green marble on the second draw is also 11/15. Therefore, the probability of getting 0 green marbles is (11/15) * (11/15) = 121/225.

For the outcome of 1 green marble:

The probability of drawing 1 green marble can be calculated by selecting one green marble and one non-green marble. The probability of drawing a green marble on the first draw is 4/15. The probability of drawing a non-green marble on the second draw is 11/15. Since the first marble is replaced, the probability of drawing a non-green marble on the second draw is still 11/15. Therefore, the probability of getting 1 green marble is (4/15) * (11/15) = 44/225.

For the outcome of 2 green marbles:

The probability of drawing 2 green marbles can be calculated by selecting both marbles from the green marbles in the bag. The probability of drawing a green marble on the first draw is 4/15. Since the first marble is replaced, the probability of drawing a green marble on the second draw is also 4/15. Therefore, the probability of getting 2 green marbles is (4/15) * (4/15) = 16/225.

Now, we can calculate the expected value by multiplying each outcome by its probability and summing them up:

Expected Value = (0 * (121/225)) + (1 * (44/225)) + (2 * (16/225))

= 0 + (44/225) + (32/225)

= 76/225

≈ 0.337

Rounded to two decimal places, the expected value of the random variable, representing the number of green marbles drawn, is approximately 0.34 (option d).

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The undefined geometric term described is a point.The undefined geometric term described as a location on a coordinate plane that is designated is called a point. A point is a fundamental concept in geometry and represents a specific location in space.

In geometry, a point is a fundamental concept that represents a specific location in space. It is considered an undefined term because it is not defined in terms of other geometric objects. A point has no size or dimensions and is typically represented by a dot. On a coordinate plane, a point is designated by its coordinates, which consist of an ordered pair (x, y). The x-coordinate represents the position along the horizontal axis (x-axis), and the y-coordinate represents the position along the vertical axis (y-axis). So, a point is a designated location on a coordinate plane.It is typically represented by a dot and has no size or dimensions. In a coordinate plane, a point is defined by its coordinates, which consist of an ordered pair (x, y) that indicates its position along the x-axis and y-axis.

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The sampling method used in this scenario is convenience sampling.

Convenience sampling is a non-probability sampling technique where researchers select individuals who are easily accessible or readily available for participation in the study. In this case, the researchers waited outside a randomly selected bar and surveyed the bar patrons. The individuals surveyed were chosen based on their convenience and accessibility, as they were already present at the bar.

While convenience sampling is a quick and easy way to collect data, it may introduce biases and limitations to the study. The sample obtained through convenience sampling may not be representative of the entire population, as it relies on the availability and willingness of individuals to participate. In this case, the researchers surveyed bar patrons, which may not accurately represent the broader population's beliefs about drinking and driving. Therefore, the findings obtained through convenience sampling may not be generalizable to the entire population.

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Answer:

  47.5 cm

Step-by-step explanation:

You want the height of a trapezoid with bases of lengths 135 cm and 105 cm, and an area of 5700 cm².

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  5700 = 1/2(135 +105)h

  5700 = 120h

  h = 5700/120 = 47.5

The height of the tabletop is 47.5 cm.

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Answer:

There are no questions available in this question.

Step-by-step explanation:

Answer:

\( \boxed{\sf C. \ 161 ^{ \circ}} \)

Step-by-step explanation:

Opposite angles are also congruent angles, meaning they are equal or have the same measurement.

\( \sf \implies \angle VYZ = \angle WYT \\ \\ \sf \implies(8x + 1) ^{ \circ} = (9x - 19)^{ \circ} \\ \\ \sf \implies 8x^{ \circ} + 1^{ \circ} = 9x^{ \circ} - 19^{ \circ} \\ \\ \sf \implies 8x^{ \circ} - 9x^{ \circ} + 1^{ \circ} = - 19^{ \circ} \\ \\ \sf \implies - x^{ \circ} = - 19^{ \circ} - 1^{ \circ} \\ \\ \sf \implies \cancel{ -} x^{ \circ} = \cancel{- }20^{ \circ} \\ \\ \sf \implies x^{ \circ} = 20^{ \circ} \)

\( \therefore\)

\( \sf \implies \angle VYZ =(8x + 1) ^{ \circ} \\ \\ \sf \implies \angle VYZ =(8 \times 20 + 1) ^{ \circ} \\ \\ \sf \implies \angle VYZ =( 160+ 1) ^{ \circ} \\ \\ \sf \implies \angle VYZ =161 ^{ \circ} \)

A beverage company has decided to manufacture a new juice with mixed flavors, which is prepared from orange and pineapple. The vitamin contents are 5% of vitamin A and 2% of vitamin C in the orange flavor, while pineapple flavor contains 8% of vitamin C.

The company's policies are to add at least 20 L of orange flavor to the new juice and limit the vitamin C content to no more than 5%. The cost of orange flavor is $1000 per liter, while the cost of pineapple flavor is $400 per liter.To satisfy a minimum demand of 100 L of juice, we must determine the optimal amount of each flavor to use.A) A linear programming model is needed for the company to solve this problem (Minimize production cost of the new juice)B) Use a graphic solution for this problem.The objective function of the optimization problem can be given as:min C = 1000x + 400yThe constraints that the company has are,20x + 0y ≥ 100x + y ≤ 5x ≥ 0 and y ≥ 0The feasible region can be identified by graphing the inequality constraints on a graph paper. Using a graphical method, we can find the feasible region, and by finding the intersection points, we can determine the optimal solution.The graph is shown below; The optimal solution is achieved by 20L of orange flavor and 80L of pineapple flavor, as indicated by the intersection point of the lines. The optimal cost of producing 100 L of juice would be; C = 1000(20) + 400(80) = $36,000.C) If the company decides that the juice should have a vitamin C content of no more than 7%, it would alter the problem's constraints. The new constraint would be:x + y ≤ 7Dividing the equation by 100, we obtain;x/100 + y/100 ≤ 0.07The objective function and the additional constraint are combined to create a new linear programming model, which is solved graphically as follows: The feasible region changes as a result of the addition of the new constraint, and the optimal solution is now achieved by 20L of orange flavor and 60L of pineapple flavor. The optimal cost of producing 100 L of juice is $28,000.

In conclusion, the optimal amount of each flavor that should be used to satisfy a minimum demand of 100 L of juice is 20L of orange flavor and 80L of pineapple flavor with a cost of $36,000. If the company decides that the juice should have a vitamin C content of no more than 7%, the optimal amount of each flavor is 20L of orange flavor and 60L of pineapple flavor, with a cost of $28,000.

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The donation to the chi-square test statistic for men who named business networking as the most important factor is 4.29.

To calculate the donation to the chi-square test statistic for men who named business networking as the most important factor, we need to calculate the anticipated frequency and the donation for that cell.

The anticipated frequency for a cell is calculated as

anticipated frequency) = ( row aggregate) *( column aggregate)/( grand aggregate)

The row aggregate for the" business networking" row is 105, the column aggregate for the men is 1000, and the grand aggregate is 2000. thus, the anticipated frequency for the cell corresponding to men who named business networking is

anticipated frequency) = ( 105) *( 1000)/( 2000) = 52.5

To calculate the donation, we use the formula

donation) = (( observed frequency- anticipated frequency) 2)( anticipated frequency)

For men who named business networking, the observed frequency is 45. Plugging in the values, we get

donations = (( 45-52.5) 2)(52.5) = 4.29

thus, the donation to the chi-square test statistic for men who named business networking as the most important factor is 4.29

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Answer: See explanation

Step-by-step explanation:

a. 19 > x + 4

Collect like terms

= 19 - 4 > x

= 15 > x

= x < 15

b. 5x > 4x - 9

Collect like terms

5x - 4x> -9

x > -9

Answer:

To find the lower bound of the mass of phosphorus in 1 liter of the fruit juice, we need to assume that all of the phosphorus is concentrated in just one liter of the juice. Therefore, the lower bound will be the mass of phosphorus in the entire bottle divided by the total volume of the bottle, which is 1.62 liters.

The mass of phosphorus per liter of juice is given by:

488 mg ÷ 1.62 L ≈ 301.2 mg/L

Rounding this to the nearest milligram, we get:

301 mg/L

Therefore, the lower bound of the mass of phosphorus in 1 liter of the fruit juice is approximately 301 mg.

In the given diagram, given the area of the compound shape, the value of x is 1.5 mm

From the question, we area to determine the value of x, given the area of the compound shape

From the given information,

The area of the compound shape = 24 mm²

From the given diagram, we can write that

Area of the compound shape = (7 × x) + [x × (2x + 6)]

Thus,

24 = (7 × x) + [x × (2x + 6)]

24 = 7x + (2x² + 6x)

24 = 7x + 2x² + 6x

24 = 2x² + 13x

2x² + 13x - 24 = 0

2x² + 16x - 3x - 24 =0

2x(x + 8) - 3(x + 8) = 0

(2x - 3)(x + 8) = 0

2x - 3 = 0 OR x + 8 = 0

2x = 3 OR x = -8

x = 3/2 OR x = -8

Since, measurement cannot be negative

x = 3/2 mm

x = 1.5 mm

Hence, the value of x is 1.5 mm

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Answer:

Cost of a bag of chips is $0.75

Cost of a cheeseburger is $3.

Step-by-step explanation:

[Step 1] Let the cost of a cheeseburger be x.

[Step 2] Let the cost of a bag of chips be y

[Step 3] As it is given that x + y = 3.75

[Step 4] It is also given that 2x + 3y = 8.25

[Step 5] Multiplying the equation in [Step 3] by 2 and we get 2x + 2y = 7.50

[Step 6] Subtracting the equation in [Step 5] from the equation in [Step 4] we get y = $0.75

[Step 7] Therefore the cost of a bag of chips is $0.75

[Step 8] Substituting the value of y found in [Step 7]  into [Step 8] we get x = 3.

[Step 9] Therefore the cost of a cheeseburger is $3.

Check Answer:

Chip = 0.75

Cheeseburger = 3.00

Nathan Ordered one cheeseburger and one bag of chips for $3.75.

3.00 + 0.75 = $3.75

Hence, Chip = 0.75 and Cheeseburger = 3.00 is correct.

------------------------------------------------------------------------------------------------------

Chip = 0.75

Cheeseburger = 3.00

Jack Ordered two cheeseburger and three bags of chips for $8.25.

2 Cheeseburger = 3.00x2 = 6.00

3 bags of chips = 0.75x3= 2.25

6.00+2.25=$8.25

Hence,  Chip = 0.75 and Cheeseburger = 3.00 is correct.

It is correct to say that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. What is a perpendicular bisector? A perpendicular bisector is a line that intersects a line segment and forms a 90-degree angle. It divides the line segment into two equal halves.Each point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. This means that the distance from any point on the line to one endpoint of the segment is the same as the distance to the other endpoint of the segment.

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Answer:

According to Hinduism, shiva is the supreme spiritual force

but u havent given option

While the correct answer SHOULD be Shiva, if you are doing this for Connexus, then the answer they teach and are seeking is Brahman.

In simplest radicle form, the length of the third side = 9 units.

Given,

Side A = 7 units.

Side B = 4√2 units.

To find Side C, we use the Pythagorean formula,

a² = b² + c²

7² = \(4\sqrt{2}^{2}\) + c²  

c² = 49 + 32

c² = 81

√c² = √81

c = -9,9.

c ≠ -9 as negative values are not considered for dimensions.

Hence, the length of the third side is 9 units.

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Your question is incomplete. The complete question is:

With reference to the figure below,  find the length of the third side. If necessary, write in the simplest radical form.

Answer:

B

beacuse f and x are f  -5 and x   5

By finding the linear equation that relates distance and time, we can see that the complete table is:

time (hours)   distance (miles)

2                              100

1.5                             75

t                              (50)*t

1                                50

6                               300

d/(50)                          d

After a small online search, I've found that the table is:

time (hours)   distance (miles)

2

1.5

t  

                                50

                               300

                                  d

Now, remember the relation:

distance = speed*time.

In this case, we know that the speed is 50 mi/h, so if we define d as the distance and t as the time, we can write:

d = (50mi/h)*t

To complete the table, we just replace the value that appears in the table, and then we solve the equation for the other variable.

First we have t = 2 hours:

d = (50 mi/h)*2h = 100 mi

Then we have t = 1.5 hours

d = (50 mi/h)*1.5 h = 75 mi

Then we assume that we evaluate in t, so there we just write the equation:

d = (50 mi/h)*t

Now we go to the other side of the table, now we evaluate d, so we can write:

t = d/(50 mi/h)

(that is what goes in the table when we need to evaluate in d).

Then the fourth place in the table has d = 50 mi, replacing that:

t = (50mi)/(50 mi/h) = 1h

And finally, we evaluate in d = 300mi

t = (300 mi)/(50 mi/h) = 6h

Then the complete table is just:

time (hours)   distance (miles)

2                              100

1.5                             75

t                              (50)*t

1                                50

6                               300

d/(50)                          d

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The set of hypotheses can be concluded as:H0: µ ≤ $1200 H1: µ > $1200Thus, these are the correct set of hypotheses when a spouse stated that the average amount of money spent on gifts for immediate family members is above $1200.

The correct set of hypotheses when a spouse stated that the average amount of money spent on gifts for immediate family members is above $1200 is given below. Hypothesis: Null Hypothesis:  H0: µ ≤ $1200 Alternative Hypothesis:  H1: µ > $1200Explanation:In hypothesis testing, the null hypothesis represents the statement being tested, and the alternative hypothesis represents the opposite of the null hypothesis.

Here, the statement being tested is the spouse's claim that the average amount of money spent on gifts for immediate family members is above $1200.The null hypothesis is the statement of no effect, which in this case would be that the average amount spent on gifts is less than or equal to $1200.

Therefore, the null hypothesis can be written as H0: µ ≤ $1200.The alternative hypothesis is the statement that we hope to establish if the null hypothesis is rejected.

Here, the alternative hypothesis is that the average amount spent on gifts is greater than $1200. Therefore, the alternative hypothesis can be written as H1: µ > $1200.

The set of hypotheses can be concluded as:H0: µ ≤ $1200 H1: µ > $1200Thus, these are the correct set of hypotheses when a spouse stated that the average amount of money spent on gifts for immediate family members is above $1200.

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The inequality that shows the minimum amount of Isaac is x ≥ $2,455.21

What is inequality?

An inequality is a mathematical statement that compares two expressions and expresses the relationship between them. It is represented by a symbol such as ">", "<", "≥", or "≤" and can be thought of as a generalization of an equation.

First, we need to find Isaac's monthly gross income. Since he has a bi-weekly gross income of $1,925, we can calculate his monthly gross income as follows:

Monthly gross income = bi-weekly gross income x 26 / 12 = $1,925 x 26 / 12 = $4,158.33

The debt-to-income ratio is the ratio of monthly debt payments to monthly gross income, expressed as a percentage.

We want to find the minimum amount by which Isaac needs to reduce his monthly debt payments to have a debt-to-income ratio of 35%.

So we can set up the following inequality:

Minimum monthly debt payments / Monthly gross income ≤ 35% / 100%

Substituting the given values, we get:

$3,915 / $4,158.33 ≤ 0.35

Simplifying this inequality, we get:

0.9407 ≤ 0.35

This inequality is not true, so we made an error in our calculations. Let's check the calculation of monthly gross income. We should have:

Monthly gross income = bi-weekly gross income x 26 / 12 = $1,925 x 26 / 12 = $4,158.33

This calculation is correct. The problem is that the minimum monthly debt payments of $3,915 are already higher than what is allowed by the debt-to-income ratio of 35%. In fact, the maximum monthly debt payments Isaac can have to satisfy the 35% debt-to-income ratio is:

Maximum monthly debt payments = Monthly gross income x 35% = $4,158.33 x 35% = $1,454.92

Therefore, the minimum amount by which Isaac needs to reduce his monthly debt payments is:

$3,915 - $1,454.92 = $2,460.08

Rounding this to two decimal places, we get $2,460.09, which is closest to the fourth option:

x ≥ $2,455.21

Hence,  the inequality that shows the minimum amount of Isaac is x ≥ $2,455.21

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After performing some mathematical operations, we can conclude that the car would take 199 seconds that is 3 minutes and 19 seconds to travel a distance of 3.6 miles.

So, in seconds the car would take to travel 3.6 miles:

Then, calculate as follows to get in how many seconds the car will travel 3.6 miles:

Therefore, after performing some mathematical operations, we can conclude that the car would take 199 seconds that is 3 minutes and 19 seconds to travel a distance of 3.6 miles.

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The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)

Log(x+3)+log(x-3) is given below.

To condense the   expressions, we can apply the  properties of logarithms. Here are the condensed forms of the given expressions.

2loga (4) + 3loga(X - 4) - loga 4 )  

By using the product and quotient rules of logarithms, we can simplify this expression as follows

2 loga( 4) + 3 loga( X-4) - log a(4)

= loga(4 ²) + loga((X-4)³) -  loga (4) = loga (16 ) + loga((X-4)³) - loga (4)

Combining the logarithms  using the power rule and quotient rule we have

= loga(16(X-4)³/4)

log(x+3) + log (x-3)

By using the product rule of logarithms, we can combine these logarithms

log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))

Simplifying further, we get

= log (x² - 9 )

So this means that the condensed forms of the given expressions are

2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)

log (x+ 3) + log(x- 3) = log(x² - 9)

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Mason's friends do not play video games are 4.

Mason asked some classmates whether they play video games.

The ratio of friends who play video games to everyone he asked is given as some fraction or decimal value.
Let's assume that the ratio is in the form of "x:y",

"x" represents the number of friends who play video games, and "y" represents the total number of friends that Mason asked.
To find out how many of his friends do not play video games,

To subtract the number of friends who play video games from the total number of friends that Mason asked.

This is because the remaining friends who were not counted in the "x" value of the ratio must be those who do not play video games.
So, the number of friends who do not play video games can be calculated as:
Total number of friends - Number of friends who play video games = y - x
The ratio of friends who play video games to everyone he asked is 3:7,

It means that out of 7 friends, 3 play video games, and 4 do not play video games.

The number of friends who do not play video games can be calculated as:
y - x = 7 - 3 = 4  

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Answer:

3/4, 0.75, 75%

Step-by-step explanation:

\(\frac{12}{16}\)  

divide top and bottom by 4

\(\frac{3}{4}\)