Write an equation of the line that passes through (−5, −1) and is parallel to the line y = 4x − 6.

The required solution of the equations is given as (2, 3, 0).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
So we are given a system,
3x -2y + 3z = 0
-3x-5y-5z = -21

Substitute x =2, and we get the system,
-2y + 3z = -6
-5y -5z = -15

Multiply equation 1 by -5 and equation 2 by 2 we get the system,
10y - 15z = 30
-10y -10z = -30

Adding the above equations,
z = 0

Now,
-2y = -6
y = 3

Thus, the required solution of the equations is given as (2, 3, 0).

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the car is approximately 22.4 meters away from the tower.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

we can write:

tan(55 degrees) = 32 / d

To solve for "d", we can rearrange the equation:

d = 32 / tan(55 degrees)

Using a calculator, we can evaluate the tangent of 55 degrees:

tan(55 degrees) = 1.428

d = 22.4 meters

Therefore, the car is approximately 22.4 meters away from the tower.

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A tessellation is a pattern made by repeating geometric shapes without any gaps or overlaps. These shapes, called tiles or polygons, fit together perfectly to cover a plane or a surface. Tessellations can be found in various forms of art, architecture, and design. They are used to create visually appealing patterns and decorations, as well as to explore mathematical concepts.

Tessellations are utilized in various practical applications, such as tiling floors, walls, and pavements, designing mosaics and quilts, and creating computer graphics and textile patterns. They are also studied in mathematics to understand concepts like symmetry, geometry, and transformations.

For polygons to tessellate, certain conditions must be met at their vertices. At each vertex, the angles formed by the polygons must add up to a whole number of degrees, typically 360 degrees. In other words, the sum of the interior angles of each polygon meeting at a vertex must be a multiple of 360 degrees.

This ensures that the polygons can fit together seamlessly without leaving any gaps or overlaps. Examples of polygons that tessellate include equilateral triangles, squares, and hexagons, as their angles add up to 360 degrees at each vertex.

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A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

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Answer:

17

Step-by-step explanation:

At a store;

PRICE OF GREEN APPLES:

Then, a pound of green apples cost:

But;

PRICE OF RED APPLES:

Then, a pound of red apples cost:

Thus, GREEN APPLES are cheaper.

Answer:

719.95392

the final answer is this

so you round it off to where you want

Answer:

t= 2p+5/p-1

Step-by-step explanation:

The question is not well writen

Assume p = t+5/t-2

We are to make t the subject of the formula

Cross multiply

p(t-2) = t+5

pt - 2p = t+5

pt - t = 2p+5

t(p-1) = 2p+5

t= 2p+5/p-1

Hence the value of t is 2p+5/p-1

The values that used to create the box and whisker plot

[using these values]

Minimum value: Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

Here, we have,

Step 1: Order the data set from smallest to largest:

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

Step 2: Calculate the lower quartile (Q1), median (Q2), and upper quartile (Q3):

Q1 (25th percentile): The value that separates the lowest 25% of the data from the rest. Since we have 10 data points, the first quartile will be the average of the 2.5th and 3.5th data points. In our case, it's the average of the 2nd and 3rd data points:

Q1 = (19 + 28) / 2 = 23.5

Q2 (50th percentile or median): The value that separates the lowest 50% of the data from the rest. Since we have an even number of data points, the median will be the average of the 5th and 6th data points:

Q2 = (34 + 38) / 2 = 36

Q3 (75th percentile): The value that separates the lowest 75% of the data from the rest. Since we have 10 data points, the third quartile will be the average of the 7.5th and 8.5th data points. In our case, it's the average of the 7th and 8th data points:

Q3 = (45 + 47) / 2 = 46

Step 3: Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 46 - 23.5 = 22.5

Step 4: Determine the whiskers:

Lower whisker: The smallest value that is not smaller than Q1 - 1.5 * IQR

Upper whisker: The largest value that is not larger than Q3 + 1.5 * IQR

Lower whisker limit: 23.5 - 1.5 * 22.5 = -10

Upper whisker limit: 46 + 1.5 * 22.5 = 79.5

Our data points are all within these limits, so the lower whisker is at the smallest value, 12, and the upper whisker is at the largest value, 56.

Now, you can plot the box and whisker plot using these values:

Minimum value : Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

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create a box and whisker plot for the following set of data

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

The Binomial probability of x = 3 for the given parameters is 0.2048

The Binomial probability relation can expressed as :

\(P(x) = nCx * p^{n} * q^{n-x}\)

where :

for x = 3

We substitute x into the equation thus :

P(x = 3) = 17C3 * (1/8)³ * (1 - 1/8)¹⁴

P(x = 3) = 0.2048

Therefore, the probability of x = 3 in the scenario given is 0.2048

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Answer:

n=1

Step-by-step explanation:

-2(6 - 3n) + 27n = -3(n - 8)

-12+6n+27n=-3n+24

-12+33n=-3n+24

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

33n=-3n+36

+3     +3

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

36n=36

----    ----

 n=1

Clara's and Stefan's pizzas did not have the same ratio of pepperoni pieces to ham pieces.

For Clara,

The number of pepperoni pieces = 4

The number of ham pieces = 6

The ratio = 4:6 = 2:3

For Stefan,

The number of pepperoni piece = 6

The number of ham piece = 10

The ratio = 6:10 = 3:5

Therefore the ratio of Clara's and Stefan's pizzas is not the same.

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student 3 i thin srry if im wrong

Answer:

student 3

Step-by-step explanation:

Answer:

negative 400 over 9−  

400

9

=negative 44 and 4 over 9− 44

4

9

≈negative 44.444−44.444

Step-by-step explanation:

The function which represents the graph is : D. y = 3sin(x)

"A function is an expression which assigns each element of X to exactly one element of Y from a set X to a set Y."

"The graph of a function f is the set of all points in the plane of the form (x, f(x))."

"The graph of y=sin(x) is like a wave that oscillates between -1 and 1, in a shape that repeats itself every 2π units.

Also, the graph of sine function passes though origin, as sin(0) = 0 ."

"The graph of y=cos(x) is like the graph of y=sin(x) but shifted horizontally by π units"

From given graph, we can observe that the graph must be of sine function.

Also, given graph represents the graph of y = sin(x) expanded 3 times.

So, the function which represents the graph is, y = 3sin(x).

Hence, the correct answer is option D. y = 3sin(x)

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Answer:

50 text messages would have to be sent or received in order for the plans to cost the same each month.

Step-by-step explanation:

x = number of text messages sent

0.2x+40=50

0.2x = 10

5(0.2x) = 5(10)

x = 50

Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.

Answer:

It should be 42.4

the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

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Answer:

r = 18 cm

Step-by-step explanation:

The formula for the circumference of a circle is 2πr.

Hence,

2πr = 36π

r = 18 cm

Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

Answer:

m∠A = 49°

Step-by-step explanation:

According to Angle Sum Property,

m∠A

Answer:

5 (less than sign) 2

Step-by-step explanation:

Answer:

5n-20

Step-by-step explanation:

Product means multiply and so the product of 5 and n is 5n. To decrease this value by 20 , means to subtract 20 from it hence: 5n - 20 is algebraic expression for the statement

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

Answer:

The answer is

\( \frac{3}{2} \\ \)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(1,-4) and (3,-1)

The slope is

\(m = \frac{ - 1 - - 4}{3 - 1} = \frac{ - 1 + 4}{2} = \frac{3}{2} \\ \)

We have the final answer as

\( \frac{3}{2} \\ \)

Hope this helps you

The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

The required details for null hypothesis in given paragraph

The null hypothesis and alternative hypothesis in this case would be:

H₀: The distribution of hockey players' birth months is uniformly distributed.

H₁: The distribution of hockey players' birth months is not uniformly distributed.

The expected counts for each birth month can be calculated as follows:

Expected Count = (Total Number of Players) * (Proportion of Total Players for Each Birth Month)

Since there are 4 birth months and the distribution is assumed to be uniform, the proportion of total players for each birth month is 1/4 = 0.25. Therefore, the expected count for each birth month is:

Expected Count = 188 * 0.25 = 47

To test the null hypothesis, we can then calculate the chi-square statistic using the following formula:

χ² = ∑((O - E)² / E)

where O is the observed count, E is the expected count, and the sum is taken over all birth months.

Plugging in the observed and expected counts, we get:

χ² = ((66 - 47)² / 47) + ((59 - 47)² / 47) + ((34 - 47)² / 47) + ((29 - 47)² / 47)

= 3.87 + 2.04 + 3.87 + 5.57

= 15.35

In this case, df = 3.

Looking up the critical value in the chi-square table with df = 3 and a = 0.05, we find that the critical value is 7.815. Since the chi-square statistic (15.35) is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to suggest that the distribution of hockey players' birth months is not uniformly distributed.

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The likelihood of an event is expressed as a number between zero (the event will never occur) and one (the event is certain). For example, the probability of an outcome of heads on the toss of a fair coin is ½ or 0.5.

A single toss of a coin is an event (also called a trial) that is not connected to or influenced by other events. When a coin is tossed twice, the coin has no memory of whether it came up heads or tails the first time, so the second toss of the coin is independent.

In this case we don't have two consecutive tosses, we instead flip two coins. Nevertheless the same rule stated above apply for this case.

Now the proability of something to happen is always 1, this means that the sum of all the possible outcomes have to be equal to 1.

We also need to remember the Product Rule. This states that the probability of the occurrence of two independent events is the product of their individual probabilities. The probability of getting two heads on two coin tosses is 0.5 x 0.5 or 0.25.

With this in mind it is easier to think of this problem like this: The probability of getting one or more heads is equal to 1 minus the probability of obtaining two tails. But this last proability is equal to 0.5 x 0.5=0.25; therefore the probability we are looking for is:

Hence the probability of obtaining one head or more is 0.75.

Answer:

C = 31.4159

A = 78.5398

Step-by-step explanation:

diameter = 10

radius = 5

plug into formula: C = 2π5

A = π * 5²

To graph the function g(x) = (x + 2)²2 + 3 on the same coordinate grid as f(x) = x²2, we need to apply a horizontal shift of 2 units to the left and a vertical shift of 3 units up to the graph of f(x).

What are the steps?

Here are the steps to obtain g(x):

Start with the graph of f(x) = x²2 on the coordinate grid.

To apply a horizontal shift of 2 units to the left, subtract 2 from x in the equation of f(x). This gives us f(x + 2) = (x + 2)²2.

The graph of f(x + 2) is shifted 2 units to the left compared to the graph of f(x).

To apply a vertical shift of 3 units up, add 3 to the equation of f(x + 2). This gives us g(x) = (x + 2)²2 + 3.

The graph of g(x) is shifted 2 units to the left and 3 units up compared to the graph of f(x).

Therefore, the function g(x) = (x + 2)²2 + 3 will be obtained by applying a horizontal shift of 2 units to the left and a vertical shift of 3 units up to the graph of f(x) = x²2.

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Answer:

Pull terms out from under the radical, assuming positive real numbers.

0

Step-by-step explanation: