two angles form a linear pair. one angle measure is 36° more than the other. find both angle measures.​

x=7

Step-by-step explanation:

median is the middle no.=6 and x

it will be 6+x=13

take 6 to the other side=7, hence x=7

Answer:

105°

Step-by-step explanation:

X and 75 has to add up to 180

so 180 - 75 = 105°

Answer:

20+r +r = 256

Step-by-step explanation:

Let r = rabbits

c = chickens

c = 20 +r  since there are 20 more chickens than rabbits

Together there are 256

c+r = 256

Replacing c with 20+r

20+r +r = 256

The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4.

A box plot, also known as a box-and-whisker plot, is a graphical representation of numerical data that displays the distribution of a dataset. It provides a visual summary of the minimum, first quartile, median, third quartile, and maximum values, as well as any outliers that may be present.

To construct a box plot from the given data (diameters of cans in an assembly line: 5.7, 5.6, 5.1, 5.4, 5.2, 5.6, 5.7, 5.3, 5.8, 5.2), follow these steps:

1. Sort the data in ascending order: 5.1, 5.2, 5.2, 5.3, 5.4, 5.6, 5.6, 5.7, 5.7, 5.8.

2. Find the median (middle value) of the dataset, which is 5.4.

3. Determine the first quartile (Q1), which is the median of the lower half of the data. In this case, it is the median of the numbers below 5.4: 5.2.

4. Find the third quartile (Q3), which is the median of the upper half of the data. In this case, it is the median of the numbers above 5.4: 5.7.

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 5.7 - 5.2 = 0.5.

6. Identify any outliers in the dataset. Outliers are values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. In this case, there are no outliers.

7. Construct the box plot using a number line. Draw a box from Q1 to Q3, with a line inside representing the median. Add whiskers (lines) extending from the box to the minimum value (5.1) and the maximum value (5.8).

The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4. The whiskers would extend from 5.1 to 5.8. This visual representation provides an overview of the distribution and key statistical measures of the diameters of cans in the assembly line.

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Answer:

Sum of Interior Angles = (Number of Sides -2) • 180 degrees

Sum = (12 -2) * 180

Sum of the interior angles = 1,800 degrees

Source:  http://www.1728.org/polygon.htm

Step-by-step explanation:

Answer:

y==1/4

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Answer:

The second method is correct because in the first method she eliminates a solution by dividing through by x and assuming she graphed correctly, the solutions she gave are correct.

Step-by-step explanation:

Answer:

Yes she's correct

Step-by-step explanation:

Let's check

Cancel one x

Another root is 0

So as a quadratic equation it's correct

The probability of picking a card less than 7 from a standard deck of cards is 2/13.

To find the probability (P) of picking a card less than 7, we need to determine the number of favorable outcomes (cards less than 7) and divide it by the total number of possible outcomes.

In this case, the favorable outcomes are the cards with values less than 7, which are 5 and 6. The total number of possible outcomes is the total number of cards in the deck, which depends on the specific deck being used.

Assuming a standard deck of 52 cards, there are four 5s and four 6s, making a total of eight favorable outcomes.

Therefore, P(less than 7) = favorable outcomes / total outcomes = 8 / 52.

Simplifying the fraction, we find that P(less than 7) = 2 / 13.

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Answer:

R = 35.0

Step-by-step explanation:

We know tan theta = opp/ adj

tan R = r/s

tan R = 7/10

Take the inverse tan of each side

tan ^-1 tan (R) = tan ^-1 (7/10)

R =34.9920202

R = 35.0

Answer:

A. 35º

Step-by-step explanation:

Answer:

Answer 10 to the power of 4

Step-by-step explanation:

10 to the power of 6 = 1000000 and 10 to the power of 2 = 100, so if you divide them you get 10000 which is 10 to the power of 4

Answer:  

10³

Step-by-step explanation:  

Don mind the ten just look at the numbers above the ten. Well what is 6 divided by 2 answer 3 so your answer would be 10³.

Answer:

See below

Step-by-step explanation:

\(1\cdot24=2\cdot12=3\cdot8=4\cdot6=24\)

Answer:

1. 24

2. 12

3. 8

4. 6

Step-by-step explanation:

2 x 12 = 24, 3 x 8 = 24, 4 x 6 = 24

The study described is a retrospective study.

A retrospective study, also known as a historical study, involves the collection and analysis of data from past events or behaviors. In this case, the study involves collecting and analyzing data on the different types of shoe designs by the designer Calvin Klein over the years from 1987 to 2014. The data has already been collected in the past, and the researcher is analyzing it to draw conclusions or make inferences about the shoe designs.

In contrast, a cross-sectional study involves the collection of data from a population at a specific point in time, while a prospective study (also known as a longitudinal study) involves the collection of data over a period of time to observe changes or trends in a population. An experiment involves the manipulation of one or more variables to observe their effect on a dependent variable, with the aim of establishing cause-and-effect relationships.

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Inferential statistics is one of the three basic ways of explaining the results of a research investigation. Group of answer choices Comparing variable quantities Graphing relationships between variables Comparing group percentages Making precise statements about data by correlating the scores of individuals on two variables.

Making precise statements about data by correlating the scores of individuals on two variables is one of the three basic ways of explaining the results of a research investigation.

This is also known as inferential statistics, which involves making predictions or generalizations about a larger population based on sample data.

The other two basic ways of explaining research results are descriptive statistics, which involves summarizing and describing the characteristics of a sample, and graphical representation, which involves using visual aids to display data and relationships between variables.

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Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.

Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:

x + kx + lx = 2r

Simplifying this equation, we get:

x(1 + k + l) = 2r

So, we have:

x = (2r)/(1 + k + l)

y = kx = k(2r)/(1 + k + l)

z = lx = l(2r)/(1 + k + l)

The circumference of the triangle is the sum of its three sides:

C = x + y + z

Substituting the expressions for x, y, and z, we get:

C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)

Simplifying this expression, we get:

C = (2r(1 + k + l))/(1 + k + l)

C = 2r

Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.

Let the lengths of the triangle be, 3x,4x,5x

Square of largest side = \(25x^{2}\)

Sum of square of other sides = \(3x^{2} + 4x^{2} = 25x^{2}\)

It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.

The circumference of a right-angled triangle has a diameter equal to its hypotenuse.

hence, 5x=6 or x= \(\frac{6}{5}\)

Now, two perpendicular sides are then,  \(\frac{18 }{5} , \frac{24}{5}\)

\(Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64\)

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Question

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

A. 8.64

B. 12

C. 6

D. 10.5

f(t) = (t + 7)^2 / t

To solve this problem, we need to simplify the expression on the left-hand side and then equate it with the expression on the right-hand side.

First, we can factor the denominator of the left-hand side using the quadratic formula:

S^2 + 14s + 49 = (S + 7)^2

So,

S/S^2+14s+49 = S/(S + 7)^2

Now, we can equate this with the expression on the right-hand side:

S/(S + 7)^2 = FI/(s + 7)

To solve for FI, we can cross-multiply:

S(FI) = (S + 7)^2

FI = (S + 7)^2 / S

To find f(t), we simply substitute t for S in the expression for FI:

f(t) = (t + 7)^2 / t

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The graphs are identified as follows

1. the domain is option G

2. the range is option E

3. the domain is option D

4. the range is option C

In coordinate geometry, the domain and range are concepts used to describe the set of possible inputs (x-values) and outputs (y-values) of a function, respectively.

The domain of a function is the set of all possible x-values for which the function is defined. In other words, it is the set of all values that can be plugged into the function and produce a meaningful output.

The range of a function is the set of all possible y-values that the function can take on as x varies over its domain. In other words, it is the set of all values that the function can output.

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Using the properties of exponents we can write the given expression as \(x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}\). Therefore, option E is the correct answer.

The given expression is \(\frac{\sqrt{x^3} \sqrt{y^5} }{\sqrt[3]{z^2} }\).

We can square root as 1/2.

So the expression becomes \(\frac{x^\frac{3}{2} y^\frac{5}{2} }{z^\frac{2}{3} }\)

=  \(x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}\)

Therefore, option E is the correct answer.

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The supplement of the angle that measures 112 degrees is 68 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

In other words, two angles are supplementary when they add up to 180 degrees.

Therefore,

let the other supplement  = x

Hence,

x + 112 = 180

x + 112 = 180

subtract 112 from both sides of the equation

x + 112 - 112 = 180 - 112

x = 68 degrees

x = 68 degrees

Therefore, the supplement of the angle that measures 112 degrees is 68 degrees.

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Answer:

(5, 20)  

Step-by-step explanation:

We can find the slope of the line

m = (y2-y1)/(x2-x1)

  = (40-0)/(10-0)

  = 40/10

  =4

Since the line goes through (0,0) the y intercept is 0

y = mx+b

y = 4x

Lets check the points  by substituting into the equation

40, 10)     10 = 4*40   10 =160  no

(–5, –10)    -10 = 4*-5    10 = -20   no

(5, 20)       20 = 4*5    20 = 20  yes

(–10, –20)    -20 = 4*-10    -20 = -40   no

Answer:

l:6   w:9

Step-by-step explanation:

       54        

 1          54

 2         27

 3          18

 6          9

Answer:

126

Step-by-step explanation:

Blue : White =  21 : 4

(ratio of Blue/ sum of ratio) * total marbles

This gives us the number of blue marbles

so:

21/25 * 150 = 126

Therefore the total number of blue marbles is 126

Answer: 126 blue marbles

Step-by-step explanation:

We don't know how many marbles there are, so we can call it x. 21 of a certain number of blue marbles, plus 4 of a certain number of white marbles is 150.

1. Make an equation: 21x+4x=150

2. Simplify. 25x=150

3. Divide to both sides. x=6

4. Plug in 6 to the ratio. 21 x 6=126 blue marbles

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

A. (7, 5)

Step-by-step explanation:

Plug each set into line equation, and A. is the only one that makes both sides equal.

5 - 5 = 6 (7 - 7)

0 = 0

The polynomials listed, x² - 36, x² + 16, x² - 7x + 12, and x² - x - 20, are all examples of polynomials that are not prime.

None of the polynomials listed are prime, as prime numbers are only divisible by 1 and themselves, while polynomials are mathematical expressions that can have multiple factors. However, some of these polynomials may have prime factorizations. For example, the polynomial x²- 7x + 12 factors into (x - 4)(x - 3), which are both prime numbers.

A prime number is a number that is only divisible by 1 and itself. Polynomials, on the other hand, are mathematical expressions that can have multiple factors. In general, polynomials are not prime numbers and cannot be expressed as the product of two or more smaller polynomials. For example, x² - 7x + 12 can be factored as (x - 4)(x - 3), but it cannot be expressed as a product of two smaller polynomials. The polynomials listed, x² - 36, x² + 16, x² - 7x + 12, and x² - x - 20, are all examples of polynomials that are not prime, as they can be factored into multiple terms. However, some of the terms in their factorizations may be prime numbers.

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Complete question is in the image attached

Answer:

It's B (x2+6)

Step-by-step explanation:

I'm just chill like that

We need to know the shape of the figure and/or additional information to solve this problem.

Firstly, we need to know how many sides the shape has in order to find the difference between the longest and shortest sides. Assuming it's a quadrilateral, we can use the formula: perimeter = sum of all sides.

Let's say the four sides are a, b, c, and d. We know that a + b + c + d = 22.

To find the difference between the longest and shortest sides, we need to find the values of a and d. However, we don't have enough information to do this.

Without more information, we cannot find the answer to your question. Perhaps there was a mistake in the problem statement, or more information needs to be provided.

In summary, we need to know the shape of the figure and/or additional information to solve this problem.  

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Answer:

A

Step-by-step explanation:

Answer:

(a) 4.875 minutes

(b) 1.86 minutes

Step-by-step explanation:

The length of fence = 150 feet.

Rate of painting by Tyler = 11ft/min

Rate of painting by Benito = 15ft/min

(a) Let after time t minutes  both have painted equal number of feet.

As Taylor has already painted 19.5 feet. So,

\(15t=19.5+11t\)

\(\Rightarrow 4t=19.5\)

\(\Rightarrow t=\frac{19.5}{4}\)

\(\Rightarrow t=4.875\) minutes.

(b)The length of fencs to be painted by Tylor=150-19.5=130.5 feet.

So. time taken by Tylor to finish the painting

\(=\frac{130.5}{11}=11.86\) minutes.

Time taken by Benito to finish the painting

\(=\frac{150}{15}=10\) minutes

Here, tome taken by Benito is less, so Benoto finishes first.

Benoto will get the time to rest for 11.86-10=1.86 minutes.

Answer:

3) The value of k is 8. 5) The slope of the line y=-17x+47/3 is -17.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(k-5)/(2-1)

m=(k-5)/1

m=k-5

k-5=3

k=3+5

k=8

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

5) y=mx+b where m=slope and b=y-intercept.

On solving the system of equations 1x + 4y = 73 and 9x + 5y = 192, the value for one plain and one shiny wrapping paper is obtained as $13 and $15 respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let the cost of plain wrapping paper be x.

Let the cost of shiny wrapping paper be y.

Stephanie sold 1 roll of plain wrapping paper and 4 rolls of shiny wrapping paper for a total of $73.

The equation for Stephanie is -

1x + 4y = 73 ..... (1)

Aliyah sold 9 rolls of plain wrapping paper and 5 rolls of shiny wrapping paper for a total of $192.

The equation for Aliyah is -

9x + 5y = 192 ....... (2)

Multiply equation (1) by 9 -

9x + 36y = 657 ....... (3)

Subtract equation (2) form (3) -

9x + 36y - (9x + 5y) = 657 - 192

9x + 36y - 9x - 5y = 465

31y = 465

y = 465 / 31

y = 15

Therefore, the cost of one shiny wrapping paper is $15.

Substitute the value of y in equation (1) -

1x + 4(15) = 73

x = 73 - 60

x = 13

Therefore, the cost of one plain wrapping paper is $13.

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