Consider reflections of ΔJKL. What line of reflection maps point K to point K' at (–5, 2)? What line of reflection maps point L to point L' at (–2, 3)?

There are no vectors among the options provided that are parallel to (1²2).

To determine if two vectors are parallel, we can compare their direction ratios.

Two vectors are parallel if their direction ratios are proportional.

Let's compare the given vector (1²2) with each of the options provided:

Vector (7²) (12²) (-22) (3) 12/ (ő) 4 24 3 13/​:

Comparing the direction ratios, we have:

1/7 = 2/12 = 2/-22 = 3/4 = 24/3 = 12/13.

Since the direction ratios of the given vector (1²2) are not proportional to the direction ratios of any of the options, none of the options are parallel to (1²2).

summary, none of the vectors (7²) (12²) (-22) (3) 12/ (ő) 4 24 3 13/​ are parallel to the given vector (1²2).

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The probability of getting an even number is 1/2 while the probability of getting a factor of 6 is 1/6

The probability of an even number

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of even numbers, x = 3

The probability of getting an even number is then calculated as

P(Even) = Number of even numbers/Sample size

This gives

P(Even) = 3/6 = 1/2

The probability of a factor of 6

From the question, the sample space of the number cube is given as

Space = 1, 2, 3, 4, 5, and 6

The above means that

Sample size, n = 6 ---- i.e. the number of observations

Number of factor of 6, x = 1

The probability of getting a factor of 6 is then calculated as

P(factor) = Number of factor of 6/Sample size

This gives

P(factor) = 1/6

Hence, the probability is 1/2 and 1/6

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The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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The domain of the relation is {-9, 1, 3, 8, 9}

All the values that go into a relation or a function are called the domain.

Given is a relation, (-3, -7), (8, -7), (1, 10), (-9, -8) and (9, -6)

The domain of a function or relation is the set of all possible independent values the relation can take.

Hence, the domain of the relation is {-9, 1, 3, 8, 9}

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                                                  (17)

Answer:

\(h(-6) = -457\)            

Step-by-step explanation:

Given the function

\(h(x)= 72 x-25\)

Put \(h = -6\) to in the function

\(h(x)= 72 x-25\)

\(h\left(-6\right)=\:72\left(-6\right)-25\)

           \(=-432-25\)

           \(=-457\)

Therefore,

\(h(-6) = -457\)                            

                                                   (18)

Answer:

\(g(2)=25\)            

Step-by-step explanation:

Given the function

\(g\left(x\right)\:=\:5x^2\:+\:4x\:-\:3\)

\(g\left(2\right)\:=\:5\left(2\right)^2\:+\:4\left(2\right)\:-\:3\)

        \(= 20 + 8 - 3\)

        \(= 25\)

Therefore,

\(g(2)=25\)

The value of A has been illustrated, computed and proven based in the triangle given.

It should be noted that that a triangle is a shape that has three sides and the value of the addition of all the angles are equal to 180°.

Based on the information that's given, it should be noted that the value of angle A, angle B, and angle C will be equal to 180°.

In this case, the following can be deduced:

A = 5x

B = 90°

C = x + 10°

Therefore, A + B + C = 180° (sum of angles in a triangle)

5x + 90 + x + 10 = 180°

6x = 180° - 90° - 10°

6x = 80°

x = 80/6

x = 13 1/3

Therefore, the value of A will be:

= 5x

= 5 × 13 1/3

= 66 2/3

Therefore, A is 66 2/3.

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Answer:

$2415.76

Step-by-step explanation:

\(compound \: interest \: = ({ \frac{10 + 100}{100} })^{5} \times 1500\)

1.6 * 1500 = $2415.76

Answer:

C/7 = 20

Step-by-step explanation:

Answer:

10.72

Step-by-step explanation:

a²+b²=c²

->

25²-16²= y²

625-256=y²

V369=y

y≈ 19.21

x²= 22²-y²

x²= 484-369

x= V115

x≈ 10.72

By using Pythagoras theorem the value of x is, 10.7 units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The figure is shown.

Let the unknown side = y

Now, For upper triangle, we can use Pythagoras theorem as;

⇒ 25² = y² + 16²

⇒ 625 = y² + 256

⇒ y² = 369

⇒ y = √369

⇒ y = 19.2

Hence, The value of x is find as by using Pythagoras theorem as;

⇒ 19.2² + x² = 22²

⇒ 368.6 + x² = 484

⇒ x² = 484 - 368.6

⇒ x² = 115.4

⇒ x = √115.4

⇒ x = 10.7 units

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Answer:

1) 678.24

2)366.333.... repeating

3) 254.34

Step-by-step explanation:

1) 3.14 x 6² = 113.04 ---> 113.04 x 6 = 678.24

2) 3.14 x 5² = 78.5 ---> 78.5 x 14 = 1099 ---> 1099/3 = 366.333.... repeating

3) 3.14 x 9² = 254.34

Answer:

Complementary angles are those that sum up to 90o.Vertical angles have equal measures. Therefore, if vertical angles measure 45o each, they are complementary.

Explanation: Here how it might look if angles ∠1 and ∠3 are measured at 45o.

I think the answer is b

I think the answer is b

I think the answer is b

I think the answer is b

The ratio is (J/W) = 7/6. Or. J= (7/6)• W .

Second line: J= (7/6)• 24. J= 28.

Third line: J= (7/6)• 18. J= 21

Answer:

\(-3(x+3)\)

Factor the expression

\(-3x-9\)

\(-3(x+3)\)

I hope this helps you :D

Answer:

Hello

Step-by-step explanation:

Two different ways are:

–3(x + 3) & 3(–x – 3)

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The formula possible formula for the trigonometric function whose values are in the following table is  y = 6 x sin(π/2 * x) - 4.

Trigonometric functions are described as the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

The formula for a trigonometric function is typically written as :

y = a sin (bx + c) + d

where a, b, c, and d are constants which tells us  the amplitude, frequency, phase shift, and vertical shift of the function, respectively.

From the above table,  the amplitude = 6,

the frequency is 2π/4 = π/2

the phase shift = 0, and

the vertical shift = -4.

Therefore, we can write  the formula for the function as Y = 6 * sin(π/2 * x) - 4.

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Answer: 20

Calculator helps lol

The probability that fewer than 4 are independent = 0.971

Let X be a random variable representing the number of independent people out of 12 people.

Then X follows binomial distribution.

A binomial distribution considers two possibilities in 'n' trials -  success or  failure. Here the case of success is being independent and the case of failure is being either republican or democrat.

The probability distribution function of a binomial distribution is,

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

Where n is the number of trials, p - the probability of success

Here, n = 12

Since 6% of voters are independent, probability of being an independent = 6/100 = 0.06

Probability that fewer than 4 are independent = P( X = 0 or 1 or 2 or 3)

                                                                             = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Now, P(X=0) = ¹²C₀ (0.06)⁰ (1-0.06)¹²⁻⁰

                      = 1 x 1 x 0.4759

                      = 0.4759

P(X = 1) = ¹²C₁ (0.06)¹ (1-0.06)¹²⁻¹

           = 12 x 0.06 x 0.94¹¹

           = 0.3645

P(X = 2) = ¹²C₂ (0.06)² (1-0.06)¹²⁻²

             = 66 x (0. 06)² x 0.94¹⁰

            = 0.128

P(X = 3) =  ¹²C₃ (0.06)³ (1-0.06)¹²⁻³

             = 22 x 0.000216 x 0.94⁹

             = 0.00272

Therefore, Probability that fewer than 4 are independent = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3) =  0.4759 + 0.3645 +  0.128 + 0.00272 = 0.971

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tan(35) = 0.70020753821 = Perpendicular(BC)/Base(AB)

0.70020753821 = BC/15000

BC = 10503 ft.

AC² = AB² + BC²

AC = √15000² + 10503²

AC = √225000000 + 110313009

AC = √335313009

AC = 18311.5 ft

10503 ft is the height of the jet after traveling due east 15,000ft from the point of liftoff and  18311.5 ft is the distance the jet has traveled.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that a jet took off from a runway and flew a constant 35° upward

We have to find the height of the jet after traveling due east 15,000ft from the point of liftoff

We know that tan is the ratio of opposite side and adjacent side

tan(35) = BC/15000

0.70020753821 = BC/15000

BC = 10503 ft.

B) By pythagoras theorem we find the distance the jet has traveled.

AC² = AB² + BC²

AC = √15000² + 10503²

AC = √225000000 + 110313009

AC = √335313009

AC = 18311.5 ft

Hence, 10503 ft is the height of the jet after traveling due east 15,000ft from the point of liftoff and  18311.5 ft is the distance the jet has traveled.

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Answer:

- 1/2

Step-by-step explanation:

In order to find a slope intercept we need to use,

Equation : y= mx + b to find the slope (m)

Answer:

D- Neither graph is a funvtion.

Step-by-step explanation:

A function can only have one input to one output.  These have more than one output for each input.  You can also do the vertical line test, if it touches more than two points at the same time while going horizontally across, it is not a function.

Answer: x= -5

Stexp-by-step explanation:

If you look at the table given, G(x) -20 is alligned with x=-5

The probability that a sample of 60 families from Alberta will have a mean income between $28,000 and $29,500 can be determined by calculating the z-scores corresponding to the given income values and using the standard normal distribution.

To find the probability, we need to convert the income values into z-scores. The z-score measures the number of standard deviations a given value is from the mean. The formula for calculating the z-score is:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the sample mean is $28,500, the population mean is also $28,500, the population standard deviation is $2600, and the sample size is 60. Using these values, we can calculate the z-scores for $28,000 and $29,500.

z1 = (28000 - 28500) / (2600 / sqrt(60))

z2 = (29500 - 28500) / (2600 / sqrt(60))

Once we have the z-scores, we can look up the corresponding probabilities from the standard normal distribution table or use statistical software to find the area under the curve between the two z-scores. This area represents the probability that the sample mean falls between $28,000 and $29,500.

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Answer:

A.

Step-by-step explanation:

when you distribute it you keep the subtraction sign and have to multiply 6 by 50 and then 6 by 1

The standard deviation of a distribution of sample means, also known as the standard error of the mean, is a measure of the variability or dispersion of the sample means from different samples taken from the population.

It is related to the standard deviation of the population and the sample size.When creating a distribution of sample means, each sample mean is calculated by taking a random sample from the population and computing the mean of that sample.

The standard deviation of this distribution, denoted as the standard error, is typically smaller than the standard deviation of the population. This reduction in variability is due to the effect of sample size.

As the sample size increases, the standard error decreases because larger sample sizes provide more representative information about the population, leading to less variability in the sample means. Therefore, the standard deviation of the distribution of sample means is inversely related to the square root of the sample size.

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The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.

In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:

Each term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.

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The full question is:

How many terms are in the following expression 6 + 2 x - 4 y + 5 z

:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.

During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.

According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes

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The function y=540(1.04)^x represents exponential growth. The rate of increase can be determined by finding the value of 1.04^x.

For example, if x=1, then the value of 1.04^1 is 1.04, which represents a 4% increase. If x=2, then the value of 1.04^2 is 1.0816, which represents an 8.16% increase. If x=3, then the value of 1.04^3 is 1.1265, which represents a 12.65% increase.

In general, as the value of x increases, the value of 1.04^x increases at a faster rate, resulting in an exponential growth curve. The percentage rate of increase is determined by the value of 1.04. In this case, the percentage rate of increase is 4% per unit increase in x.

To find the total number of different routes from town A to town C, we can first find the number of different routes from A to B and then multiply it by the number of different routes from B to C. There are 7 different roads between A and B and 4 different roads between B and C. Therefore, the total number of different routes from A to C is 7 x 4 = 28.

(b) To find the total number of different routes from town A to town C and back, we can use the product rule. There are 28 different routes from A to C (as calculated in part a) and 28 different routes from C to A (since we can use any road once in each direction). Therefore, the total number of different routes from A to C and back is 28 x 28 = 784.

(c) To find the total number of different routes from town A to town C and back in part (b) that visit town B at least once, we can use the principle of inclusion-exclusion. There are 28 different routes from A to C and 28 different routes from C to A. However, we need to subtract the routes that do not visit B at all. To find this number, we can use the product rule again, since there are 5 different roads between A and C that do not go through B (2 from A to C and 3 from C to A). Therefore, the number of routes that do not visit B at all is 2 x 3 = 6. So, the total number of different routes from A to C and back in part (b) that visit B at least once is 28 x 28 - 6 = 784 - 6 = 778.

(d) To find the total number of different routes from town A to town C and back in part (b) that do not use any road twice, we can use the principle of permutations. Since we cannot use any road twice, we need to find the number of permutations of the roads. There are 7 roads between A and B, 4 roads between B and C, and 2 roads between A and C. Therefore, the total number of different routes from A to C and back in part (b) that do not use any road twice is 7P2 x 4P2 x 2P2 = 126 x 12 x 2 = 3024.

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