Answer:
To solve 34x23 ≡ r (mod 13), we can first calculate the product 34x23 = 782. Next, we need to find the remainder when 782 is divided by 13. To do this, we can divide 782 by 13 and find the remainder: 782 ÷ 13 = 60 remainder 2 Therefore, 782 is equivalent to 2 (mod 13). So, the solution to the original equation is r ≡ 2 (mod 13).
The length of the longer leg of a right triangle is 22cm more than six times the length of the shorter leg. The length of the hypotenuse is 23cm more than six times the length of the shorter leg. Find the side lengths of the triangle.
The length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.
what is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Let's denote the length of the shorter leg by "x".
According to the problem statement, the length of the longer leg is 22cm more than six times the length of the shorter leg, so:
longer leg = 6x + 22
Also, the length of the hypotenuse is 23cm more than six times the length of the shorter leg, so:
hypotenuse = 6x + 23
Now, we know that this is a right triangle, so we can use the Pythagorean theorem to relate the side lengths:
shorter leg² + longer leg² = hypotenuse²
Substituting the expressions we found earlier, we get:
x² + (6x + 22)² = (6x + 23)²
Expanding the squared terms and simplifying, we obtain:
x² + 36x² + 264x + 484 = 36x² + 276x + 529
Subtracting 36x² + 276x + 529 from both sides, we get:
x² - 12x - 45 = 0
Now, we can solve for x by factoring the quadratic equation:
(x - 15)(x + 3) = 0
So, either x = 15 or x = -3. Since we're dealing with lengths, we discard the negative solution and take x = 15.
Therefore, the length of the shorter leg is 15cm, the length of the longer leg is 6x + 22 = 6(15) + 22 = 112cm, and the length of the hypotenuse is 6x + 23 = 6(15) + 23 = 113cm.
So the side lengths of the right triangle are 15cm, 112cm, and 113cm.
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Use the graph to answer the question.
Graph of a polygon ABCD with vertices at 6 comma 3, 15 comma 3, 15 comma 9, 6 comma 9 and a second polygon A prime B prime C prime D prime with vertices at 2 comma 1, 5 comma 1, 5 comma 3, 2 comma 3.
Determine the scale factor used to create the image.
3
one third
one half
2
The distance between point A (6,3) and A' (2,1) is half of the original distance between A and B (6,3) and (15,3). Therefore, the scale factor is one half.
To determine the scale factor used to create the image of the second polygon A'B'C'D' from the original polygon ABCD, we can compare the side lengths of the two polygons.
The scale factor used to create the image is one half. This is because the distance between each vertex in the original polygon and the corresponding vertex in the image polygon is half of the original distance. For example,
Let's take the horizontal sides:
Side AB in polygon ABCD has length 15 - 6 = 9 units.
Side A'B' in polygon A'B'C'D' has length 5 - 2 = 3 units.
Now, we can find the scale factor by dividing the side length of A'B' by the side length of AB:
Scale factor = (A'B') / (AB) = 3 / 9 = 1/3
So, the scale factor used to create the image is one third.
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Much help is needed asap!
1. Identify each premise and the conclusion in the following argument. Determine whether the argument is an example of inductive or deductive reasoning.
Our house is made of brick. Both of my next-door neighbors have brick houses. Therefore, all houses in our neighborhood are made of brick.
Premises:
Conclusion:
Inductive or deductive?
2. Use the list of equations and inductive reasoning to predict the next multiplication fact in the list:
37 × 3 = 111, 37 × 6 = 222 , 37 × 9 = 333, 37 × 12 = 444 , ....
Use inductive reasoning to determine the probable next number in the list below. An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence.
5, 9, 13, 17, 21, 25, 29, .....
3. Successive Differences
Use the method of successive differences to find the next number in the sequence.
(a) 20, 31, 45, 62, 82, ... (Hint: Start with 31 - 20 = 11, use the subsequent term subtract the previous term)
(b) 8, 6, 3, 1, 2, 8, 21, ... (Hint: start with 6 - 8= -2, use the subsequent term subtract the previous term)
4. Find the sum using the special sum formula.
1 + 2 + 3 + ... + 48
5. Use the formula given on the first section to find
a) the sixth pentagonal number.
b) the eighth triangular number.
6. A vending machine accepts nickels, dimes, and quarters. Exact change is needed to make a purchase. How many ways can a person with four nickels, three dimes, and two quarters make a 30-cent purchase from the machine?
7. Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12.
He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week?
8. Use inductive reasoning to determine the units digit (or ones digit):
Example: Use inductive reasoning to determine the units digit of the number
3^55 .
The question is not about giving the exact value, but rather than applying the inductive reasoning to figure out the units digit.
The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, ... repeating meaning that every power that is divisible by 4 will end in 1. 56 is divisible by 4. Using this inductive reasoning 3 to the 56th power would end in a 1, then moving backward to the 55th power would give you a units digit of 7. This is inductive reasoning because we are using the smaller sample size of 4 repeating unit digits to make broad theories about all powers of 3.
Another similar approach: The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, ... repeating. If the power is a multiple of four, the units digit is 1. Power 52 is a multiple of 4 and it's close to power 55.
Power 52 ends with units digit of 1, next 53 ends with 3, 54 ends with 9, and 55 ends with 7
(a) The ones digit (also called the units digit) in 2^4000 . The question is not about giving the value to the expression,
but rather than applying the inductive reasoning to figure out the units digit. The answer is just a single digit.
(b) The units digit of the number 3^41
9. Kathy stood on the middle rung of a ladder. She climbed up 2 rungs, moved down 5, and then climbed up 6. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder?
10. If you ask Batman’s nemesis, Catwoman, how many cats she has, she answers with a riddle: “Five-sixth of my cats plus seven.” How many cats does Catwoman have?
11. A birdhouse for swallows can accommodate up to 8 nests. How many birdhouses would be necessary to accommodate 58 nests?
12. Use the circle graph below to determine how many of the 140 students made an A or a B.
(see picture of circle graph attached below)
13. The bar graph shows the number of cups of coffee, in hundreds of cups, that a professor had in a given year.
a) Estimate the number of cups in 2004.
b) What year shows the greatest decrease in cups?
(see picture of bar graph below)
14. The line graph shows the average class size of a first grade class at a grade school for years 2001 through 2005. (see picture line graph below)
In which years did the average class size increase from the previous year?
How much did the average size increase from 2001 to 2003?
The premise is that both of my next-door neighbors and I have brick homes. So, all of the homes in our area are brick construction. A good illustration of inductive reasoning is this.
How to use equations to answer the rest?2. Given that the pattern appears to be multiplying by 3, then 6, then 9, then 12, and so on, the next multiplication fact is probably 37 x 15 = 555.
3.
(A) The number 101 comes next in the list.
(b) The following digit in the series is -10.
4. According to the formula n(n+1)/2, the first n positive integers are added together. Hence, 48(48+1)/2 = 1176 is the sum of the first 48 positive integers.
5.
(A) The formula n(3n-1)/2 yields the nth pentagonal number. Thus, 6(3x6-1)/2 = 91 is the sixth pentagonal number.
(b) The expression n(n+1)/2 yields the nth triangular number. Hence, 8(8+1)/2 = 36 is the eighth triangular number.
6. There are ten ways to use the four nickels, three dimes, and two quarters to make a 30-cent purchase from the vending machine.
7. The first week, Ronnie had $12 to his name.
8.a.The ones digit in the number 24000 is 6.
(b) 341's units digit is 3.
9. 19 rungs make up the ladder.
10. Catwoman owns 42 felines.
11. 58 nests would require 8 birdhouses, plus 2 additional nests.
12. A total of 60 pupils received an A or a B.
13.
(a) 550 cups are anticipated to be consumed in 2004.
(b) The year 2003 exhibits the biggest decline in cups.
14. Since 2001, the typical class size has risen.
15. During 2001 and 2002, as well as between 2004 and 2005, the average class size increased. From 2001 to 2003, the average class size grew by two pupils.
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A manufacturer sells its products to a wholesaler for $73 each. The
wholesaler then marks up those products and sells them to retailers
for $80.43. What is the wholesaler's markup rate? Round to the
nearest hundredth.
The wholesaler's markup is the difference between the selling price and the cost price, which is $80.43 - $73 = $7.43.
The markup rate can be found by dividing the markup by the cost price and multiplying by 100 to get a percentage:
markup rate = (markup / cost price) x 100%
markup rate = ($7.43 / $73) x 100%
markup rate = 10.17%
Therefore, the wholesaler's markup rate is 10.17%, rounded to the nearest hundredth.
Question 1 of 5
You're putting together a student poetry book and want to create it as an EPUB book that you
can read in the Books app. How can you make an EPUB book and open it in the Books app?
Identify the correct order of the following steps.
1 Create a new document using a book template.
2 Choose Copy to Books.
3 Enter EPUB information, then tap Export.
4 Tap Export, then choose EPUB.
5 Add text to the book, then tap the More button in the upper-right corner
Choose Download as ePub or Download as PDF from the Personal Books screen's export icon. The Apple Ibooks icon will say Transfer to Books when you select Open in.
What, in plain terms, are books?A book is a device for storing data in the form either writing or images. Books are often made up of several pages that are bound together and covered in reeds, parchment, vellum, or paper.
Why are books essential to our lives?Books are important in life, especially for young people. Reading books helps pupils learn more, improves their intelligence, and raises their awareness of the diverse nations and civilizations throughout the world.
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The correct order of the steps is:
1. Create a new document using a book template.
2. Add text to the book, then tap the More button in the upper-right corner.
3. Enter EPUB information, then tap Export.
4. Tap Export, then choose EPUB.
5. Choose Copy to Books to open the EPUB book in the Books app
.Your answer: To create an EPUB book and open it in the Books app, follow these steps in the correct order: 1. Create a new document using a book template. 2. Add text to the book, then tap the More button in the upper-right corner. 3. Tap Export, then choose EPUB. 4. Enter EPUB information, then tap Export. 5. Choose Copy to Books.
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Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her allowance every day.
Formulate and then graph the equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, x.
The equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, x, can be represented as y = 2x + 125, where 2x represents the total amount she saves from her allowance and 125 represents the initial amount she saved.
This is a linear equation in slope-intercept form, where the slope of the line is 2, indicating that she saves $2 per day, and the y-intercept is 125, indicating that she had already saved $125 before starting to save from her allowance. To graph this equation, we can plot the y-intercept at (0, 125) and use the slope to find other points on the line. For example, after 5 days, she would have saved y = 2(5) + 125 = 135 dollars, giving us the point (5, 135). Plotting this point and connecting it with the y-intercept will give us a straight-line graph.
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Colby’s art class is 50 minutes. She spends 21 minutes cutting paper and the rest of the time making a collage. How much time did Colby spend making her collage?
Colby spends 29 minutes making her collage.
50 is the total amount of minutes and 21 minutes is a part of that total.
This means we have to subtract.
50 - 21 = 29.
Solve for s.
3s + 1 = 10
S=
Submit
Answer:
S ========================= 9
because 9+ 1= 10
simple
Answer:
s=3
Step-by-step explanation:
3s+1 = 10
To solve for s in this two step equation, we must first subtract 1 from each side.
3s+1-1 = 10-1
3s = 9
Then divide by 3 on each side.
3s/3 = 9/3
s=3
using arithmetic sum formula
Find the sum of the first 6 terms.
2,5,8,11,14,17
Therefore, the sum of the first 6 terms of this arithmetic sequence is 57.
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant number to the previous term. The fixed constant number is called the common difference (d) of the sequence.
Here,
To find the sum of the first 6 terms of this arithmetic sequence, we can use the arithmetic sum formula:
Sn = n/2 * [2a + (n - 1)d]
where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
In this case, we have:
a = 2 (the first term)
d = 3 (the common difference, since each term is 3 more than the previous term)
n = 6 (the number of terms)
Substituting these values into the formula, we get:
S6 = 6/2 * [2(2) + (6 - 1)3]
= 3 * [4 + 15]
= 3 * 19
= 57
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Trigonometry dba
100 points need in 1 hour
Answer: I thank it is 200 point in 2 hour
Step-by-step explanation:
This is due at midnight can I have some help :>
The distance between town 1 and 2 is 83 miles
What is word problem?Word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
The distance between Town 1 and 3 is 110 miles and the distance between Town 2 and town 3 is 27miles.
Therefore the distance between town 1 and 2 is the difference between distance between town 1 and 3 and distance between town 2 and 3
This means that distance between town 1 and 2 = 110-27 = 83 miles.
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The triangle below is equilateral. Find the length of side
�
x to the nearest tenth.
Value of side x in equilateral triangle is 6units.
Define equilateral triangleAn equilateral triangle is a type of triangle in which all three sides are of equal length. Equilateral triangles are also equiangular, meaning all three angles are of equal measure and are each 60 degrees. Because all three sides and angles are equal, equilateral triangles are symmetric about their center point, and their three medians, altitudes, and angle bisectors are all the same line.
Area of equilateral triangle = √3/4×a²
Given side length=12
So, area of equilateral triangle =√3/4×12²=62.35383
We know that
Area of triangle= ½×base×height
Given
Base=12
let height of triangle be=y
Area=½×12×y
62.35383=½×12×y
y=10.39
Using pythagoras' theorem,
c²=a²+b²
122=x²+10.392
x=√144-107.95
x=6
Hence, value of side x in equilateral triangle is 6units.
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In need of help ! Thank you
Since the two equations represent the same line, there are infinitely many solutions to the system.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, each containing one or more terms, separated by an equal sign. The terms may contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. Equations are used to represent relationships between variables and to solve problems in mathematics, science, engineering, and many other fields. They can be classified based on their degree, number of variables, and the types of functions they involve. Linear equations, for example, involve only first-degree terms and are used to represent straight lines; quadratic equations involve second-degree terms and are used to represent parabolas.
Here,
To determine whether the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point, we can first put the equations in slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.
10y + 8x = 10
10y = -8x + 10
y = (-4/5)x + 1
5y - 5 = -4x
5y = -4x + 5
y = (-4/5)x + 1
Notice that the two equations have the same slope of -4/5 and the same y-intercept of 1. Therefore, the two lines are identical and intersect at every point on the line.
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in a hurry need help on these questions
The length of the ramp is approximately 4.95 meters and the angle the ladder makes with the ground is approximately 58.21 degrees.
Solving the equationTo solve x^2 + 8x - 20 = 0 using the Zero Product Property, we first need to factor the quadratic equation into two linear factors:
So, we have
(x + 2)(x - 10) = 0
This gives
x = -2 and x = 10
The length of the rampTo find the length of the ramp, we can use the trigonometric ratio of tangent.
We know that the vertical height (opposite side) of the ramp is 1.8 meters and the angle between the ramp and the ground (angle of elevation) is 20
So, we have
tan(20) = opposite / adjacent
tan(20) = 1.8 / adjacent
This gives
adjacent = 1.8/tan(20)
Evaluate
adjacent = 4.95
Therefore, the length of the ramp is approximately 4.95 meters.
The angle with the groundWe know that the ladder is 20 feet long and reaches a point 17 feet up the wall.
Let the angle the ladder makes with the ground be θ.
Using the trigonometric ratio of sine, we have:
sin(θ) = opposite / hypotenuse
sin(θ) = 17 / 20
Taking the arc sine of both sides, we get:
θ = sin^(-1)(17/20)
Using a calculator, we get:
θ ≈ 58.21 degrees
Therefore, the angle the ladder makes with the ground is approximately 58.21 degrees.
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With the aid of appropriate diagrams, compare and contrast the demand for several or multiple variable inputs under perfect competitive and imperfect markets?
In a perfectly competitive market, firms are price takers, meaning they have no market power and must accept the market price for their output.
What is market price?A market price is the price at which a good or service is sold in a specific market. The forces of supply and demand determine market price in a competitive market.
Firms in a perfectly competitive market are price takers, which means they lack market power and must accept market prices for their output.
As a result, in a perfectly competitive market, the demand for multiple variable inputs is derived from the marginal product of each input.
The marginal product is the extra output generated by adding one more unit of an input while holding all other inputs constant.
Thus, the value of the marginal product, which is the marginal product multiplied by the market price of the output, is the demand for an input.
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find geomatic series for a1
the first term of the geometric series is approximately 105.294.
How to solve the problem?
The formula for the sum of a geometric series is given by:
Sn = a1(1 - rⁿ)/(1 - r)
where a1 is the first term, r is the common ratio, n is the number of terms, and Sn is the sum of the series.
We are given that Sn = 3045, r = 2/5, and An = 120, where An is the nth term of the series. We can use these values to solve for a1.
First, we can use the formula for the nth term of a geometric series:
An = a1 * rⁿ⁻¹
Substituting An = 120 and r = 2/5, we get:
120 = a1 * (2/5)ⁿ⁻¹
We also know that the sum of the series is Sn = 3045. Substituting the formula for Sn and solving for n, we get:
3045 = a1(1 - (2/5)ⁿ)/(1 - 2/5)
12180 - 4(2/5)ⁿ = 5a1
a1 = (12180 - 4(2/5)ⁿ)/5
Now we can substitute this expression for a1 into the equation we obtained for An:
120 = [(12180 - 4(2/5)ⁿ)/5] * (2/5)ⁿ⁻¹
Simplifying and solving for n, we get:
n = log(12/5) / log(2/5)
Substituting this value of n back into the expression for a1, we get:
a1 = (12180 - 4(2/5) power (log(12//log(2/5))) / 5
Using a calculator, we can evaluate this expression to get:
a1 ≈ 105.294
Therefore, the first term of the geometric series is approximately 105.294.
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The table shows the relationship between the depth, in meters, of a submarine and the time, in
minutes, since it started a dive.
The relation between time and depth is not prοpοrtiοnal as 2/100 ≠ 4/180 ≠ 6/260 ≠ 8/340.
What is prοpοrtiοnal relation?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality"
To solve questions that involve a table showing the relationship between two variables, such as depth and time in this case, you may want to consider the following steps:
A quick check οf table values shοws the relatiοnship is nοt prοpοrtiοnal:
100/2 = 50 ≠ 45 = 180/4
That is, the ratiοs οf table values are nοt cοnstant.
2/100 ≠ 4/180 ≠ 6/260 ≠ 8/340
Therefore, the relation between time and depth is not prοpοrtiοnal.
When the values are graphed, the line thrοugh the pοints dοes nοt intersect the οrigin. This is further indicatiοn the relatiοnship is nοt prοpοrtiοnal.
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Complete question:
Find√b2-4ac when a = 2, b = −5, c = -3.
Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.
The answer to this problem: 7
5(2 +2f)
U need to simplify this expression how do I get the answer and what is the answer pls help I’m so stuck on this
Remika just got a new job!
• The job pays $8.50 per hour
During the first year, every 4 months there is a 2% raise in hourly pay.
At the end of one year, how much would Remika be paid hourly, to the nearest cent?
●
Do not enter the dollar sign ($).
Answer: 9.01
Step-by-step explanation: 8.5*0.02= 0.17 *3= 0.51+8.5=9.01
Rewrite in simplest rational exponent form √x-4x Show each step of your process.
Answer:
[tex]x {}^{ \frac{5}{8} } [/tex]
Step-by-step explanation:
[tex]1. \: \sqrt{x {}^{ \frac{5}{4} } } \\ 2. \: x {}^{ \frac{5 \times 1}{4 \times 2} } \\ 3. \: x {}^{ \frac{5}{4 \times 2} } \\ 4. \: x {}^{ \frac{5}{8} } [/tex]
Jake and carry 6 and 1/4 lb of wood in from the barn his father can carry one and five seven times as much as Jake how many pounds can Jake's father carry
Answer:
Jake's father can carry 10 and 5/7 lb of wood.
Step-by-step explanation:
Jake carried 6 and 1/4 lb of wood.
Let's convert this to an improper fraction:
6 and 1/4 = (4 * 6 + 1)/4 = 25/4
So, Jake carried 25/4 lb of wood.
Jake's father can carry 1 and 5/7 times as much as Jake.
Let's convert this to a fraction:
1 and 5/7 = (7 * 1 + 5)/7 = 12/7
So, Jake's father can carry 12/7 times as much as Jake.
To find out how many pounds Jake's father can carry, we need to multiply Jake's weight by 12/7:
Jake's father can carry = (25/4) * (12/7)
= (25 * 12) / (4 * 7)
= 300/28
= 10 and 5/7 lb (when simplified to a mixed number)
Select the correct answer from each drop-down menu.
AABC is similar to ADEF. The ratio of the perimeter of AABC to the perimeter of ADEF is 1:10. The longest side of ADEF measures 4
The length of the longest side of AABC is
2
4
16
30
units. The ratio of the area of AABC to the area of ADEF is 1:100 v
Reset
Next
The length of the longest side of AABC is 4 units, and the area of AABC is equal to the area of ADEF.
What is angle ?An angle is the figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. The measure of an angle is usually given in degrees or radians and is determined by the amount of rotation between the two rays or lines. Angles are used in geometry and trigonometry to study shapes, distances, and other properties of objects.
According to the given information:Since AABC is similar to ADEF, the corresponding sides of the two triangles are proportional. Let the longest side of AABC be x. Then:
x/4 = 1/10 (since the ratio of the perimeters is 1:10)
Solving for x, we get:
x = 4/10 * 10 = 4
Therefore, the length of the longest side of AABC is 4 units.
Since the ratio of the areas of AABC to ADEF is 1:100, and we know that the longest side of ADEF measures 4, we can use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths:
Area of AABC / Area of ADEF =[tex](x/4)^2 = 1/100[/tex]
Substituting x = 4, we get:
Area of AABC / Area of ADEF[tex]= (4/4)^2 = 1[/tex]
So, the area of AABC is equal to the area of ADEF.
Therefore, The length of the longest side of AABC is 4 units, and the area of AABC is equal to the area of ADEF.
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6x2+15x=0
use the quadratic formula to solve. and describe the solution. show work
Answer: x = -2.5
Step-by-step explanation:
I think you meant 6x^2 + 15x = 0
6x^2 + 15x = 0
3x(2x + 5) = 0
2x + 5 = 0
2x = -5
x = -2.5
Let A={1,2,3,4,5,6,7 } and let R be the “has the same parity as“ relation on A. Write down R in set listing notation.
The answer of the given question based on the relation is R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}.
What is Set listing notation?Set listing notation is a way to represent a set by listing all of its elements between curly braces { }. If a set has a large or infinite number of elements, it may not be practical to list all the elements. In such cases, we can use set-builder notation to describe the set using a condition or a rule.
The "has the same parity as" relation on set A means that any two elements in A are related if they have the same parity (either both even or both odd).
So, we can write the relation R as a set of ordered pairs where each pair consists of two elements that have the same parity.
R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}
In this set, the ordered pair (x, y) indicates that x and y have the same parity. For example, (1, 3) is in R because 1 and 3 are both odd. Similarly, (2, 4) is in R because 2 and 4 are both even.
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Given vectors u = (8, 1) and v = (-7, -1), find the sum u + v and write the
result in component form.
According to the solution we have come to find that, The sum of the given vectors u and v is (1, 0).
What is vector?In mathematics, a vector is a mathematical object that has both magnitude (or length) and direction. It is usually represented as a directed line segment, where the length of the segment corresponds to the magnitude of the vector, and the direction of the segment represents the direction of the vector.
A vector can be specified in terms of its components or coordinates, which are typically expressed as a sequence of numbers or symbols. For example, a two-dimensional vector can be written as (x, y), where x and y are the components of the vector along the x-axis and y-axis, respectively.
To find the sum of two vectors, we simply add their corresponding components.
So, for the given vectors u = (8, 1) and v = (-7, -1), their sum u + v can be computed as:
u + v = (8, 1) + (-7, -1) = (8 - 7, 1 - 1) = (1, 0)
Therefore, the sum of the given vectors u and v is (1, 0).
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Find the coordinates of the circumcenter of the triangle with the given vertices. R(-2,5), S(-6,5), T(-2,-1).
Answer:
the circumcenter of triangle RST is (-4, 3).
Step-by-step explanation:
To find the circumcenter of a triangle, we need to find the intersection of the perpendicular bisectors of its sides.
Let's first find the midpoints of the sides RS, ST, and RT.
Midpoint of RS:
x-coordinate = (-2 + (-6))/2 = -4
y-coordinate = (5 + 5)/2 = 5
Midpoint of RS is (-4, 5).
Midpoint of ST:
x-coordinate = (-6 + (-2))/2 = -4
y-coordinate = (5 + (-1))/2 = 2
Midpoint of ST is (-4, 2).
Midpoint of RT:
x-coordinate = (-2 + (-2))/2 = -2
y-coordinate = (5 + (-1))/2 = 2
Midpoint of RT is (-2, 2).
Now, let's find the equations of the perpendicular bisectors of RS and ST, and then find their point of intersection.
Perpendicular bisector of RS:
The slope of RS is (5 - 5)/(-6 - (-2)) = 0.
The midpoint of RS is (-4, 5).
So, the equation of the perpendicular bisector of RS is x = -4.
Perpendicular bisector of ST:
The slope of ST is (5 - (-1))/(-6 - (-2)) = -3/2.
The midpoint of ST is (-4, 2).
So, the equation of the perpendicular bisector of ST is y = (-3/2)(x + 4) + 2, which simplifies to y = (-3/2)x - 1.
Now, let's find the point of intersection of these two lines.
x = -4 for the perpendicular bisector of RS, so we substitute that into the equation of the perpendicular bisector of ST:
y = (-3/2)(-4) - 1 = 4 - 1 = 3.
Therefore, the circumcenter of triangle RST is (-4, 3).
Calculate the difference between the offensive and defensive
Offensive is 81.8 and defensive is 31.57
Answer:
50.23
Step-by-step explanation:
To calculate the difference between the offensive and defensive values, we simply subtract the defensive value from the offensive value:
81.8 - 31.57 = 50.23
The difference between the offensive and defensive values is 50.23.
limit (2n)! as n goes to 0.
The limit of (2n)! as n goes to 0 does not exist.
What is Limit?Limits are a fundamental concept in mathematics that describe the behavior of a function as the input variable approaches a certain value, either from one or both sides. They are used to determine values that a function can get arbitrarily close to but not necessarily equal to.
The limit of (2n)! as n goes to 0 does not exist, as the factorial function is not defined for non-negative integers less than 1. The factorial function is defined as the product of all positive integers up to and including the argument. Therefore, for non-negative integers less than 1, the factorial function is undefined. The limit does not exist because the function is undefined for the given value of n.
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Prove that Limit (2n)! as n goes to 0 does not exist.
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an
elephant weighs 3300 pounds on Planet A, find the elephant's weight on Planet B.