61 = 7 - 6x
this is 8th grade math ​

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5

We have to given that;

the terminal side of theta in standard position contains the point (6,-8)

Hence, For given condition we get;

The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

Here, x = 6, y = - 8

Hence, We get;

r = √x² + y²

r  = √6² + 8²

r = √36 + 64

r = √100

r = 10

So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,

cos θ = x / r

cos θ = 6 / 10

cos θ =  3 / 5

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The correct transformation that describes why rectangles ABCD and A′B′C′D′ are similar is Rectangle ABCD was dilated by a scale factor of 5 to form rectangle A′B′C′D′.

Dilation is a transformation that changes the size of an object while maintaining its shape. In this case, the coordinates of rectangle ABCD were multiplied by a scale factor of 5 to obtain the coordinates of rectangle A′B′C′D′.

This means that each side length of rectangle ABCD was multiplied by 5 to get the corresponding side length of rectangle A′B′C′D′.

The reflection across the y-axis and the rotation of 90° counterclockwise would result in different shapes and orientations, not maintaining the similarity between the two rectangles.

The dilation by a scale factor of 15 or 1/5 would also change the proportions and not result in a similar rectangle.

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9514 1404 393

Answer:

Step-by-step explanation:

Usually, we write an equation for each side of the inequality.

Left-side equation:

  y = x^2 +6x

Right-side equation:

  y = x^2

So, the system of two equations in two variables is ...

_____

Additional comment

The solution of this system is (x, y) = 0.

Carlos

Alberto Ricarlos

Answer:63 games

Step-by-step explanation:

Answer:

I think its A ratio reduced, since a scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

Answer:

It isn't either of the first two. My best guess would be the units of a ratio, (sorry if it's actually a ratio reduced). It's worded very weirdly

Answer:

Step-by-step explanation:

Given that:

A list of 25 recently sold paintings in an auction house is available, and eight artists were represented in the sales.

The objective is to determine if the correlation coefficient would be an appropriate way to summarize the relationship between the artist (x) and sale price (y).

From the information given;

NO, The correlation coefficient would not be an appropriate way to summarize the relationship between artist (x) and sale price (y).

The reason is being that since variable (x) is the artist and which is regarded as the categorical variable even though it is attributed to numerical values, it cannot and will not be used in quantitative studies like correlation.  

The length of AB is 0.605 units and it is derived from both the point (1, -2) and line 2y + 3x = 6.

Length of AB is the distance between point A and point B and we need to determine the coordinates.

Let's find the equation of the line parallel to the given line:

2y + 3x = 6

[Note: two parallel lines will have the same slope]

Express the equation in straight line form as:

2y = -3x + 6

y = (-3/2)x + 3

Now, let's find the equation of the line passing through the point (1, -2) with a slope of -3/2. We can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

where

(x₁, y₁) = (1, -2)  

m = (-3/2).

Substitute the values

y - (-2) = (-3/2)(x - 1)

y + 2 = (-3/2)x + 3/2

y = (-3/2)x + 3/2 - 2

y = (-3/2)x - 1/2

Now, to find point A, we need to determine where the line intersects the x-axis.

Set y = 0 0 = (-3/2)x - 1/2

(3/2)x = -1/2

x = (-1/2) * (2/3)

x = -1/3

So, point A is (-1/3, 0).

Next, to find point B, we need to determine where the line intersects the y-axis.

Set x = 0

y = (-3/2)(0) - 1/2

y = -1/2

So, point B is (0, -1/2).

Now, the distance between points A and B is given as:

d = \(\sqrt{(x_{2} - x_{1} )^2 + (y_{2} - y_{1} )^2}\)

d = \(\sqrt{(0 - (-1/3)^2 + (-1/2 - 0)^2}\)

d = \(\sqrt{((-1/3)^2 + (-1/2 )^2}\)

d = \(\sqrt{-1/9 + 1/4}\)

d = \(\sqrt{13/36}\)

d = 0.605

Therefore, the length of AB is approximately 0.605 units.

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The sum of the first 31 terms of the arithmetic series is 114.

What is arithmetic series?

In mathematics, arithmetic series is the sequence of the number whose common difference between the two consecutive number is always constant. And the sum of the series is depend on the first term as well as on the last term.

According to the question, the given series is an arithmetic series. In the common difference is same.

The given series is:

4, 11, 18,....4, 11, 18,....4, 11, 18,....

To know the sum of the given series, first calculate the sum of the first three numbers. And later multiply by ten.

Using standard formula for the sum of the arithmetic series:

\(S_{3} =\frac{(first term + last term)}{2} = \frac{4+18}{2} =11\)

Therefore to calculate the sum of the 31 terms:

s(31 terms) = 10(11) + first term = 110 + 4 = 114

Hence, the sum of the first 31 terms of the arithmetic series is 114.

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Step-by-step explanation:

sin theta = 12/13

cos theta = 5/13

tan theta = 12/5

cosec theta = 13/12

sec theta = 13/5

cot theta = 5/12

Fun fact:

The longest word in any of the major English language dictionaries is pneumonoultramicroscopicsilicovolcanoconiosis, a word that refers to a lung disease contracted from the inhalation of very fine silica particles, specifically from a volcano; medically, it is the same as silicosis.

Cool right? Here are more fun facts.

1 “I am” is the shortest complete sentence in the English language.

2 Supercalifragilisticexpialidocious (*breath*) is NOT the longest word in English.

Like that?

Banging your head against a wall for one hour burns 150 calories.

In Switzerland it is illegal to own just one guinea pig.

The total number of pencils that is available all together = 684 pencils.

Number of boxes of pencils found = 12

Each box contains = 12 pencils

The total number of students = 54

Each student brought = 10 pencils

The total number of pencils all together = Total number of pencils from all students + total number of pencils in all boxes

Total number of pencils in all boxes:

Total number of pencils from all students:

The total number of pencils all together = 144 + 540

The total number of pencils that is available all together = 684 pencils

The derivative of the function \(y = 5^x + e^7\) with respect to 'x'

is  \(\frac{dy}{dx} = 5^xln5 + 0\).

Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function also known as the slope.

We know, \(\frac{dy}{dx} a^x = a^xlna\), where 'a' is a constant.

Given, \(y = 5^x + e^7\).

Now, The derivative of the function with respect to 'x' is,

\(\frac{dy}{dx} = 5^xln5 + 0\), As \(e^7\) is a constant, and the derivative of any constant term is zero because the slope of a constant term is zero.

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Answer: 12

Step-by-step explanation: 35 - 23

Answer:

472.2 km

Step-by-step explanation:

Answer:

3 balls of wool

Step-by-step explanation:

8/4=2

6/2=3

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Answer: No. Zeke found the LCM to be the product of two and eight but because eight is a multiple of two the LCM is eight so the first day he will have both clubs is the 8th day of the month

Step-by-step explanation:

all you have to do is fine the least common multiple of 2 and 8 which is eight so obviously zeke is incorrect because they said the least common multiple was 16 and it is not. zeke multiplied 2 and 8 which is not what you’re supposed to do to get the lcm.

Answer:

28 yd²

Step-by-step explanation:

finding the area of a triangle is (base * height) / 2.

(14*4)=56

56/2=28

The surface area of the triangular prism is 137ft².

To get the surface area of a triangular prism, we will calculate the area of each face and then sum them up.

Base area = (4 ft * 5 ft) / 2

Base area = 20ft/2

Base area = 10 ft²

Since triangular prism has two triangular bases, the total area of the triangular bases is:

= 2 * Base area

= 2 * 10 ft²

= 20 ft².

Perimeter of the triangular base:

= 4 ft + 5 ft + 4 ft

= 13 ft

Face area = Perimeter * Height

Face area = 13 ft * 3 ft

Face area = 39 ft²

The total area of the rectangular faces is:

= 3 * Face area

= 3 * 39 ft²

= 117 ft².

The Surface area of the triangular prism will be:

= Total area of triangular bases + Total area of rectangular faces

= 20 ft² + 117 ft²

= 137 ft².

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The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

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To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Answer:

A. Bin(40,0.65)

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have a cell phone, or they do not. The probability of an adult having a cell phone is independent of any other adult having a cell phone. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

In function of its parameters, the distribution is written as: Bin(n,p).

The proportion of adults who own a cell phone in a certain Canadian city is believed to be 65%

This means that \(p = 0.65\)

Forty adults are to be selected at random from the city.

This means that \(n = 40\).

Thus, we have Bin(40,0.65), and the correct answer is given by option A.

Answer:

3(C + 5) = 7

Step-by-step explanation:

Let C = unknown number

The sum of a number and 5:

C + 5

Three times the sum of a number and 5:

3(C + 5)

Three times the sum of a number and 5 is 7:

3(C + 5) = 7

To solve

Use the distributive law:  a(b + c) = ab + ac

⇒ 3C + 15 = 7

Subtract 15 from both sides:

⇒ 3C = -8

Divide both sides by 3:

⇒ C = -8/3

So

The expression is

On solving

The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

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Answer: Diameter: 8

              Area:  201.1

Step-by-step explanation:

Diameter: Use the formula for the area of a circle:

Use the formula for the area of a circle:

A=πr2

Here, the area is 16π:

16π=πr^2

Divide both sides by  π:

16=r^2

Take the square root of both sides:  √16=√r^2

4=r

Since the radius of the circle is 4, the diameter is twice that:

d=4×2=8

Area:

Formula:

A = π r^2

A= Area R= Radius

Add Radius

A= π 8^2

Solve:

Simplify  π⋅8^2

Exact Form:

A=64π

Decimal Form:

A=201.06192982

Answer: 137 lies between 136 and 138

Hope this helps!!

Answer:

11 and 12

Step-by-step explanation:

The square root of 137 lies between 11 and 12 because 11^2 = 121 and 12^2 = 144. 137 lies between 121 and 144.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

 ~ ren ⚘

The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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The 25% of the shaded checker board has pieces on it.

To check that, we need to solve the expression below:

Percent = 100%*(# shaded squares with pieces)/(total # of shaded squares)

There are a total of 32 shaded squares, and in 8 of them we can see pieces, then we can replace these values in the formula above to get:

Percent = 100%*(8/32) = 25%

That is the percent of the shaded checker that has pieces.

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