find the equation of the circle below

The units digit of the 5857th triangular number is 8.

A series of numbers known as triangular numbers may be modelled as the sum of a series of positive integers. The equation Tn = (n(n+1))/2 yields the nth triangular number. The first few triangular numbers, for instance, are 1, 3, 6, 10, 15, and so on. Many mathematical and non-mathematical applications exist for triangular numbers. They can be found, for instance, in the study of geometry, combinatorics, and number theory. They are utilised in algorithms for data searching and sorting in fields like computer science, where they have practical applications.

The nth triangular number is given by the formula:

Tn = (n(n+1))/2

For the given sequence 1,3,6,10,15,21,28,36, the units digit are:

1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, ...

The value of 5857 is congruent to 7 modulo 10.

Thus, the units digit is seventh number in the cycle above, that is 8.

Hence, the units digit of the 5857th triangular number is 8.

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The range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.

A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.

To find the range of the function f(x) = x + 3, we need to apply the function to each value in the given domain and collect the resulting outputs.

When the domain is {-1, 3, 5, 7}, we have:

f(-1) = -1 + 3 = 2

f(3) = 3 + 3 = 6

f(5) = 5 + 3 = 8

f(7) = 7 + 3 = 10

Therefore, the range of the function is the set of all possible output values, which are {2, 6, 8, 10}. So the correct answer is option C.

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To find where the line crosses the x-axis, we need to find the value of x the line crosses the x-axis at the point   [tex](-5/3, 0).[/tex]

a) The gradient of a line is the coefficient of the x term in its equation in the form y = mx + c, where m is the gradient. Therefore, the gradient of the line with equation [tex]y = 3x + i is 3[/tex]  .

b) Since the line passes through the point (2, 11), we can substitute these values into the equation  [tex]y = 3x + i[/tex] to find the value of i:

[tex]11 = 3(2) + i[/tex]

[tex]11 = 6 + i[/tex]

[tex]i = 11 - 6[/tex]

[tex]i = 5[/tex]

Therefore, the equation of the line can be written as   [tex]y = 3x + 5.[/tex]

c) The value of k in the equation   [tex]11 = 6 + k[/tex] is simply the y-intercept of the line. From the equation [tex]y = 3x + 5[/tex]  , we can see that the y-intercept is 5. Therefore, k = 5, and the equation of the line is [tex]y = 3x + 5.[/tex]

d) To find where the line crosses the x-axis, we need to find the value of x when y = 0. Substituting y = 0 into the equation [tex]y = 3x + 5[/tex]  , we get:

[tex]0 = 3x + 5[/tex]

[tex]x = -5/3[/tex]

Therefore, the line crosses the x-axis at the point  [tex](-5/3, 0).[/tex]

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a) The gradient of the line is 3.

c) The Value of k is 6.

d) The line crosses the y-axis at (0, 5).

The line's equation is y = 3x + k,

a) Compare this with the standard equation of line y = mx + c

where 3 is the coefficient of x.

The slope or gradient of a line is represented by the coefficient of x in its equation.

As a result, the gradient of the line y = 3x + k is 3.

b) We now know that the line goes through the point. (2, 11). Using the equation y = 3x + k, we can find the value of the y-intercept (k) at this moment. When we substitute x = 2 and y = 11 into the equation, we get:

11 = 3(2) + k

When we simplify the right side, we get:

11 = 6 + k

c) When we subtract 6 from both sides, we get:

k = 11 - 6 = 5

As a result, the equation of the line is as follows:

y = 3x + 5.

d) So, the y-intercept value is 5, indicating that the line crosses the y-axis at the location. (0, 5).

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Answer:

3. ( 3, -1 )

Step-by-step explanation:

Therefore, the best prediction for the number of times the spinner will land on blue in 6 spins is 1. However, it's important to note that this is just a prediction based on probability, and the actual number of times the spinner lands on blue may vary from this prediction.

Probability refers to the measure or quantification of the likelihood of an event or outcome occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event (never occurring) and 1 represents a certain event (always occurring).

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we flip a fair coin, the probability of getting heads is 0.5, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

by the question.

Assuming that the spinner is fair and unbiased, and that the probability of landing on blue is equal to the probability of landing on any other color, the best prediction for the number of times it will land on blue is simply the expected value of the number of times it will land on blue in 6 spins.

Since there are six equally likely outcomes each time the spinner is spun, the probability of landing on blue is 1/6. Thus, the expected number of times the spinner will land on blue in 6 spins is:

Expected number of times landing on blue = probability of landing on blue × number of spins

Expected number of times landing on blue = 1/6 × 6

Expected number of times landing on blue = 1

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Answer: 25

Step-by-step explanation:

Let x represent the number of pages Broonzy read last night. Then, 5x represents the number of pages she will read tonight. According to her plan, after reading 5x pages tonight and 10 pages tomorrow night, she will complete the remaining 40 pages. The equation can be expressed as:

x (last night) + 5x (tonight) + 10 (tomorrow night) = 40 (total remaining pages)

Combining the terms, we get:

6x + 10 = 40

Now, let's solve for x:

6x = 30

x = 5

So, Broonzy read 5 pages last night. To determine the number of pages she needs to read tonight, we multiply x by 5:

5x = 5 * 5 = 25

Therefore, Broonzy has to read 25 pages tonight to finish her book according to her plan.

The equation of line that is parallel to y = -4 and passes through the point (3,7) is y = 7

Since the line we want to find is parallel to y = -4, it has the same slope as y = -4, which is 0 (since the line is horizontal).

Now we can use the point-slope form of the equation of a line to find the equation of the line passing through the point (3,7) with slope 0

y - y1 = m(x - x1)

where (x1, y1) is the given point, and m is the slope.

Plugging in the values, we get

y - 7 = 0(x - 3)

Simplifying, we get

y - 7 = 0

y = 7

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I have solved the question in general, as the given question is incomplete.

The complete question is:

What is the equation of a line that is parallel to y = -4 and passes through the point (3,7)?

a. Sketch of a rhombus that is not a square, the line segment JK as one of its diagonals is mentioned below. b. The polygon formed , connecting the consecutive midpoints of each side of a rhombus is a rectangle.

A line segment is a part of a line that is bounded by two distinct endpoints. In geometry, a line is an infinite straight path that extends indefinitely in both directions, but a line segment is a finite portion of that path with a measurable length. The length of a line segment can be determined by measuring the distance between its two endpoints using a ruler or other measuring tool.

a. Here is a sketch of a rhombus that is not a square, using the line segment JK as one of its diagonals. I've labeled the midpoint of each side of the rhombus with M1, M2, M3, and M4:

        M2       x         M3

        .___________.  

        |                        |  

        |                        |  

   M1x          .             x  M4

        |                        |  

        |___________|  

        M4       x           M3

b. The polygon formed by connecting the consecutive midpoints of each side of a rhombus is a rectangle. To see why, let's look at the diagonals of the rhombus. Since the diagonals of a rhombus are perpendicular bisectors of each other, we know that they intersect at right angles, dividing the rhombus into four congruent right triangles. Let's call the point where the diagonals intersect P.

Now, let's look at the line segments that connect the midpoints of opposite sides of the rhombus. These line segments are parallel to each other, and each one connects two midpoints that are equidistant from the intersection point P. Therefore, these line segments are also equidistant from each other, and they divide the rhombus into four congruent rectangles.

Finally, we can see that the polygon formed by connecting the consecutive midpoints of each side of a rhombus is simply a subset of the lines that connect the midpoints of opposite sides. Since these lines form congruent rectangles, we know that the polygon formed by the midpoints is also a rectangle.

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a. Sketch of a rhombus that is not a square, the line segment JK as one of its diagonals is mentioned below.

b. The polygon formed , connecting the consecutive midpoints of each side of a rhombus is a rectangle. Whose image is attached below.

A line segment is a part of a line that is bounded by two distinct endpoints. In geometry, a line is an infinite straight path that extends indefinitely in both directions, but a line segment is a finite portion of that path with a measurable length. The length of a line segment can be determined by measuring the distance between its two endpoints using a ruler or other measuring tool.

a. Here is a sketch of a rhombus that is not a square, using the line segment JK.

b. The polygon formed by connecting the consecutive midpoints of each side of a rhombus is a rectangle. To see why, let's look at the diagonals of the rhombus. Since the diagonals of a rhombus are perpendicular bisectors of each other, we know that they intersect at right angles, dividing the rhombus into four congruent right triangles. Let's call the point where the diagonals intersect P.

Now, let's look at the line segments that connect the midpoints of opposite sides of the rhombus. These line segments are parallel to each other, and each one connects two midpoints that are equidistant from the intersection point P. Therefore, these line segments are also equidistant from each other, and they divide the rhombus into four congruent rectangles.

Finally, we can see that the polygon formed by connecting the consecutive midpoints of each side of a rhombus is simply a subset of the lines that connect the midpoints of opposite sides. Since these lines form congruent rectangles, we know that the polygon formed by the midpoints is also a rectangle.

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From a point 100m from a building the angles of elevation to the top and the bottom of a flagpole atop the building are 54.5 degrees and 51.8 degrees. Therefore, the height of the flagpole is 125.6m.

we can use the trigonometric ratios of Sine, Cosine, and Tangent.

First, we need to draw a right triangle with the given information.

The triangle will have two sides:

the 100m side and the side to the flagpole. We can use the angle of elevation of 54.5 degrees to calculate the side of the triangle opposite the flagpole.

To do this, we use the Tangent ratio and solve for the side opposite the flagpole (the height of the flagpole):

Tangent(54.5) = Height/100

Height = 100*Tangent(54.5)

Height = 100*1.256

Height = 125.6m

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Answer: variables

Step-by-step explanation:

mathmeticians made this to where it would leave things out of questions, so factoring would just be your variables my guy

The five number summary is: Minimum: 60 Q1 (first quartile): 63 ,Median: 70Q3 (third quartile): 75, Maximum: 79

To find the five number summary of the data set 72, 60, 64, 75, 79, 63, 70, 61, 78, follow these steps:

1. Arrange the data in ascending order: 60, 61, 63, 64, 70, 72, 75, 78, 79

2. Identify the minimum value (smallest number): 60

3. Identify the maximum value (largest number): 79

4. Calculate the median (middle number): There are 9 data points, so the median is the 5th number: 70

5. Calculate the first quartile (Q1): The lower half of the data set is 60, 61, 63, 64, 70. The median of this lower half is the

middle number, which is 63.

6. Calculate the third quartile (Q3): The upper half of the data set is 70, 72, 75, 78, 79. The median of this upper half is

the middle number, which is 75.

The five number summary is:

Minimum: 60

Q1 (first quartile): 63

Median: 70

Q3 (third quartile): 75

Maximum: 79

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Answer: y=-3/4x-11

Step-by-step explanation: slope= -3/4

y+8=-3/4x+4

y+8=-3/4x-3

y=-3/4x-11

Answer:

31

Use Bodmas to solve it

7*3 + 10
21 +10
31

31

You can use BODMAS by arranging it multiplication comes first so 7 times 3 which is 21 so agter that addition comes next so that will be 21 plus 10 which gives 31

Answer:

13 x 5 = 65

65 + 7 = 72

Explanation:

First set up the equation with ‘x’ being the unknown number. Then set up an inequality where the actions done to x equal 13.

[tex](x-7)\div5=13[/tex]

Now solve for x

First multiple both sides by 5 That gives us

[tex]x-7=65[/tex]

Now add seven to both sides to isolate and solve for x

[tex]\bold{x=72}[/tex]

Answer:

4.4 m

Step-by-step explanation:

Area of the wheel of a car= 1.54 m²

Area of a circle= [tex]\pi r^{2}[/tex]

                 1.54= 3.14 x r²

                     r²= [tex]\frac{1.54}{3.14}[/tex]

                     r²= 0.49

                      r= 0.7 m

Circumference of the wheel= [tex]2\pi r[/tex]

                                              = 2 x 3.14 x 0.7

                                              = 4.4 m

∴ the circumference of the wheel is 4.4 m

Answer:

Step-by-step explanation:

Para encontrar el precio del videojuego después de que primero aumentó un 25 % y luego se redujo un 20 %, debemos seguir estos pasos:

Paso 1: Calcular el nuevo precio después del aumento del 25%.

Para ello, podemos multiplicar el precio original por 1,25 (que representa el 25% de incremento):

Nuevo precio tras la subida del 25% = 55,32€ x 1,25 = 69,15€

Paso 2: Calcula el precio después de la reducción del 20%.

Para ello, podemos multiplicar el nuevo precio (después de la subida del 25 %) por 0,80 (que representa la rebaja del 20 %):

Precio después de la reducción del 20% = 69,15 € x 0,80 = 55,32 €

Por lo tanto, el precio final del videojuego tras subir un 25% y luego reducirlo un 20% es de 55,32€. Este es el mismo que el precio original del videojuego.

1 centimeter on the scale drawing of rectangular park represents 15 feet of the actual parking lot.

What is rectangle?

A rectangle is a four-sided flat shape with four right angles. It is a type of quadrilateral. Rectangles have opposite sides that are parallel and equal in length, and all four interior angles are right angles (90 degrees).

We know that the width of the actual parking lot is 48 feet. We also know that on the scale drawing, the width is represented by 3.2 cm. Therefore, we can set up a proportion to find out how many feet are represented by 1 centimeter on the scale drawing:

[tex]$\frac{48 \text{ feet}}{3.2 \text{ cm}} = \frac{x \text{ feet}}{1 \text{ cm}}$[/tex]

where x is the number of feet represented by 1 centimeter on the scale drawing.

We can solve for x by cross-multiplying:

[tex]$48 \text{ feet} \times 1 \text{ cm} = 3.2 \text{ cm} \times x \text{ feet}$[/tex]

Simplifying, we get:

[tex]$x = \frac{48 \text{ feet} \times 1 \text{ cm}}{3.2 \text{ cm}} = 15 \text{ feet}$[/tex]

Therefore, 1 centimeter on the scale drawing represents 15 feet of the actual parking lot.

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Answer:

Step-by-step explanation:

irregular quadrilateral

Answer:

The name of this shape is (Irregular Pentagon)

A straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.

This graph represents the solution to this inequality.

What is inequality?

An inequality in mathematics is a relation that compares two integers or other mathematical statements in an unequal way. The majority of the time, height comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.

Given inequality:

(-1/4)*(12x + 8) < -2x + 11

First, we need to solve it for knowing the value of x,

So,

(-1/4)*(12x + 8) < -2x + 11

Or, -3x - 2 < -2x + 11

Or, -2 - 11 < -2x + 3x

Or, -13 < x

A ray with a red dot at minus 13, and it passes through minus 5.

Hence the correct answer is C; a straight line passing from minus 17 to minus 5, A ray with a red dot at minus 13, and it passes through minus 5.

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When examining the plots, only one displays a straight line going from -17 to -5 and a ray going from -13 to -5. (indicating that x can be any value greater than or equal to -13) Thus, option C is correct.

To solve the inequality, we can simplify it by first distributing the -1/4 on the left side:

[tex]-3x - 2 ≤ -2x + 11[/tex]

Next, we can isolate the variable on one side by subtracting -2x from both sides:

[tex]-x - 2 ≤ 11[/tex]

Finally, we can isolate the variable by adding 2 to both sides:

[tex]-x ≤ 13[/tex]

And since we want to solve for x, we need to multiply both sides by -1, which will flip the direction of the inequality:

[tex]x ≥ -13[/tex]

This means that x can be any value greater than or equal to  [tex]-13[/tex] .

Therefore, Looking at the graphs, the only one that shows a straight line passing from -17 to -5 and a ray starting at -13 and passing through -5 (indicating that x can be any value greater than or equal to -13)

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Answer: 298.41 K

Step-by-step explanation:

given from the problem: T=VPC

where C is a constant

plug in knowns to get C

294= (8000)(0.75)C

C=0.049

T=VP(0.049)

T = (7000)(0.87)(0.049)

T = 298.41 K

The percentage of the lawn that John still needs to mow, (x / L) multiplied by 100. The specific value of x and L will depend on the dimensions of the lawn shown in the model.

To determine the percent of the lawn that John still needs to mow, we need to find the ratio of the area of the un-mowed section to the total area of the lawn, and then multiply by 100 to express the result as a percentage.

Let's assume that the lawn is a rectangular shape, and let's label the length of the lawn as L and the width of the lawn as W. If the dark green section represents the part of the lawn that John has already mowed, then the light section represents the part of the lawn that he still needs to mow. Let's label the length of the un-mowed section as x.

The area of the un-mowed section can be found by multiplying the length x by the width W, which gives us xW. The area of the entire lawn is L times W. Therefore, the area of the mowed section is (LW - xW) since the un-mowed section is xW.

To find the percentage of the lawn that John still needs to mow, we can use the following formula:

percentage un-mowed = (area un-mowed / area of entire lawn) x 100

Substituting the expressions we found for the area of the un-mowed section and the area of the entire lawn, we get:

percentage un-mowed = (xW / (LW)) x 100

Simplifying the expression, we get:

percentage un-mowed = (x / L) x 100

Therefore, the percentage of the lawn that John still needs to mow is equal to (x / L) multiplied by 100.

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As a result, Class B's average math test score is roughly 57.67 as rounded to 2 decimal places.

The word "mean" is typically used in mathematics to describe one of the various averages that are used to represent a set of numerical data. The arithmetic mean, usually referred to as the average, is the most widely used kind of mean. For calculating the arithmetic mean, all the values in a set of data are added up, and the sum is then divided by the total number of values. It provides a general understanding of the "core" value in a collection of data. For instance, adding up each person's height and dividing it by the total number of individuals would yield the average height of the group.

given

Use this equation to determine the mean (average) of a group of numbers:

mean = (all numbers added together) / (number of numbers)

Since we are aware that the mean score for Class A is 21, we can use the following calculation to determine the total of all Class A scores:

Sum of Class A Grades = Mean * Number of Class A Students = 21 * 28 = 588

Also, we are aware that the average score for both classes is 39, thus we can use the following formula to determine the total score for both classes:

Average of the students' combined test results in both classes is 39 * (28 + 27) = 39 * 55, or 2145.

Lastly, we can apply the mean calculation to determine the mean grade in Class B:

Sum of Class B students' scores divided by the total number of Class B students equals 1557 divided by 27.

= 57.67 (rounded to 2 decimal places) (rounded to 2 decimal places)

As a result, Class B's average math test score is roughly 57.67 as rounded to 2 decimal places.

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Answer:

x^2 + 7x - 18 = (x + 9)(x - 2)

The difference between length and width is x + 9 - (x - 2) = x + 9 - x + 2 = 11.

Answer:

Step-by-step explanation:

First, we have to solve g(1)

g(1) = 9(1) + 3

g(1) = 12

f(g(1)) = f(12)

f(12) = -3(12)²+6

f(12) = -3(144) + 6

f(12) = -426

Therefore, f(g(1)) = -426

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

What is the Pythagorean theorem?

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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After answering the provided question, we can conclude that As a result, equation the cost of 2 pounds of candy is $7.00.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9"[/tex] asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Claim: To calculate the cost of 2 pounds of candy, multiply the cost per pound of candy by 2.

According to the data provided, the cost per pound of candy is $3.50.

Reasoning: In order to determine the cost of 2 pounds of candy, we must first determine the total cost of 2 pounds of candy. Because the price per pound of candy is $3.50, we can calculate the total cost by multiplying the price per pound by the number of pounds. In this case, we want to know how much it costs for two pounds, so we multiply $3.50 by two to get:

2 pounds of candy = $3.50 per pound x 2 pounds = $7.00

As a result, the cost of 2 pounds of candy is $7.00.

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Answer:

-24

Step-by-step explanation:

Hey there!

First we need to find the ratio

ratio = -6/-3 = 2

r = 2

-3, -6, -12, ? , -48

T1 = a

T2 = ar

T3 = ar²

T4 = ar³

T5 = ar⁴

And so on...

T1 means first term, T2 means second term

We're finding the fourth term which is T4

Remember T1 = a = -3

So, T4 = ar³

= -3 × 2³

= -3× 8

= -24

Therefore, the fourth unknown term is -24

You're welcome y'all

Step-by-step explanation:

Step 1 :

Break down the fraction with the H.C.F of the numerator and the denominator.

For instance, in Question 5 , the HCF of 20 and 8 is 4. So, 4 will go into 20 five(5) times and 4 will go into 8 two(2) times, leaving 5/2.

Step 2 :

Then 2 (denominator) will go into 5(numerator) two(2) times.

So, you'll get 2 as the whole number .

Step 3:

Multiply the denominator by the whole number (2×2) to get 4.

Then subtract 4 from 5 to get 1 and to form a proper fraction by making 1 the numerator and the 2 the denominator to get 1/ 2

Step 4 :

Then put the 2( whole number) and the 1/2 ( proper fraction) together to get the mixed fraction

Answer:

Step-by-step explanation:

the measurements are a Pythagorean triple, therefore it is a right triangle, where 3 and 4 are the legs and 5 is the hypotenuse, we use the formula 1/2 × b × h

A = 1/2 × b × h.

A = 1.5 × 4

A = 6"^2