Which type of triangle can be constructed with a 50° angle between two 8-inch sides? A. Equilateral B. Isosceles C. Scalene D. Obtuse.

Answer:

Step-by-step explanation:

m

=

1

;  

n

=

−

2

Explanation:

Given:

4

m

+

n

=

2

-------------------------------Equation (1)

m

−

4

n

=

9

..........................................Equation (2)

Determine the value of n

Showing every step in the first part to demonstrate method

Consider Equation (2)

Add 4n to both sides

m

−

4

n

+

4

n

=

9

+

4

n

But

4

n

−

4

n

=

0

m

=

9

+

4

n

.....................................(3)

Substitute for m in (1) using (3)

4

m

+

n

=

2

→

4

(

9

+

4

n

)

+

n

=

2

Multiply out the bracket

⇒

36

+

16

n

+

n

=

2

36

+

17

n

=

2

Subtract 36 from both sides

17

n

=

−

34

Divide both sides by 17

n

=

−

34

17

=

−

2

'.........................................................

Determine the value of m

Substitute

n

=

−

2

into (2)

m

−

4

n

=

9

→

m

−

4

(

−

2

)

=

9

m

+

8

=

9

m

=

9

−

8

m

=

1

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check

4

m

+

n

=

2

→

4

(

1

)

+

(

−

2

)

=

2

m

−

4

n

=

9

→

1

−

4

(

−

2

)

=

9

Answer: the answer would be

 $ 784.96

Step-by-step explanation:

Answer:

Step-by-step explanation:

The discount rate = 12%

The retail price= $892

The discount = the retail price*the dicount

                      =  12/100*892= $107.4

You'll need a drill bit with a diameter slightly smaller than 0.249325 inches.

A chart or formula can be used to determine the correct drill bit size for a 1/4-20 tap.

The following formula is a common method:

drill bit size = tap's major diameter - (constant x pitch)

The major diameter of a 1/4-20 tap is 0.250 inches, and the pitch (distance between threads) is 0.050 inches. Using 0.0135 as a constant (a common value for coarse threads), the calculation would be:

0.250 drill bit size (0.0135 x 0.050)

Size of drill bit = 0.250 - 0.000675

0.249325 in drill bit size

As a result, you'll need a drill bit with a diameter slightly smaller than 0.249325 inches. In practice, a drill bit size of 7/32 inch would suffice for the majority of applications.

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Answer:

Step-by-step explanation:

true

The length of each side of the octagon with area of 576 square centimeters and an apothem of 16 centimeters is  9  centimeters .

Compared to lower sided shapes, an octagon's area is a little more complicated. A normal octagon's area is equal to 4 as. Where "s" stands for the octagonal side and "a" for the apothem, which runs straight from the pentagon's center to one of its sides.

The formula for the area of a regular octagon is:

A = 4 × apothem × side

Using this formula and the given values, we can solve for the length of each side of the octagon:

576 = 4 × 16 × side

Dividing both sides by 4 × 16, we get:

side = 576 ÷ (4 × 16)

Simplifying the right-hand side, we get:

side = 576 ÷ 64 = 9 cm.

Therefore, the length of each side of the octagon is  9 cm .

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Answer:

Step-by-step explanation:

The amount having half life=27 days  left after 54 days will be 122 gm.

What is a substance's half-life?

When we refer about half life, we mean the time it takes for exactly half of the radioactive material in question to decay.

More specifically, the time it takes for the radioactive material to lose exactly half of its mass.

Now,

As half-life=27 days

initial amount=488 gm

after 27 days, amount=488/2=244 gm

and after next 27 days amount=244/2

=122 gm

So, After 27+27=54 days the left substance will be 122gm of total initial amount=488gm.

hence,

           The amount left after 54 days will be 122 gm.

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The smallest angle θ1 for which a laser beam can undergo total internal reflection on the hypotenuse of a glass prism is 41.8°, expressed with two significant figures

The smallest angle θ1 for which a laser beam can undergo total internal reflection on the hypotenuse of a glass prism can be calculated using the law of total internal reflection. This law states that when a ray of light is incident on the surface separating two media of different refractive indices, the angle of incidence (θ1) must be greater than a certain critical angle (θc) in order for total internal reflection to occur.

Calculating the critical angle of the hypotenuse of a glass prism can be done by using Snell’s Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. In this case, the two media are air and glass, with refractive indices of 1 and 1.5 respectively.

Using Snell’s Law, we can calculate the critical angle of the hypotenuse as θc = sin⁻¹ (1/1.5) = 41.8°.

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Answer:

y = x + 8  (second option)

Step-by-step explanation:

If Chris's age is x , then Stephanie who is 8 years older should be x + 8

y = x + 8

The probability of at least one of the cars starting on a cold morning is 0.84 or 84%.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is used to quantify the chances or odds of a particular event happening or not happening.

In probability theory, the probability of an event is represented as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. The probability of an event that is neither impossible nor certain is represented by a number between 0 and 1, where a probability of 0.5 indicates that the event is equally likely to happen or not happen.

Probability can be calculated using various methods, including empirical or experimental probability, theoretical probability, and subjective probability. Empirical or experimental probability is based on observations or experiments, while theoretical probability is based on mathematical models or formulas. Subjective probability is based on personal beliefs or opinions.

Probability is used in many areas of study, including statistics, economics, engineering, and physics, among others. It is also used in everyday life, such as when making decisions or predicting outcomes. For example, probability can be used to determine the likelihood of winning a game of chance, the chances of an accident happening, or the probability of a disease occurring.

To find the probability of at least one of the two cars starting on a cold morning, we can use the complement rule, which says that the probability of an event happening is equal to 1 minus the probability of the event not happening.

In this case, the event of interest is at least one car starting on a cold morning. The complement of this event is neither car starting on a cold morning. The probability of neither car starting on a cold morning is:

0.4 * 0.4 = 0.16

Therefore, the probability of at least one car starting on a cold morning is:

1 - 0.16 = 0.84

So the probability of at least one of the cars starting on a cold morning is 0.84 or 84%.

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Therefore , the solution of the given problem of linear equation comes out to be the linear equation of the image is y = 3x + 22.

The formula y = mx+b is used to produce a simple regression curve. The slope is B, and the y-intercept is m. The preceding line indicates independent components, yet is commonly referred to as a "math equation combining many variables". In bivariate linear equations, there are just two variables. Application problems involving linear equations have no known solutions. Y=mx+b.

Here,

Let's first find the coordinates of two points on the original line. We can choose any two points, but for simplicity, let's choose (0,4) and (1,7), which lie on the line y=3x+4.

The distance between these two points is:

d = √((1-0)² + (7-4)²) = √(10)

To find the new coordinates of these points after dilation, we multiply the distance by 4 and use the center of dilation (1,1) as the reference point:

New coordinates of (0,4):

x' = 1 + 4(0-1) = -3

y' = 1 + 4(4-1) = 13

New coordinates of (1,7):

x' = 1 + 4(1-1) = 1

y' = 1 + 4(7-1) = 25

So the image of the line y=3x+4 after dilation by scale factor 4 centered at (1,1) is the line passing through the points (-3,13) and (1,25). We can find the equation of this line by finding the slope and the y-intercept.

Slope:

m = (y2-y1)/(x2-x1) = (25-13)/(1-(-3)) = 12/4 = 3

Y-intercept:

y = mx + b

13 = 3(-3) + b

b = 22

Therefore, the linear equation of the image is y = 3x + 22.

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Answer:

24.413

Step-by-step explanation:

Break the shape up into 2 triangles and 1 rectangle, then add up the 3 areas.

Rectangle:  4.6 x 3.15 = 14.49

Triangle 1:  1/2(3.3)(3.15) = 5.1975

Triangle 2: 1/2(3)(6.3 - 3.15) = 4.725

Total area = 14.49 + 5.1975 + 4.725 = 24.413

Answer

True, True, False

Step-by-step explanation:

I am not quite sure but I hope this helps in any way.

I say True to the Increasing from minute to 25 because Clayton’s time starts at 0 and the time increases to 25 minutes.

I say True because if you see the point where it shows 25 minutes and stops at 60 minutes until Clayton goes back up, it shows the line regularly occurring which would make him be constantly moving to 60 minutes. (Constant means to regularly occur)

I say false because Clayton’s time is increasing into 90 minutes, not decreasing. Also its kinda like the same concept as the Increasing from minute 0 to 25.

In this list, 10 is the largest number and -1 is the smallest number, so it is also ordered from greatest to least.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Without a list of options to choose from, it is difficult to determine which list Janet could have created. However, generally speaking, a list of numbers in order from greatest to least would start with the largest number and end with the smallest number.

For example:

10, 8, 5, 3, 1

In this list, 10 is the largest number and 1 is the smallest number, so it is ordered from greatest to least. Other examples could include:

-1, 2, 4, 7, 10

Therefore, In this list, 10 is the largest number and -1 is the smallest number, so it is also ordered from greatest to least.

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The fraction n/8 is between 4/5 and 1. To calculate all the possible values of n, use the following equation:  n = (4/5)*8 = 6.4

Since n is a fraction, the possible values are 6, 6.4, 6.8, 7.2, 7.6, 8, and 8.4.
The possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.

To find the possible values of n, we can cross-multiply and compare the fractions.

1/2 < n/8 < 4/5

Cross-multiplying gives us:

8 < 2n < 32

Dividing by 2 gives us:

4 < n < 16

The possible values of n are the integers between 4 and 16, which are 5, 6, and 7.

Therefore, the possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.

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The age of Jane is 22 years.

Janes age is 10 more than three times her son's age. In two years, her age will be 12 less than the square of her son's age. Therefore, let's find Jane's age as follows:

Hence, using equation,

let

son's age = x

Jane age = 3x + 10

In two years,

(x + 2)² - (3x + 10 + 2)  = 12

(x + 2)(x + 2) - 3x - 12 = 12

x² + 2x + 2x + 4 - 3x - 24 = 0

x² + x - 20 = 0

x² - 4x + 5x  - 20 = 0

x(x - 4) + 5(x - 4) = 0

(x + 5)(x - 4) = 0

Therefore,

x = -5 and x = 4

We can only use positive numbers.

Therefore,

Jane's age = 3x + 10

Jane's age = 3(4) + 10

Jane's age = 12 + 10

Jane's age = 22

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The mass of 1 whole pizza will be 384 g.

What is Proportion ?

A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. It is a formula or claim that shows that two ratios or fractions are equivalent.

He has cut 1st pizza into 24 slices and other pizza into 8 slices.

Let the mass of small slice to be "x" g

So, the mass of large slice will be " 32+x " g

Now, Ben has two identical pizzas, it means the mass of both pizzas will be same.

So, mass of 1st pizza = mass of other pizza

                        24 x   =  8 ( 32+x )

                        24x = 256 + 8x

                        16x = 256

                         x = 16

Hence, the mass of 1 whole pizza = 24 × 16 = 384 g.

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The required in the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y, which represents the amount of money in the savings account after x weeks.

The value of y depends on the value of x, so y is dependent on x. However, the value of x does not depend on the value of y, so x is independent.

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The function g(x) = 4∛(x+2) - 5 is a transformation of the cube root parent function f(x) = ∛x. The transformation involves a vertical stretch by a factor of 4, a horizontal shift to the left by 2 units, and a vertical shift downwards by 5 units.

The cube root parent function f(x) = ∛x has a single x-intercept at the origin (0,0) and is symmetric about the origin. It has a gradual increase as x moves from negative to positive values.

In contrast, the function g(x) = 4∛(x+2) - 5 has a vertical stretch by a factor of 4, making the graph steeper than the parent function. The horizontal shift to the left by 2 units moves the x-intercept to (-2,0). The vertical shift downwards by 5 units moves the entire graph downward, so the new y-intercept is at (0,-5).

Overall, the function g(x) has been vertically stretched, horizontally shifted to the left, and vertically shifted downward from the parent function f(x).

Answer:

5.6

Step-by-step explanation:

Answer:

5.6

Step-by-step explanation:

5.6 to the nearest 10th

Generally, a size 1 diaper will weight around 8-14 lbs may it be for infants or adults.

By absorbing or containing waste materials to prevent soiling of outer clothing or the surrounding environment, diapers are a type of underwear that enable the wearer to urinate or defecate without using a toilet.

Diapers must be changed when they become soiled or wet, usually by a second person like a parent or caregiver. Skin issues around the diapered area can arise from failing to change a diaper as frequently as necessary.

Cloth or synthetic disposable materials are used to create diapers. Infants, toddlers who haven't learned to use the toilet, and kids who have bedwetting issues are the main groups of people who wear diapers. Adults who have incontinence or other conditions that call for their use may also do so.

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We may use the formula 1Hp = 735Watt to convert watts to horsepower.

Watt and horsepower are both units of power.

But horsepower is a more powerful unit of power. We use horsepower to measure the power of electrical instruments such as turbines, motors, and a variety of other devices.

Thus, according to normal unit conversion rates, 1 Horsepower Equals 735 Watt.

1 Hp = 735 W

As a result, we have the conventional relationship 1Hp = 735 W. We may now simply convert any power supplied in horsepower to the unit of Watt.

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Measures of centre are used to describe the typical or average value of the data, while measures of spread describe the variability or dispersion of the data around the centre. Some common measures of centre and spread include:

Mean: the arithmetic average of the data. It is appropriate for symmetric distributions without outliers.

Median: the middle value of the data. It is appropriate for skewed distributions and distributions with outliers.

Mode: the most common value in the data. It is appropriate for distributions with a prominent peak or mode.

Range: the difference between the maximum and minimum values in the data. It is appropriate for describing the spread of the data, but it can be influenced by outliers.

Interquartile range (IQR): the range of the middle 50% of the data, from the 25th percentile (Q1) to the 75th percentile (Q3). It is appropriate for describing the spread of the data, and it is less influenced by outliers than the range.

Standard deviation: a measure of the average distance of the data from the mean. It is appropriate for symmetric distributions without outliers, and it is used to describe the spread of the data in the context of the mean.

The choice of which measures to use depends on the characteristics of the distribution and the goals of the analysis.

In general, it is important to consider multiple measures of centre and spread in order to obtain a complete understanding of the distribution of the data.

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The statement that must be true is option (f) "The equation Ax = b has a solution for all b precisely when it has more columns than rows".

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

This is because if the matrix has more columns than rows, then the system of equations cannot be underdetermined, meaning that there is a unique solution for the equation.

On the other hand, if the matrix has more rows than columns, then it is possible that the equation Ax = b could have no solutions, which would mean that it is an overdetermined system.

Furthermore, if the matrix is a square matrix, then it will have the same number of rows and columns, and it is possible that the equation Ax = b could have either one solution or no solutions.

Therefore, the statement "The equation Ax = b has a solution for all b precisely when it has more columns than rows" is the only one out of the six given that must be true

Hence the option (f) is correct.

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Pick B. The graph's name and shape as expressed by the equation y = c is known as its constant function.

Theoretical physicists use graphs to graphically represent or chart facts or values in a logical way. Usually, a plot point will reveal the connection between three or more objects. A graph is a quel data structure made up of nodes, also known as triangles, and edges. The nodes, sometimes referring to as vertices, should have been joined with glue. Edges in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of advances in statistical charts, such as charts and graphs, pie charts, and line graphs. a circle logarithmic graph

given

The function illustrated is a horizontal straight line which is often represented by the equation y = c which is a constant function; consequently, the right answer is B.

By considering alternative options, we can determine that the function cannot be an identity function (since the function is not y = x), an absolute value function (because the graph is flat), or a cubic function (because the graph is flat).

Pick B. The graph's name and shape as expressed by the equation y = c is known as its constant function.

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Therefore , the solution of the given problem of expression comes out to be the simplified expression is 8n³ + 6n - 20.

There is a requirement for mathematical operations as addition, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an expression. A statement of fact contains values, parameters, and mathematical operations including additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

Given :

2n² + 4n + 4

    x 4n - 5

    -----------

    8n³ - 10n² + 16n² - 20n + 16n - 20

    -----------

    8n³ + 6n - 20

Thus, the simplified expression is 8n³ + 6n - 20.

Therefore , the solution of the given problem of expression comes out to be the simplified expression is 8n³ + 6n - 20.

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The total area of the composite figure represented by the scale drawing is 2,168.1 square yards.

Measurements refer to the process of assigning numerical values to physical quantities such as length, mass, time, temperature, and many others. These numerical values are expressed in units, which are standardized and accepted values used for comparison and communication.

Measurement is an essential part of science, engineering, and many other fields where precise and accurate data is required. Measurements allow us to make quantitative comparisons, analyze data, and draw conclusions.

There are different methods of measurement depending on the physical quantity being measured. For example, length can be measured using a ruler or tape measure, mass can be measured using a scale, and time can be measured using a clock or stopwatch.

It is important to note that measurements can have errors due to various factors such as limitations of the measuring instruments, environmental factors, and human error. Therefore, it is crucial to understand the limitations of the measuring instruments and to take steps to reduce errors as much as possible.

Overall, measurements are an important tool for gaining knowledge and understanding of the physical world, and they play a critical role in many aspects of our daily lives.

To find the total area of the composite figure represented by the scale drawing, we need to use the scale to convert the measurements in inches to measurements in yards, and then use these measurements to calculate the areas of the individual shapes and add them together.

Let's assume that we have labeled the various shapes in the composite figure A, B, C, and D, as shown in the scale drawing.

To convert the measurements in inches to yards, we need to divide each measurement in inches by 36 (since there are 36 inches in a yard) and then multiply by the scale factor of 9 yards per inch. This gives us the measurements in yards:

Shape A: 3 inches x 9 yards/inch = 27 yards (length), 2 inches x 9 yards/inch = 18 yards (width)

Shape B: 5 inches x 9 yards/inch = 45 yards (length), 3 inches x 9 yards/inch = 27 yards (width)

Shape C: 3 inches x 9 yards/inch = 27 yards (diameter)

Shape D: 2 inches x 9 yards/inch = 18 yards (length), 2 inches x 9 yards/inch = 18 yards (width)

Now we can calculate the areas of each shape using the appropriate formulas:

Area of Shape A: length x width = 27 yards x 18 yards = 486 square yards

Area of Shape B: length x width = 45 yards x 27 yards = 1,215 square yards

Area of Shape C: (pi x (diameter/2)^2)/4 = (pi x (27/2)^2)/4 = 143.1 square yards (using the formula for the area of a circle)

Area of Shape D: length x width = 18 yards x 18 yards = 324 square yards

Finally, we can add up the areas of all four shapes to get the total area of the composite figure:

Total area = 486 square yards + 1,215 square yards + 143.1 square yards + 324 square yards

Total area = 2,168.1 square yards

Therefore, the total area of the composite figure represented by the scale drawing is 2,168.1 square yards.

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