True False x-sqrt6 is a factor of x^4-36

Answer:

1. 9

2. 12

3. 26

Step-by-step explanation:

Answer:

1. 9

2. 12

3. 26

Step-by-step explanation:

An easy way to solve problems like this is to convert the percentage into a decimal, then multiply that decimal by the whole. For example, if I had the question "What is 10% of 100?", I would first convert the 10% to a decimal. 10% is the same as 10/100, which in decimal form is 0.1. I would then multiply 0.1 by  100 to find out how much 10% of 100 is. I get 10, so my answer is 10. Hope this helps!

Answer: (c)

(√2-√3)(√2+√3)

Step-by-step explanation:

An irrational number is one that cannot be expressed as the ratio of two integers. In other words it cannot be expressed as \(\frac{x}{y}\) where x and y are integers

\(\sqrt{2}\) is irrational

\(\sqrt{3}\) is irrational

In fact the square root of any prime number is irrational. So \(\sqrt{5}\), \(\sqrt{7}\) etc are irrational. But \(\sqrt{9}\) is not irrational since it evaluates to 3 which can be expressed as \(\frac{3}{1}\)

Any expression that contains the square root of a prime number is also irrational

Looking at the choices we see that choices (a), (b) and (d) all evaluate to expressions containing square roots of primes

(a)  (2-√3)2 = 4 - 2√3  . Hence irrational

(b) √2+√3)2 = 2√2+2√3. Hence irrational

(d) 27√7​ is irrational

Let's look at choice (c)

(√2-√3)(√2+√3)

An expression \((a+b)(a-b)\)  can be evaluated as \(a^{2} - b^{2}\)

Here a = √2, \(a^{2}\) =\(a = \sqrt{2}\\ a^2 = (\sqrt{2} )^2 = 2\\\\b = \sqrt{3} \\b^2 = (\sqrt{3} )^2 = 3\\\\a^2 - b^2 = 2-3 = -1\\\)

This is a whole number(integer) and all integers are rational numbers

Hence correct answer is (c)

Answer:

The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.

In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.

The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:

Σ_{i=1}^{11} (6i + 2)

To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:

The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.

The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.

The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.

Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).

Answer:

116 / 45

Step-by-step explanation:

To add fractions with unlike denominators, we need to find their common denominator.

One way to do this is by finding the least common multiple (LCM) of the denominators.

The LCM of 3, 5, 9 and 15 is 45.

We then convert each fraction so that its denominator is 45:

1/3 = 15/45

3/5 = 27/45

7/9 = 35/45

13/15 = 39/45

Now we can add the fractions:

15/45 + 27/45 + 35/45 + 39/45

To simplify, we can add the numerators and keep the common denominator:

(15 + 27 + 35 + 39) / 45

Which gives us:

116 / 45

Therefore, the sum of the fractions 1/3 + 3/5 + 7/9 + 13/15 is, 116 / 45.

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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In mathematics, a sequence is an ordered list of elements, often denoted by brackets or parentheses.

The term "a sequence of length n" refers to a sequence that contains a specific number of elements, where the number of elements is denoted by "n."

When the domain of a function is the set of natural numbers (N), it is called an infinite sequence. An infinite sequence can be thought of as an ordered list that continues indefinitely.

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Answer:

Step-by-step explanation:

The statement that is true for the given figure will be AD/DC = AB/CB.

So the correct option is A.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

The triangle ABC is divided into two triangle by a median DB that are;

Triangle ADB and Triangle ADC

So here the proportion form as;

AD/DC = AB/CB.

Therefore, The statement that is true for the given figure will be AD/DC = AB/CB.

So the correct option is A.

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Answer:

Either 4+4=8 then take 1 away to get 7 or 3+3=6 then add 1 to get 7.

Step-by-step explanation:

The ratio of the number of baskets scored by team A to the number of baskets by team B is 2: 5. Then the correct option is B.

In a basketball game, team B scored 5 baskets for every 2 that team A scored.

The utilization of two or more additional numbers that compares is known as the ratio.

Assume that Team A scored two baskets while Team B netted five.

The problem statement states that for every two baskets Team A scored, Team B scored five. This may be expressed as the ratio shown below:

Ratio = 2x : 5x

Ratio = 2: 5

Thus, the correct option is B.

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Answer:

The difference between the first and second friends' total earnings is $154.

BRAINLIEST, PLEASE!

Step-by-step explanation:

32 x $17 = $544

26 x $15 = $390

$544 - $390 = $154

The correct expression of the inequality expression is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

From the question, the expression is given as

18 ÷ 6 + 3 □ 6 + 12 ÷ 3

We start by converting the above expression to the same form

So, we start by solving the quotients

This gives

3 + 3 □ 6 + 4

Next, we evaluate the sum

So, we have

6 □ 10

In the above expression, we have

6 and 10

By convention, the number 6 is less than the number 10

This is so because 6 has a smaller value and 10 has a higher value

When the above numbers are compared, we have

6 is less than 10

This means that we make use of the inequality symbol <

So, we have

18 ÷ 6 + 3 < 6 + 12 ÷ 3

Hence, the complete inequality is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3

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Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

We have,

Let's start by finding the total number of points that Carlos can earn in the class:

Total points

= 5 quizzes x 20 points per quiz

= 100 points

If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.

Total points earned.

= 18 + 19 + 17 + 20

= 74 points

To find the minimum score Carlos needs on the final quiz, we can set up an inequality:

(74 + x) / 5 ≥ 0.9

where x is the score on the final quiz.

Simplifying this inequality.

74 + x ≥ 90

x ≥ 16

Therefore,

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

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I’m sorry but I could not find a pdf version of the Envision volume 2 book for 5th grade online. However, I found some websites that have answer keys and lesson plans for the book. You can check them out by searching for the following queries:

I hope this helps you with your homework.

The perimeter of the shaded part is 18 units

In order to determine the perimeter of the shaded portion, we will take the difference between the external rectangle and the triangle that was not shaded below;

The formula for calculating the perimeter of rectangle is expressed according to the equation below:

Perimeter of a rectangle = 2(length +width)

Perimeter of external rectangle = 2(7+ 10)

Perimeter of external rectangle = 34 units

Perimeter of the unshaded smaller rectangle = 2(2 + 6)

Perimeter of the unshaded smaller rectangle = 16 square units

Determine the perimeter of shaded part

Perimeter of the shaded part = 34 - 16

Perimeter of the shaded part = 18 units

Hence the perimeter of the shaded part is 18 units

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Answer:

We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write:

m∠A + m∠B + m∠C = 180

Substitute the given values:

5x+6 + 7x-18 + m∠C = 180

Combine like terms:

12x-12 + m∠C = 180

Add 12 to both sides:

12x + m∠C = 192

Subtract 12x from both sides:

m∠C = 192 - 12x

Therefore, m∠C is equal to 192 minus 12 times x.

Answer: A = 132 . 93 cm 2

Step-by-step explanation:

A = lw

A = 8.7

A = 56cm2

A=2

A=(3.14)(7) 2

A 153 . 86 cm 2

76. 93 cm 2

A = 56cm 2 + 76.93 cm 2

A = 132 . 93 cm 2

Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

Answer:

Sorry I could only find the answer to the second part.

y=56x

Answer:

3a-21

Step-by-step explanation:

3(a-7)

3a-3x7

3a-21

Answer:

a)2.7

b)1.65289256

c)3.12

Answer:

  = -1/2

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

   = (11-10)/(8-10)

    = 1/-2

  = -1/2

Answer:

160

Step-by-step explanation:

Angle ABE is a 180 as ABE forms a line

so angle ABC + ANGLE CBE = 180

x + 20 = 180

x = 180-20

= 160

I hope im right!!

Step-by-step explanation:

answer is 160

hope it helps

Answer:

AD = 15

Step-by-step explanation:

Based on the Pythagoras Theorem, the longest side of a right-angled triangle is: \(\sqrt{a^{2}+b^{2}}\) where a and b are the legs of the triangle.

In triangle BDC, we can put in the formula to find BD.

85 = \(\sqrt{77^{2}+BD^{2}}\)

85² = 77² + BD²

7225 = 5929 + BD²

BD² = 7225 - 5929

       = 1296

BD = \(\sqrt{1296}\)

BD = 36

In triangle ABD, we can put in the formula to find AD.

39 = \(\sqrt{36^{2}+AD^{2}}\)

39² = 36² + AD²

1521 = 1296 + AD²

AD² = 1521 - 1296

       = 225

AD = \(\sqrt{225}\)

AD = 15