Write an equation of the line in point-slope form that is perpendicular to the given line
and passes through the given point.
y = −3x + 4; (−1, 3)

In order to plot points H I and J on the coordinate planeIdentify the x-coordinate and y-coordinate of each point (H, I, and J). For example, let's say the coordinates are as follows:

Point H: (xH, yH)

Point I: (xI, yI)

Point J: (xJ, yJ)

Locate the origin (0, 0) on the coordinate plane. This is the starting point for plotting any point.

Move along the x-axis according to the x-coordinate of each point. If the x-coordinate is positive, move to the right; if it's negative, move to the left. Mark a point on the x-axis at the appropriate location.

Move along the y-axis according to the y-coordinate of each point. If the y-coordinate is positive, move upward; if it's negative, move downward. Mark a point on the y-axis at the appropriate location.

The point where the x and y axes intersect is the location of the point. Mark that point on the coordinate plane.

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How to Plot points H I and J on the coordinate plane

If a = 6 - \(\sqrt{35} \), find the value of a² + \( \frac{1}{a²} \)

a = 6 - \(\sqrt{35} \) (Given)

Now, first of all we have to find the value of \( \frac{1}{a} \).

So, \( \frac{1}{a} \) = \( \frac{1}{6 \: - \: \sqrt{35}} \)

\( \frac{1}{a} \) = \( \frac{6 \: + \sqrt{35}}{(6 \: - \: \sqrt{35})(6 \: + \: \sqrt{35})} \)

\( \frac{1}{a} \) = \( \frac{6 \: + \sqrt{35}}{(6)² \: - \: (\sqrt{35})²} \)

\( \frac{1}{a} \) = \( \frac{6 \: + \sqrt{35}}{36 \: - \: 35} \) \( (\because \sqrt{35} \: × \: \sqrt{35} \: = \: 35) \)

\( \frac{1}{a} \) = \( \frac{6 \: + \: \sqrt{35}}{1} \)

\( \frac{1}{a} \) = 6 + \(\sqrt{35} \)

Now, we have to find the value of a² + \( \frac{1}{a²} \)

So, a² + \( \frac{1}{a²} \) = \( (a \: + \frac{1}{a})² \) - 2.a.\( \frac{1}{a} \)

a² + \( \frac{1}{a²} \) = \( (6 \: - \sqrt{35} \: + \: 6 \: + \sqrt{35})² \) - 2

a² + \( \frac{1}{a²} \) = (12)² - 2

a² + \( \frac{1}{a²} \) = 144 - 2

a² + \( \frac{1}{a²} \) = 142

The value of a² + \( \frac{1}{a²} \) is 142. [Answer]

The slope of a plot of ln k versus 1/t equal to: −E_a/R

The Arrhenius equation is one that describes the relation between the rate of reaction and temperature for many physical and chemical reactions.

Arrhenius equation is expressed as:

k = \(Ae^{-E_{a}/RT }\)

Taking natural log on both sides,

ln k = ln \(Ae^{-E_{a}/RT }\)

In k = In A - E_a/RT

In k = In A - (E_a/R * (1/T))

This equation is in the form of y = mx + c

The plot of ln k vs 1/T gives a straight line with negative slope.

Slope = −E_a/R

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Answer:

x = 68

y = 90

Step-by-step explanation:

The angles inside any quadrilateral add up to 360

For the first shape, it is a parallelogram, meaning the opposite angles are equal.

360 - 112 - 112 = 2x

2x = 136

x = 68

Second shape:

z = 360 - 110 - 85 - 75

z  = 90 <- y is the outside angle, meaning y is not (always) equal to z

y = 180 - z

y = 90

Answer:

for e, x = 68

i dont know where the x is on f.. but the missing inner angle should be 90

Step-by-step explanation:

the parallel lines means that the opposite interior angles are the same, so 112 + 112 = 224

360 - 224 = 136

136 ÷ 2 = 68

Answer:

A. The first five terms in Pattern A are 2, 7, 12, 17, 22.

Step-by-step explanation:

I will just write out the first five terms for both patterns so it is easier to see.

Pattern A:   2, 7, 12, 17, 22

Pattern B:   2, 5, 9, 12, 15

C and D are both false. B is also false because it adds 4 from 5 to 9 instead of 3. "A" is the correct answer since it matches the correct terms.

Answer:

A. The first five terms in Pattern A are 2, 7, 12, 17, 22

Step-by-step explanation:

Pattern A

Start at 2 and follow the rule "add 5"

\(\sf 2 \underset{+5}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+5}{\longrightarrow} 17 \underset{+5}{\longrightarrow} 22\)

So the first five terms in Pattern A are 2, 7, 12, 17, 22

Pattern B

Start at 2 and follow the rule "add 3"

\(\sf 2 \underset{+3}{\longrightarrow} 5 \underset{+3}{\longrightarrow} 8 \underset{+3}{\longrightarrow} 11 \underset{+3}{\longrightarrow} 14\)

So the first five terms in Pattern B are 2, 5, 8, 11, 14

True Statement

Therefore, the statement that is true is:

A. The first five terms in Pattern A are 2, 7, 12, 17, 22

Answer:

9

Step-by-step explanation:

12 divided by 4 is 3

3 multiplied by 3 is 3

The maximum area of the rectangle that has a perimeter of 12 meters would be equal to 6x - x^2.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be the length of the rectangle and y be the width of the rectangle

The perimeter of a rectangle = 2( l + b)

                                         12   =   2(x + y)

                                         (x +y) = 6

                                             y = 6- x

The area of the rectangle = length × Width

                                          = x × y

                                          = x ( 6- x)

                                          = 6x - x^2

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Answer:

2000 represents the original amount of butterfly's

3/4 represents the change in butterfly's

To find c) plug 3 in for t and solve.

The probability of making the wrong decision is approximately 0.0082.

According to the central limit theorem, the distribution of the sample mean of a large number of independent and identically distributed random variables approaches a normal distribution. In this case, the random variable is the number of odd outcomes in 100 rounds of the roulette.

As each outcome has an equal probability of being odd, the distribution of the number of odd outcomes is binomial with parameters n=100 and p=1/2.

Using the mean and variance of a binomial distribution, we have:

mean = np = 100 x 1/2 = 50

variance = np(1-p) = 100 x 1/2 x (1 - 1/2) = 25

The standard deviation of the distribution is the square root of the variance, which is 5. Therefore, the z-score for a count of 55 is:

z = (55 - 50) / 5 = 1

Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1 (i.e., a count of 55 or more) is approximately 0.1587. However, we are interested in the probability of making the wrong decision, which is the probability of a count of 55 or more given that the roulette is fair.

This probability is equal to the significance level of the test, which is the probability of rejecting the null hypothesis (fair roulette) when it is actually true.

Assuming a significance level of 0.05, the probability of making a Type I error (rejecting a true null hypothesis) is 0.05. Therefore, the probability of making the wrong decision is approximately 0.05 x 0.1587 = 0.0082.

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Answer:

11. 10x^2 - 13x - 3

12. 5x^2 + 18x + 5

Step-by-step explanation:

11. Product means multiplication, so you can multiply (5x + 1) and (2x - 3).

\((5x + 1) * (2x - 3)\) - Using the FOIL (First+Outer+Inner+Last)

So: \((5x*2x) + (5x*-3) + (1*2x) + (1*-3)\\10x^{2} -15x + 2x -3\\10x^{2} -13x -3\)

12. \(3x^{2} + 8x - 1 + 2(x^{2} +5x + 3)\) (So, you distribute the 2 to x^2 + 5x + 30, then combine like terms).

\(3x^{2} + 8x - 1 + 2(x^{2} +5x + 3)\\3x^{2} + 8x - 1 + 2x^{2} +10x + 6\\(3x^{2} +2x^{2}) + (8x + 10x) + (-1+6)\\5x^{2} + 18x + 5\)

Hopefully, this helped you. Good luck & have a good day!

The recurrence relation for the number of ways to arrange cars in a row with n parking spaces if we can use Cadillacs, Hummers, or Fords can be written as: A(n) = 3A(n-1) .

Let A(n) be the number of ways to arrange cars in a row with n parking spaces. We can place either a Cadillac, Hummer, or Ford in the first parking space. If we place a Cadillac, then we have A(n-1) ways to arrange the remaining (n-1) parking spaces.

Similarly, if we place a Hummer or a Ford in the first parking space, we have A(n-1) ways to arrange the remaining parking spaces. Therefore, the recurrence relation can be written as: A(n) = 3A(n-1)

with initial condition A(1) = 3. This recurrence relation tells us that the number of ways to arrange cars in a row with n parking spaces is three times the number of ways to arrange cars in a row with (n-1) parking spaces.

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Answer:

72√2

Step-by-step explanation:

3√2 × 2√8 × √3 × √6

The above can be simplified as follow:

3√2 × 2√8 × √3 × √6

Recall

a√c × b√d = (a×b)√(c×d)

3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)

= 6√288

Recall

288 = 144 × 2

6√288 = 6√(144 × 2)

Recall

√(a×b) = √a × √b

6√(144 × 2) = 6 × √144 × √2

= 6 × 12 × √2

= 72√2

Therefore,

3√2 × 2√8 × √3 × √6 = 72√2

Answer:

5/2y - 8

Step-by-step explanation:

Step 1: Add -7 to both sides.

2x+7+−7=5y−9+−72x=5y−16

Step 2: Divide both sides by 2.

2x2=5y−162x=52y−8

Answer:

too lazy to do the math but yk

Step-by-step explanation:

ok so first you wanna make sure you isolate variables, to find x you get

2x+7=5y-9

2x=5y-2

x=(5y-2)/2

plug that into the equation, then you get the y value, which you can put into the equation again (by equation i mean 2x+7=5y-9)

then you have both x and y

Answer: D

Step-by-step explanation:

a^2 +b^2 = c^2

\(3\sqrt{2}^2\)= 18

3\sqrt{2}^2= 18

18 + 18 = 36

The square root of 36 is 6

Answer:

D no is correct ans

Step-by-step explanation:

using pythagoras thoerem h^2=p^2+b^2

and put the value P=3root 2 and b =3root2 and take out h

The probability that a particular death is due to an automobile accident is 4%

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

total deaths in recent years = 1158

automobile accident resulted = 46 accidents

cancer deaths resulted = 226 accidents

heart disease deaths resulted = 388 accidents

the probability that a particular death is due to an automobile accident = 46/1158

                     = 0.04 or 4 % chances

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Answer:

A vector graphic consists of a set of instructions for creating a picture is a true statement.

Step-by-step explanation:

A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.

These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.

Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.

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a) No, the relation (a, b) ∈ R if a is taller than b does not form a poset on the set of all people in the world. b) Yes, the relation (a, b) ∈ R if a is not taller than b forms a poset on the set of all people in the world. c) Yes, the relation (a, b) ∈ R if a = b or a is an ancestor of b forms a poset on the set of all people in the world. d) No, the relation (a, b) ∈ R if a and b have a common friend does not form a poset on the set of all people in the world.

a) The relation (a, b) ∈ R if a is taller than b does not form a poset on the set of all people in the world. This is because the relation is not reflexive, as a person cannot be taller than themselves.

b) The relation (a, b) ∈ R if a is not taller than b does form a poset on the set of all people in the world. This relation is reflexive, antisymmetric, and transitive. Every person is not taller than themselves, and if a person is not taller than another person and that person is not taller than a third person, then the first person is also not taller than the third person.

c) The relation (a, b) ∈ R if a = b or a is an ancestor of b does form a poset on the set of all people in the world. This relation is reflexive, antisymmetric, and transitive. Every person is an ancestor of themselves, and if a person is an ancestor of another person and that person is an ancestor of a third person, then the first person is also an ancestor of the third person.

d) The relation (a, b) ∈ R if a and b have a common friend does not form a poset on the set of all people in the world. This relation is not antisymmetric, as two people can have a common friend without being equal to each other.

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Answer: A random variable.

Step-by-step explanation:

a numerical description of the outcome of an experiment is called a random variable.

The probability that the baseball player has exactly 1 hit in his next 7 at-bats is 0.2908, rounded to 4 decimal places.

It is a statistic that measures the performance of baseball players. It is the ratio of the number of hits to the number of at-bats.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1.

Static means the precise value of something, without approximation or estimation.

It is a process of approximating a number to a specific number of decimal places.

A baseball player has a batting average of 0.365. The probability that he has exactly 1 hit in his next 7 at-bats is to be found.

Step 1: Calculate the probability of getting a hit in one at-bat. The probability of getting a hit in one at-bat is equal to the batting average of the player.

P(hit) = 0.365

Step 2: Calculate the probability of not getting a hit in one at-bat. The probability of not getting a hit in one at-bat is equal to the difference between 1 and the batting average.

P(not hit) = 1 - 0.365 = 0.635

Step 3: Calculate the probability of getting exactly 1 hit in 7 at-bats. The probability of getting exactly 1 hit in 7 at-bats can be calculated using the binomial probability formula:

P(1 hit in 7 at-bats) = 0.2908 (rounded to 4 decimal places)

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The value of f(x) = x³ - x² -5x - 3 will be (x-3)³ +8(x-3)² + 16(-3).

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

f(x) = x³ - x² -5x - 3

= (x - 3)³ +9x² - 27x +27- x² -5x -3

= (x-3)³ +8x² - 32x + 24

= (x-3)² +8(x-3)² + 48x -72-32x +24

= (8-3)² + 8(8-3)² + 16x-48

= (x-3)³ + 8(x-3)² + 16(x-3)+48-48 =

= (x-3)³ +8(x-3)² + 16(-3).

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Answer:

Part A; Initial dosage is 10 milligrams

Part B:

8.4113 milligrams after 1 hour

5.0057 milligrams after 4 hours.

Step-by-step explanation:

It is given M(h)= 10 \(e^{-0.173h}\)

Initial dosage is the 10 milligrams

After 1 hour, plug in h as 1

So, M(1)=10\(e^{-0.173*1}\)

Simplify the right side

M(1)=10(0.84113)

M(1)= 8.4113 milligrams.

Now, after 4 hours

M(4)=10 \(e^{-0.173*4}\)

M(4)=10(0.50057)

M(4) =5.0057 milligrams

Answer:

620

Step-by-step explanation:

12-1=11

11x50

1x70

add the two totals and you should get 620

Hope this helps!

Answer:

∠I ≅ ∠F

Step-by-step explanation:

Since, F is common vertex in the sides GF and FE of triangle FGE and I is common vertex in the sides IJ and IH of triangle IJH.

Hence, ∠I ≅ ∠F will be the required information to prove that △FGE ~ △IJH by the SAS similarity theorem.

The other information needed to prove that △FGE ~ △IJH by the SAS similarity theorem will be  ∠I ≅ ∠F

The ratio of similar sides of similar triangles are equal.

According to the given question, the angle F serves as a common vertex with the sides GF and FE of triangle FGE and also I serve as the common vertex with the sides IJ and IH of triangle IJH.

The other information needed to prove that △FGE ~ △IJH by the SAS similarity theorem will be  ∠I ≅ ∠F

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The solution to the quadratic equation x² + 4x + 4 = 0 is x = -2 and x = -2

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The standard form of a quadratic equation is:

y = ax² + bx + c

Where a, b and c are constants

Given the quadratic equation:

x² + 4x + 4 = 0

x² + 2x + 2x + 4 = 0

x(x + 2) + 2(x + 2) = 0

(x + 2)(x + 2) = 0

x + 2 = 0; and x + 2 = 0

x = -2 and x = -2

The solution to the quadratic equation is x = -2 and x = -2

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Answer:

option A by symmetry of figure.and then using formula of triangle and rectangle.

Answer: 8

Step-by-step explanation: Divide 224 by 28

Answer:

??

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Firstly we find the x value. x-7=0; x=7

Secondly we introduce x value in 1st ecuation. So

(7-3)^2 +(y+1)^2=16, 16+y^2+2y+1=16,

Consider this ecuation: y^2+2y+1=0

y1=( -b+Δ)/ 2a, y2= (-b-√Δ)/2a, Δ=√b^2-4ac=√4-4=0

y1,2= -2/2= -1  

1 Real solution x=7 and y= -1.

Answer:

8 > u > 6

Step-by-step explanation:

We have to solve this inequality as 2 separate inequalities.

==============================================================

Inequality 1 :

⇒ 10 > 5u/4

⇒ 5u < 10 × 4

⇒ 5u < 40

⇒ u < 8 [Box 1]

============================================================

Inequality 2 :

⇒ 5u/4 > 15/2

⇒ 5u/2 > 15

⇒ u/2 > 3

⇒ u > 3 × 2

⇒ u > 6 [Box 2]

============================================================

Solution :

⇒ 8 > u > 6

The probability that individual ii-2 exhibits the disease given a 75% penetrance is 0.75 or 75%.

Penetrance refers to the probability of an individual expressing a particular trait or disease given their genetic makeup. In this case, the penetrance of the disease is 75%, which means that there is a 75% chance that an individual with the genetic mutation for the disease will actually exhibit the disease. Therefore, the probability that individual ii-2 exhibits the disease given this penetrance is also 0.75 or 75%.

1. Penetrance is the probability that an individual with a specific genotype will express the associated phenotype or disease.
2. In this case, the penetrance of the disease is 75%, which means there is a 75% chance that an individual with the disease-associated genotype will exhibit the disease.
3. Given this penetrance, the probability that individual ii-2 exhibits the disease is 0.75 or 75%.

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