Suppose point D were moved to (–3, –2). Quadrilateral ABCD would then be a ____.

The length of the longest side of the isosceles triangle is 5 inches.

An isosceles triangle is a type of triangle in which two sides have the same length. The two equal sides are called the legs, and the third side, which is the base, is called the hypotenuse. The angle between the legs is called the vertex angle.

An isosceles triangle can be acute, meaning that the vertex angle is less than 90 degrees, right, meaning that the vertex angle is exactly 90 degrees, or obtuse, meaning that the vertex angle is greater than 90 degrees.

It's important to note that all equilateral triangles are isosceles but not all isosceles triangles are equilateral.

Given,

The length of the rod is 13 inches.

The length of the sides are x, x-1 and x-1.

We know that,

The rod length is 13 inches the mean perimeter is 13 inches.

So,

x + x-1 + x-1 = 13

=> 3x- 2 = 13

=> 3x= 15

=> x= 5 inches

Therefore, the other two sides = x-1 = 5-1 = 4 inches

So the length of the longest side of the isosceles triangle is 5 inches.

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The logarithmic function is a mathematical function that expresses the exponent of a number to produce a given value, with the property of simplifying multiplication to addition and it is the inverse of the exponential function.

A logarithmic function is a mathematical function that expresses the power to which a number (the base) must be raised in order to produce a given value. The logarithm of a number is the exponent to which the base must be raised to produce that number.

A logarithmic function can be represented in the form of log_b(x) or logb(x), where b is the base of the logarithm and x is the value being evaluated.

For example, the logarithm of 1000 to the base 10 is 3, because 10^3 = 1000. It can be written as log10(1000) = 3.

The logarithm function has the property that log_b(x*y) = log_b(x) + log_b(y), which means that logarithms simplify the multiplication of numbers to the addition of logarithms.

The logarithmic function also has an inverse function, which is the exponential function, that's why logarithms and exponents are inverses of each other.

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The total area of metal that can be seen on the surface of the wood is 43.2 square millimeters.

To find the total area of metal that can be seen on the surface of the wood, we need to find the area of one nail head and then multiply that by the number of nails.

The area of a circle is given by the formula:

A = πr²,

where π is the mathematical constant pi (estimated as 3 in this case) and r is the radius of the circle (half of the diameter).

So, the area of one nail head in square millimeters is:

A = 3 ×(2.4/2)² = 3 × 1.2² = 3 × 1.44 = 4.32 square millimeters

As there are 10 nails, so the total area of metal that can be seen on the surface of the wood in square millimeters is:

Total area = 4.32 square millimeters/nail × 10 nails = 43.2 square millimeters

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Answer:

There are 9 green candies in the jar

Step-by-step explanation:

The lines which are parallel among the given answer choices are; line 1; y = 1/2x - 6 and line 2; x - 2y = -1.

Recall that parallel lines are described by the feature such that; they have equal slopes but different y-intercepts.

Hence, by representing the equations in slope-intercept form; we have;

line 1; y = 1/2x - 6

line 2; x - 2y = -1;. y = 1/2x + 1

line 3; y = 4x + 6

line 4; y + 3 = 1/4 (x-6);. y = 1/4x - 9/2.

By comparison with the slope-intercept form equation; it follows that the lines which have equal slopes but different y-intercepts is the pair; line 1 and 2.

Hence, the parallel lines are; lines 1 and 2.

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Answer:

14

Step-by-step explanation:

35/100= .35

.35 x 40= 14

Not red skittles: 14

Answer:

14

Step-by-step explanation:

35/100= .35

.35 x 40= 14

Not red skittles: 14

Antionette can purchase a maximum of 56 adult-sized t-shirts.

What is algebraic ?

Algebraic refers to anything that pertains to algebra, which is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebraic concepts include using variables (such as x or y) to represent unknown values, using operations such as addition, subtraction, multiplication and division.

Let x be the number of adult-sized t-shirts that Antionette purchases.

We know that ,

The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

We can set up the equation to represent the total cost of all the t-shirts and the money Antionette has ,

(x6.25) + (454.50) = 550

To solve for x, we can simplify the equation by multiplying the number of adult-sized t-shirts by the cost per t-shirt and the number of youth-sized t-shirts by the cost per t-shirt, and then set it equal to the total money Antionette has ,

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

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The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

(x*6.25) + (454.50) = 550

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

The player's chances of scoring a goal on their next shot are 0.205, or 20.5%.

This is calculated by dividing the number of goals they scored (16) by the number of shots they took (78).

The formula for finding the probability:

P(A) = number of favorable outcomes / total number of possible outcomes

16 / 78 = 0.205

Probability is a mathematical concept that quantifies the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is unavoidable.

A probability of 0.5 (or 50%) means that the event is equally likely to occur or not occur.

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The relationship between these two numbers is 3 > 2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An expression:

3 is greater than 2.

Here, we will use the inequality symbol.

3 > 2.

Therefore, the expression is 3 > 2.

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The complete question:

Which symbol correctly describes the relationship between these two numbers?

And the expression: 3 is greater than 2.

A 30-degree angle is a measure of an angle, which is one-sixth of a full rotation or circle.

The measure of an angle is the amount of rotation between the two rays that form the angle, measured in degrees. The full rotation of a circle is 360 degrees, so one-sixth of a full rotation is 360 degrees divided by 6, which equals 60 degrees. However, a 30-degree angle is half of a 60-degree angle, so it is half of one-sixth of a full rotation, which is 30 degrees. It's also a right angle's complement angle, meaning that the sum of the 30 and 60 degrees angles is 90 degrees, a right angle. In geometry, 30-degree angles are often used in various calculations and constructions, such as finding the measure of complementary and supplementary angles, solving trigonometric problems, and drawing geometric figures.

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Answer:

66

Step-by-step explanation:

First find AD:

AD² + 9² = 41²

AD² = 1681-61=1600

AD = √1600 = 40

Now find BD:

BD² + 40² = 85²

BD² = 7225-1600=5625

BD = √5625 = 75

BC = BD - 9 = 75 - 9 = 66

By applying discounted price concept, the original cost of the jersey can be determined from this equation 83.39 = 37.89 + 0.70x. The original cost of the jersey is $65.

Discounted price is a price obtained after a reduction by a certain percentage from the normal price. Thus, a discounted price is lower than the normal price.

The formula: discounted price = original price × (100% - %discount)

Some information given from the problem:

Jersey discount = 30%

Hat cost = $37.89

Total spent = $83.39

Let's say the cost of the jersey = x

Total spent = hat cost + discounted jersey cost

        83.39 = 37.89 + (x * (100% - 30%))

        83.39 = 37.89 + (x * (70%))

        83.39 = 37.89 + (x * 0.7)

        83.39 = 37.89 + 0.7x

Thus this is the equation.

If we want to know the original cost of the jersey, we can continue the calculation:

            83.39 = 37.89 + 0.7x

83.39 - 37.89 = 0.7x

              45.5 = 0.70x

                    x = 45.5/0.70

                    x = 65

Thus, the original cost of the jersey is $65.

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This article will demonstrate how to use Data Frame in the R programming language to calculate the mean by group.

Mean by A, B, and C group:

To determine the mean from a frequency table, follow these steps: Divide the values of the numbers by the frequencies. Determine the sums.

Divide the total by n.

Three distinct series can be used to calculate it: viz., Frequency, discrete, and individual series of distributions. "The Standard Deviation is the square root of the arithmetic mean of the squares of all deviations," Spiegel states.

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7. 2n^2 - 5n + 10 = 7, is true.This means that if we substitute the value of n in the given equation we will get 7.

The Remainder Theorem states that if a polynomial is divided by a linear function, then the remainder is equal to the value of the polynomial at the root of the linear function.

In this case, we have the polynomial p(x) = 2x^2 - 5x + 10, which is being divided by x-n, and we are told that the remainder is 7. This means that when we substitute the root of x-n (which is n) into p(x), we get a remainder of 7. 2n^2 - 5n + 10 = 7, so this statement is true.

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Since lines m and n are parallel lines, the value of x in the image above is equal to 19.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

In Mathematics, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair.

By applying the Linear Pair Postulate to the two (2) alternate interior angles, we have the following:

6x + 4 + (4x - 14) = 180

10x - 10 = 180

10x = 180 + 10

10x = 190

x = 190/10

x = 19.

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Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given. The f(x) is 1.2x.

Its value is expressed as f(x). The line has a slope of m.In the coordinate plane, the point where the line crosses the y-axis is where the function's value, or b, is determined when x is equal to zero.The coordinate's value, x, is given.

Detailed explanation:

Given:

f(x - 5) = 1.2x - 6

Required:Find f (x) In order to solve f(x), we must translate f(x - 5) into terms of f. (x). The procedure is as follows.

f(x - 5) = 1.2x - 6

The expression to the right should be factored.

f(x - 5) = 1.2(x - 5) (x - 5)

Now that we have changed x for x - 5 in the previous formula, we may solve for f(x) (on the right hand side and the left hand side).

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Answer:

the number would be anything over 59.50

Step-by-step explanation:



By AAS congruence theorem, triangle QXP is congruent to triangle SXR.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, X is the midpoint of QS and ∠P≅∠R.

Consider, ΔQXP and ΔSXR

QX=XS (X is the midpoint of QS)

∠P≅∠R (Given)

∠QXP ≅ ∠SXR (Vertical angle theorem)

By AAS congruence theorem,

ΔQXP ≅ ΔSXR

Hence, proved.

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The order pairs to the given equations are (-3, 18) and (3, 6)

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given are two equation, f(x) = x²-2x+3 and f(x) = -2x+12

For solving, equate them,

x²-2x+3 = -2x+12

x² = 2x-2x+12-3

x² = 9

x = ±3

Put x = -3 in f(x) = -2x+12

f(-3) = -2(-3)+12

f(-3) = 18

And, Put x = 3 in f(x) = -2x+12

f(3) = -2(3)+12

f(3) = 6

Therefore, the ordered pairs are (-3, 18) and (3, 6)

Hence, the order pairs to the given equations are (-3, 18) and (3, 6)

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There were 1,278 people at the last basketball game and the stands were divided into 6 sections. Each section had 213 people.

The question asked how many people were in each section, and it was given that there were 1,278 people at the game and the stands were divided into 6 sections. To find out how many people were in each section, I divided the total number of people by the number of sections. This concept of division is used to find out how many times a quantity (in this case, the number of people) is divided into a certain number of equal parts (in this case, the number of sections). The result is the number of people per section.

This is represented mathematically as:

1,278 people / 6 sections = 213 people per section

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The number is 10 more than 8910+89 = 99

given that

One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them. Three apples and two apples are combined to make five apples in the example in the adjacent image. This observation is analogous to the formula "3 + 2 = 5" in mathematics (that is, "3 plus 2 is equal to 5").

In addition to counting things, addition can also be defined and performed using abstractions known as numbers, such as integers, real numbers, and complex numbers. A branch of mathematics called arithmetic includes addition. Addition can also be done on abstract objects like vectors, matrices, subspaces, and subgroups in algebra, another branch of mathematics.

10 more than 89

more than means plus or addition or sum

10+89 = 99

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Answer:

The area of the training field is 16,966 m2. The area of the rectangle is 83 x 62 = 5,146 m2, and the area of each semicircle is (3.14 x (83/2)2) / 2 = 1,652 m2. Therefore, the total area of the training field is 5,146 + (2 x 1,652) = 16,966 m2.

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There are three important steps to graph a line when an equation is given to us.

Let us look at an example for the same.

Let us graph the equation 6x + 2y = 12

Finding the x-intercept (the x-intercept has a y-value of 0),

6x + 0 = 12

⇒ x = 2

Hence, x-intercept is (2,0)

Finding the y-intercept (the y-intercept has an x-value of 0),

0 + 2y = 12

⇒ y = 6

Hence, y-intercept = (0,6).

The graph is shown in the diagram after plotting the 2 intercepts on a graph and a line drawn through them.

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Answer:

These two equations are equivalent to each other because they both represent the same mathematical operation and they both yield the same result.

The first equation, 88 + 32, is adding 88 to 32, which results in the sum of 120.

The second equation, 90 + 30, is adding 90 to 30, which also results in the sum of 120.

In other words, both equations represent the same mathematical operation (addition) of two numbers (88 and 32 or 90 and 30) and both yield the same result (120).

Step-by-step explanation:

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The difference between the largest and the smallest of these three numbers is 95.

in mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Let the common multiple of ratio be x.

then, according to given condition, the ratio of three numbers is 7 : 3 : 2 and these three numbers have a sum of 228. i.e.

7x + 3 x + 2x = 228

12x = 228

x = 19

so, the largest number is

= 7x

= 7 × 19

= 133

and the smallest number is

= 2x

= 2 × 19

= 38

so, the Difference between the largest and  the smallest number is

= 133 - 38

= 95

Therefore, the difference between the largest and the smallest of these three numbers is 95.

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For the linear equation 12 = 2x+4y, the value of ordered pairs are (0,3) and (6,0).

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The given linear equation is 12 = 2x + 4y

Substitute the value of x as 0 to find the value of y -

12 = 2x + 4y

12 = 2(0) + 4y

12 = 4y

y = 12/4

y = 3

Therefore, the value for y is obtained as 3.

Substitute the value of y as 0 to find the value of x -

12 = 2x + 4y

12 = 2x + 4(0)

12 = 2x

x = 12/2

x = 6

Therefore, the value for x is obtained as 6.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

Therefore, two ordered pairs are obtained as (0,3) and (6,0).

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Your normal hourly rate is $40.50 and you earned $612.50 for working 46 hours this week, which is 1.5 times your normal hourly rate for each hour over 40.

Your normal hourly rate is the amount of money you get paid per hour for working. The overtime rate is For every hour you work over 40 in a week, your hourly wage will increase by 1.5.This means that if you work 46 hours in a week and your normal hourly rate is $40.50, you would receive $40.50 for each hour up to 40 hours, and then an additional $60.75 for each hour after that. This means that you would have earned a total of $612.50 for working 46 hours this week, with $405 for 40 hours and $207.50 for the 6 hours of overtime.

Normal hourly rate (40 hours) = 40 hours x $40.50/hour = $1,620

Overtime rate (6 hours) = 6 hours x $60.75/hour = $364.50

Total earned = $1,620 + $364.50 = $1,984.50

Total paid = $612.50

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Lines 16-20 suggest that the speaker imagines his future as one in which he will look back on the decision he made to take the less traveled road with a sense of regret or longing.

He states that he will be "telling this with a sigh," indicating that the memory is not a happy one. Additionally, the phrase "ages and ages hence" implies that a significant amount of time has passed since the speaker made the decision, further emphasizing the sense of regret or longing. Overall, these lines suggest that the speaker believes that taking the less traveled road has had a significant impact on his life and that he will continue to reflect on this decision in the future.

"The Road Not Taken" is a famous poem by Robert Frost, in which the speaker reflects on a decision to take a different path in the woods. The poem does not give specific details of the speaker's future but rather reflects on the idea of choices and regrets.

This question should be written as:

What do lines 16-20 tell you about how the speaker imagines his future? Explain using text evidence to support your answer.

Lines 16-20  from "The Road Not Taken:

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6 acres are used for growing crops

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Word problems can involve arithmetic operations, geometry, algebra, and other mathematical areas.

Since the farm has 15 acres of land and four-tenths of the farmland is used for growing crops. we can say:

acres used for growing crops = 4/10 * 15

acres used for growing crops = 6 acres

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