What are the coordinates of the vertices of d(3, a)(△abc) for a(0, 4), b(−2, 5), and
c(3, 7)? does the perimeter increase or decrease?

The perimeter of a rectangle is 34 units.

To find the perimeter of the rectangle with vertices (3,2), (13,2), (13,9), and (3,9), you need to determine the lengths of its sides.

The distance between (3,2) and (13,2) is the length of the base: 13 - 3 = 10 units.
The distance between (3,2) and (3,9) is the height: 9 - 2 = 7 units.

The perimeter of a rectangle is given by the formula P = 2*(length + width). In this case, P = 2*(10 + 7) = 2*17 = 34 units.

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The value of x is 26.5, found using the property of intersecting chords in a circle and the Pythagorean theorem.

To find the value of x, we can use the property that states that if two chords intersect in a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

In this case, we can draw radii from O to points P and S, and label their lengths as 19. Then, we can label the segments of chords FG and RS as follows:

                     Let a = FG and b = GP

                      Let c = RS and d = SP

Since OP is a radius of the circle, we know that a + b = 19. Similarly, since OS is a radius of the circle, we know that c + d = 19.

Using the property mentioned above, we can write:

                      a * b = c * d

Substituting the given values, we get:

                   25 * (19 - b) = 28 * (19 - d)

Expanding and simplifying, we get:

                      475 - 25b = 532 - 28d

Substituting a + b = 19 and c + d = 19, we get:

                 b = 19 - a and d = 19 - c

Substituting these values, we get:

                 25a - 25(19 - a) = 28c - 28(19 - c)

Simplifying, we get:

                    53a - 475 = 28c - 532

Rearranging, we get:

                       53a - 28c = -57

We also know that a + c = 25 + 28 = 53.

We can solve these two equations simultaneously to find the values of a and c:

                        a = 13.8

                        c = 39.2

Therefore, the length of the segment RS is 39.2, and the length of the segment RP19S is 58.2.

Using the Pythagorean theorem, we can find the length of the segment OP:

                  (OP)²= (RP19S)² - (19)²

                  (OP)² = (58.2)² - (19)²

                  (OP)² = 3136.24

                        OP = 56

Finally, we can find x using the fact that the chords FG and RS are parallel:

                           x = (1/2) * (FG + RS)

                           x = (1/2) * (25 + 28)

                           x = 26.5 (rounded to the nearest tenth)

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The minimum value of k that satisfies this inequality is k = 9.

To find the value of k for which the area of the triangle is a minimum, we'll use the following terms: vertices, non-degenerate triangle, and area of a triangle. Here's the step-by-step explanation:

1. The vertices of the triangle are $(1, 7), (13, 16),$ and $(5, k)$.
2. A non-degenerate triangle means it has a positive area.
3. The area of a triangle can be calculated using the formula: Area = (1/2) * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Now, let's find the area of the triangle with the given vertices:

Area = (1/2) * |1(16 - k) + 13(k - 7) + 5(7 - 16)|

We want to minimize the area, so let's simplify the expression:

Area = (1/2) * |-9 + 13k - 104|

Since we want a non-degenerate triangle, the area must be greater than 0. Therefore, the expression inside the absolute value must be positive:

-9 + 13k - 104 > 0
13k > 113
k > 113/13
k > 8.69

Since k is an integer, the minimum value of k that satisfies this inequality is k = 9.

The sum of the values of k for which the area of the triangle is a minimum is just the single value we found, which is 9.

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The exact length of the curve is 112/3(√3 + 1), or approximately 96.666.

To find the exact length of the curve, we can use the formula for arc length:

L = ∫a^b √(1 + [f'(x)]²) dx

where f(x) = (x² - 4)^(3/2)/6, 5 ≤ x ≤ 9.

First, we find f'(x):

f'(x) = 3x(x² - 4)^(1/2)/12 = x(x² - 4)^(1/2)/4

Then we substitute f'(x) into the formula for arc length:

L = ∫5^9 √(1 + [x(x² - 4)^(1/2)/4]²) dx

L = ∫5^9 √(1 + x²(x² - 4)/16) dx

L = ∫5^9 √(16 + 16x²(x² - 4)/16) dx

L = ∫5^9 √(16x² + x^4 - 4x²) dx

L = ∫5^9 √(x^4 + 12x²) dx

L = ∫5^9 x²√(x^2 + 12) dx

We can use the substitution u = x^2 + 12, which gives du/dx = 2x and dx = du/2x, to simplify the integral:

L = (1/2)∫37^93 √u du

L = (1/2) [(2/3)u^(3/2)]_37^93

L = (1/3)[(125 + 108√3) - (13 + 36√3)]

L = (1/3)(112√3 + 112)

L = 112/3(√3 + 1)

Therefore, the exact length of the curve is 112/3(√3 + 1), or approximately 96.666.

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Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

To answer your question about how many cups of water Abby should add to make 1 gallon of punch, let's first convert all the given measurements to cups. One gallon is equivalent to 16 cups.

1. Orange juice: Abby uses 2 quarts of orange juice. Since there are 4 cups in a quart, she uses 2 x 4 = 8 cups of orange juice.

2. Lemon juice: Abby uses 1 cup of lemon juice.

3. Pineapple juice: Abby uses 2 1/2 pints of pineapple juice. There are 2 cups in a pint, so she uses (2 1/2) x 2 = 5 cups of pineapple juice.

Now, let's add up the cups of orange juice, lemon juice, and pineapple juice: 8 + 1 + 5 = 14 cups. Since Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

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The solution to the inequality is x ≥ -1.

We solve the inequality 1/3(2x-1)≤1-2/5(2-3x).

Let's go step by step:
Begin by distributing the fractions to the terms inside the parentheses:
  (1/3 * 2x) - (1/3 * 1) ≤ 1 - (2/5 * 2) + (2/5 * 3x)
  (2x/3) - (1/3) ≤ 1 - (4/5) + (6x/5)
Combine like terms on each side of the inequality:
  (2x - 1)/3 ≤ (1 - 4/5) + 6x/5
  (2x - 1)/3 ≤ (1/5) + 6x/5.

To eliminate the fractions, find a common denominator, which in this case is 15.

Multiply each term by 15:
  15 * (2x - 1)/3 ≤ 15 * (1/5) + 15 * 6x/5
  5(2x - 1) ≤ 3 + 18x
Distribute and simplify:
  10x - 5 ≤ 3 + 18x
Move the variables to one side and constants to the other side:
  10x - 18x ≤ 3 + 5
  -8x ≤ 8
Divide both sides by -8 (remember to flip the inequality sign since we are dividing by a negative number):
  x ≥ -1.

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Answer:3:58 p.m.

Step-by-step explanation:

Answer: x = 10

Step-by-step explanation: To solve this equation, you can use the logarithmic property that states loga(b) + loga(c) = loga(bc). So, you can rewrite the left side of the equation as log2((x-6)(x+6)). Then, you can use the property that states loga(b) = c is equivalent to a^c = b to solve for x.

So, you have log2((x-6)(x+6)) = 6, which is equivalent to 2^6 = (x-6)(x+6). Simplifying the left side gives you 64, and expanding the right side gives you x^2 - 36 = 64. Solving for x gives you x = ±√100, which is x = ±10. However, since the original equation includes logarithms.

The statement mentions that the kitchen sink has a capacity of 108.460 L of water and it is important to round up the amount to the nearest liter. When we round up the capacity of the sink, it comes out to be 108 liters. This means that the sink can hold up to 108 liters of water at maximum capacity.

It is important to have an idea of the sink’s capacity in terms of liters because it helps in managing the amount of water used while washing dishes or other household items. It is also beneficial to know the capacity of the sink while filling it with water for cleaning purposes, as it prevents the sink from overflowing.

Overall, the capacity of a sink is an important factor to consider while designing a kitchen or bathroom as it ensures proper functionality and prevents any damage to the surrounding areas due to overflowing water. So, it is always advisable to check the capacity of a sink before installing it in a household.

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Complete Question  :  Mirrors kitchen sink holds up to 108.460 L of water. Round this amount to the nearest liter.

Susan earns $9.50 per hour. This is found by dividing her earnings by the number of hours worked for each corresponding row in the table.

To find how much money Susan earned per hour, we need to divide the total earnings by the total number of hours worked. For finding the Total earnings we need to add the money earned in every hour,

Total earnings = $47.50 + $66.50 + $85.50 + $104.50 = $304

Total hours worked = 5 + 7 + 9 + 11 = 32

Money earned per hour = Total earnings / Total hours worked

= $304 / 32

= $9.50

Therefore, Susan earned money of $9.50 per hour.

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When Krissa exercises daily by walking and she aims to walk at a steady rate of 3.4 miles per hour:

a) The equation is d = 3.4t;

b) Krissa will walk 2.13 miles;

c) It will take Krissa 1.6 hours to walk 5.44 miles.

When Krissa exercises daily by walking and she aims to walk at a steady rate of 3.4 miles per hour:

a. The equation that models the relationship between time and distance is:

d = 3.4t

where d is the distance Krissa walks in miles and t is the time she spends walking in hours.

b. To calculate the distance Krissa will walk in 5/8 of an hour, we can substitute t = 5/8 into the equation from part a:

d = 3.4(5/8) = 2.125 miles

Therefore, Krissa will walk 2.125 miles in 5/8 of an hour, rounded to the hundredths.

c. To calculate how long it will take Krissa to walk 5.44 miles, we can rearrange the equation from part a to solve for t:

t = d/3.4

Substituting d = 5.44 into this equation, we get:

t = 5.44/3.4 = 1.6 hours

Therefore, it will take Krissa 1.6 hours to walk 5.44 miles.

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The cost of two oranges is 1.1 dollars.

One Sunday, Cory bought 4 apples and 6 oranges and paid $5.10. Dalia bought 2 apples and 5 oranges and paid $3.65.

Therefore, using equation,

let

x = cost of each apples

y = cost of each oranges

Hence,

4x + 6y = 5.10

2x + 5y = 3.65

Multiply equation(ii) by 2

4x + 6y = 5.10

4x + 10y = 7.3

4y = 2.2

y = 2.2 / 4

y = 0.55 dollars

Therefore,

cost of 2 oranges = 0.55(2) = 1.1 dollars

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Variable expenses are expenses that fluctuate from month to month, and are typically not a fixed amount. Examples of variable expenses include groceries, fuel, clothing, and entertainment. These expenses can be influenced by various factors such as personal choices, seasonality, and external events.

In Luis's expenses, the following expenses are variable expenses:

On the other hand, the following expenses are fixed expenses:

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Answer:

groccieries is the answer for plato 2023

Answer: 45 (depends on what the rightmost angle is)

Step-by-step explanation:

All angles of a triangle add up to 180 degrees.

Two angle measures are provided, 100 and 35 (?)

Add up the two to get 135, and subtract from 180

180 - 135 = 45 degrees.

I might be seeing the rightmost angle measure wrong but I think it's 35, if it's not you can still apply the same strategy, just add the two given angles and subtract that from 180 to find x.

Let the fraction be x/y.

We know that x + y = 12, and that (x) / (y + 3) = 12.

Multiplying both sides of the second equation by (y + 3), we get:

x = 12(y + 3)

Substituting this into the first equation, we get:

12(y + 3) + y = 12

Expanding and simplifying, we get:

13y + 36 = 12

Subtracting 36 from both sides, we get:

13y = -24

Dividing both sides by 13, we get:

y = -24/13

Substituting this value of y into the equation x + y = 12, we get:

x - 24/13 = 12

Multiplying both sides by 13, we get:

13x - 24 = 156

Adding 24 to both sides, we get:

13x = 180

Dividing both sides by 13, we get:

x = 180/13

Therefore, the fraction is 180/13 divided by -24/13, which simplifies to -15/2.

The ferris wheel will take a total time of 10 seconds for the platform to reach the 11 o'clock position and the diver's height off the ground when he is at the 11 o'clock position is 50 feet.

To determine the time it takes for the platform to reach the 11 o'clock position and the diver's height off the ground, we will use the given information about the ferris wheel.

1. The ferris wheel has a radius of 50 ft and turns counterclockwise at a constant speed with a period of 40 seconds.
2. The center of the wheel is 65 ft off the ground.
3. The platform is at the 3 o'clock position when it starts moving (t=0).

The ferris wheel has a period of 40 seconds, which means it takes 40 seconds for it to make a full rotation. The distance between the 3 o'clock position and the 11 o'clock position is 90 degrees out of 360, which is one-fourth of the total distance around the circle.

Therefore, it will take 1/4 of the total time for the platform to reach the 11 o'clock position, which is 40/4 = 10 seconds.

To find the diver's height off the ground at the 11 o'clock position, we can use the sine function. Let's call the angle formed by the radius from the center of the ferris wheel to the diver and the radius from the center of the ferris wheel to the 3 o'clock position θ.

Since the platform starts at the 3 o'clock position and rotates counterclockwise, θ will increase as time passes. At the 11 o'clock position, θ will be 90 degrees.

We know that the radius of the ferris wheel is 50 feet and the center of the ferris wheel is 65 feet off the ground. Let's call the height of the diver off the ground h. Then we have:

sin θ = h / (50 ft)

h = (50 ft) * sin θ

At the 11 o'clock position, θ = 90 degrees, so we have:

h = (50 ft) * sin 90°

h = 50 ft

Therefore, the diver's height off the ground when he is at the 11 o'clock position is 50 feet.

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The height of the right circular cone ,candle is approximately 6.8 inches.

To find the height of the third candle, which is a right circular cone with a volume of 16 cubic inches and a radius of 1.5 inches, we will use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

1. Substitute the given values into the formula: 16 = (1/3)π(1.5)^2h
2. Simplify the equation: 16 = (1.5^2 * π * h) / 3
3. Solve for h:
  a. Multiply both sides by 3: 48 = 1.5^2 * π * h
  b. Divide by π: 48/π = 1.5^2 * h
  c. Divide by 1.5^2: (48/π) / 1.5^2 = h
4. Calculate the height, and round to the nearest tenth: h ≈ 6.8 inches

The height of the candle is approximately 6.8 inches.

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The result of 19 minus a negative 29 is 48. Expressed as a fraction in simplest form, this would be 48/1.

To find the difference between 19 and negative 29, we can use the rule that subtracting a negative number is the same as adding its absolute value. So, 19 - (-29) is the same as 19 + 29, which equals 48.

To write this as a fraction in simplest form, we simply put 48 over 1, since any integer can be expressed as a fraction with a denominator of 1. We don't need to simplify any further, so our final answer is 48/1.

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Answer:  D.  7/15 or

Step-by-step explanation:

You have 15 possible outcomes

Probability= possibilities/outcomes

Possible numbers that are multiples of 3 are: 3, 6, 9, 12, 15.  There are 5 possibilities.

P(multiple of 3) = 5/15

Possible numbers that are multiples of 7 are: 7, 14, .  There are  2 possibilities.

P(7) = 2/15

Because of the or you add th e probabilities

P(multiple of 3 or multiple of 7) = 5/15 +2/15 =7/15

D

Answer:

b+24

Step-by-step explanation:

the sum of a number represented by variable b

-- b+

and 24

-- b+24

Answer: b + 24

Step-by-step explanation:

The sum of .. and ➜ addition between two values

a number b ➜ b (represented by a variable)

24 ➜ the number 24

         The sum of a number b and 24 ➜ b + 24

Answer:

It is C

Step-by-step explanation:

It cannot be d bc - 7-4=-11 so rejected

Not b bc the first number is - 7

The same w a

The missing step in solving the inequality 4(x – 3) /4 < 10/6x is to divide both sides by 2.

Apply the distributive property to get 4x - 12 /4 < 10/6x.

Combine like terms to obtain 4x - 3 < 5/3x.

Add 3/3x to both sides to get 4x < 8/3x + 3.

Subtract 8/3x from both sides to get 4/3x < 3.

Divide both sides by 4/3 to get x < -9/4.

Simplify the result by dividing both sides by 2 to get x < -9/2 or x > -4/3.

Therefore, the missing step is to divide both sides by 2, which gives x < -9/2 or x > -4/3.

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The solution of the graphs of the equations is; )(6, 3 2/3)

A system of equation consists of two or more equations that share the same variables.

The solution of a system of equations obtained graphically can be obtained from the point of intersection of the lines of the graph of the equations

Taking the axis as the lowermost and  leftmost white lines, we get;

The points on the function f are (0, 1), and (9, 5)

The slope is; (5 - 1)/(9 - 0) = 4/9

The y-intercept is; (0, 1)

The equation is; y = (4/9)·x + 1

The equation of the line g is; x = 6

Therefore, the point of intersection is; y = (4/9)×6 + 1 = 8/3 + 1 = 11/3 = 3 2/3

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The equation that represents the asymptote of the function, y = tan x is: C. x = π/4.

Option A, x = -π, and Option D, x = (3π)/2, do not represent asymptotes of the graph of the function y = tan x.

Option B, x = 0, represents a vertical asymptote of the graph of y = tan x because tan x is undefined at x = π/2 + kπ, where k is an integer. Therefore, tan x is undefined at x = π/2, 3π/2, 5π/2, etc. and there is a vertical asymptote at x = 0.

Option C, x = π/4, represents a linear asymptote of the graph of y = tan x. As x approaches π/4 from either side, the tangent function approaches a straight line with slope 1 and x-intercept 0. Therefore, the equation of the asymptote is y = x - π/4.

Thus, the answer is C. x = π/4.

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The chef will use 43.5 pounds of ingredients to make soup for 40 people. Your answer is 43.5..

Step 1: Calculate the pounds of beef for 40 people using the expression 0.3n.
0.3 * 40 = 12 pounds of beef

Step 2: Calculate the pounds of carrots, which is 7 fewer than the pounds of beef.
12 - 7 = 5 pounds of carrots

Step 3: Calculate the pounds of potatoes, which is twice the pounds of beef.
2 * 12 = 24 pounds of potatoes

Step 4: Calculate the pounds of onions, which is half the pounds of carrots.
0.5 * 5 = 2.5 pounds of onions

Step 5: Add up the pounds of all ingredients to find the total pounds for 40 people.
12 (beef) + 5 (carrots) + 24 (potatoes) + 2.5 (onions) = 43.5 pounds

The chef will use 43.5 pounds of ingredients to make soup for 40 people. Your answer is 43.5.

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Answer:

y = 5x + 5

Step-by-step explanation:

If x is the number of boxes sold and y is the cost

The first box costs $10

Each additional box costs $5.

If the total number of boxes sold is x, then after selling the first box for $10, there will be x - 1 boxes left to be sold

The cost of x -1 boxes at $5 per box = 5(x - 1) = 5x - 5

Therefore for a total of x boxes sold the total cost, y in dollars is
y = 10 (for the first box)  +  5x - 5 (for the remaining x - 1 boxes)

= 10 + 5x - 5

= 5 + 5x

which in standard form is written as
y = 5x + 5

We can verify our equation using specific numbers for x
For x = 1
y = 5 + 5(1) = 10   ; since only one box has been sold, the cost is fixed at $10

For x = 2 y = 5 + 5(2) = 5 + 10 = $15
This works out to since first box is sold at $10 and the second box at $5

Leave it to you to work out for other numbers

Answer: $193.42

Step-by-step explanation:

Based on the given designs, the cost to make the triangular and circular street signs would be $68.60 and $124.42 respectively, making the total cost of making both signs $193.02.

To calculate the cost of making the two street signs, we need to first find the area of each sign. The area of a triangle is given by the formula 1/2 x base x height. So, for the triangular street sign, the area would be 1/2 x 3 x 2.6 = 3.9 square feet.

The area of a circle is given by the formula π x radius². So, for the circular street sign, the area would be π x (1.5)² = 7.065 square feet.

Now that we have the areas of both signs, we can calculate the total cost of the material needed. The cost per square foot of material is $17.64, so we need to multiply this by the total area of the signs.

For the triangular sign, the cost would be 3.9 x $17.64 = $68.60.

For the circular sign, the cost would be 7.065 x $17.64 = $124.42.

Therefore, the total cost to make both signs would be $68.60 + $124.42 = $193.02.

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1. The skirt cost using Mai's method is $21.68.

2. The skirt cost using Elena's method is $21.

3. Mai's method is correct because she correctly calculates the discounts sequentially while Elena combines the discount.

We'll examine the methods suggested by Mai and Elena for finding the new price of the skirt and determine which one is correct.

1. Using Mai's method (30 x 0.85 x 0.85):

1: Calculate the first 15% off discount: 30 x 0.85 = 25.50

2: Calculate the additional 15% off discount: 25.50 x 0.85 = 21.675

So, the skirt will cost $21.68 using Mai's method (rounded to the nearest cent).

2. Using Elena's method (30 x 0.70):

Elena suggests taking 30% off the original price. To do this, we multiply the original price by 0.70:

30 x 0.70 = 21

So, the skirt will cost $21 using Elena's method.

3. Explanation of the difference in expressions and the correct method:

Mai's method is correct because she correctly calculates the discounts sequentially. The first 15% off is applied to the original price, and then the additional 15% off is applied to the reduced price. This results in a final price of $21.68.

Elena's method is incorrect because she combines the two discounts into a single 30% off, which does not accurately reflect the sequential discounts. By doing this, she finds a final price of $21, which is not correct.

In conclusion, Mai's method (30 x 0.85 x 0.85) is the correct way to calculate the new price of the skirt, resulting in a final cost of $21.68.

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The maximum concentration of the antibiotic between hours 1 and 7 is 1.03 mg/ug, which occurs at t = 1/39 hours.

To find the maximum concentration of the antibiotic between hours 1 and 7, we need to find the maximum value of the function C(t) on the interval [1, 7]. We can do this by taking the derivative of C(t), setting it equal to zero, and solving for t.

C(t) = 4te^{-39t}

C'(t) = 4e^{-39t} - 156te^{-39t}

Setting C'(t) equal to zero, we get:

4e^{-39t} - 156te^{-39t} = 0

4e^{-39t}(1 - 39t) = 0

1 - 39t = 0

t = 1/39

We can now evaluate C(t) at t = 1/39 and the endpoints of the interval [1, 7] to determine the maximum concentration:

C(1) = 4e^{-39} ≈ 0.00011 mg/ug

C(7) = 28e^{-273} ≈ 0.000000003 mg/ug

C(1/39) = 1.0256 mg/ug

Therefore, the maximum concentration of the antibiotic between hours 1 and 7 is 1.03 mg/ug, which occurs at t = 1/39 hours.

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The value of x as an improper fraction in its simplest form is 14/5.

To solve the inequality 5x - 4 < 10, we need to isolate x on one side of the inequality. First, we add 4 to both sides:

5x - 4 + 4 < 10 + 4

5x < 14

Then, we divide both sides by 5:

5x/5 < 14/5

x < 2.8

Therefore, the solution to the inequality is x < 2.8. However, the question asks for the answer as an improper fraction in its simplest form. To convert 2.8 to an improper fraction, we multiply both the numerator and denominator by 10 to get rid of the decimal:

2.8 * 10 / 1 * 10 = 28 / 10

To simplify the fraction, we divide both the numerator and denominator by their greatest common factor, which is 2:

28 / 10 = 14 / 5

Therefore, the answer is 14/5.

Learn more about improper fraction at https://brainly.com/question/27847209

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