By similarity ratio of triangles, we have;
ΔPQR ∼ ΔPSR ∼ ΔRSQ
PS/PR = PR/PQ
PQ/RQ = RQ/SQ
How to solve similar triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Thus, applying the concept of similar triangle ratio we can say that;
ΔPQR ∼ ΔPSR ∼ ΔRSQ
Similarly, by similarity ratio of triangles, we have;
PS/PR = PR/PQ
We also have;
PQ/RQ = RQ/SQ
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Answer:
what kinda question is this?
Step-by-step explanation:
A golfer hits a golf ball off a tee. A quadratic function models the height of the golf ball in the coordinate plane, with the origin representing the initial location of the golf ball. Which of the following features can be used to determine the height that the golf ball travels from its initial location to the point where the golf ball starts falling towards the ground? Select ALL that apply.
Responses
zeros
vertex
y-intercept
end behavior
Zeros, vertex, and end behavior can all be used to determine the height that the golf ball travels from its initial location to the point where the golf ball starts falling towards the ground.
What is graph?Graph is a data structure that consists of a set of nodes and edges that connect those nodes. Nodes are used to represent entities, such as people, places, or objects, and edges are used to represent the connections between those entities. Graphs are used to represent relationships between data, such as in networks, social media, and biological systems. Graphs can also be used to represent mathematical equations, as in function graphs.
Zeros, or x-intercepts, are the points where the graph of the quadratic function crosses the x-axis. The vertex is the highest point of the graph and can be used to determine the peak of the golf ball's trajectory. Finally, the end behavior of the graph can be used to determine how the graph will change as x increases or decreases without bound. This can be used to determine the point at which the golf ball begins to fall towards the ground.
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Missing digits 5,62,2,2
Using the rules of writing a pattern, we found the missing numbers and found the pattern:
52, 62, 72, 82
What is a pattern?
A pattern in mathematics is a series of recurring figures, shapes, or numbers. Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the items that are part of the pattern and those that are not. There are many distinct kinds of patterns, including word patterns, logic patterns, image patterns, and number patterns. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series. The number of patterns can be limitless or finite.
We are asked to find the missing digits to complete the pattern.
5_, 62, _2, _2
So the numbers have two digits.
For this pattern, the last three numbers end with the digit 2.
So the first number should be 52.
Now the difference between 52 and 62 is 10.
Since the last two numbers also have an ending digit as 2, the difference between two consecutive numbers should be 10.
Then the pattern is:
52, 62, 72, 82.
Therefore using the rules of writing a pattern, we found the missing numbers and found the pattern:
52, 62, 72, 82
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in quadrilateral QRST, QS is congruent to RT. is QRST a rectanglr
Answer:
Step-by-step explanation:
14.7 N
What is the volume of the composite figure?
The volume of the composite figure is 408 cm³
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
The volume of the composite figure is:
Volume = area of base * height
Substituting:
Base area = (14 * 3) + (1/2)(5 + (14-6))(7 - 3) = 68 cm²; height = 6 cm
Volume = area of base * height = 68 cm² * 6 cm = 408 cm³
The volume is 408 cm³
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Question 1-25
Look at the recursive formula given for a sequence.
f(1) = 4
f(n) = f(n-1) +6
What is the fifth term in the sequence? Enter the answer in the box.
Answer:
[tex]1 - 25xy2256xx28( [/tex]
Complete the square
x^2 =−8x−7
super important
The solutions to the equation x²= -8x - 7 are x = -1 or x = -7.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
To complete the square for this equation x^2 = -8x - 7
Adding the square of half the coefficient of x (which is (-8)/2 = -4) to both sides of the equation:
x² + 8x + (-4)²= -7 + (-4)^2
This gives us:
x² + 8x + 16 = 9
Now we can write the left-hand side as a perfect square:
(x + 4)² = 9
Taking the square root of both sides gives us:
x + 4 = ±3
Solving for x, we get:
x = -4 ± 3
Therefore, the solutions to the equation x²= -8x - 7 are: x = -1 or x = -7.
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1) equivalent expression of 3(2x-1)
2) expression of there are 5,280ft in 1 mile.
3) expression of there are 16oz in `pound
Therefore , the solution of the given problem of expressions comes out to be 16 ounces are equal to 1 pound.
Expression : What is it?There is a need for mathematical operations like multiplying, splitting, joining, and currently removing. If they were combined, it would read as follows: A mathematical formula, some data, and an equation Values, elements, and mathematical operations like additions, deductions, errors, subdivisions, and algebraic formulas all go into making a declaration of truth. It is possible to assess and analyse words and sentences.
Here,
=> 6x - 3 is an expression that is equal to 3(2x-1).
We can spread the 3: to see why this is true.
=> 3(2x-1) = 6x - 3
There are 5,280 feet in a mile, as the saying goes.
5280 feet make up a mile.
Simply put, this phrase means that 5,280 feet is equal to 1 mile.
One way to say "there are 16 ounces in a pound" is:
A pound weighs 16 ounces.
Simply put, this phrase means that 16 ounces are equal to 1 pound.
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An adult pass at the amusement park costs 1.6 times as much as a child’s pass.
How many dollars does an adult pass cost if a child’s pass costs:
By answering the supplied question, we may infer that the response is equation 1.6 x 30 Equals $48 for an adult pass if the price is $30.
so on.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Let's assume that a child's pass costs $x.
The issue states that the price of an adult pass is 1.6 times that of a kid pass. Thus, an adult pass costs:
$1.6 times
So, if a child's pass is expensive:
a) If an adult pass costs $10, then 1.6 x 10 equals $16.
b) $20, then 1.6 x 20 Equals $32 for an adult pass.
1.6 x 30 Equals $48 for an adult pass if the price is $30.
so on.
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Tell whether the ordered pair is a solution of the equation.
7=y-5× (4,28)
The answer is "no," the ordered pair (4, 28) is not a solution of the equation.
What is equation?A solution of an equation is a value or set of values that makes the equation a true statement when substituted for the variable(s) in the equation.
To determine if the ordered pair (4, 28) is a solution of the equation 7 = y - 5x, we need to substitute the values x = 4 and y = 28 into the equation and check if it is a true statement:
7 = y - 5x
7 = 28 - 5(4) // Substitute x = 4 and y = 28
7 = 28 - 20
7 = 8
The statement 7 = 8 is not true, which means that the ordered pair (4, 28) is not a solution of the equation 7 = y - 5x. Therefore, the answer is "no," the ordered pair (4, 28) is not a solution of the equation.
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The city has decided to build a circular outdoor amphitheater in the new park. The architects would like to surround the amphitheater with a low brick wall and lay turf inside. They would like the diameter of the amphitheater to be 140 feet.
Each pallet of turf comes with 100 rolls of turf and each roll will cover about 30 square feet. What is the minimum number of pallets that the city must order to have enough turf to fill in the amphitheater?
Therefore, unitary method solution is in order to have enough turf to cover the amphitheatre, the city must purchase at least 6 pallets of it.
What is unitary method ?Take the lengths of this minute subsection and split the sum by two to complete a task using a variable unitary technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.
Here,
A is equal to (70)2/4, which is 15,386.78 square feet.
We split the area by the area covered by each roll of turf to determine the quantity of rolls necessary to cover this area:
Rolls Equals A / Rolls' surface area
Given that the size per roll is 30 square feet, we have:
15,386.78 rolls divided by 30 equals 512.89 rolls.
Ceil(number of rolls / 100) = minimal number of pallets
the smallest number larger than or equal to x, ceil(x), is. If we replace the value we discovered with the quantity of rolls, we get:
Ceil (512.89 / 100) = Ceil (5.1289) = Minimum number of boxes = 6
Therefore, in order to have enough turf to cover the amphitheatre, the city must purchase at least 6 pallets of it.
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Which of the following is common both ADC and BCD
The segment CD is common on both ΔACD and ΔBCD.
What is a Triangle?Polygon, which has three sides and three vertices, is called a triangle.
The sum of all the angles of the triangle is 180°.
Given:
Two triangles ΔACD and ΔBCD in the given image.
To find the commonality between two triangles ΔACD and ΔBCD:
The sides of the triangle ΔACD are AC, CD, and AD.
The sides of the triangle ΔBCD are BC, CD, and BD.
From the diagram,
we can clearly see that the segment CD is common on both ΔACD and ΔBCD.
CD ≅ CD (reflexivity)
Therefore, the common segment is CD.
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Use the graph to answer the question. Graph of polygon ABCD with vertices at 1 comma negative 1, 3 comma negative 5, 7 comma negative 5, 5 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 1 comma negative 6, 3 comma negative 10, 7 comma negative 10, 5 comma negative 6. Determine the translation used to create the image. 5 units down 5 units up 1 unit down 1 unit up
The image was created by translating 5 units down, 5 units up, 1 unit down, and 1 unit up. ABCD and A'B'C'D' are two polygons on the graph.
The first polygon, ABCD, has vertices at (1,-1), (3,-5), (7,-5), and (8,-5). (5,-1). The vertices of the second polygon, A'B'C'D', are located at (1,-6), (3,-10), (7,-10), and (8,-10). (5,-6).
What exactly are vertices?Vertices are points in a geometric figure that define its shape. A vertex is defined mathematically as the intersection of two or more lines, edges, or curves.
We can compare the coordinates of the two polygons to determine the translation that was used to create the image. The first coordinate of the two polygons is (1,-1) and the second coordinate is (1,-1). (1,-6). The y-coordinate difference is 5 units, so the translation is 5 units down. The two polygons' second coordinate is (3,-5) and (3,-10). The y-coordinate difference is 5 units, so the translation is 5 units down.
The second polygon's third coordinate is (7,-5) and (7,-10). The y-coordinate difference is 5 units, so the translation is 5 units down. (5,-1) is the fourth coordinate of both polygons (5,-6). The y-coordinate difference is 5 units, so the translation is 5 units down.
The image was translated 5 units down, 5 units up, 1 unit down, and 1 unit up.
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Which of the e-values satisfy the following inequality?
3e ≤ 6
Choose all answers that apply:
B
e = 1
e = 2
e = 3
Stuck? Review related articles/videos or use a hint.
Report a problem
The e values that satisfy the inequality 3e ≤ 6, are e = 1 and e = 2.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
To determine which values of e satisfy the inequality 3e ≤ 6, we can divide both sides by 3 -
3e/3 ≤ 6/3
e ≤ 2
Therefore, any value of e that is less than or equal to 2 will satisfy the inequality.
Out of the given choices, e = 1 and e = 2 satisfy the inequality, but e = 3 does not, because 3 is greater than 2.
Therefore, the correct answers are -
e = 1 and e = 2
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2 step equation first person to answer gets...
An equation can be solved by finding the value of the variables.
How do you solve an equation?Solving an equation involves finding the value(s) of the variable(s) that make the equation true. The process for solving an equation depends on the type of equation and the specific instructions or conditions given.
1) 18 - a/16 = 17
18 - a = 16 * 17
18 - a = 272
a = 18 - 272
a = -254
2) 15 - n/-10 = -21
15 - n = (-21) * (-10)
15 - n = 210
n = 15 - 210
n = -195
3) 12 + y/-20 = 18
12 + y = 18 * (-20)
y = -372
4) c + 17/-26 = -5
c + 17 = (-5) (-26)
c = 113
5) 3c + 12 = 36
c = 36 - 12/3
c = 8
6) 1/5 f - 9 = -24
1/5 f = -24 + 9
1/5 f = -15
f = -15 * 5
f = -75
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Can you please solve?
Answer:
19 and - 8
Step-by-step explanation:
( u ○ w )(3)
evaluate w(3) then substitute the value obtained into u(x)
w(3) = - 2(3)² = - 2(9) = - 2 × 9 = - 18 , then
u(- 18) = - (- 18) + 1 = 18 + 1 = 19
-----------------------------------------------
( w ○ u )(3)
evaluate u(3) then substitute the value obtained into w(x)
u(3) = - 3 + 1 = - 2 , then
w(- 2) = - 2(- 2)² = - 2(4) = - 2 × 5 = - 8
Lynette bought a new car for $34,000 . She paid a 20% down payment and financed the remaining balance for 60 months with an APR of 4.4% . Assuming she made monthly payments, determine the total cost of Lynette's car. Round your answer to the nearest cent, if necessary. Formulas
Answer:
The down payment Lynette made is:
Down payment = 20% of $34,000 = $6,800
The amount financed is:
Amount financed = Total price - Down payment
Amount financed = $34,000 - $6,800 = $27,200
To calculate the monthly payment, we can use the following formula:
Monthly payment = (Pr(1+r)^n) / ((1+r)^n - 1)
where:
P = amount financed
r = monthly interest rate
n = number of months
First, we need to calculate the monthly interest rate:
Monthly interest rate = APR / 12
Monthly interest rate = 4.4% / 12 = 0.0036667
Now, we can calculate the monthly payment:
Monthly payment = ($27,200 * 0.0036667 * (1+0.0036667)^60) / ((1+0.0036667)^60 - 1)
Monthly payment = $501.47
The total cost of the car is the sum of the down payment and the total of all the monthly payments over 60 months:
Total cost = Down payment + Monthly payment * 60
Total cost = $6,800 + $501.47 * 60
Total cost = $37,688.20
Therefore, the total cost of Lynette's car is $37,688.20.
3x + 6x help!!
Need this quicklllyh
Answer: 9x
Step-by-step explanation:
You combine like terms.
What is the distance between the points shown? Show your work.
Round your answer to the nearest tenth.
Answer:
8.3 units
Step-by-step explanation:
To find the distance between the two points, use the distance formula.
Distance = [tex]\sqrt{(x-x)^2+(y-y)^2}[/tex]
(x, y)
(-1.5, 4)
(-5, -3.5)
[tex]\sqrt{(x-x)^2+(y-y)^2}[/tex] - Formula
[tex]\sqrt{(-1.5--5)^2+(4--3.5)^2}[/tex] - Plug in values
[tex]\sqrt{(3.5)^2+(7.5)^2}[/tex] - Simplify parenthesis
[tex]\sqrt{12.25+56.25}[/tex] - Simplify
[tex]\sqrt{68.5}[/tex] = 8.27647267862 = 8.3
1. Graph the function f(x)=sin (x) - 2.
Answer:
See Picture
Step-by-step explanation:
The original sin(x) function starts at (0,0) and oscillates around the x-axis between y=1 and y=-1, intercepting it in intervals of π.
To graph sin(x)-2 then, we simply need to graph a sin(x) function 2 units lower.
Name the reference angle for -300°
The reference angle for A = -300° is given by R = 60°
What is Reference Angle?Every angle is measured from the positive part of the x-axis to its terminal line (the line that determines the end of the angle) traveling counterclockwise. For angles in the first quadrant, i.e., angles less than or equal to 90 degrees, the reference angle is equal to the original angle.
The reference angle is always positive
0° to 90°: reference angle = angle
90° to 180°: reference angle = 180° - angle
180° to 270°: reference angle = angle - 180°
270° to 360°: reference angle = 360° - angle
Given data ,
Let the reference angle be represented as R
Now , let the given angle be A
A = -300°
And , for 270° to 360°: reference angle = 360° - angle
when the angle is negative and less than -270°
The reference angle is given by adding 360° to it and the angle lies in the first quadrant
So , the reference angle R = A + 360°
R = -300 + 360
R = 60°
Hence , the reference angle is 60°
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The perimeter of a square is 36 inches. Find the length of the diagonal. Round answer to nearest tenth
Answer:
12.7 inches
Step-by-step explanation:
We know that the length of a diagonal is :
[tex]d=a\sqrt{2}[/tex]
Here d = Diagonal of a square
a = Side of a square
Given:
The perimeter of a Square is 36 inches.
Since the formula for the perimeter of a square is 4a
Thus, 4a = 36
⇒ a = 36÷4 = 9 inches
Now,
d = 9×√2 = 12.7 inches
Hence the length of a square is 12.7 inches.
Solve -7(1-4m)=13(2m-3)
Answer:
To solve the equation -7(1-4m)=13(2m-3), we can start by simplifying each side of the equation:
-7(1-4m) = 13(2m-3)
-7 + 28m = 26m - 39 (distributing the -7 and 13)
Next, we can simplify further by combining like terms:
28m - 26m = -39 + 7
2m = -32
Finally, we can solve for m by dividing both sides of the equation by 2:
m = -16
Therefore, the solution to the equation -7(1-4m)=13(2m-3) is m = -16.
Answer:
[tex] \sf \: m = - 16[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of m.
The equation is,
→ -7(1 - 4m) = 13(2m - 3)
Then the value of m will be,
→ -7(1 - 4m) = 13(2m - 3)
→ -7(1) + 7(4m) = 13(2m) - 13(3)
→ -7 + 28m = 26m - 39
→ 28m - 26m = 7 - 39
→ 2m = -32
→ m = -32 ÷ 2
→ [ m = -16 ]
Hence, the value of m is -16.
Selina is remodeling her home. She installed a low-flow toilet in her home that flushes 0.8 gallon each time. She replaced her showerhead with a low-flow showerhead that releases 1.5 gal/min. She flushes 12 times a day and showers for 10 minutes a day. On average, her appliances use 40.2 gal/day. Assuming no other appliance use, how much less water will she use than the average U.S. citizen?
The average U.S. citizen uses approximately 88 gallons of water a day.
What is Frequency?
Frequency is a measure of how often an event occurs within a given period of time. It is typically expressed as the number of occurrences of a given event per unit of time. Frequency can be used to measure a variety of phenomena such as the frequency of sound in a given environment or the frequency of a particular chemical element in a given sample.
Selina's low-flow toilet and showerhead will reduce her total water use to just 48.4 gallons per day, a savings of 39.6 gallons of water each day. This is a 44.8% reduction in her water consumption, saving her almost 40 gallons of water per day.
By making these improvements, Selina is helping to conserve a precious resource and limit her environmental impact. Not only is she helping to conserve water, but she is also saving money on her water bill. It is estimated that a typical household can expect to save about $170 annually by making these simple changes.
In addition to her low-flow fixtures, Selina can take additional steps to reduce her water consumption. She can install a water-efficient dishwasher, reduce the frequency of her laundry loads, and install a rain barrel to collect rainwater for gardening. By making these changes, she can reduce her water consumption even further and save even more money.
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K
The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total
amount due at time t.
P = $9000, r = 5.5%, t = 8 months
The future value is $
(Simplify your answer. Type an integer or a decimal.)
ew an example
Get more help.
Clear all
Check answer
orrect
Answer:
the future value or total amount due at the end of 8 months is $9,330.00
Step-by-step explanation:
To find the future value of a loan that is borrowed at a simple interest rate, we use the formula:
A = P(1 + rt)
where A is the future value or total amount due, P is the principal or initial amount borrowed, r is the simple interest rate as a decimal, and t is the time period in years.
In this case, the principal is $9000, the simple interest rate is 5.5% or 0.055 as a decimal, and the time period is 8 months or 8/12 = 2/3 years.
Substituting these values into the formula, we get:
A = 9000(1 + 0.055 × 2/3)
= 9000(1.0375)
= $9,330.00
Therefore, the future value or total amount due at the end of 8 months is $9,330.00
we know that a year has 12 months, so 8 months is really 8/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\to \frac{8}{12}\dotfill &\frac{2}{3} \end{cases} \\\\\\ A = 9000[1+(0.055)(\frac{2}{3})] \implies A = 9330[/tex]
How to solve (x-4)^2-9=0
Answer:
Step-by-step explanation:
(x-4)^2-9=0
Let's assume a=x-4 and b=3
We know that,
[tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]
substituting values a, and b in above equation we get,
(x-4+3)(x-4-3)==
(x-1)(x-7)=0
x=1,7
Answer:
[tex]\displaystyle{x=7,1}[/tex]
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{\left(x-4\right)^2-9=0}[/tex]
Add 9 both sides:
[tex]\displaystyle{\left(x-4\right)^2-9+9=0+9}\\\\\displaystyle{\left(x-4\right)^2=9}[/tex]
Square root both sides:
[tex]\displaystyle{\sqrt{\left(x-4\right)^2}=\sqrt{9}}[/tex]
Cancel square root for left side and add plus-minus to right side:
[tex]\displaystyle{x-4=\pm \sqrt{9}}[/tex]
Evaluate the surd of 9:
[tex]\displaystyle{x-4=\pm 3}[/tex]
Add 4 both sides:
[tex]\displaystyle{x-4+4=\pm 3 +4}\\\\\displaystyle{x=\pm 3 +4}[/tex]
Two solutions can be either:
[tex]\displaystyle{x=3+4}[/tex] or [tex]\displaystyle{x = -3+4}[/tex]
Hence:
[tex]\displaystyle{x=7,1}[/tex]
Show that a binary operation has at most one identity element?
binary operation has at most one identity element.
What is the binary operation?A binary operation is a mathematical operation that takes two elements from a set and combines them to produce a third element in the same set. In other words, it is an operation that involves two operands, which can be numbers, variables, or other mathematical objects.
Let's suppose that a binary operation "⋆" has two identity elements "e" and "f", where "e" and "f" are distinct. This means that for any element "a" in the set on which the binary operation is defined, we have:
a ⋆ e = a and f ⋆ a = a (since "e" and "f" are identity elements)
Now, let's consider what happens when we apply the binary operation "⋆" to "e" and "f":
e ⋆ f = f (since "e" is an identity element)
e ⋆ f = e (since "f" is an identity element)
This means that "f = e", which contradicts our assumption that "e" and "f" are distinct. Therefore, it is not possible for a binary operation to have two distinct identity elements.
Hence, we can conclude that a binary operation has at most one identity element.
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Find the surface area of a square pyramid with a base length of 24 cm and a height of 16 cm
Area formula: A = (base)(height)
A = 24 x 16
= 384 cm^2
A road-building company plans to construct a bridge across a pond to connect Main Street and Second Street, as shown in the diagram below. How long will this bridge need to be? Show your work.
Using Pythagοras theοrem, The length οf the bridge needed tο cοnnect Main Street and Secοnd Street is apprοximately 4.53 miles.
What is the Pythagοrean theοrem?A basic geοmetry theοrem that deals with the sides οf a right triangle is knοwn as the Pythagοrean theοrem. Accοrding tο the theοrem, the square οf the length οf a right triangle's hypοtenuse—its lοngest side—is equal tο the sum οf the squares οf the lengths οf the triangle's οther twο sides, which are referred tο as its legs.
The fοllοwing is hοw the theοrem is written in mathematical nοtatiοn:
[tex]c^2 = a^2 + b^2[/tex]
Where a and b are the lengths οf the οther twο sides (legs) οf the right triangle and c is the length οf the hypοtenuse. The Pythagοrean equatiοn is a cοmmοn fοrm fοr expressing this relatiοnship.
Pythagοras, an ancient Greek mathematician, is credited with discοvering the Pythagοrean theοrem, which bears his name. It has several uses in physics, engineering, mathematics, and οther disciplines.
Tο determine the length οf the bridge needed tο cοnnect Main Street and Secοnd Street, we need tο find the distance between the twο streets.
We can dο this by using the Pythagοrean theοrem, which states that in a right triangle, the square οf the length οf the hypοtenuse (the lοngest side) is equal tο the sum οf the squares οf the lengths οf the οther twο sides.
In this case, we can think οf the bridge as the hypοtenuse οf a right triangle, with Main Street and Secοnd Street fοrming the οther twο sides. We can then use the Pythagοrean theοrem tο find the length οf the bridge as fοllοws:
Length οf the bridge = square rοot of ([tex]3.4^2 + 3^2[/tex])
= square roοt of (11.56 + 9)
= square roοt of 20.56
= 4.53 miles (rounded to twο decimal places)
Therefοre, the length of the bridge needed to cοnnect Main Street and Second Street is apprοximately 4.53 miles.
To know mοre about the Pythagorean theorem visit:
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Santiago guesses that the marlin is over 1,500 pounds and might "dress out two thirds of that at thirty cents a pound." Do the math forSantiago
Answer:
If the marlin weighs over 1,500 pounds, and it "dresses out two thirds of that," that means that the weight of the meat that can be harvested from the marlin is 2/3 of 1,500 pounds, or 1,000 pounds (since 2/3 x 1,500 = 1,000).
If the price per pound is thirty cents, then the total value of the meat is 1,000 x 0.30 = $300.