The height of the TV would be 61.27 inches.
What is Pythagoras theorem?
The hypotenuse's square length is equal to the sum of the squares of the lengths of the other two sides of the right-angled triangle, according to the Pythagorean theorem, commonly known as the Pythagoras theorem.
Here, The 75 inches represents the length of diagonal of the TV because the length of TV is always measured diagonally. So, the diagonal's length is 75 inches.
We've width as 43.25 inches.
Since TV is of the shape of rectangle, we can calculate the height by applying Pythagoras theorem.
So, we've hypotenuse² = (side 1)² + (side 2)²
It can be written as,
diagonal² = height² + width²
(75)² = height² + (43.25)²
height² = (75)² - (43.25)²
= 5625 - 1870.5625
= 3754.4375
height = √3754.4375 = 61.27 inches.
Hence, height will be 61.27 inches.
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unit 1 geometry basics homework 2 segment addition postulate answer key
The segment addition postulate holds true in this example.
The segment addition postulate states that if two line segments have the same end points, then the two segments are congruent. This postulate can be expressed using the following formula: AB + BC = AC. This formula states that the sum of the lengths of two segments with the same endpoints (AB and BC) is equal to the length of the third segment (AC). To illustrate this rule, imagine a line segment AB with a length of 5 units. If we add another line segment BC to the same line segment, with a length of 3 units, then the combined length of the two segments (AB + BC) would be 8 units, which is also the length of the third segment (AC). Therefore, the segment addition postulate holds true in this example.
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Complete question:
Is the Segment Addition Postulate true?
What is the product of 4 and 0 answer?.
The product of 4 and 0 is zero.
We know that a product is an operation where two or more numbers are multiplied together to get a single result.
In case of small numbers a multiplication is considered repeated addition, and we can solve simple multiplication problems by adding repeatedly.
Generally, the types of multiplication method : addition method, long multiplication, grid method, drawing lines and by splitting two digit numbers into Tens and Ones
We know that if we multiply any non-zero real number by zero then the result / product is always 0.
This property of multiplication is called as the Zero property of multiplication.
So, the product of 4 and 0 is always zero.
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Is the inverse of a parabola a function?.
There is no inverse of the parabola function
An open curve or conic section known as a parabola is created when a right circular cone and a plane perpendicular to one of the cone's elements cross. It is a quadratic equation-defined symmetric U-shaped curve. A function's inverse is the graph of the function projected over the line y=x.
There is no inverse function for the parabola because it is not a one-to-one function. A one-to-one function is one in which every element in its domain corresponds to precisely one element in its range. It's not a one-to-one function in a parabola because as the x value increases, the y value might take a variety of values and vice versa. It can't be inverted because of this.
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can the maximum value for a quadratic function be negative?
can the minimum value for a quadratic function be positive? justify your answer
The quadratic equation has a negative value that is a maximum if vertex constant is negative but vertex y-coordinate is negative, while it has a positive value that is a minimum if vertex constant is positive by vertex y-coordinate is positive.
How to understand absolute extremes in quadratic functions
Graphically speaking, quadratic functions are parabolae and their absolute extremes are called vertices. There are three ways to describe quadratic functions:
Standard form
y = a · x² + b · x + c
Factor form
y = a · (x - r₁) · (x - r₂)
Vertex form
y - k = C · (x - h)²
Where:
a - Lead coeffcientb, c - Other coefficients.r₁, r₂ - RootsC - Vertex constanth, k - Vertex coordinates.Vertex form offers us a quick possibility to answer this question, from its understanding we get the following conclusions:
Maximum value can be a maximum and negative if C < 0 and k < 0.Minimum value can be a minimum and positive if C > 0 and k > 0.To learn more on parabolae: https://brainly.com/question/21685473
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Express the lengths a and b in the figure in terms of θ.
The lengths a and b be value of a = 24 sinθ, and b = 24 cosθ.
What is meant by SOHCAHTOA?
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
tanθ = opposite / adjacent
The side that touches the angle but is not the hypotenuse is referred to as the adjacent side, while the side that is immediately across from the angle is referred to as the opposite side and does not touch the angle. The triangle's longest side is always the hypotenuse.
This information allows us to identify an as the opposing side and b as the neighboring side. Now all you have to do is utilize your angle to get the value of these lengths using SOHCAHTOA.
Since an is the opposite side, we shall utilize sine for it. Keep in mind that your hypotenuse is 24; therefore, we can enter in the data we have and solve for the missing lengths:
sinθ = opposite / hypotenuse
= a / 24
a = 24sinθ
For b, because it is the adjacent side, we will use cosine.
cosθ = adjacent / hypotenuse
= b / 24
b = 24cosθ
Therefore, the value of a = 24sinθ, and b = 24cosθ.
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A box containing 300 similar chocolates weighs 6150 g. The same box containing 250 similar chocolates weighs 5.15 kg. What is the mass of the empty box? Give your answer in kilograms.
Answer:
Step-by-step explanation:
as the there is a box one time had :
300-----> 6150g
2150----> 5150g ( 5.15 kg converted to grams which is time 1000)
divide each number on its weight you will find the difference is 20.5 g which is the weight
6150/300= 20
5150/250= 20
How do you write an equation of a parabola with vertex at the origin and the given Directrix?.
The parabola's conventional form is y^2=4ax, which results in a parabola with an axis parallel to the x-axis, a vertex at the origin, a focus at (a,0), and a directrix at (x=a).
Since a=2 in your example, y^2=4ax is the result. The y-axis serves as the parabola's axis. The directrix equation is y = -a, which is equivalent to y = -12. There is a parabola's vertex at (0,0).
You must be aware that a parabola's equation in a vertex form is y=a(xh)^2+k, where a stands for the equation's slope, in order to determine the focus of a parabola. We can deduce from the formula that the parabola's focus lies at (h, k+1/4a).
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A triangular prism has an equilateral triangle base whose sides are 7 meters. The height of the prism is 4 meters
What is the lateral surface area
The lateral surface area of the prism is 81m².
All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area.
The total area of all of its faces is reduced to the lateral area. It can also be explained by multiplying the prism's height by the base's circumference.
The base's sides are each 7 meters long, which is a given.
Phase 7+7+7 = 21 meters is the perimeter.
We also know that the prism is 4 meters tall.
The lateral area is therefore
L = P base × h
L = 21m x4m
L = 81m²
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An online furniture store sells chairs for $100 each and tables for $450 each. Every day, the store can ship no more than 18 pieces of furniture and must sell no less than $3200 worth of chairs and tables. Also, the store must sell a minimum of 8 tables. If xx represents the number of tables sold and yy represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.
PLEASE HELP THIS IS AN EMERGENCY
The inequality expression and solution to a system of inequalities graphically is xx + yy <= 18
We can represent the system of inequalities as follows:
xx + yy <= 18 (representing the maximum number of pieces of furniture that can be shipped)
A possible solution could be:
xx = 8 (number of tables sold)
yy = 10 (number of chairs sold)
How do we express the inequality?100yy + 450xx >= 3200 (representing the minimum amount of money that must be made from the sale of chairs and tables)
xx >= 8 (representing the minimum number of tables that must be sold)
To graphically represent this system of inequalities, we can begin by graphing the first inequality in a coordinate plane. The inequality xx + yy <= 18 can be represented by a line with the equation y = -x + 18.
Next, we can graph the second inequality. The inequality 100yy + 450xx >= 3200 can be represented by a line with the equation y = -(4.5/5)x + 80.
Finally, we can graph the third inequality, which is a horizontal line at y = 8.
Now we can graph these three inequalities, one line for each inequality, and see where they intersect. The point where all three lines intersect is one possible solution for the system of inequalities.
A possible solution could be:
xx = 8 (number of tables sold)
yy = 10 (number of chairs sold)
However, this solution is within the constraints of the problem and satisfies all three inequalities.
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Please help, its geometry and its multiple choice question.
In the given figure the Δ LHK is similar to ΔL'H'K' and also ΔL'H'K' is the dilation of Δ LHK centered at the origin with a scale factor of 3/2.
What are Similar triangles?Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.
Here,
As shown in the figure,
Two triangles are given,
Δ LHK and ΔL'H'K'
Scale factor,
L'H'/LH = L'K'/LK = H'K'/HK = 3/2 [from the figure]
Thus, In the given figure the Δ LHK is similar to ΔL'H'K', and also ΔL'H'K' is the dilation of Δ LHK centered at the origin with a scale factor of 3/2.
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i need help finding the vertex please i don’t understand anything
The vertex, Minima or maxima, Domain and range of the all given graphs are obtained.
Explain the minima and maxima of the function?The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, respectively.For the given question-
Part a:
Vertex : (-1, -4)
Minima or maxima: minima at x = -1
Domain: All real number.
Range: [-4, ∞)
Part b:
Vertex : (3, 4)
Minima or maxima: Maxima at x = 3
Domain: All real number
Range: [4, -∞)
Part c:
Vertex : (4, -4)
Minima or maxima: minima at x =4
Domain: All real number
Range: [-4, ∞)
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What is the first step in solving the equation 20=6x-4 solving for x ?
Subtract 4 from both sides.
Subtract 20 from both sides.
Add 4 to both sides.
Divide both sides by 6 .
Answer: Add 4 to both sides
Hope this helps :)
Step-by-step explanation:
20=6x-4
+4 +4
24=6x
/6 /6
4=x
The dimensions of a cylinder are shown in the diagram. Which measurement is closest to the lateral surface area in square centimeters of the cylinder
The lateral surface area of a cylinder is 1110.8 cm².
Derive the formula for the volume of cylinder.Consider a very thin cross section of a cylinder whose thickness is [dh] {differential or very small value}. The volume of this cross section would be -
dV = πr² dh
For complete cylinder -
∫dV = πr² ∫dh
[V - 0] = πr² [h - 0]
V = πr²h
Given are the dimensions of a cylinder are shown in the diagram.
We can write the lateral surface area as -
LSA = 2πrh
LSA = 2 x 3.14 x 8.8 x 20.1
LSA = 1110.8 square centimeters.
Therefore, the lateral surface area of a cylinder is 1110.8 cm².
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its D if that was too confusing
Answer: D
Step-by-step explanation: ? question
You are sent out of the cave next.. You find a third species of alien monster. It's not drooling, but it does have a serious breath problem. You find that this species is 2 cm tall at birth and gets five times as tall with each day that passes.
Create a formula to describe the monster's growth.
How tall will the monster be after 3.7 days?
The exponential equation that describes the monster's growth, in meters, is given as follows:
y = 0.02(5)^x.
The height of the monster after 3.7 days is given as follows:
19.3 meters.
How to define an exponential function?An exponential function is defined as follows:
y = ab^x.
For which the parameters are given as follows:
a is the initial value.b is the rate of change.Considering the initial height of the monster and the fact that the height is multiplied by five each day, the function is given as follows:
y = 0.02(5)^x.
Hence the height after 3.7 days is given as follows:
y = 0.05(5)^3.7
y = 19.3 meters.
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This is meant to be easy apparently, help please
The value of the function f ( g ( 6 ) ) = -6
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
Let the second function be represented as g ( x )
Now , the value of f ( x ) = 6 - x
The value of g ( x ) = x + 6
To calculate the value of f ( g ( 6 ) )
Substitute the value of x = 6 in the equation , we get
g ( 6 ) = 6 + 6 = 12
Substitute the value of x = 12 in f ( x ) , we get
f ( g ( 6 ) ) = f ( 12 )
The value of the composition function , we get
f ( 12 ) = 6 - 12
f ( 12 ) = -6
Hence , the value of the composition function f ( g ( 6 ) ) is -6
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Four friend went to the movie. Each ticket cot $8 and each peron brought popcorn and a oda for $5 dollar. How much did they pend in all? Show two way to write the expreion or equation and olve
They spend $52 in total for the movie ticket and popcorn.
The substitution method is a simple way to solve a system of linear equations algebraically and find the solutions of the variables.
Given that,
Tickets (t) = $8
Popcorn & Soda (s)= $5
Friends = 4
Since all friends bought the same thing the equation will be set as
4(t +s) = m OR 4t +4s = m
Using substitution, you plug each variable
t = 8 and s = 5
4((8) + (5)) = m
4(8+5) = m => 4(13) =m => 52=m
OR
4(8) + 4(5) = m => 32 + 20 = m =>
52 =m
Thus, They spend $52 in total for the movie ticket and popcorn.
Complete question: Four friends went to the movies each ticket cost $8 and each person bought popcorn and a soda for $5 how much did they spend in all? let m stand for the amount of money spent
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Is √ 64 a real number?.
Yes. 64 is a real number. Real numbers can be expressed as infinite decimal expansion.
Real numbers includes integers, natural numbers. Real numbers can be of positive and can be of negative numbers. Real numbers can be both a rational number or a irrational numbers. These two are the main groups of real numbers. Rational numbers are written as the ratio of two integers. Irrational numbers are not written as the ratio of two integers. Irrational numbers are the type of real numbers. 64 is a real number as well as a perfect square of a number. It is a perfect square of the 8. This explains the properties of Real numbers.
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What number is one more than 39?.
The number is one more than 39 is 40
Number:
Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number.
Greater than Number:It is a mathematical term used to compare two quantities and to establish a relationship between two quantities in which one term is greater than the other. The terms greater than, less than, and equal are used to compare two numbers, amounts, or amounts. Each term has a separate letter. B. "greater than" is represented by ">".
According to the Question:
To better understand this question,
It can be expressed as 1 more than 39, 1 more than 39, 39 plus 1.
Thus,
1 more than 39 is the same as 39 plus 1. So the answer for 1 greater than 39 is calculated as:
Therefore,
1 + 39 = 40.
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Alex i planting flower. She want to put 3 flower in each pot. Write an expreion to how how many pot he need to buy. Ue x for your variable
Alex needs to buy x / 3 pots to put 3 flowers in each pot.
What is variable ?
A variable is a value or a quantity that can change or take on different values in a mathematical expression or a scientific experiment. In mathematics and computer science, variables are often represented by letters or symbols, such as x, y, z, etc. These letters or symbols are used to represent an unknown value.
The expression to find the number of pots Alex needs to buy to put 3 flowers in each pot is ,
x = 3 flowers per pot
Number of pots = Total number of flowers / Flowers per pot
Number of pots = x / 3
So, Alex needs to buy x / 3 pots to put 3 flowers in each pot.
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x = 3 flowers per pot
Number of pots = Total number of flowers / Flowers per pot
Number of pots = x / 3
So, Alex needs to buy x / 3 pots to put 3 flowers in each pot.
What is range of values for X?.
A function's range is the set of values which that function can take. This represents the collection of values that the function returns after we enter an x value.
The domain of a procedure is the set of values that can be plugged into it. This set contains the x values in a function like f. (x).
A function's range is indeed a set of integers that it can generate.
In certain terms, this is the set of y-values obtained by plugging all possible x-values into the function. The domain is the set of all potential x-values.
A function in mathematics is a defined interaction between this and an autonomous variable (x) and a completely reliant variable (y).
A function's range refers to all of the potential values for y. The method used to calculate a function's range is y = f. (x).
The distinction between the lowest and highest numbers is called the range. When there are extraordinarily high or low values, the range can be deceiving.
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large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant
height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
Answer: i am really sorry but no whts
In a mall hockey arena with 8000 eat there are 3000 upper level eat which are $10 cheaper than the remaining lower ection eat
The cost of lower and upper level seats are $28 and $18 each, respectively.
Let x be the cost of the lower level seats
We know that the upper level seats are $10 cheaper, so their cost can be expressed as the algebraic expression x - 10.
We also know that the total number of seats is 8000, and 3000 of them are upper level seats, and a sellout has a total revenue of $194 000.
So we can set up the following algebraic equation:
(8000 - 3000)x + 3000(x - 10) = 194 000
Simplify the equation and solve for the value of x.
5000x + 3000x - 30 000 = 194 000
8000x = 224 000
x = 28
So, the cost of the lower section seats is $28 and the cost of the upper level seats is $18.
The problem seems incomplete, it must have been
"In a small hockey arena with 8000 seats there are 3000 upper level seats which are $10 cheaper than the remaining lower section seats. For a sellout to a Memorial Cup game the total revenue was $194 000. Find the cost of each type of ticket."
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Evaluate 1/2yz
if y= 3/5
and z= −1 7/8
Write your answer as a fraction in simplest form.
To evaluate 1/2yz when y = 3/5 and z = -17/8, we first substitute the given values for y and z into the expression:
1/2(3/5)(-17/8)
Next, we can simplify this by multiplying the fractions:
1/2 * 3/5 * -17/8 = (-3/10) * (-17/8)
To multiply the fractions we multiply the numerators and denominators separately:
(-3/10) * (-17/8) = (-3 * -17)/(10 * 8)
Then we can simplify the numerator by combining like terms:
(-3 * -17)/(10 * 8) = 51/40
So the final result of the expression is 51/40.
Answer:
_51/80
Step-by-step explanation:
1/2*3/5*_17/8
1/2×3/5×(_17/8)
3/10×(_17/8)
_51/80
Put thee in acending order
A
7. 9
×
10
2
B
0. 0079
×
10
3
C
790
×
10
−
3
D
79
When we put the following numbers in ascending order, the order becomes 790×10^-3 < 0.0079 × 10^3 < 79 < 7.9 × 10^2.
In ascending order, we need to arrange any given set of data in such a way that the smallest number comes first, and then comes the next bigger number, and then the next bigger, and so on. The largest number in that given data set comes at the end. We have to arrange the following in such a manner as well.
Since we can deduce that 790×10^-3 is the smallest of the lot, it comes first. The next bigger number is 0.0079 × 10^3 and so, it comes right after that. Just after this is the number 79 and then, the largest number of this data set is 7.9 × 10^2 and so, it is at the last. Hence, the order is as such -
= 790×10^-3 < 0.0079 × 10^3 < 79 < 7.9 × 10^2.
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The area of trapezoid TRAP is 100. Furthermore, TR = 32, AP = 8, and TP = RA. If
∠T = ∠R, what is the length of segment TP?
The length of the longer base of the trapezoid is TP = 13 units
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the area of the trapezoid be A = 100 units²
Now , the length of the longer base b = 32 units
The length of the shorter base a = 8 units
Let the height of the trapezium be = h
Area of Trapezoid = ( ( a + b ) h ) / 2
Substituting the values in the equation , we get
100 = ( 32 + 8 ) x h / 2
200 = 40h
Divide by 40 on both sides of the equation , we get
h = 5 units
Now , the height be PE , where E lies 12 units from T
Now , from the Pythagoras equation , we get
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
TP² = PE² + TE² , where PE is the height of the triangle
TP² = 5² + 12²
TP² = 169
Taking square roots on both sides of the equation , we get
TP = 13 units
Hence , the length of the trapezium is 13 units
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12 of the 30 watermelons were ripe.
a. what fraction of the Watermelons were right?
b. what percent of the Watermelons were ripe?
c. If one of the Watermelons is picked at random, which is more likely: That the watermelon is ripe or is not ripe. Why?
The fraction of the watermelons that is ripe is 2 / 5.
The percentage of the watermelons that is ripe is 40%.
The water melons that is not rip is more likely to be picked at random because it is more in number
How to find the fractions of watermelon?12 of the 30 watermelons were ripe. The fractions of the watermelon that are ripe can be calculated as follows:
fraction of watermelon that are ripe = 12 / 30
fraction of watermelon that are ripe = 6 / 15
fraction of watermelon that are ripe = 2 / 5
Hence, the percentage of the water melon that are ripe can be calculated as follows:
percentage of water melon that is ripe = 2 / 5 × 100
percentage of water melon that is ripe = 200 / 5
percentage of water melon that is ripe = 40%
If one of the watermelons is picked at random. It is more likely the watermelon that is not ripe is picked. This is because the unripe watermelon has a higher probability of been picked because it is high in number.
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Rounding Money
Round the nearest hundredth.
33.333
What is the nature of roots of the quadratic equation 5?.
The nature of roots of the quadratic equation 5x^2 - 2x + 3 = 0 is complex number.
The nature of roots of a quadratic equation is determined by the discriminant, which is the value of b² - 4ac. In this case, the quadratic equation is 5x^2 - 2x + 3 = 0.
To find the discriminant, we can use the formula: b² - 4ac. In this case, a = 5, b = -2 and c = 3, so the discriminant is:
Discriminant = (-2)² - 4*5*3 = 4 - 60 = -56
The discriminant can be used to determine the nature of the roots:
If the discriminant is greater than 0, the roots are real and distinct.
If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).
If the discriminant is less than 0, the roots are complex and not real numbers.
In this case, the discriminant is negative, so the roots of the equation 5x^2 - 2x + 3 = 0 are complex. The roots can be found by factoring the equation into (x + a + bi)(x + a - bi), where a and b are real numbers, and i is the imaginary unit (i² = -1).
--The question is incomplete, answering to the question below--
"What is the nature of roots of the quadratic equation 5x^2 - 2x + 3 = 0?"
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Need help on this question!!!
The area of the composite figure is 124 square miles.
How to determine the area of a composite figure
Composite figures are the result of uniting two or more geometric figures, in this case, we need to determine the area of a composite figure that results from the union of two right triangles and two rectangles, whose area formulas are described below:
Rectangle
A = w · l
Right triangle
A = 0.5 · w · l
Where:
w - Width, in miles.l - Length, in miles.A - Area, in square miles.Now we proceed to calculate the area of the composite figure:
A = 0.5 · (6 mi) · (18 mi) + 0.5 · (8 mi) · (3 mi) + (6 mi) · (5 mi) + (4 mi) · (7 mi)
A = 124 mi²
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