Show that the equation has no rational root. 11. x3 + 3x2 - 4x + 6 = 0 12. 3x3 - 4x2 + 7x + 5 = 0 13. 5x4 + 3x2 - 5 14. x4 - 9x + 7 15. x5 – 3x3 + 4x2 + x - 2 = 0 16 2x5 + 3x3 + 7 = 0

The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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To determine the number of pattern block rhombuses needed to create 2 hexagons, we need to understand the relationship between the two shapes.

A pattern block rhombus is a rhombus-shaped tile commonly used in geometry and math education. It is composed of two equilateral triangles joined together.

A hexagon, on the other hand, is a polygon with six sides. Each side of a regular hexagon is congruent to the others, and all its angles are equal.

In order to create a hexagon using pattern block rhombuses, we need to consider the arrangement of the rhombuses. Let's assume that the hexagons we want to create are regular hexagons.

A regular hexagon can be divided into six equilateral triangles. Each equilateral triangle can be formed using two pattern block rhombuses. Therefore, to create one regular hexagon, we need a total of 6 equilateral triangles x 2 rhombuses per triangle = 12 pattern block rhombuses.

Since we want to create 2 hexagons, we multiply the number of rhombuses required for one hexagon by 2:

12 pattern block rhombuses per hexagon x 2 hexagons = 24 pattern block rhombuses.

Therefore, we would need 24 pattern block rhombuses to create 2 regular hexagons.

Answer:

0.70

Step-by-step explanation:

The nine is in the hundreths place, and it is over five, so you would round the number to the left of it up (the six). Basically, ignore the 8.

The number 0.698, when rounded off to the nearest hundredth, will become 0.70.

For the Rounding, some number to a specific value is making its value, mostly done for better readability or accessibility.

We need to round 0.698 to the nearest hundredth.

The hundredth place in the number is 9, that is greater than or equal to 5.

Since, we round up the tenths place to 7 + 1 = 8 and drop all other digits after the hundredth place and replace them with zeros.

0.698 rounded to the nearest hundredth is 0.70.

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In the context of calculating sample variance (s²), the following results on summations can be helpful.

These results state that for any constant c, the sum of the squared deviations from c is equal to the sum of the squared values minus 2c times the sum of the values, plus c squared times the count of values.

To calculate the sample variance (s²), which measures the variability of a set of values, it is necessary to compute the sum of the squared deviations from the mean. The following results on summations can aid in this calculation:

Sum of Squares: The sum of the squared values is equal to the sum of each value squared.

∑(x²) = (x₁)² + (x₂)² + ... + (xₙ)²

Deviation from a Constant: If we have a constant value c, the sum of the squared deviations from c is obtained by subtracting 2c times the sum of the values from the sum of the squared values and adding c squared times the count of values.

∑((x - c)²) = ∑(x²) - 2c∑(x) + c²n

These results can be utilized in calculating the sample variance (s²) by considering c as the mean of the values. By applying these formulas, we can efficiently compute the necessary summations and obtain the desired variance measurement for the given dataset.

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Answer:

1960

Step-by-step explanation:

1880 unknown

1990 $1.23

2016 $1

1960 $8

The numerical length of the line segment FG is 10 units.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Point G is on FH, hence:

FH = FG + GH

Given that GH = 8, FH = 3x + 3, FG = 2x, hence:

3x + 3 = (2x) + 8

x = 5

FG = 2x = 2(5) = 10

The numerical length of the line segment FG is 10 units.

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To calculate how long it would take to pay off 60% of the debt,

we can use the same facts as in problem #16. Let's go through the steps:

1. Determine the total amount of debt: Find the original debt amount given in problem #16.

2. Calculate 60% of the debt: Multiply the total debt by 0.6 to find the amount that represents 60% of the debt.

3. Divide the amount obtained in step 2 by the monthly payment: This will give us the number of months it will take to pay off 60% of the debt.

Now, let's apply these steps to the options provided:

a. About 45 months: To determine if this is the correct answer, we need to perform the calculations outlined above using the original debt amount and the monthly payment given in problem #16.

b. About 50 months: Same as option a, perform the calculations using the original debt amount and the monthly payment.

c. About 55 months: Perform the calculations outlined above using the original debt amount and the monthly payment.

d. About 37 months: Perform the calculations outlined above using the original debt amount and the monthly payment.

After performing the calculations for each option, compare the results with the options provided to find the correct answer.

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Based on the computation, the series \(\sum \frac{(-1)^n}{n^3}\) converges

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

\(\sum \frac{(-1)^n}{n^3}\)

From the above series, we can see that:

Using the above as a guide, we have the following:

We can conclude that the series converges

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Given:

Aim:

We need to find the trigonometric function and the quadrant of the angle.

Explanation:

Take inverse trigonometry on both sides of the equation.

Final answer:

Answer: 219

Step-by-step explanation: hope this helps!!!!

Answer:

$24.20

Step-by-step explanation:

2 examples where a system of equations could describe a real-life situation are given below.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.


1.Modeling a business’s profit: A business can be represented by a system of equations to find the maximum profit. The equations can include the cost of the product, the price of the product, the number of units of the product sold, and other variables such as taxes and shipping costs. By representing the business with a system of equations, a business can optimize the equation to achieve the maximum profit.

2. Modeling the housing market: A system of equations can be used to model the housing market. The equations can include variables such as housing prices, the number of houses on the market, the number of buyers, the supply of housing, and the demand for housing. By using a system of equations, economists can better understand the housing market and make predictions about future trends in the market.

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Answer:

D

Step-by-step explanation:

it's D I don't have a full step by step

Answer:

if im not mistaken the andswer is D

The expression was written using the associative property of addition.

[(-2) +8] +3 equals 6 + 3 which equals 9.

(-2) + [8+3] equals (-2) + 11 which equal 9.

Given,

[(-2) +8] +3 equals ______ + 3 which equals _____  

(-2) + [8+3] equals (-2) +  _____  which equal _____

We need to see which operation is used and fill in the blanks.

It states that (a+ b) + c = a + (b + c).

We have,

[(-2) +8] +3 equals ______ + 3 which equals _____  

(-2) + [8+3] equals (-2) +  _____  which equal _____

We can write it as:

[(-2) +8] +3  = 6 + 3 = 9

(-2) + [8+3] = -2 + 11 = 9

We see that,

[(-2) +8] +3 = (-2) + [8+3]

This is in the form: (a+b)+c = a+(b+c)

Thus the expression was written using the associative property of addition.

[(-2) +8] +3 equals 6 + 3 which equals 9.

(-2) + [8+3] equals (-2) + 11 which equal 9.

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Answer:

The length is 22.5 and the width is 19.5

Step-by-step explanation:

          2L + 2W = P

                     \/

          2L + 2W = 84

                     \/

W + 3 + W + 3 + W + W= 84

                     \/

          4W + 6 = 84

                     \/

                4W = 78

                     \/

     W = 19.5      L = 19.5 + 3 = 22.5

I hope this helps, have a nice day! :D

Answer:

27

Step-by-step explanation:

Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

To find the perimeter (p) of a parallelogram, you need to know the length of all four sides. However, in this case, you are given the ratio of the base (b) to one of the sides (a), which is n/a.
Since a parallelogram has two pairs of parallel sides, the opposite sides are equal in length. Therefore, if the base is b, then the opposite side is also b. Using the given ratio, you can find the length of the other side (n) by multiplying a by n/a, which is n.
So, the length of the other side is also n, and the perimeter can be calculated by adding up all four sides: p = 2b + 2n.
However, if given the ratio of the base to one of the sides, you can use this to find the length of the other side. For this problem, if the base is b, then the opposite side is also b, and the length of the other side is n (where n/a = b/a).

Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

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Answer:1/7

Step-by-step explanation: You take the amount that are springer spaniels and you put them with the whole of the dogs in the park 14 so you would have 2/14. You can reduce this fraction to 1/7 by dividing both the top and bottom of the fraction by 2.

Answer:

C = 18π cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Circumference Formula: C = 2πr

Step-by-step explanation:

Step 1: Define

Identify variables

r = 9 cm

Step 2: Find C

The function f(x) has at most one relative extremum on the interval 2 < x < 4, based on the behavior of its derivative f'(x) = sin(x^2 + 1). Therefore, the correct option is a. One.

To determine the number of relative extrema of the function f(x) on the interval 2 < x < 4, we need to analyze the behavior of its derivative f'(x).

We have that f'(x) = sin(x^2 + 1), we need to examine where the derivative changes its sign within the interval (2, 4) to identify the relative extrema.

Since the sine function oscillates between -1 and 1, we can observe that sin(x^2 + 1) will also oscillate between -1 and 1 as x^2 + 1 varies.

However, since the interval (2, 4) is relatively small, the value of x^2 + 1 will not vary significantly, and the sine function will not complete multiple oscillations within this interval.

Therefore, there will be at most one sign change for sin(x^2 + 1) within the interval (2, 4), indicating that f(x) may have at most one relative extremum within this interval.

Hence, the correct answer is: a. One.

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Answer:

Right-angled triangle

Step-by-step explanation:

It has a square angle, meaning it is a right angle, which is \(90^{o}\), making it a right angled triangle

The height of the pyramid from the base and the volume is h = 3V/B

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

Volume and base area are known

This means that we make the height the subject of the formula

The volume of a pyramid is calculated as

V = 1/3Bh

Where

B  Base area

h - height

So, we have

h = 3V/B

By making the height the subject of the formula

Hence, the height of the pyramid from the base and the volume is h = 3V/B

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Answer:

For the first question, D is the correct answer.

For the second question, B is the correct answer.

Step-by-step explanation:

First question:

\(5.89 + .61(30) = 24.19\)

\(5.89 + .61(35) = 27.24\)

So D is the correct answer.

Second question:

A function is a relation in which each element in the domain corresponds to one and only one element in the range. That said, relations A, C, and D are not functions since in each of these relations, one element in the domain corresponds to two elements in the range. Only relation B is a function.

Answer:

D.

Step-by-step explanation:

Because 36:20 simplified is 9:5.

Answer:

It is D 9:5

Step-by-step explanation:

Beacuse 9x4= 36

and 5x4= 20

so 36:20 or 9:5

Answer:

\(A=54.95\ ft^2\)

Step-by-step explanation:

The angle of shaded sector = 360-332 = 28°

The radius of sector, r = 15 ft

We need to find the area of the shaded sector. The formula for the area of the sector is given by :

\(A=\dfrac{\theta}{360}\times \pi r^2\\\\=\dfrac{28}{360}\times 3.14\times (15)^2\\\\A=54.95\ ft^2\)

So, the area of the shaded sector is equal to \(54.95\ ft^2\).

Answer:

k=2

Step-by-step explanation:

1. 48+5k=58

2. 5k=58-48

3. 5k=10

4. k=10/5

5. k=2