After the raise, the salary of woman becomes $2700.
Salary Reduction and RaiseThe answer was determined through simple arithmetic calculations.
First, the initial salary of $2500 was reduced by 10%, which is calculated as $2500 * 0.1 = $250.So the new salary after the reduction was $2500 - $250 = $2250.Next, a 20% raise was given over the reduced salary of $2250, which is calculated as $2250 * 0.2 = $450.Finally, the raise was added to the reduced salary, resulting in $2250 + $450 = $2700.So, the woman's salary after the raise is $2700.This method of calculation can be applied to any similar scenario where an initial salary is reduced by a certain percentage and then increased by another percentage. The formula used can be generalized as:
Final Salary = (Initial Salary - Initial Salary * Reduction Percentage) * (1 + Raise Percentage)
It's a simple and straightforward method that can be easily applied to find the final salary in similar cases.
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A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 10 feet less than 3 times the height. Find the width and the
height if the carpenter expects to use 30 feet of lumber to make it.
what are the measures of the angels in the right triangles formed by the two regular pentagons are
The measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.
Right triangles and regular pentagonsThe interior angles of a regular pentagon measure 108 degrees each. Therefore, if we have two regular pentagons, the right triangle formed by the two pentagons will have two angles that are equal to 108 degrees each.
These two angles are the complement of each other, meaning they add up to 90 degrees. Therefore, one of the angles in the right triangle formed by the two pentagons is 72 degrees, and the other is 18 degrees.
So, the measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.
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superior segway tours gives sightseeing tours around chicago, illinois. it charges a one-time fee of $60, plus $28 per hour. what is the slope of this situation?
So the slope of the scenario is $28 per hour, which indicates that the expense of the tour increases by $28 for every extra hour spent on it.
What is slope?The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, while the y-intercept is (0, 7).
Here,
In this situation, the slope represents the rate of change in the cost of the tour with respect to the time spent on the tour. The slope of the situation can be calculated as the change in cost divided by the change in time.
Since the one-time fee is a fixed cost, it does not change with respect to the time spent on the tour. Therefore, the slope can be calculated as the rate of change in the cost due to the hourly fee of $28.
The slope can be represented as:
slope = Δcost/Δtime = $28/hour
So, the slope of the situation is $28 per hour, which means that for every additional hour spent on the tour, the cost of the tour increases by $28.
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simplify 2m exponent of 0 n exponent of 6 over 3n exponent of 5
The simplified expression is equal to 2/3.
Simplifying Math ExpressionThe expression can be simplified as follows:2m⁰ * n⁶ / (3n⁵)
Since m⁰ is equal to 1, the expression becomes:2 * n⁶ / (3n⁵)
Dividing both numerator and denominator by n⁵ gives:2 * n / (3n) = 2/3
So the simplified expression is equal to 2/3.
The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.
For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.
In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.
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What is the greatest common factor between 18 and 30 and 54
Answer: 1, 2, 3, 6, 1
Step-by-step explanation:
When listing all the factors for 18, 30 ,54....
18 , 30 , 54 to find the common factors. The common factors for 18,30,54 18 , 30 , 54 are 1,2,3,6 1 , 2 , 3 , 6 . The GCF (HCF) of the numerical factors 1,2,3,6 1 , 2 , 3 , 6 is 6 .
( Hope this helps )
The line y= 2x+3 and y=-3x+3 intersect at the point:
The point of intersection of the two equations will be ( 0, 3 ). The correct option is C.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the two equations are y= 2x+3 and y=-3x+3. The value of x and y will be calculated as:-
y= 2x+3
y=-3x+3
Equate the equations and solve,
2x + 3 = - 3x + 3
2x +3x = 0
x = 0
The value of y is,
y = 2x+3
y = 2 x 0 + 3
y = 3
Therefore, the two equations points of intersection will be ( 0, 3 ). The right answer is C.
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The scatter plot and line of best fit below shows the length of two peoples femur (the long leg bone in thigh) and their height in centimeters. Based on the line of best fit, what would be the predicted femur length for someone with a height of 218 cm.
The predicted femur length is 69 cm
How to determine the predicted femur lengthFrom the question, we have the following parameters that can be used in our computation:
The scatter plot
On the scatter plot, we have
x = the length of two peoples femur (the long leg bone in thigh)
y = height in centimeters
So, we have
Height = 218 cm
From the graph, we have
x = 69
Hence, the femur length is 69 cm
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Determine whether ABC with vertices A(-3, 6), B(0, 10), and C (3, 8) is similar to XYZ with vertices X(-1, 3), Y(2, 7) , and Z(5, 5) .
Using Pythagorean theorem and the vertices given, the two triangle are similar
What are vertices of a triangleTwo triangles are similar if and only if the ratios of their corresponding sides are equal. So, to determine if triangle ABC is similar to triangle XYZ, we need to compare the ratios of corresponding sides.
One way to do this is to calculate the lengths of the sides in both triangles and compare the ratios. For example, the length of side AB in triangle ABC can be found using the Pythagorean theorem:
AB = √((0-(-3))^2 + (10-6)^2) = √(3^2 + 4^2) = √25 = 5
Similarly, the length of side XY in triangle XYZ can be found:
XY = √((2-(-1))^2 + (7-3)^2) = √(3^2 + 4^2) = √25 = 5
Next, we can compare the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ. If the ratios are equal for all corresponding sides, then the triangles are similar.
In this case, we find that the ratios of corresponding sides AB and XY, BC and YZ, and AC and XZ are all equal, so triangles ABC and XYZ are similar.
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8
Helen thinks of two numbers.
The Highest Common Factor (HCF) of her two numbers is 5
The Lowest Common Multiple (LCM) of her two numbers is a multiple of 12
Write down two possible numbers that Helen could be thinking of.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
what is HCF ?The biggest integer that is able to divide two or more quantities is known as the highest common factor (HCF) or greatest common factor. Highest refers to the biggest or greatest number. The sharing a common meaning of two or more integers. Feature is an integer that can be used to divide a whole number (a divisor). Write each integer as the sum of one's main characteristics in step one. Step 3: The HCF of said given integers is the greatest number that can be found among the common factors.
given
1. It is assumed that when Helen thinks of two numbers, they have corresponding HCF and LCM values of 5 and 12.
2. The smallest common multiple shared by two numbers is referred to as the least common number.
LCM of 4 and 6 is 12, for instance.
3. The highest number that divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.
HCF of 6 and 8 is 2, for instance.
4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.
5.The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values other than 5. 60 and 120 have an HCF of 60, but not 5.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
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how many -digit numbers are there with unique digits from to such that the first five digits form an increasing series and the last five digits form a decreasing series?
The number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.
For the first five digits to form an increasing series, we can choose the first digit in 9 ways (it can't be 0), the second digit in 8 ways, the third digit in 7 ways, the fourth digit in 6 ways, and the fifth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the first five digits.
For the last five digits to form a decreasing series, we can choose the sixth digit in 9 ways (it can't be 0), the seventh digit in 8 ways, the eighth digit in 7 ways, the ninth digit in 6 ways, and the tenth digit in 5 ways. So, there are 9 × 8 × 7 × 6 × 5 = 15, 120 ways to choose the last five digits.
Therefore, the number of 10-digit numbers with unique digits from 1 to 9 such that the first five digits form an increasing series, and the last five digits form a decreasing series is 15, 120 * 15, 120 = 227, 528, 000.
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Bacteria can multiply at an alarming rate when each bacterium splits into two new cells, thus doubling. If a single bacterium is discovered at 9 a.m. and doubles every hour, how many bacteria will there be at the end of the day (midnight)? Write an equation and show the calculations that represent this situation.
The equation we get for the amount of bacteria with with time T
T(t)=15×2ⁿ where n is the number of hours.
What are exponents?Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.
Given here: A certain type of bacteria doubles every hour
Now number of hours between 9-12 pm
is 15 hours
if at 9 a.m the amount of bacteria is x then we have in 15 hours
at t=1 we have the number of bacteria was
T=2×15
=30
Similarly we have for t=15 we get
T=15×2¹⁵
Hence, The equation we get for the amount of bacteria with with time T
T(t)=15×2ⁿ where n is the number of hours.
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A bobsled team is practicing runs on a track. Their first run takes 4.85 minutes. On each of the next two runs, the team’s time changes by −512% compared to the previous time.
A photo of a bobsled on a track is shown.
Question 1
Part A
What was the team’s time, rounded to the nearest hundredth of a minute on their final run?
Answer: The team's time on the final run can be found by successively multiplying their first time by (1 - 0.512) twice:
First run time: 4.85 minutes
Second run time: 4.85 * (1 - 0.512) = 2.37 minutes
Third run time: 2.37 * (1 - 0.512) = 1.15 minutes (rounded to the nearest hundredth)
So the team's time on their final run was 1.15 minutes.
Step-by-step explanation:
Paula's Pizza Parlor uses the following ingredients to make pizza
Number of Pizzas
2
5
Sauce
18
Cheese
12
At this Rate how many sauce and cheese will paula use to make 5 pizzas?
To make 5 pizzas, Paula will use 45 sauce and 30 cheese.
What are multiplication and division?Multiplication is used to find the product of two or more numbers. Multiplication is also known as repeated addition.
The division is the opposite operation of multiplication. It is how one tries to determine how many times a number is contained into another.
Given,
Paula uses 18 sauce and 12 cheese to make two pizzas.
Ingredients needed to make one pizza = 18/2 sauce and 12/2 cheese
= 9 sauce and 6 cheese
Ingredients needed to make 5 pizzas = 9 × 5 sauce and 6× 5 cheese
= 45 sauce and 30 cheese
Hence, 45 sauce and 30 cheese is needed to make 5 pizzas.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The two sequences of transformations of ΔABC that exhibit the congruence between the two triangles include the following:
A. a rotation of 180° about the origin and a translation of 1 unit left.
E. a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left.
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Point A = (-6, 2) → Point A' = (-(-6), -(2)) = (6, -2).
By translating the pre-image of triangle A'B'C' horizontally left by 1 unit, the coordinate A" of the image of triangle A'B'C' include the following:
(x, y) → (x - 1, y - 7)
Coordinate A' = (6, -2) → Coordinate A'' (6 - 1, -2) = (5, -2)
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properties of equality
if you could figure out this it would be great but its a whole worksheet
Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.
what is inequality ?A relationship of two expresses or integers that is neither equal in mathematics is referred to as an inequality. Furthermore, inequity results from imbalance. In math and science, an inequalities establishes the connection between two ou alors elements. Egality and inequality are not the same. Use the not equal symbol most frequently when two quantities are not equal (). Values of any size can be examined using a variety of inequalities. By changing the two sides until only the variables are left, many straightforward inequalities can be solved. However, a number of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.
given
2(x- 9 ) = -10 ( given )
= 2x - 18 = -10 ( multiplication property )
= 2x = -10 + 18 ( subtraction property )
2x = 8 ( division property )
x = 4
Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.
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2=e-1 help me I'm stuck it on a math book page 541 question 20
Answer:
[tex]3=e[/tex]
Step-by-step explanation:
I know this might be late but I can help if you still need it
So in the equation [tex]2=e-1[/tex], we need [tex]e[/tex] by itself. To do that we need to add [tex]1[/tex] to each side. We do this because the side that [tex]e[/tex] is on, the [tex]1[/tex] is being subtracted and we need to do the opposite of subtraction which is addition.
[tex]2=e-1[/tex]
[tex]+1[/tex] [tex]+1[/tex]
So the new equation:
[tex]3=e[/tex]
Hope this helped!
Stay safe and have a great day/night! (:
HELLP PLEASE!!!! I WILL MARK BRAINLIEST!!!
Answer:
No Solution.
Step-by-step explanation:
To solve for x in this equation, we need to simplify both sides of the equation and make them equal.
Starting with the left-hand side:
5 + x - 14 = x - 7
Adding 14 to both sides:
5 + x = x + 7
Subtracting x from both sides:
5 = 7
5 does not equal 7.
Therefore, the value of x is no solution.
Answer:
there is no solution for this, if you solve you will get 0=2 (This is also called a contradiction)
Step-by-step explanation:
5+x-14=x-7
5-14 = -9
-9+x=x-7
x-9=x-7
+9 +9
x=x+2
-x -x
0 = 2
A. 829.6 mi³
B. 891.6 mi³
C. 437.8 mi³
D. 694.8 mi³
Answer:
b
Step-by-step explanation:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²
the students in mr. juarez's homeroom collected more cans than students in ms. wade's homeroom. write an expression that represents how many more cans were collected.
The expression that can represent how many more cans were collected is 8n - 7 > 6n + 3, which is in fact an inequality.
An inequality in math is an algebraic expression that represents, well, inequality. It shows a relationship between two values or expression, which aren't equal to each other. It is used to compare two values/expression, showing if one is greater than, less than, or simply not equal to another. Thus, we would use a mathematical symbol of <, >, ≤, ≥, or ≠ to express an inequality.
Since students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom do, you can use the symbol > in your inequality. The number of cans collected in Mr. Juarez's homeroom is 8n − 7, while the number of cans collected in Ms. Wade's homeroom is 6n + 3. Therefore, your inequality would be 8n - 7 > 6n + 3.
This question is missing some parts, which are most probably these:
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Chapter 4 Lesson 3 Solving System of Equations Using Elimination
1) 2x + 5y = 17
+ 6x – 5y = -9
────────
8x = 8
divide both sides by 8 :
Answer : x = 1 (one solution)
2) (3x – y = 0) * 4
(4x + 2y = 14) * 3
12x – 4y = 0
- 12x + 6y = 14
────────
-10y = -14
Divide both sides by -10
Answer : y = 1.4 (one solution)
3) 6x + 5y = 39
- 3x + 5y = 27
────────
3x = 12
Divide both sides by 3
Answer : x = 4 ( one solution )
4) 4x – 7y = 3
+ x – 7y = -15
────────
5x = -12
Divide both sides by 5
Answer : x= -2.4 (one solution)
Find the mean of these numbers:
2,6,9,56,63,68
Explanation:
First we add up those numbers
2+6+9+56+63+68 = 204
Then divide by 6 because there are 6 values in this list.
204/6 = 34
Answer:34
Step-by-step explanation:It's obtained by simply dividing the sum of all values in a data set by the number of values.
Plsssss help and show work
The vertex form of quadratic equation is y = a(x - 0)² + 7 and the standard form of quadratic equation is y = 0x² + 7
What do you mean by Vertex form?The vertex form of a quadratic equation is an equation written in the form:
f(x) = a(x - h)² + k,
where (h, k) is the vertex of the parabola represented by the equation. The variable x represents the input value, f(x) represents the output value, a represents the coefficient of the x² term, h represents the x-coordinate of the vertex, and k represents the y-coordinate of the vertex. The vertex form of a quadratic equation is useful for easily identifying the location and shape of the parabola represented by the equation, especially if the parabolic function has a vertex that is not at (0,0).
The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
To find the vertex form of this equation, we need to find the vertex first. To do this, we can average the x-values of the maximum and minimum points in the table, which gives us the x-coordinate of the vertex. In this case, the maximum and minimum points are (1, 7) and (-1, -9), so the x-coordinate of the vertex is (1 + -1)/2 = 0.
Next, we can find the y-coordinate of the vertex by evaluating f(0), which gives us 7.
So, the vertex of the parabola is (0, 7).
Using this information, we can write the vertex form of the equation:
y = a(x - 0)² + 7
To find the standard form of the equation, we need to expand the vertex form and simplify.
y = a(x² - 0x) + 7
y = ax² + 7
We can then find the value of a by using any one of the points in the table. Let's use the point (1, 7):
7 = a(1²) + 7
7 = a + 7
a = 0
So, the standard form of the equation is:
y = 0x² + 7
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There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
The probability of getting 2 same colour balls in a row = 41/81
Probability:The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.
Probability of an event P(E)
= [ No of favorable outcomes ]/ Total No of outcomes
Here we have
There is a bag filled with 5 blue and 4 red marbles.
Number of balls = 5 + 4 = 9
Marble is taken at random from the bag,
The probability of getting the red ball = 4/9
The probability of getting the blue ball = 5/9
The color is noted and then it is replaced.
Another marble is taken at random.
The probability of getting the red ball 2nd time = 4/9
The probability of getting the blue ball 2nd time = 5/9
The probability of getting red ball in 2 attempts = (4/9)(4/9) = 16/81
The probability of getting blue ball in 2 attempts = (5/9)(5/9) = 25/81
Hence the probability of getting 2 of the same color
= 16/81 + 25/81
= 41/81
Therefore,
The probability of getting 2 same colour balls in a row = 41/81
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Find the sum of the series. Make sure to use the formula and show your work.
The summation of the series ¹³∑ₙ₎ ₁ (3n - 1) is 260.
What is the sum of the series?Given the summation in the question;
¹³∑ₙ₎ ₁ (3n - 1)
First, we split the summation into smaller summations that fits the summation rule.
¹³∑ₙ₎ ₁ (3n - 1) = 3 ¹³∑ₙ₎ ₁ (n) + ¹³∑ₙ₎ ₁ (- 1)
Now, lets evaluate 3 ¹³∑ₙ₎ ₁ (n).
Using the formula for the summation of a polynomial with degree 1
ⁿ∑ₐ₎ ₁ (a) = n( n + 1 ) / 2
Plug in the values
3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(13+1))/2)
3 ¹³∑ₙ₎ ₁ (n) = (3) (( 13(14))/2)
3 ¹³∑ₙ₎ ₁ (n) = (3) (182/2)
3 ¹³∑ₙ₎ ₁ (n) = (3) (91)
3 ¹³∑ₙ₎ ₁ (n) = 273
Next, evaluate ¹³∑ₙ₎ ₁ (- 1)
Using the formula for the summation of a constant
ⁿ∑ₐ₎ ₁ (c) = cn
Plug in the values
¹³∑ₙ₎ ₁ (- 1) = (-1)(13)
¹³∑ₙ₎ ₁ (- 1) = -13
Now, we add the results of the summation.
273 - 13
260
Therefore, the sum of the series is 260.
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I need some help ! The options are 25,50,65,130
Answer:
XZ=65
Step-by-step explanation:
so half of the circle would be 180
we need XZ and we know that YW+WX+XZ= 180
we also know that WX and YZ are parallel
WX=50
YW=XZ
YW+XZ=2XZ
WX+2XZ=180
50+2XZ=180
2XZ=130
XZ=65
Answer:
25
Step-by-step explanation:
diameter YZ = 50
OZ = OX = 25
thus, mXZ= 25
Subtract and reduce to lowest terms: 3 1/4 - 1 1/8
A. 2 1/8
B. None
c. 2 0/4
d. 17/8
The correct answer is option A. 2 1/8 when reduced to the lowest terms.
To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.
Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.
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what is the length of the line? the first quadrant of an x- y- coordinate plane. a line segment extends from two, eight to twelve, two.
The length of the line segment is approximately 12.04 units. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows: d = √((x2 - x1)^2 + (y2 - y1)^2)
The length of a line segment in a two-dimensional x-y coordinate plane can be found using the distance formula. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the line segment extends from the point (2, 8) to the point (12, 2). By plugging these values into the formula, we find that:
d = √((12 - 2)^2 + (2 - 8)^2) = √(100 + 36) = √136 = 12.04
So, the length of the line segment is approximately 12.04 units. This formula is useful for finding the distance between any two points in a two-dimensional plane and can be used in various fields such as geometry, physics, and engineering. The formula is based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
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Complete question:
What is the length of the line segment in the first quadrant of an x-y coordinate plane that extends from (2, 8) to (12, 2)?
Answer:
its D 136
Step-by-step explanation:
khan
maya earns £3672 each month before tax is taken out . this amount is then split into three parts:She doesnt pay tax on £972 of it. she pays 20% tax on £2665 of it. she pays 40% tax on the rest of it. How much of mayas monthly earnings are left after tax has been taken out? please help
Answer:
£ 3125
Step-by-step explanation:
Tax amount on £ 2665 = 20% of 2665
= 0.2 * 2665
= £ 533
Rest amount = 3672 - (972 + 2665)
= 3672 -3637
= £ 35
Tax amount of £ 35 = 40% * 35
= 0.4 * 35
= 14
Total tax = 533 + 14
= £ 547
Money left after paying tax = 3672 - 547
= £ 3125
In the triangle DEF, the length DX = 3cm, XE = 7cm, and EF = 8cm.
a. Using a pair of compasses only and a ruler, construct the triangle DEF. Leave in your
construction arcs. Be sure to include these for the perpendicular line at X.
b. Measure the length of the side DF.
c. Measure the height of the triangle, XF.
d. Describe in words the locus of the point that is 2cm from E and draw this onto your diagram.
e. Use compasses to bisect the angle D. You must leave your construction arcs in.
Answer:
This question is asking for a construction problem, which involves using a pair of compasses and a ruler to draw the triangle DEF and then measure certain aspects of the triangle, such as the length of DF, the height of XF, and the locus of a point 2cm from E. It also requires bisecting the angle D.
Step-by-step explanation:
a. To construct the triangle DEF, use the compasses to draw arcs with radii of 3cm and 7cm from points D and E respectively, so that the arcs intersect. Then, connect the points of intersection with a straight line to form the side DE. Next, use the compasses to draw an arc with a radius of 8cm from point F and intersect it with the previous arcs. Connect the points of intersection with a straight line to form the side DF. Finally, use the ruler to connect the points D, E, and F to form the triangle. To draw the perpendicular line at X, draw a line segment parallel to DE passing through the midpoint X, and then use the compasses to draw arcs centered at X and intersecting the sides DE and DF. Connect the points of intersection to form the perpendicular line at X.
b. Measure the length of DF using a ruler.
c. Measure the height of the triangle XF by measuring the distance from X to DF.
d. The locus of the point that is 2cm from E can be found by drawing an arc with a radius of 2cm centered at E and intersecting the sides DE and DF. The points of intersection represent the points that are 2cm from E.
e. To bisect the angle D, use the compasses to draw two arcs centered at D that intersect the sides DE and DF. Connect the points of intersection to form the bisector of angle D.
It is important to note that these steps are only a general guide and may need to be adjusted slightly depending on the specifics of the problem.
four numbers; 3, 2, 4 ,7
use all four cards to make smallest number
use all four cards to make the number closest to 5000 as possile
Answer:
To make the smallest number with the cards 3, 2, 4, and 7, you can arrange them as 2, 3, 4, 7 to get the number 237.
To make the number closest to 5000, arrange the cards as 7, 4, 2, 3 to get the number 7243.
Step-by-step explanation: