1. The square of a number equals nine times that number. Find the number.
2. Suppose that four times the square of a number equals 20 times that num-
ber. What is the number?
3. Twice the square of the sum of a number and 3 is 98. Find the number.
​

The function combines the standard function type of a linear equation (2x) with an arithmetic operation (subtracting 3) to create the desired relationship.

A relationship between two quantities can be effectively modeled using a mathematical function. Functions are fundamental tools in mathematics that establish a connection between inputs and outputs. By combining standard function types with arithmetic operations, we can create a versatile function that captures the desired relationship.

To build such a function, we can start by identifying the two quantities we want to relate, let's call them "x" and "y". We can then express their relationship using a combination of standard function types, such as linear, quadratic, exponential, or trigonometric functions, and apply arithmetic operations like addition, subtraction, multiplication, or division to modify the function's behavior.

For example, let's say we want to model a relationship where "y" is twice the value of "x" minus three. We can define this relationship using a linear function as follows:

**f(x) = 2x - 3**

Here, the function "f(x)" represents the relationship between "x" and "y". By substituting different values of "x" into the function, we can determine the corresponding values of "y" and observe how the two quantities are related.

In this case, the function combines the standard function type of a linear equation (2x) with an arithmetic operation (subtracting 3) to create the desired relationship.

By employing various standard function types and applying different arithmetic operations, we can construct functions that model relationships between two quantities in a wide range of scenarios. The key is to understand the nature of the relationship we want to represent and utilize appropriate function types and arithmetic operations to accurately capture that relationship.

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The next two numbers of the geometric sequence will be 27 , 81.

Geometric Sequence or Geometric Progression is defined as a sequence where every term is multiplied by a constant fixed number to get the next term except the first term.

For Example ; 2,6,18,54,.....  This is a Geometric sequence as every next term except the first term is multiplied with 3.

Geometric Sequence is denoted by \(a,ar,ar^{2} ,ar^{3} ,.....\)

Its general term is denoted by \(a_{n} =a.r^{n-1}\), where a is the first term

r is the common ratio

n is the number of term in the sequence.

According to the given question

given the first two term = 3,9

So   a=3     …..(1)

next we need common ratio "r" for this we divide second term by first term .

that is \(\frac{a_{2} }{a_{1} }\).

r=9/3

r=3.

The next term of the sequence will be third and fourth term i.e. \(a_{3} ,a_{4}\).

\(a_{3} =a*r^{3-1}\)       ( using general formula for GP)

Substituting the value as a=3 and r=3

\(a_{3} =3^{3} \\ \\ a_{3} =27\)

Now

\(a_{4} =a*r^{4-1}\)

Substituting the value as a=3 and r=3

\(a_{4} =3*3^{3}\)

\(a_{4} =3^{4}\\ \\ a_{4} =81\)

Therefore , The next two numbers of the geometric sequence will be 27 , 81.

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Step-by-step explanation:

Everything is written in the photo and the answer and the solution (I had to write some text so that I could send it)

• The intersection of lines n and k is point V.

• Point X is the intersection of line m and plane A.

We can infer  the following from the diagram :

We can see that the intersection of any two planes will produce a line at the intersection point of plane A and plane S, the line CW is formed and also the lines intersect at a point, the intersection point of line n and line k is point V.

• The point X in the diagram is brought about by the intersection of line m on the plane A .

In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line.

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Answer:

2

Step-by-step explanation:

In an arithmetic sequence, the common difference refers to the constant amount added or subtracted between consecutive terms. To find the common difference, we can subtract any term from the following term.

Let's subtract the second term (-13) from the first term (-15):

-13 - (-15) = -13 + 15 = 2

So, the common difference in the arithmetic sequence -15, -13, -11, ... is 2.

Answer:

x-intercept:  (-56, 0)

y-intercept:  (0, -14)

Step-by-step explanation:

The x-intercept is the point at which the line crosses the x-axis, so when y=0.  To find the x-intercept, substitute y=0 into the given equation:

\(\begin{aligned}y=0\implies x+4(0)&=-56\\x+0&=-56\\x&=-56\end{aligned}\)

Therefore, the x-intercept of the given linear equation is:

The y-intercept is the point at which the line crosses the y-axis, so when x=0.  To find the y-intercept, substitute x=0 into the given equation:

\(\begin{aligned}x=0\implies 0+4y&=-56\\4y&=-56\\y&=\dfrac{-56}{4}\\y&=-14\end{aligned}\)

Therefore, the y-intercept of the given linear equation is:

1) In this question, we can notice that theta is in Quadrant IV. In this quadrant, the cosine of theta yields a positive value.

2) So, let's make use of a Pythagorean Identity to find the value of the cosine of theta, given the sine of that same angle:

3) Thus the cosine of theta is 4/5 for in Quadrant IV cosine is positive.

Answer:

B' (2,3)

Step-by-step explanation:

See the pictures below.  B was two units below y = 1 so B' needs to be 2 units above y = 1.  That places the point at (2,3)

Answer:

70

Step-by-step explanation:

20 km times 3 plus 10 km

Answer:

D

Step-by-step explanation:

Let's call the original diameter x. Then, the circumference would be xπ. If the diameter is 2x, the circumference is 2xπ. 2xπ / xπ = 2 so the answer is D.

Answer:

D. 2 times the circumference of the original circle

Step-by-step explanation:

The circumference of a circle is represented by the formula C = 2(r)pi (where is r is the radius), which can also be written as C = (d)pi, where d is the diameter, (since 2r is equivalent to d). If the diameter is doubled, the original equation can be rewritten as C = 2(d)pi. Therefore, the circumference of the new circle is double the original circle.

You can plug in a sample number to further prove this point. Pretend r = 3 so d = 6. C = 6pi. Now when the diameter is doubled, d = 12 and C = 12pi which is double 6pi.

So the answer is D. 2 times the circumference of the original circle  

The width of the rectangular walkway is 3 feet around.

The walkway has a uniform width around the rectangle.

Let the width of walkway be x

The total length of the garden and walkway will be (12+2x) feet

The total width of the walkway and garden would be (8+2x) feet

Area of the garden and the walkway together are 252 square

Let’s express this mathematically:

(8+2x)(12+2x) = 252

Let’s open the brackets;

96+ 16x+ 24x + 4x^2 = 252

4x^2 + 40x + 96 = 252

4x^2 + 40x + 96-252 = 0

4x^2 + 40x - 156 = 0

Let’s divide all through by 10. We have;

x^2 + 10x -39 = 0

X^2 +13x-3x-39 = 0

x(x + 13) -3(x+ 13) = 0

(x-3)(x + 13) = 0

x -3 = 0 or x + 13 = 0

x = 3 or -13

We ignore x = -13 since width cannot be negative in size

Therefore, the width of the rectangular walkway is 3 feet around.

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The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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Focus groups are not appropriate for generating statistics and making scientific generalizations.

The given statement is True.

Focus groups are qualitative research methods used to gather in-depth insights and subjective opinions from a small group of participants.

They typically involve a moderator guiding a discussion among a selected group of individuals to explore their perspectives, attitudes, and experiences on a specific topic.

The main objective of focus groups is to obtain rich, contextual information rather than to produce statistical data.

Focus groups usually consist of a small number of participants, typically ranging from 6 to 12 individuals, which makes it difficult to achieve statistical significance or representativeness.

The participants are not randomly selected, but rather purposively chosen based on specific criteria relevant to the research focus.

While focus groups offer valuable qualitative insights, they are not designed to generate statistically reliable data or make generalizations to a larger population.

The results obtained from focus groups are specific to the participants involved and their unique perspectives.

Therefore, it is not appropriate to use focus group findings as a basis for making scientific generalizations or drawing statistically significant conclusions about a broader population.

To make scientific generalizations and produce statistical data, researchers typically employ quantitative research methods, such as surveys or experiments, with larger and more diverse samples that allow for statistical analysis and inference.

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When the line of slope of 3 passes through two points, the value of y is -8.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

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

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of y is -8 when the line of slope of 3 is passing through 2 points as given.

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Answer:

6/2

2/6

6/6

2/2

Step-by-step explanation:

Answer:

where is the rest of the question

Answer:

D Standard Deviation

Step-by-step explanation:

Edge 2022

Subtraction is a mathematical operation that reflects the removal of things from a collection. The difference between −9 4/5 and −3 2/3 is -6 2/15.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The difference between −9 4/5 and −3 2/3 is,

−9 4/5 − (−3 2/3)

= −9 4/5 + 3 2/3

= (−9+3) + (−4/5 + 2/3)

= −6 + (-2/15)

= -6 2/15

Hence, The difference between −9 4/5 and −3 2/3 is -6 2/15.

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The value of i where remainder of n/ 4 is 2 is :

i² = -1 .

i² = -1

i⁰ = 1

i¹ = i

i² = -1

i³ = i² x i

  = -1 x i

  = -i

i⁴ = i² x i²

   = -1 x -1

   = 1

The pattern repeats.

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Answer:

10

Step-by-step explanation:

\(-5(x-3)+7x=35\)

Distribute the 5

\(-5x+15+7x=35\)

Combine like terms

\(2x+15=35\)

Subtract 15 to isolate the variable

\(2x=20\)

Divide by 2

\(x=10\)

Answer:

x = 10

Step-by-step explanation:

I hope this helps!

I don't know how to write it in index form but I can Rationalize the Denominator.

Rationalize the Denominator:        \(\frac{\sqrt{x} }{3}\)

Answer:

popcorn is 5.5 and drink is 4

Step-by-step explanation:

It just is my g

Answer: what is the question? I will gladly sovle it

Step-by-step explanation:

tell me your questions and i will solve it asap. i know the area is 40 square millmetres but if you have a question i will gladly answer it.

Two triangles are congruent because the sides of two triangles and angles are congruent and the transformation applied to map triangle EBD onto triangle CBA is rotation of 90 degrees.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

There are two triangles in the coordinate plane.

Triangle ABC and triangle EBD are in plane.

We need to find the transformation applied to EBD onto triangle CBA.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

The triangle EBD undergoes a rotation of 90 degrees in clockwise direction to get triangle CBA.

The two triangles are congruent because the sides of two triangles and angles are congruent. So we conclude that the two triangles are congruent.

Hence, rotation of 90 degrees is the transformation (s) could be applied to map triangle EBD onto triangle CBA.

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The expression for sin(θ + ϕ), we get sin(θ + ϕ) = (-15 - 8sqrt(24))/85 under the conditions.

Using the trigonometric identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b), we have:

sin(θ + ϕ) = sin(θ)cos(ϕ) + cos(θ)sin(ϕ)

We are given that sin(θ) = 15/17 with θ in Quadrant I, so we can use the Pythagorean identity to find cos(θ):

cos(θ) = sqrt(1 - sin^2(θ)) = sqrt(1 - (15/17)^2) = 8/17

We are also given that cos(ϕ) = -5/5 with ϕ in Quadrant II, so we can use the Pythagorean identity again to find sin(ϕ):

sin(ϕ) = -sqrt(1 - cos^2(ϕ)) = -sqrt(1 - (5/5)^2) = -sqrt(24)/5

Substituting these values into the expression for sin(θ + ϕ), we get:

sin(θ + ϕ) = (15/17)(-5/5) + (8/17)(-sqrt(24)/5) = (-15 - 8sqrt(24))/85

Therefore, sin(θ + ϕ) = (-15 - 8sqrt(24))/85 under the given conditions.

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The P-value in each of the given situations for testing the null hypothesis H₀: p = 0.6 using a z-test can be determined as follows:

A. Hₐ: p > 0.6, z = 1.47: The P-value is the probability of observing a z-score greater than 1.47, which can be found by calculating the area under the standard normal curve to the right of 1.47.

B. Hₐ: p < 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70, which can be found by calculating the area under the standard normal curve to the left of -2.70.

C. Hₐ: p ≠ 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70 or greater than 2.70, which can be found by calculating the sum of the areas under the standard normal curve to the left of -2.70 and to the right of 2.70.

D. Hₐ: p < 0.6, z = 0.25: The P-value is the probability of observing a z-score less than 0.25, which can be found by calculating the area under the standard normal curve to the left of 0.25.

To determine the P-value, we need to calculate the corresponding areas under the standard normal curve based on the given z-scores. The P-value represents the probability of observing a z-score as extreme or more extreme than the given value, assuming the null hypothesis is true.

By using standard normal distribution tables or statistical software, we can find the probabilities associated with the given z-scores. These probabilities represent the P-values for each scenario, providing a measure of evidence against the null hypothesis.


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The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

The if statement evaluates the test expression inside the parenthesis ().

If the test expression is evaluated to true, statements inside the body of if are executed.

If the test expression is evaluated to false, statements inside the body of if are not executed.

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

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In conditional statements, the part of the statement following 'if' is called the antecedent.

The antecedent is the condition that needs to be true for the consequent to occur.

The consequent is the part of the statement that follows 'then.'

An antecedent is a noun or pronoun that denotes a specific being, place, object, or clause.

It's also referred to as a referent. Without an antecedent, a sentence may be insufficient or nonsensical since it is

required to establish what or to whom a pronoun in a sentence is referring.

In summary, a conditional statement is structured as "if (antecedent) then (consequent)."

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Answer:

yes

Step-by-step explanation:

Answer:

It is rational

Step-by-step explanation:

1.52 = 1 + 52/100 = 152/100 which is rational, because it can be expressed as a fraction

a) This sample of 27 share prices represents cross-sectional data because it includes a snapshot of share prices from different stocks at a specific point in time.

b) The 95% confidence interval for the mean share price is $43.16 ± $3.39.

c) The 95% confidence interval suggests that we can be 95% confident that the true mean share price of stocks listed on this stock exchange falls within the range of $39.77 to $46.55.

d) The 99% confidence interval would be wider than the 95% confidence interval because a higher confidence level requires a larger margin of error, resulting in a broader range of values.

a) This sample of 27 share prices represents cross-sectional data because it captures a snapshot of share prices from different stocks on the stock exchange at a specific point in time, allowing for comparison and analysis.

b) To construct a 95% confidence interval for the mean share price, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / Square Root of Sample Size)

Given the sample mean share price of $43.16, the standard deviation of $8.75, and a sample size of 27, we need to determine the critical value associated with a 95% confidence level from a t-distribution table or statistical software.

c) The 95% confidence interval constructed for the mean share price indicates that we can be 95% confident that the true population mean share price falls within the calculated interval.

In the context of this question, it provides a range of values within which we estimate the average share price for stocks listed on this stock exchange to be.

d) The 99% confidence interval would be wider than the 95% confidence interval.

This is because a higher confidence level requires a larger range of values to capture the true population mean with a higher degree of certainty, leading to a wider interval.

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Answer:

The zeroes are (-1/3, 0) (2/3, 0) and (2, 0)

Step-by-step explanation:

i graphed it on desmos :)