Find the equation of the line perpendicular to the line x + 2y = 6 and passing through the point (1, 2). Provide full working out please. Thanks :)

Answer:

one obtuse angle is the answer

Step-by-step explanation:

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The patch's area is 2.47 × 10^(-6) km².

The cost of the patch is $14.61.

(a) The area of the patch in square kilometers (km²) can be found by converting the given area in square centimeters (cm²) to square kilometers.

1. Convert cm² to m²: Divide the given area by 10,000 since 1 m² is equal to 10,000 cm².
24.7 cm² ÷ 10,000 = 0.00247 m²

2. Convert m² to km²: Divide the area in m² by 1,000,000 since 1 km² is equal to 1,000,000 m².
0.00247 m² ÷ 1,000,000 = 2.47 × 10^(-6) km² (scientific notation)

The patch's area is 2.47 × 10^(-6) km².

(b) To find the cost of the patch, we need to multiply the area of the patch by the cost of the patching material.

1. Convert the cost of the patching material to cost per cm²: Divide the given cost by 1 square inch since 1 square inch is approximately equal to 6.4516 cm².
$3.82/in² ÷ 6.4516 cm²/in² = $0.592/cm² (rounded to the nearest cent)

2. Multiply the cost per cm² by the area of the patch in cm² to find the total cost of the patch.
$0.592/cm² × 24.7 cm² = $14.61 (rounded to the nearest cent)

The cost of the patch is $14.61.

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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The area of the shaded region and the area of the unshaded region are the same.

The square can be divided into quarters, and the quarter circles can then be moved.

When the quarter's circle move which means the shaded portion completes the half portion of the square and the remaining half portion is completed by the unshaded part of the square.

Therefore the square is divided into two equal rectangles as shown in the fig below.

The colored and un-shaded portions are then equal, as can be seen:

Therefore the area of the shaded region is equal to the combined area of the unshaded region.

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The correct matching relating the correlation coefficients are given as follows:

A correlation coefficient is an index that measures the association between multiple variables.

The closer the absolute value of the correlation coefficient is of 1, the stronger is the association, meaning that the statement has more certainity.

Closer to zero, the correlation coefficient gives no confidence of the assessment, and values above 0.6 are considered as indicating strong correlation.

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If triangles 1 and 2 are similar then ratio of two sides is 25:52

A triangle is a polygon with edges and three terminals. It belongs to the basic geometric shapes. A triangle containing the angles A, B, and C is referred to by the term ABC.

Any three Euclidean points that are not collinear result in a triangle and a rectangle. In other words, any triangle is exclusively covered by that plane and is contained within that plane.

We know that any two triangles are similar by three axioms:

SSS , AAS , SAS or AAA axiom of similarity.

In the Euclidean plane, every triangle is contained within a single plane, but in higher-dimensional Euclidean spaces, this is no longer the case. This article addresses triangles in terms of geometry, more specifically the Euclidean plane, unless otherwise stated.

ratio of the sides of two triangle are in same ration when the triangles are similar

Now given ratio is 25:52, hence the ratio of the sides will be same.

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9514 1404 393

Answer:

  9.  ±1, ±2, ±3, ±6

  11.  ±1, ±2, ±3, ±4, ±6, ±12

Step-by-step explanation:

The possible rational roots are (plus or minus) the divisors of the constant term, divided by the divisors of the leading coefficient.

Here, the leading coefficient is 1 in each case, so the possible rational roots are plus or minus a divisor of the constant term.

__

9. The constant is -6. Divisors of 6 are 1, 2, 3, 6. The possible rational roots are ...

  ±{1, 2, 3, 6}

__

11. The constant is 12. Divisors of 12 are 1, 2, 3, 4, 6, 12. The possible rational roots are ...

  ±{1, 2, 3, 4, 6, 12}

_____

A graphing calculator is useful for seeing if any of these values actually are roots of the equation. (The 4th-degree equation will have 2 complex roots.)

The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.

The statement is true.
Let's first understand the terms used:
Linearly independent:

A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:

The span of a set of vectors is the set of all linear combinations of those vectors.

In this case, Span\({x, y}\) is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span\({x, y}.\)

This means that z can be expressed as a linear combination of x and y:
\(z = ax + by\), where a and b are scalar constants.
Let's analyze the set\({x, y, z}\). We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set \({x, y, z}\)is linearly dependent, because one vector (z) can be expressed as a linear combination of the others \((x and y)\).

Thus, the statement is true: If x and y are linearly independent, and if z is in Span\({x, y}\), then\({x, y, z}\) is linearly dependent.

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Answer:

B (lmk if you want me to explain)

Step-by-step explanation:

the point slope form is

y-y1=m(x-x1)

y-12=5/6(x--9)

y-12=5/6(x+9)

Answer:

1. 7

2.13

3.92

4.23

Step-by-step explanation:

P- parentheses

E- exponents

MD- Multiplication and division

AS- addition and subtraction

1. 3+3^2-5

3+9-5

12-5=7

2. 2^3-5x1+10

8-5x1+10

8-5+10

13

3. 24\2+10^2-20

24/2+100-20

12+100-20

92

4. 6x^3+25/5

18+25/5

18+5

23

Answer:

c. \(3(10)^{6}\)

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

-4x>8

x<-2

-4>-2x

8<x

8<x<-2

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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1. The characteristic equation for the differential equation y" - 9y' = 0 is r² - 9r = 0, which simplifies to r(r - 9) = 0. The roots are r = 0 and r = 9.

2. The characteristic equation for the differential equation t²y" + 16y = 0 is r² + 16 = 0. There are no real roots, but there are complex roots given by r = ±4i.

1. To find the characteristic equation for the differential equation y" - 9y' = 0, we assume a solution of the form y = e^(rt). Substituting this into the differential equation, we get r²e^(rt) - 9re^(rt) = 0. Factoring out e^(rt), we have e^(rt)(r² - 9r) = 0. Since e^(rt) is never zero, we can divide both sides by e^(rt), resulting in r² - 9r = 0. This equation can be further factored as r(r - 9) = 0, which gives us two roots: r = 0 and r = 9. These are the solutions to the characteristic equation.

2. For the differential equation t²y" + 16y = 0, we again assume a solution of the form y = e^(rt). Substituting this into the differential equation, we have r²e^(rt)t² + 16e^(rt) = 0. Dividing both sides by e^(rt), we obtain r²t² + 16 = 0. This equation does not have real roots. However, it has complex roots given by r = ±4i. The characteristic equation is r² + 16 = 0, indicating that the solutions to the differential equation have the form y = Ae^(4it) + Be^(-4it), where A and B are constants.

In summary, the characteristic equation for the differential equation y" - 9y' = 0 is r² - 9r = 0 with roots r = 0 and r = 9. For the differential equation t²y" + 16y = 0, the characteristic equation is r² + 16 = 0, leading to complex roots r = ±4i. These characteristic equations provide the basis for finding the general solutions to the respective differential equations.

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To eliminate the unknown variable a1 from the system of equations, we need to select two equations that can be combined in a way that eliminates a1 when the equations are subtracted or added. The specific choice of equations depends on the structure of the system and the coefficients of a1 in each equation.

To determine which equations can be used to eliminate a1, we need to examine the coefficients of a1 in each equation. If the coefficients are of equal magnitude but opposite signs, subtracting the equations will result in the elimination of a1. Conversely, if the coefficients have the same sign, adding the equations can eliminate a1.

Given the system of equations, eq.2, eq.3, and eq.4*, we should analyze the coefficients of a1 in these equations. By comparing the coefficients, we can determine which combination of equations can be used to eliminate a1. It is essential to select two equations where the coefficients of a1 have opposite signs or equal signs, depending on whether we are subtracting or adding the equations, respectively.

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Step-by-step explanation:

 the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .

Answer:

therefore the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .........

Answer:

x= 43/2

2x-4+4=39+4

2x=43

2x/2=43/2

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

The side lengths of the original square was 2.  2 x 2 = 4

.25 x 2 = .5

The squares are now 1/2 x 1/2.  One of the 4 original squares will now need 4 new smaller size squares to cover the one square.

4 x 4 = 16

Answer:

x = .464

Step-by-step explanation:

Assumptions: Equation is \(-2x^3+20\). Thus having an asymptote at the value x=0.

The linear function that describes the relationship is y = -2x + 3

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

x f(x)

−1 5

0 3

1 1

A linear function is represented as

y = mx + c

Where

c = y when x = 0

This means thar

c = 3

So, we have

y = mx + 3

From the table, we can see that

As x increases by 1, y decrease by 2

This means that

m = -2

So, we have

y = -2x + 3

Hence, the equation is y = -2x + 3

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The primary code we use to signal identity, according to Remland, is nonverbal communication.

Nonverbal communication refers to the transmission of messages without the use of words. It involves various forms of communication such as facial expressions, body language, gestures, posture, eye contact, and tone of voice. Remland, a researcher in the field of communication, emphasizes the significance of nonverbal cues in signaling identity.

Nonverbal cues play a crucial role in expressing our cultural, social, and personal identities. They can convey information about our emotions, attitudes, status, and affiliations. For example, the way we dress, our choice of accessories, and our body language can communicate aspects of our identity such as our gender, social group, or profession.

Nonverbal communication is particularly powerful because it often operates at an unconscious level and can convey messages that are difficult to express through words alone. These nonverbal signals can shape impressions, establish connections, and influence how others perceive and respond to us.

According to Remland, nonverbal communication is the primary code we use to signal identity. Understanding and interpreting nonverbal cues are essential for effective communication and for navigating social interactions, as they provide valuable insights into the identities and intentions of individuals.

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Answer:

Designate the remaining pair of coordinates as "set 2." Using the previous coordinates (3, 4) and (1, 2), the coordinate pair (1, 2) becomes "set 2" and will be your x2 and y2 values in the formula. Therefore, x1 is 3, y1 is 4, x2 is 1 and y2 is 2. Now that you have your values, you can plug them into the formula.

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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Answer:

Step-by-step explanation:

Remark

If you strip away DJ you can see for yourself which angle is opposite <EGH

Vertically Opposite angles are the angles opposite one another created by two crossed lines.

Answer: The answer to your question is <LGI

\(36:9+48-10:2=\\\\=4+48-5=52-5=\boxed{47}\)

Answer:

Step-by-step explanation:

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

Step-by-step explanation:

Given:

System as per question:

Or

Step-by-step explanation:

Let the number of apples be a and lemons be l . Then ,

=> a + l = 17

Also ,

=> 35a + 15l = $ 3.95

The value of l is 75cm

Similar figures are two figures having the same shape. The objects which are of exactly the same shape and size are known as congruent objects.

The ratio of corresponding sides of similar shapes are equal

In the diagram, It consist of bigger cone to smaller cone.

Represent the slant height of the smaller cone by x, the remaining part is 35cm

Therefore l = 35 + x

Therefore (35+x)/x = 15/8

= 8( 35+x) = 15x

280+8x = 15x

280 = 15-8x

280 = 7x

divide both sides by 7

x = 280/7

x = 40

Therefore l = 35+x

l = 35 + 40

l = 75cm

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Answer:

volume = 2850.9 in³

Step-by-step explanation:

volume of a cylinder = \(\pi r^2h\)

where r is the radius and h is the height

Given:

⇒ volume = 3.14 x 12.2² x 6.1 = 2850.9 in³

x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given equation is nine times of x plus four y equal to fifty one

9x+4y=51

We have to convert this equation to slope intercept form

4y=51-9x

4y=9x-51

Divide both sides by 4

y=9/4x-51/4

x intercept is 9/4 and y intercept is -51/4

Hence x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.

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