for what value(s) of a does the system have nontrivial solutions?

If angles a and b are supplemented, they add up to 180 degrees. If angles a and c are supplements, they add up to 180 degrees.

Since angle a is a common angle in both of these equations, you can conclude that angles b and c must also be supplemented and add up to 180 degrees. Supplemented means that two angles add up to 180 degrees. In other words, they are supplementary angles.

Supplementary angles are two angles that add up to 180 degrees. They are considered "complementary" to each other as they "complete" a straight line, which measures 180 degrees. A straight line is a geometric object with no curvature, consisting of an infinite set of points that extends infinitely in both directions. It is the shortest distance between two points and has the property of being perfectly straight. In geometry, straight lines are a basic building block to define and measure other shapes and figures.

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Answer:

Step-by-step explanation: P = (2, 3, 5, 7, 11, 13, 17, 19), Q = (1, 3, 5, 7, 9)

PnQ = (3,5,7)

(I think your N means intersection)

The letter of protest from the Standing Rock Sioux Tribe to the federal government is likely to concern the construction of the Dakota Access Pipeline, which threatened the Tribe's water supply and cultural sites.

The Standing Rock Sioux Tribe is a Native American tribe located primarily in North and South Dakota. The tribe is known for its opposition to the Dakota Access Pipeline, a controversial oil pipeline that would cross the tribe's reservation and potentially impact its water supply and cultural sites. In 2016, the Standing Rock Sioux Tribe and its supporters held a series of protests and demonstrations against the pipeline, attracting national attention and leading to its temporary halt.

The Dakota Access Pipeline (DAPL) is a

n oil pipeline that runs from the Bakken oil fields in North Dakota to Illinois. The tribe and its supporters held protests, leading to confrontations with law enforcement. In 2016, the US Army Corps of Engineers declined to grant the pipeline an easement, but this decision was later reversed by the Trump administration.

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Answer:

The area of the base of the rectangular box is 2x² + 4x - 3 square units and the height is x units.

So the volume of the box can be found by multiplying the area of the base by the height:

V = (2x² + 4x - 3) x (x)

V = 2x³ + 4x² - 3x

Therefore, the polynomial expression for the volume of the box is 2x³ + 4x² - 3x.

Answer:

2x^3 + 4x^2 - 3x

Step-by-step explanation:

area of base = 2x^2 + 4x - 3 = Length x Breadth

Height of box = x

volume of box = Height x Length x Breadth

= (2x^2 +4x - 3) x

= 2x^3 + 4x^2 - 3x

Answer:

original number Jacob wrote = 78

Step-by-step explanation:

basically Jacob wrote a 3 digit number, let's call it "x" and then he added 230 to x which resulted in 1011.

this can be written simple as an equation:

x + 230 = 1011

now just solve for x:

x = 1011 - 230

x = 781

finally we know that Jacob initially wrote a two digit number and then an additional digit to its right, hence the original number Jacob wrote would be:

78

First, find the product of the numbers:

Now, rewrite the given expression as:

Proved that the given expression is divisible by 3, 7, 13 and 37.

The distance between the car and Johnstown is decreasing at a rate of 33 miles per hour.

After travelling 63 miles, the distance between the car and Johnstown is changing at a rate of 33 miles per hour, and the distance between the car and Johnstown is 100 miles

To calculate the distance between the car and Johnstown after travelling 63 miles, we need to first find the starting distance.

The car starts off 163 miles directly north from the city of Johnstown, so the starting distance is 163 miles.

We then need to subtract the distance travelled from this starting distance. Since the car is travelling at a rate of 33 miles per hour, it has travelled 63 miles in the given time.

Therefore, the distance between the car and Johnstown is 100 miles

(163 - 63 = 100).

Finally, we need to calculate the rate of change of this distance. Since the car is travelling at a rate of 33 miles per hour, the rate of change of the distance between the car and Johnstown is also 33 miles per hour.

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In order for a graph to be considered a time series graph, it must have a series of data points that are displayed in chronological order over a period of time.

Graph is a data structure which is used to represent a set of connected objects. It is composed of nodes and edges which represent the relationships between the objects. Graphs are used to represent different types of data such as networks, trees, and more. They can be used to model different types of relationships such as relationships between people, objects, and even ideas. Graphs are also used in a variety of applications including route-finding, graph theory, and data mining.

This means that the data must be plotted on the graph according to when it was collected, with the earliest data points on the left and the most recent data points on the right. The data points must be consistently spaced apart; for example, if the data points represent daily measurements, then the data points should be one day apart. Additionally, the graph should show the overall trend of the data over the period of time. Ideally, the graph should also show the variability of the data points over the period of time.

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As per the given triangle RT = AS, RS = AT, the statement < TSA = < STR is proved.

Given two triangles, if the length of one side is proportional to the length of a corresponding side in another triangle, then the two triangles are similar.

This relationship is expressed as "RT = AS," where R and S are corresponding vertices in the two triangles and T is the point where the two sides intersect.

To prove that < TSA = < STR, we need to show that corresponding angles in the two triangles are equal.

This is because corresponding angles in similar triangles are equal, and this is one of the ways to prove that two triangles are similar.

To prove that RT = AS and RS = AT, we can use the function of proportionality. This function states that if two sides are proportional, then the ratio of corresponding lengths will be equal.

Therefore, if RT = AS and RS = AT, then we can conclude that < TSA = < STR and the two triangles are similar.

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Answer:

-0.25

Step-by-step explanation:

rise/run=2/8

= 0.25

ans is negative because line is going down

Answer:

2/-8 = -1/4 or -0.25 in decimal

Step-by-step explanation:

To find the slope take two distinguishable points on the graph(integer values preferred).

Find the difference in the y values and divide by the corresponding difference in the x values

You can identify 2 points with integer coordinates as

(-5, 3) and (3, 1)

Difference in y values = 3 - 1 = 2

Corresponding difference in x values : -5 - 3 = -8

So slope is 2/-8 = -1/4 or -0.25 in decimal

There are 9600 different ways to choose a lunch special at the starlight diner.

In the given question, there are:

Number of appetizers = 6

Number of salads = 5

Number of meat dishes = 4

Number of sides = 4

Number of breads = 4

Number of drinks = 5

We know that the number of ways to choose r elements from n elements is equal to nCr.

Since, the starlight diner's lunch special includes a choice of one each, then the number of ways in which we can choose a lunch special at the diner will be:

6C1 x 5C1 x 4C1 x 4C1 x 4C1 x 5C1 = 9600

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The area painted is 376.8 sq. inches (approximately)

We can start solving the problem by calculating the radius of the base of the rod. We can use the formula for the circumference of a circle:

circumference = 2πr

Where r is the radius of the circle.

Given that the circumference of one of the bases of the rod is 12π inches, we can set up the equation:

12π = 2πr

r = 12π/2π = 6

So the radius of the base of the rod is 6 inches.

Now we can use the radius to find the area of one base of the rod. The area of a circle is given by the formula:

A = πr²

So the area of one base of the rod is:

A = π × 6² = 36π

Now we can use the length and radius of the rod to find the lateral surface area of the rod.

The formula for the lateral surface area of a cylinder is :

L.S.A = 2πrh

Where h is the height of the cylinder. In this case, the height of the cylinder is 4 inches.

L.S.A = 2π × 6 × 4 = 48π

So the lateral surface area of the rod is 48π inches.

Finally, to find the total area painted, we can add the area of the two bases and the lateral surface area.

Total area painted = 2 × 36π + 48π = 120π sq inches.

Now we can use π≈3.14 and get the area painted to the nearest tenth.

Total area painted = 120×3.14 = 376.8 sq. inches

Therefore, the area painted is 376.8 sq. inches (approximately)

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The percent markdown is 22.58% for the given DVD player.

The percentage is defined as a ratio expressed as a fraction of 100.

We can determine the value of the  percent markdown by the following formula,

percentage decrease = (initial value - reduced value) / initial value × 100%

As per the given question, we have

initial value = $175.80, and reduced value = $153.67

Substitute the values in the above formula, and we get

percent markdown = (175.80 - 153.67) / 175.80 × 100%

percent markdown = (22.13) / 175.80 × 100%

percent markdown = 0.1258 × 100%

Apply the multiplication operation, and we get

percent markdown = 12.58 %

Thus, the percentage decrease of the given item would be 12.58%.

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Answer:

R92.463

Step-by-step explanation:

100% - 20% = 80% = 0.8

0.8 times 124.95 = R99.96

7.5% = 0.075

99.96 - (99.96 x 0.075) = R92.463

So, Maria pay R92.463 for the swimming costume.

The measures of two supplementary angles are 110° and 70°.

The sum of two or more angle is 180 degree then the angle is called the supplementary angle.

We have to given that;

One angle is 40 degrees more than the measure of the supplement.

Let measure of one angle = x

Then, Measure of its supplement = 180 - x

Here, One angle is 40 degrees more than the measure of the supplement.

Hence, We get;

⇒ x = 40 + (180 - x)

⇒ x + x = 220

⇒ 2x = 220

⇒ x = 110

Thus, Measure of one angle = x = 110°

Then, Measure of its supplement = 180 - x

                                                    = 180° - 110°

                                                    = 70°

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Using the definition of continuity and the properties of limits to show that the function is continuous at the given number  f(x)=-5

continuity of a real function is provided generally in a calculus’s introductory course in terms of a limit’s idea.

First, a function f with variable x is continuous at the point “a” on the real line, if the limit of f(x), when x approaches the point “a”, is equal to the value of f(x) at “a”, i.e., f(a).

Second, the function (as a whole) is continuous, if it is continuous at every point in its domain.

We know that the value of f near x to the left of a, i.e. left-hand limit of f at a and the value of f near x to the right f a,

i.e. right-hand limit are equal, then that common value is called the limit of f(x) at x = a. Also,

a function f is said to be continuous at a if limit of f(x) as x approaches a is equal to f(a).

A function f is continuous at a number a if

[tex]\lim_{x \to\n} f( x) = f(a)[/tex]

f(x) = [tex]x ^3x^4 5[/tex]

     = [tex]\lim_{x \to \ a} x^3 * \lim_{x \to \ a} x^4 *5\\= (-1)^3 * (-1)^4 *5\\= -1 * 1* 5\\= -5[/tex]

Using the definition of continuity and the properties of limits to show that the function is continuous at the given number  f(x)=-5

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Answer:

1409.3

Step-by-step explanation:

Let the distance flown by the arrow in feet be [tex]d[/tex].

[tex]\sin 20^{\circ}=\frac{482}{d} \\ \\ \frac{1}{\sin 20^{\circ}}=\frac{d}{482} \\ \\ d=\frac{482}{\sin 20^{\circ}} \\ \\ d \approx 1409.3[/tex]

If 6 boys and 4 girls get off the bus at the next bus stop, the ratio of girls to total students will be 14/27.

There are 22 boys and 32 girls on a school bus, 6 boys and 4 girls get off the bus at the next bus stop.

Total boys = 22

Total girls = 32

Total Student = Total boys + Total girls

Total Student = 22 + 32

Total Student = 54

The girls gets off = 4

Now remaining girls in bus = Total girls - The girls gets off

Now remaining girls in bus = 32 - 4

Now remaining girls in bus = 28

The ratio of girls to total students = Now remaining girls in bus/Total Students

The ratio of girls to total students = 28/54

The ratio of girls to total students = 14/27

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Answer:7

Step-by-step explanation:

7

The value of n is 30.33. The thirty-fourth term can be found by solving for the common difference (d) and the number of terms (n) in the arithmetic sequence and then using the formula for the nth term of an arithmetic sequence.

Let's assume that the common ratio of the geometric sequence is r. Then, the terms of the geometric sequence are given by:

[tex]a_2 = a_1 * ra_{10} = a_1 * r^8a_{34} = a_1 * r^{32}[/tex]

Since these terms also appear in the arithmetic sequence, we can write:

[tex]a_2 = a_1 + da_{10} = a_1 + 9da_{34} = a_1 + 33d[/tex]

Substituting the expressions for a_2 and a_{10} from the geometric sequence into the arithmetic sequence, we have:

[tex]a_1 * r = a_1 + da_1 * r^8 = a_1 + 9d[/tex]

Solving for d, we get:

[tex]d = a_1 * (r - 1)d = a_1 * (r^8 - 1) / 9[/tex]

Next, we use the expression for a_{34} from the arithmetic sequence and substitute the expression for d to obtain:

[tex]a_{34} = a_1 + 33d = a_1 + 33a_1 * (r^8 - 1) / 9[/tex]

Since the first term of the arithmetic sequence is 1, we have:

[tex]a_{34} = 1 + 33 * 1 * (r^8 - 1) / 9[/tex]

The value of n can be found by using the formula for the nth term of an arithmetic sequence:

[tex]a_n = a_1 + (n-1)d[/tex]

Setting n = 34 and substituting the expression for d, we have:

[tex]a_{34} = 1 + (33) * (a_1 * (r^8 - 1) / 9)[/tex]

So the thirty-fourth term of the arithmetic sequence is:

[tex]a_{34} = 1 + 33 * (1 * (r^8 - 1) / 9) = 34 - 33/9.[/tex]

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Complete Question:

An arithmetic sequence with first term 1 and common difference not equal to 0 has second, tenth, and thirty-fourth terms that form a geometric sequence.

What is the thirty-fourth term of the arithmetic sequence?

The fourth term in the geometric sequence above appears as the nth term in the arithmetic sequence. Find the value of n.

The required factors of the number 63 is 21×3.So, option(B) is correct.

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Algebraic expressions are written as the sum of two or more expressions using factoring formulas. The following are some crucial factoring formulas: (a + b)2 = a2 + 2ab + b.

We have to find the factors of the number 63

= 63

= 9×7

= 3×3×7

= 21×3

Thus required factors of the 63 are 21×3.

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The calculated t-value of 8.77 is not statistically significant with a confidence level of 99%. This indicates that the sample does not differ significantly from the mean.

The formula for calculating a one-tailed test of significance with a sample size of 5 elements is as follows:

First, calculate the mean of the sample:

Mean = (18 + 15 + 12 + 19 + 21) / 5 = 17

Second, calculate the sample variance:

Variance = [(18-17)2 + (15-17)2 + (12-17)2 + (19-17)2 + (21-17)2] / 4 = 16

Third, calculate the standard deviation:

Standard Deviation = √16 = 4

Fourth, calculate the t-value:

t-value = (17 - 0) / (4 / √5) = 8.77

Finally, calculate the p-value:

p-value = 1 - (2 * 0.01) = 0.98

Thus, the p-value for the sample of five elements with a significance level of 0.01 is 0.98. This means that the calculated t-value of 8.77 is not statistically significant with a confidence level of 99%. This indicates that the sample does not differ significantly from the mean.

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To demonstrate the given situation, the type of chart(s) that is best to use is both an x-bar chart and an R-chart.

An x-bar chart is a statistical process control chart used to monitor the mean of a continuous data set over time. The chart plots the average (x-bar) of each subgroup of data points, rather than plotting individual data points, and provides information about process stability and control. The x-bar chart is often used in conjunction with an R-chart.

An R-chart (Range chart) is a type of statistical process control chart that is used to monitor the variability of a process by plotting the range (difference between the maximum and minimum values) of a subgroup of samples at different time periods. The R-chart provides a measure of process variability and helps detect changes in variability, which may indicate a change in the underlying process mean. The R-chart is typically used in conjunction with an X-bar chart, which monitors the process mean, to provide a comprehensive view of process performance.

The question seems incomplete, it must have been...

"Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend?

-both an x-bar chart and an R-chart

-p-chart

-an x-bar chart, but not an R-chart

-c-chart

-both a p-chart and a c-chart"

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Answer: SSS Postulate

Step-by-step explanation:

Since DF is congruent to FD, there are three congruent sides.

The rabbit travels a distance of 138 m, and the average speed of the hiker for the entire trip is 7.2 km/h.

Given that,

Speed = 12.0 m

Time = 11.5 seconds

Now we need to calculate the distance by using the formula of distance:

d=v*t

d=12.0*11.5

d=138m

The rabbit travels a distance of 138 m.

Distance = 5.10 km

Time = 1 hour

Distance 16.5 km

Time = 2 hours

To calculate the average speed of the hiker for the entire trip using the formula of average speed:

v=D/T

Where, D = Total distance

T = Total time

Put the value into the formula:

v=5.10+16.5/1+2

v=7.2km/h

Therefore, the average speed of the hiker for the entire trip is 7.2 km/h.

Hence, This is the required solution.

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Answer:The perimeter of a trapezoid is equal to the sum of the lengths of all its sides.

Let's call the height of the trapezoid "h".

Then, the length of the two sides equal (78 - 30 - 14) / 2 = 22 ft.

The area of the trapezoid is equal to (30 + 14) / 2 * h = 22 * h.

We can now find h using the formula:

h = (2 * area) / (30 + 14) = (2 * area) / 44.

We don't know the area, so we cannot find h.

Step-by-step explanation:

The point must be (-4,-4)

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here : the Point D in the graph.

Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate). The origin is located at (0,0).

we can clearly read that the point D is -4 points away from the y-axis and -4 units away from the x-axis to the right. It also lies in the third quadrant in the co-ordinate plane.

Hence, The point must be (-4,-4)

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The unit vector with the same direction as the given vector is (−0.45i, 0.9j, −1k).  This vector has been normalized so that the magnitude is equal to 1, while still preserving the direction of the original vector.

To find the unit vector with the same direction as the given vector, we need to normalize the vector. This means we need to divide each component of the vector by its magnitude. The magnitude of the vector is the square root of the sum of the squares of its components, which in this case is the square root of (9^2 + 2^2 + 1^2), or 9.64. Dividing each component of the vector by its magnitude gives us the unit vector (−0.45i, 0.9j, −1k). The magnitude of this vector is equal to 1, and the direction is the same as the original vector.

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Answer:

the answer is B or 12x +18

Answer:

first option: 12x+18

Step-by-step explanation:

You are finding the area of a rectangle so the formula you use will be

length * height

length = 4x+6

height= 3

you multiply them:

=3*(4x+6)

=3*4x + 3*6

=12x+18