Find an equation of the line that is tangent to the graph of f and parallel to the given line. See image for more

Answer:

38°

Step-by-step explanation:

142° and x° are angles on a straight line. Angles on a straight line are equal to 180°

142° + x° = 180°

x° = 180° - 142°

x° = 38°

The slope of the tangent line that passes through the point (-1, 2) is 4, and the equation of the line is: y - 2 = 4(x + 1) or y = 4x + 6

To find the slope of the tangent line to a circle, we first need to find the equation of the circle.

Given the center and radius, the equation of a circle can be written as:

(x + 5)^2 + (y - 3)^2 = 17

Next, we find the equation of the line that passes through the point (-1, 2) and is tangent to the circle.

We can use the slope-point form of the equation of a line:

y - 2 = m(x + 1)

where m is the slope of the line.

To find the value of m, we need to find the slope of the line that is tangent to the circle at the point (-1, 2).

The slope of a tangent line to a circle at a point is equal to the derivative of the equation of the circle at that point.

Taking the partial derivatives of x and y in the equation of the circle, we get:

2(x + 5)dx + 2(y - 3)dy = 0

Rearranging and solving for the slope:

dy/dx = -(x + 5)/(y - 3)

Evaluating the slope at the point (-1, 2), we get:

dy/dx = -(−1 + 5)/(2 − 3) = 4

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The range of possible side lengths that satisfy these conditions is,

⇒ { s | 45.5 < s < 49.5 }

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The perimeter of a square must be greater than 182 inches but less than 198 inches.

Now, We know that;

The perimeter of a square is given by,

⇒ P = 4s

Where, 's' represents the length of a side.

Here, The perimeter of a square must be greater than 182 inches but less than 198 inches.

Hence, We get;

⇒ 182 < P < 198

Since, P = 4s

⇒ 182 < 4s < 198

⇒ 182/4 < 4s/4 < 198/4

⇒ 45.5 < s < 49.5

Thus, The range of possible side lengths that satisfy these conditions is,

⇒ { s | 45.5 < s < 49.5 }

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The "if statement" to show that  increases pay by 3% if score is greater than 90, otherwise increases pay by 1% ; is written below .

The if statement in that implements the conditions that increases pay by 3% if score is greater than 90, otherwise increases pay by 1% is written as :

⇒ if (score > 90)

⇒  pay *= 1.03;

⇒  else

⇒  pay *=1.01;

In the above mentioned  code, the "score" is a variable that represents the value to be tested, and "pay" is a variable that represents the current pay.

The statement checks that if score is greater than 90.  pay is increased by 3% (multiplying by 1.03). If score is not greater than 90, pay is increased by 1% (multiplying by 1.01).

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On solving the provided question we can say that Area of the trapezium = 1/2 X (8+18 ) X 8 = 144 ft sq.

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is known as Trapezium in the United Kingdom and other English-speaking countries. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's base is defined as its parallel sides. An identical one set of opposite sides that are parallel to one another define a trapezoid, a convex quadrilateral. When drawn on paper, the two-dimensional trapezoid shape resembles a table. A polygon with four sides and four vertices is referred to as a quadrilateral in Euclidean geometry.

Area of the trapezium = 1/2 X (8+18 ) X 8

A = 26 X 4 = 144 ft sq.

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The probability that x a random variable is between 1.88 and 19.86 , i.e., P( 1.88< X< 19.86) is equals to the 0.9235 or 92.35%.

Let x be a random variable and it is normally distributed with a mean of 10 and a standard deviation of 5. We have to determine the probability that x is between 1.88 and 19.86 . In other words, X~ N( 10, 5) and P( 1.88< X< 19.86).

Mean, μ = 10

standard deviation, σ = 5

Normal distribution formula ,

Z = (X - μ)/σ

P( 1.88< X< 19.86) = P(( 1.88 - μ)/σ < (X- μ)/σ < ( 19.86 - μ)/σ)

= P((1.88 - 10)/5 < (X- 10)/5 < ( 19.86 - 10)/5)

= P(-8.12/5 < (X- μ)/σ < 9.86/5)

= P( - 1.624 < (X- μ)/σ < 1.972)

= P( - 1.624 < Z< 1.972)

= P( Z> 1.972) - P( Z< - 1.624)

P( 1.88< X< 19.86) = 0.92351

Hence, the required probability is 0.9235 .

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The value of the quantity negative one-third cubed all raised to the power of -3 will be -19683.

Expression in math's is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is negative third cubed all raised to the power of negative 3.

The expression can be solved as below:-

E = [ ( -1 / 3 )³ ]⁻³

E = [ (  -1 / 3 ) ] ⁻⁹

E = ( -3 )⁹

E = -19683

Therefore, the value of the quantity negative one-third cubed all raised to the power of -3 will be -19683.

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The students use simple random sampling.

In this case, every member of the population participating in the sampling has the same opportunity to become a member of the sample. Many people think that random sampling is an ideal sample to be used in a study. In fact, random sampling can be used as a basis for generalizing a conclusion.

Random sampling is selecting samples in such a way that all combinations of a unit have the same chance of being selected as a sample.

In order to make it easier what is meant by "members of the population have the same opportunity", a case example will be given. For example, in a population there are 100 members, but only 50 are needed to be members of the sample, so each member of the population has a 100/50 probability of being able to participate in sampling to become a member of the sample.

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The simple events in this ranking experiment are C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C where all of the simple events have the same probability, 1/6.

The simple events in this ranking experiment are the 6 possible ways the individual can order the three glasses of cola: C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C.

Since the individual's preferences are assumed to be random and the same cola has been put into all three glasses labeled C, D, and P, each of the 6 possible ways the individual can order the glasses (C-D-P, C-P-D, D-C-P, D-P-C, P-C-D, P-D-C) are equally likely.

This means that each of the 6 simple events has a probability of 1/6, or 0.1667. This is because if each ordering of the glasses is considered an outcome, there are 6 equally likely outcomes. The probability of any one of the outcomes is 1 divided by the total number of outcomes, or 1/6.

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In the quotation, Theodore Rhodie is expressing his resistance to the idea of giving up his membership in the ARU, as doing so would mean giving up his principles and rights as an American citizen.

Using someone else's precise words or statements as part of your writing is known as a direct quotation.

Theodore Rhodie, a former Pullman employee, is referring to the imprisonment of Eugene V. Debs in his quotation. Debs was the leader of the American Railway Union (ARU) and was a prominent figure in the Pullman Strike of 1894. The strike resulted in the shutdown of the nation's rail system, causing widespread economic disruption. In response, the federal government intervened, sending in troops to restore order. Debs was arrested and convicted of violating a federal court injunction against the strike, leading to his imprisonment.

In the quotation, Theodore Rhodie is expressing his resistance to the idea of giving up his membership in the ARU, as doing so would mean giving up his principles and rights as an American citizen. This reflects the sentiment of many workers during the Pullman Strike who felt that their rights were being violated and were willing to stand up for their principles, even if it meant facing consequences such as imprisonment.

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Answer:b

Step-by-step explanation:

The expression 1/9(-3/5) can be written in simplest form as -5/27.

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[tex]y=3^{1+x}[/tex] is the  equation of the exponential function represented by the table.

Two or more expressions with an Equal sign is called as Equation.

The given table is below

x     y

0    3

1     9

2    27

3    81

Each time x increases by 1, y increases by a factor of 3.

Thus, the required equation  has the form y = 3ˣ

If x = 0, do we get 3,

No, therefore we must modify the exponent:

[tex]y=3^{1+x}[/tex]

Hence, [tex]y=3^{1+x}[/tex] is the  equation of the exponential function represented by the table.

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Answer:

1/2

Step-by-step explanation:

On the clock from 3 to 9, the hour hand turns clockwise 1/2 of the revolution

The answer is C. There is a positive linear relationship between player height and number of points scored for basketball players in the coach's state.

A confidence interval is a range of values that is calculated from the data and is believed to contain the true population parameter with a certain level of confidence, in this case 96%. The slope of the regression line is the average change in y for a one unit change in x, which represents the direction and strength of the relationship between x and y.

The confidence interval for the slope is (−0.432,1.844), which does not include 0, which means that the slope is not equal to 0. If the slope were 0, there would be no relationship between player height and points scored. The fact that the confidence interval is positive means that the slope is positive, which indicates a positive linear relationship between player height and number of points scored.

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The proof of the statement that "any affine transformation, the ratio of parallel line segments is invariant, but the ratio of non-parallel line segments is not invariant" , is explained below .

An Affine Transformation is defined as a mapping between two vector spaces that preserves collinearity and ratios of parallel line segments, but not necessarily ratios of non-parallel line segments.

Which means that if two line segments are parallel in the original space, then their corresponding line segments in the image space will also be parallel and have the same ratio.

But , if the original line segments are not parallel, then their corresponding line segments in the image space will generally not be parallel and their ratio may change.

Therefore , it is proved that the ratio of parallel line segments is invariant under affine transformations, while the ratio of non-parallel line segments is not.

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Cost of the item in both cases are (a) $21 (b) $21.6 and (c) Lower price of the item is when applied 20% discount first and then $3 off.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

(a) Original price of the item = $30

After 20% discount, price of the item = 30 - (30 × 20%)

                                                              = 30 - (30 × 0.2)

                                                              = $24

After $3 off, price of the item = $24 - $3 = $21

(b) Original price of the item = $30

After $3 off, price of the item = $30 - $3 = $27

After 20% discount, price of the item = 27 - (27 × 20%)

                                                             = $21.6

(c) The lower price is when applied 20% discount first and then $3 off.

Hence the price of the item is lower when we apply 20% discount first and then applied $3 off.

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Answer:

5491.50575

Step-by-step explanation:

10520 x (1 - 0.15)^4
so first you subtract 1 from 0.15 and that equals 0.85 then you times 0.85 itself cuz it decreases value for a total of four years and that would make 0.85^4 =0.52200625 now you 10520 x 0.52200625= 5491.50575
ps. depending if your adding or subtracting percents it will either 1+ or 1- then whatever percent into decimal hope this helps!

The density of an irregularly shaped object with a mass of 6.05 g is 5.50 g/mL.

We have to determine the density of an irregularly shaped object with a mass of 6.05 g.

The volume of the strangely formed object is the volume it displaces.

The volume displaced is the difference between the starting volume of water and the final volume of water when the object is submerged.

The value can be taken as 3.15 mL because the final volume of water in the diagram is between 3.10 and 3.20 mL.

Volume of object = volume displaced

Volume of object = final volume - initial volume

Volume of object = 3.15 mL - 2.05 mL

Volume of object = 1.10 mL

The following formula can then be used to calculate the object's density:

Density = mass / volume

Density = (6.05 g) / (1.10 mL)

Density = 5.50 g/mL

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The complete question is:

A student needs to determine the density of an irregularly shaped object with a mass of 6.05 g.

Part A: The student fills a 10 mL graduated cylinder with deionized water. Use the image below to determine the volume of water in the graduated cylinder.

Report the answer to the correct number of significant figures. Initial volume of water = 2.05 mL

The solution is, given below.

A treatment is something that health care providers do for their patients to control a health problem, lessen its symptoms, or clear it up. Treatments can include medicine, therapy, surgery, or other approaches.

here, we have,

Part A: The appropriate design for the study includes;

Treatment used; Chamomile oil treatment

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

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Based on the histogram, 13 students held their breath for greater than 12.5 seconds but less than 15.5 seconds.

In a first-grade class, students measured how long they could hold their breath. The results were shown on a graph called a histogram. To see how many students held their breath between 12.5 and 15.5 seconds, we need to look at the bars on the graph between those times. The number of students is shown by the height of each bar.

We can see that there are 2 students who held their breath between 12.5 and 13.5 seconds. There are 5 students who held their breath between 13.5 and 14.5 seconds. And there are 6 students who held their breath between 14.5 and 15.5 seconds. To find out the total number of students, we add the heights of the bars together.

So:

Hence, there are 13 students who held their breath between 12.5 and 15.5 seconds.

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Answer:

----------------------------

After dilation by a factor of 4 the base length becomes 4 times larger:

The translation is not affecting dimensions of the figure so the base length of figure B remains as 20 units.

Answer:

 (28800 cm2) / (400 cm2/tile) = 72 tiles

Step-by-step explanation:

According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles.

According to the exterior angle theorem, the exterior angle that results from stretching a triangle side is equal to the sum of the dimensions of the triangle's two opposed interior angles. Three internal angles in a triangle or polygon always add up to 180 degrees. This theorem is applied to each of the outer angles, which total six.

Here,

Given :

With the help of the triangle's well-known features, we can validate the exterior angle theorem.

Think about an ABC.

The total of the three angles is 180 degrees (angle sum property of a triangle) ——- Equation 1: (A+B)/180 ——- Example 2 (rewriting equation 1)

e = 180 - c

——- Equivalent 3 (linear pair of angles)

Equation 3 may be solved for by substituting the value of c.

e = 180 - [180 - (a + b)]

e = 180 - 180 + (a + b)

e = a + b.

=> m∠A = m∠G

=> m∠DMG > m∠A

So , its proven that:

=> m∠DMG > m∠G

and

=> A-D-M

So,

AD = DM

=> AD <AM

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Answer:

176 miles

Step-by-step explanation:

Step 1: determine what 44% of 400 miles is

44% of 400= 176

Answer: Santiago fell asleep at 176 miles and they had 224 miles left in their trip.

Answer:

-26 and -14

Step-by-step explanation:

Let x = one number

Let y = the other number

x + y = -40

x - y = -12   Add the two equations together.

2x     = -52  Divide both sides by 2

x = -26

Substitute -26 for x to find y

x + y = -40

-26 + y = -40    Add 26 to both sides

-26 + 26 + y = -40 + 26

y = -14

Check:

x + y = -40

-26 + -14 = -40

-40 = -40 Checks

x - y = -12

-26 - (-14) = -12

-26 + 14 = -12

-12 = -12 Checks

Answer:

y = 4 and lh = 16

Step-by-step explanation:

hi again

About 68% of the area is covered by one standard deviation above and below the mean, therefore one standard deviation above the mean corresponds to 34% of the area. Thus, we have 84% after adding the 50% below the mean and the 34% above the mean.

A normality assumption with a zero mean and a standard error of one is referred to as the typical normally distributed. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.

Sixty-eight percent of the observations for the normal distribution are within one standard deviation of the mean, ninety-five percent are within two standard deviations of the mean, and ninety-nine percent are within three standard deviations of the mean.

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