Which mathematical term cannot be defined for all cases in a system of geometry?

The algebraic expression 5xy has three factors: the number 5 and the variables x and y. Factors are the multiplicative components of an expression, and factoring involves breaking down expressions into these components.

The algebraic expression 5xy has three factors: the number 5, the variable x, and the variable y. A factor is a number, variable, or a product/quotient of numbers and/or variables separated by + or - signs.

When we are factoring, we are essentially reversing the distributive law and turning the expression into its multiple components, which can also be termed as factors or multiples. For instance, expressions like 5px, 5py, or similar expressions are all made up of factors that, when multiplied together, produce the value of the expression.

When addressing expressions that can be factored, such as ax² +2hxy+by² = 0, we look for expressions that, when evaluated, produce the same value. In this particular example, it can be factored into two linear factors and represents two straight lines intersecting at the origin.

Answer:

The algebraic expression [tex]\(5xy\)[/tex] has [tex]\(8\)[/tex] factors.

Explanation:

The algebraic expression [tex]\(5xy\)[/tex] can be factored as [tex]\(5 \times x \times y\)[/tex]. To find the number of factors, we count all the unique combinations of its prime factors:

- For the factor [tex]\(5\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(5\) or \(1\).[/tex]

- For the factor [tex]\(x\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(x\) or \(1\).[/tex]

- For the factor [tex]\(y\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(y\) or \(1\).[/tex]

Therefore, the total number of factors is the product of the options for each factor, which is [tex]\(2 \times 2 \times 2 = 8\)[/tex]. So, the algebraic expression [tex]\(5xy\)[/tex] has [tex]\(8\)[/tex] factors.

The volume of the cylindrical jar, the total volume of marbles, and then find the volume not occupied by the marbles.

The volume of the jar:

Volume of the cylindrical jar = πr²h = 3.142 × (4 cm)² × 12 cm = 603.168 cm³

The total volume of the marbles:

Total volume of 20 marbles = 20 × (4/3)π(0.8 cm)³ = 214.717 cm³

The volume not occupied by marbles:

Volume not occupied = Volume of the jar - Total volume of marbles = 603.168 cm³ - 214.717 cm³ = 388.451 cm³

The amount of space between two points on a line is a distance.

In Mathematics and Geometry, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

[tex]Distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

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To convert 6.666666667 into an improper fraction, identify the whole number part and the repeating decimal part, which correspond to 18/3 and 2/3 respectively. Adding these together results in the improper fraction 20/3.

The questions asks how to express the decimal number 6.666666667 as an improper fraction. To convert a decimal to a fraction, we can identify the repeating part of the decimal, which in this case is '666...'. We know that repeating '6' corresponds to '2/3' in fraction form. To write it as an improper fraction, we first write the non-repeating part which is '6' as '6/1'. Then we add the repeating fraction '2/3' to it after converting '6/1' to have a common denominator of '3' which becomes '18/3'. Adding these gives us '20/3' which is the desired improper fraction.

To put this process into steps:

Answer:

35x>400  can be used to find the value of x

Step-by-step explanation:

Here, we have given the information employee works for 35 hours a week

Let, x be the number of hours employee can work

Here it will become 35 x since, he is working for 35 hours

Employee is earning more than $400 per week

The inequality is formed from the given information as below:

35x>400

x>80/7

Therefore, 35x>400 can be used to find the value of x which is giving value of x>80/7

Answer:

Correct choice is D

Step-by-step explanation:

Option A. The sum of two fractions is a fraction, a fraction is always rational number.

Option B. The product of a fraction and a repeating decimal can be rational number. For example,

[tex]\dfrac{3}{2}\cdot 0.\overline{3}=\dfrac{3}{2}\cdot \dfrac{1}{3}=\dfrac{1}{2}.[/tex]

Option C. The sum of a terminating decimal and the square root of a perfect square is always rational number, because the terminating decimal is a decimal that ends and the square root of a perfect square is a natural number. The product of decimal that ends and natural number is rational number.

Option D. The product of a repeating decimal and the square root of a non-perfect square is always irrational, because the square root of a non-perfect square is irrational number and when multiplying irrational number by fraction (any repeating decimal can be written as fraction) you get irrational number.

Based on conversion:

1 liter of milk is equivalent to 1.05669 US liquid quart. (1000mL)

While 1 quart of milk is equivalent to 0.946353 liters. (946.353mL)

This concluded that a liter would hold more milk by 0.053647 liters or 53.647 mL.

But if you are talking about an imperial quart, this will hold more milk than a liter. Because its measures 1136 mL which is 136mL bigger than the liter.

A liter holds more milk than a quart by approximately 0.057.

A liter holds more milk than a quart.

1 liter is equivalent to approximately 1.057 quarts. Therefore, a liter holds about 0.057 more milk than a quart.

For example, if a quart can hold 4 cups of milk, a liter can hold approximately 4.23 cups of milk.

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The total number of tests that the student has taken in the course will be 7.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

In a chemistry course, a student scored 99 on one test, 98 on another test, and 88 on each of the other tests.

Let 'x' be the total number of tests in which he scored 88. Then the equation is given as,

(99 + 98 + 88x) / (2 + x) = 91

197 + 88x = 182 + 91x

91x - 88x = 197 - 182

3x = 15

x = 5

The total number of tests is given as,

Total tests = 2 + 5

Total tests = 7

The total number of tests that the student has taken in the course will be 7.

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If quadrilateral ABCD is an isosceles trapezoid

The true statements among the given options  are written below

BC || AD

So option (1) is correct.

AB ≅ DC  

So option (3) is correct

∠CBA ≅ ∠BCD

So option (5) is correct.

In an isosceles trapezoid there is one pair of  legs of equal length and a pair of parallel  lines.

Given that quadrilateral ABCD is a isosceles trapezoid.

We have to check that out of the given options hold good for the isosceles trapezoid

[] BC ∥ AD

[] BD ⊥ AC

[] BA ≅ CD

[] BE ≅ ED

[] ∠CBA ≅ ∠BCD

In the given trapezoid ABCD

BC || AD ( pair of parallel sides )

So option (1) is correct.

AB ≅ DC  ( For an isosceles trapezoid legs are equal)

So option (3) is correct

∠CBA ≅ ∠BCD (According to  the property of isosceles  trapezoid )

So option (5) is correct.

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The average of all integers from 11 to 35 is determined by summing the first and last integers and dividing by 2. The calculation is (11 + 35) / 2, which equals to 23.

Calculating the Average of Integers

To calculate the average of all integers from 11 to 35, you sum up all the integers and then divide by the number of integers. Since the numbers form an arithmetic sequence, we can use the formula for the average, which is: (first term + last term) / 2. Therefore, the average is (11 + 35) / 2.

The calculation would then be 46 / 2, which equals 23. This value represents the mean or average of the integer set from 11 to 35. The concept of finding the average is a fundamental aspect of statistics and general mathematics that is commonly applied in various practical scenarios.

The average of all integers from 11 to 35 is 46.

To find the average of all integers from 11 to 35, we first calculate the sum of all the integers from 11 to 35. Then, we divide the sum by the total number of integers (i.e., 35 - 11 + 1 = 25). The sum of the integers from 11 to 35 is (11 + 12 + 13 + ... + 35). We can simplify this sum by using the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term. Plugging in the values, we get Sn = (25/2)(11 + 35) = 25(46) = 1150. Now, we can find the average by dividing the sum by the total number of integers: Average = 1150/25 = 46. Therefore, the average of all integers from 11 to 35 is 46.

5 x 4 x 3 x 2 x 1 = 120

120 different ways

Answer:

[tex]p(x)=-5x-x^2[/tex]

C is correct

Step-by-step explanation:

Quadratic function: A polynomial whose degree is 2 called quadratic function.

Degree = It is highest power of the polynomial.

We have to check the degree of each option.

Option 1: [tex]c(x)=6x+3x^3[/tex]

Degree = 3

Option 2: [tex]d(x)=x-8x^4[/tex]

Degree = 4

Option 3: [tex]p(x)=-5x-x^2[/tex]

Degree = 2

Option 4: [tex]k(x)=2x^2+9x^4[/tex]

Hence, [tex]p(x)=-5x-x^2[/tex] has degree 2. It would be quadratic function.