Match each quadratic equation with its solution set.
2x²-32=0
4x²-100=0
x²-55=9
x²-140=-19
2x²-18=0

{-8,8} →
{-4,4} →
{-5,5} →
{-11, 11} →

The volume of the sphere with a diameter of 6cm is 108 cm³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi

Given the data in the question:

Diameter d = 6cm

Radius is half of diameter

Radius r - 6cm/2

Radius r = 3cm

Also, π = 3

Plug the given values into the above formula.

Volume =  (4/3)πr³

Volume =  (4/3)π3³

Volume =  (4/3)(3)(27)

Volume =  108 cm³

Therefore, the volume is 108 cm³.

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Answer:

mean = 14 and standard deviation = 3.03

Step-by-step explanation:

mean = sum of all numbers ÷ by the numbers available

= (11 + 12 + 12 + 16 + 19) ÷ 5

= 70 ÷ 5

= 14

FOR STANDARD DEVIATION * USE A SCIENTIFIC CALCULATOR THEY WON'T PENALIZE YOU*

follow these steps:

1. press mode then STAT

2. then press 1-VAR

3. put all the numbers on the table in ascending order

4 after press AC

5. press shift then 1

6. you will see many things but we are only interested in standard deviation, press *Var*

7. then select the standard deviation sign and press the equal sign

Answer:

? = 8

Step-by-step explanation:

well

x/44 = 2/11

44 is greater than 11 by 4 times. so to get an equal fraction you need to multiply 2 by 4 to get 8. that way you get 8/44 which would simplify by dividing by 4 to get 2/11

The functions for this problem are defined as follows:

The functions for this problem are given as follows:

The addition and subtraction functions for this problem are given as follows:

At x = -2, the numeric value of the subtraction function is given as follows:

(t - s)(-2) = -2³ - 5(-2)²

(t - s)(-2) = -28.

The product function for this problem is given as follows:

(ts)(x) = \(5x^5\)

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Answer:

the savings is 6000

Step-by-step explanation:

We are told that the ratio of savings to expenditure is 2: 8, that is, that person saves 2 when he spends 8.

They tell us to find the savings when the cost is 24,000, so we are left with:

24000 * 2/8 = 6000

which means that when 24000 are spent the savings is 6000

The linear equation that models the average price of a new home in terms of the year x is given by y = -5600x + 294000 and the average price of a new home would be $238000 in 2014.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The line must pass through points (0, 294000) and (7, 288400) which is given in the question.

We have to determine the slope of the line :

m = (y₂ - y₁)/(x₂ -x₁ )

m = (288400- 294000)/(7 -0)

m = -5600

This represents new home per year

So with your y-intercept of 294000, your equation becomes

y = -5600x + 294000

Using this equation to predict the average price of a new home in 2014.

Let y be the average price of a new home in the year x, where x = 0 represents the year 2004.

Substitute the value of  x = 10 for the year 2014

y = -5600(10) + 294000

y = -56000 + 294000

y = 238000

Hence, the average price of a new home would be $238000 in 2014.

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Answer:

41.6

Step-by-step explanation:

32 x 0.3 = 9.6

9.6 + 32 = 41.6

41.6

i had the same question

Answer:

3/5

Step-by-step explanation:

To find the value of sinX we divide opposite side with hypotenuse

15/25 = 3/5

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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Answer:

Step-by-step explanation:

((14×3) + 1 )/3 = (43/3)

14 1/3 can be expressed as 43/3, which is an improper fraction.

To rewrite 14 1/3 as an improper fraction, we need to convert the mixed number into a fraction.

First, we multiply the whole number (14) by the denominator of the fraction (3) and add the numerator (1). This gives us the numerator of the improper fraction. The denominator remains the same.

14 × 3 = 42

Next, we add the numerator (1) to the result we obtained above.

42 + 1 = 43

Therefore, the improper fraction equivalent to 14 1/3 is 43/3.

In the fraction 43/3, the numerator (43) represents the total number of parts we have, and the denominator (3) represents the size of each part. It indicates that we have 43 equal parts of size 1/3.

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The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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Answer:

Sales Tax: $3.08

Step-by-step explanation:

When you add the price of the items up it totals $36.25. To find the sales tax you need to take 8.5% and turn it into a decimal which is 0.085. You need to take this decimal 0.085 and multiply by $36.25 which will give you $3.08 for sales tax.

Answer:

Asthenosphere

Step-by-step explanation:

The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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Answer:

400.64 is your answer

Step-by-step explanation:

I need brainlyest PLZ!!!!

Answer:

Step-by-step explanation:

The position of  √17 between 4 and 5, which is nearer 5, and the location of 6, which is between 2 and 3, which is nearer 2.

A visual representation of real numbers in a linear manner is a number line. It is a straight line that is divided into intervals or segments, each of which stands for a distinct real number value.

Number lines can be vertical or horizontally oriented, and they can also have a positive or negative orientation. Positive numbers often extend to the right or up, whereas negative numbers typically extend to the left or down. The origin of the number line, or zero, is typically situated in the middle of the line.

The number line is a crucial tool in mathematics since it offers a means of representing numerical relationships visually and carrying out fundamental arithmetic operations. For instance, positive and negative motions along a number line can be used to depict addition and subtraction, respectively, with positive movements denoting addition and negative movements denoting subtraction. On a number line, multiplication and division can alternatively be shown as repeated addition or subtraction.

If we have a number line with the proper markings, we may indicate where the square roots of 17 and 6 are located as follows:

To begin, determine the approximate square root values:

√17 is between 4 and 5, since 4² = 16 and 5² = 25.

√6 is between 2 and 3, since 2² = 4 and 3² = 9.

Place the number √17 closer to 5, between 4 and 5.

Place the number √6 between the numbers 2 and 3, closer to 2.

Since 6 and 17 are not integers and their values are not evenly spaced, it should be noted that their markings will not be evenly spaced on the number line.

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Number line attached below,

Answer:

X≤10/7

Step-by-step explanation:

7x-4≤6

add 4 both sides

7x-4+4≤6+4

7x≤10

divide 7 both sides

7x/7≤10/7

x≤10/7

hope it's helpful ❤❤❤❤

THANK YOU.

The solution of the given inequality is x≤10/7.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality can be simplified for the value of x as shown below.
7x − 4 ≤ 6

Add 4 both sides,

7x - 4 + 4 ≤  6 + 4

7x≤10

Divide 7 both sides,

7x/7 ≤ 10/7

x ≤ 10/7

Hence, the solution of the given inequality is x≤10/7.

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Answer:

Domain is all real numbers

Range is (3, ∞) or y > 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Step-by-step explanation:

I just answered this. please look at your copy post.

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:

2. A 4√3

3. B -5/3

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

because its the middle number

Answer:

4.5 m

Step-by-step explanation:

if the two triangles are similar than it would mean that zy to xy is same ratio to cb to ab which means that the second triangle is only enlarge version of the first triangle. so divide 7.2 by 1.6 and multiply 1 to get the solution of 4.5

The calculated value of k on the line is 9

From the question, we have the following parameters that can be used in our computation:

XZ is the perpendicular bisector of segment WY

This means that

WX = XY

substitute the known values in the above equation, so, we have the following representation

3k - 4 = 2k + 5

So, we have

3k - 2k = 4 + 5

Evaluate

k = 9

Hence, the value of k is 9

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