Solve the equation in the real number system: x^8-4x^7+3x^6+8x^5-15x^4+4x^3+9x^2-8x+2=0

Answer:

If you plug in -2 for x in each equation, y=1

Step-by-step explanation:

1)

y = -2x-3

y = -2(-2)-3

y = 4-3

y = 1

In the first equation y=1

2)

y = x+3

y = -2+3

y = 1

As we can see, in both equations when x is plugged in as -2, y = 1

An equation for the wheel if the center of the wheel is on the​ y-axis and y represents the height above the ground is x² + (y - 169)² = 22500.

In order to write an equation of the circle, we need two major components: the radius of the circle and the coordinates of its center. We can then express the equation in the form (x - a)² + (y - b)² = r², where r is the radius and (a, b) is the center.

Let's start by first finding the radius of the Ferris wheel. We know that the diameter of the wheel is 300 ft, and that the radius of a circle is half of the diameter. So, we have d = 300,

r = d/2

r = 300/2

r = 150 ft

Now that we know the radius, we can save that for later and move on to finding the center point.

We are told that the center of the wheel is on the y-axis; this means that the x-coordinate of our center point is a = 0.

Next, to find the y-coordinate, we can note that even though the diameter of the wheel is 300 ft, the maximum height of the wheel is actually 319 ft. That means that there must be a structure below the wheel that holds it up 19 ft above the ground (319- 300= 19).

Therefore, we must add this 19 ft to the radius of 150 ft straight up to find the center point of the circle, which is 169 ft above the ground. Thus, the y-coordinate of our center point is b = 169.

We can then plug in our radius and center point (0, 169) into our equation for a circle and simplify to get our final answer

(x - (0))² + (y - (169))² = 150²

x² + (y - 169)² = 22500

Therefore, an equation for the wheel if the center of the wheel is on the​ y-axis and y represents the height above the ground is x² + (y - 169)² = 22500.

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While finding with similar volumes, which might be volumes of figures that are similar in shape and proportion, we can find the ratio of their volumes by using the ratio of their linear dimensions.

The linear dimensions refer to the measurements of the duration, width, and height of the figures. If two comparable figures have corresponding linear dimensions inside the ratio of a:b, then their volumes could be in the ratio of [tex]a^3:b^3.[/tex] that is because the volume of a 3-dimensional determine is decided by way of multiplying its duration, width, and top collectively.

For example, if we have cubes which are similar in shape and proportion & the period of one cube is two times the period of the other dice, then the ratio in their linear dimensions is 2:1. therefore, the ratio in their volumes can be [tex](2^3):(1^3)[/tex], which simplifies to 8:1. which means the larger dice has 8 times the volume of the sm

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Answer:

1

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An equation of the line in point-slope form is y + 40 = -2(x - 70).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 100)/(50 - 0)

Slope (m) = -100/50

Slope (m) = -2

At point (70, -40) and a slope of -2, an equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 40 = -2(x - 70)

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The table shows the height of a stack of books based on the number of copies. Each copy of the book is 2.1 cm thick. Adding a new copy of the book increases the height of the stack by 2.1 cm, and the height increases by a factor of 1 for each new copy.

To complete the table, we need to find the stack height for each number of copies of the book. Since each copy of the book is 2.1 cm thick, we can use multiplication to find the total height of the stack for each number of copies

For 0 copies, the stack height is 0 cm.

For 1 copy, the stack height is 2.1 cm.

For 2 copies, the stack height is 4.2 cm (2.1 cm x 2).

For 3 copies, the stack height is 6.3 cm (2.1 cm x 3).

For 4 copies, the stack height is 8.4 cm (2.1 cm x 4).

Therefore, the completed table looks like

copies of book | 0 | 1 | 2 | 3 | 4

stack height | 0 | 2.1 | 4.2 | 6.3 | 8.4

Looking at the table, we can see that each time a new copy of the book is added, the height of the stack increases by 2.1 cm.

We can also observe that the factor by which the height of the stack changes when a new copy is added is always 1. This is because each copy of the book is the same thickness, so adding one copy always adds the same amount of height to the stack.

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The value of x for the right triangle is derived to be x = 10 using the trigonometric ratio of cosine for angle 60°

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

cos 60° = 5/x {adjacent/hypotenuse}

x = 5/cos 60° {cross multiplication}

x = 5/(1/2) {recall cos 60° = 1/2}

x = 5 × 2/1

x = 10.

Therefore, the value of x for the right triangle is derived to be x = 10 using the trigonometric ratio of cosine for angle 60°

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Answer:

the rectangular coordinates of the point (9, 150°) are approximately (-4.5, 7.794).

Step-by-step explanation:

To convert from polar coordinates to rectangular coordinates, we use the following formulas:

x = r cos θ

y = r sin θ

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point, measured counterclockwise.

In this case, r = 9 and θ = 150°. However, we need to convert θ to radians before we can use the formulas. We know that 180° = π radians, so:

150° = (5/6)π radians

Now we can use the formulas:

x = r cos θ = 9 cos (5/6)π ≈ -4.5

y = r sin θ = 9 sin (5/6)π ≈ 7.794

Therefore, the rectangular coordinates of the point (9, 150°) are approximately (-4.5, 7.794).

The reduction in reserve requirements led to an increase of $79 billion in both excess reserves and the lending capacity of Chinese banks.

According to the news accounts from March 2020, the reduction in the reserve requirement ratio (RRR) by the People's Bank of China increased the lending capacity of Chinese banks by approximately US$79 billion

(a) The excess reserves in China increased by $79 billion.

(b) As a result of the reduction in the reserve requirement, the lending capacity of Chinese banks increased by $79 billion.

This means that Chinese banks had an additional $79 billion available for lending purposes, which aimed to stimulate economic growth and support the country's economy. By lowering the reserve requirement, commercial banks were able to hold a smaller portion of their deposits as reserves, thus freeing up more funds that could be utilized for lending to businesses and individuals.

In summary, the reduction in reserve requirements led to an increase of $79 billion in both excess reserves and the lending capacity of Chinese banks.

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Answer:

16.03% increase.

Step-by-step explanation:

4.264+25%+6.396 = 16.03% increase.

The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

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There are 33,800 different four-letter passcodes that can be formed if the first letter must be an S or a T, and the last letter must not be a Z.

The English alphabet consists of 26 letters. Because the initial letter must be a S or a T, there are only two options.

There are 26 options for each letter in the second and third letters because there are no constraints. As a result, the second and third letters have a total of 26 26 = 676 potential combinations.

We have 25 options for the fourth letter (which cannot be a Z).

As a result, the total number of possible four-letter passcode combinations is:

2 × 676 × 25 = 33,800

So, if the first letter is a S or a T and the last letter is not a Z, there are 33,800 possible four-letter passcodes that may be constructed.

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The measure of angle x is 57 degrees.

Remember that the sum of the measures of two adjacent angles is always equal to 180°.

Here we can see that the angle x° and 123° are adjacent, then we can write the linear equation:

x + 123° = 180°

Solving the equation for x, we will get.

x = 180° - 123°

x = 57°

That is the value of x.

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The monument has a surface area of 432 square feet to be painted. Dividing this area by the coverage of one gallon of paint, we get a requirement of 4 gallons of paint to paint the monument.

As per the given figure, the monument has a rectangular shape with dimensions of length 12 feet, width 6 feet and height 18 feet.

The area of the monument that needs to be painted can be calculated by subtracting the area of the base that is not to be painted from the total surface area of the monument.

The area of the base that is not to be painted is 12 feet x 6 feet = 72 square feet.

The total surface area of the monument that needs to be painted is:

2 (length x height) + 2 (width x height) - area of base

= [tex]2 (12 ft x 18 ft) + 2 (6 ft x 18 ft) - 72 ft^2[/tex]

= [tex]432 ft^2[/tex]

Now, we can divide the total surface area of the monument by the area that can be covered by one gallon of paint:

[tex]432 ft^2 / 140 ft^2/gallon = 3.0857 gallons[/tex]

Since we can buy paint only by the gallon, we must round up to the nearest gallon. Therefore, we need to buy 4 gallons of paint to paint the monument.

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The requreid line plot displays a data set with an outlier given below.

The line plot with the outlier is the second one that displays the values as dots above the corresponding values on the number line. The data set has a clear outlier with one dot above the number 5, while the rest of the data points cluster around the values of 6 to 13. The other line plots do not display any clear outliers.

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We reject the null hypothesis because Hcal is greater than Hcrit

In statistics, the null hypothesis is a statement suggesting that there are no significant differences when studying two or more groups, variables, or phenomena.

Typically represented as H0 and deemed truthful until confirmed otherwise by empirical data, it can be exemplified in studies evaluating the impact of new drugs where the null hypothesis will claim that they have no effect on the outcome measured.

Here, any variations noticed between drug recipients versus those using placebos would be due to random variation rather than the drug itself causing the change.

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Answer:

A)

Step-by-step explanation:

original height- h

We are gonna add 5 to it cuz it's taller but if it was shorter we would have subtracted 5.

We are gonna add 5 to it cuz it's taller but if it was shorter we would have subtracted 5.or if it was 5 times taller we would have multiplied.

In this case it is mentioned taller so the expression would be h+5

The data shown is quantitative and continuous.

The Marcas family has listed distances to attractions in Florida as: (157, 395, 204, 150, 381, 537, 99.4, 289, 231, 246).

The data shown is quantitative and continuous.

It should be displayed in a histogram because it effectively represents the distribution of numerical data, allowing the family to visualize the distances and make an informed decision about their trip.

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The correct statement is,

⇒ The values below the X-axis are negative values of y

We have to given that;

To find true statement for the Cartesian coordinate system.

Now, We know that;

the values below the X-axis are negative values of y

And, the values above the X-axis are positive values of y.

Thus, The correct statement is,

⇒ The values below the X-axis are negative values of y

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Answer: The value of c is 8

Step-by-step explanation:

On the thing it says the c=8

The value of z is (15±5i√7)/4

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Solving x²/5 +5 = 3z/2

multiplying all terms by 10

2z²+50 = 15z

2z²-15z +50= 0

using formula method

z = -b ±√ b²-4ac)/2a

a = 2, b = -15, c = 50

(-(-15 )± √ 15²-4×2×50)/2× 2

z = 15±√225-400)/4

z = 15±√-175)/4

z = 15±√-25×7)/4

z= (15±5i√7)/4

therefore the value of z is (15±5i√7)/4

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The calculated value of the perimeter of the object is 73 inches

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

x = 12 inches, y = 24 inches, z = 34 inches, and w = 3 inches,

The value of the perimeter of the object is calculated by adding the side lengths

So, we have

perimeter = x + y + z + w

Substitute the known values in the above equation, so, we have the following representation

perimeter = 12 + 24 + 34 + 3

Evaluate

perimeter = 73

Hene, the perimeter is 73 inches

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The value of arc CD is determined as 60⁰.

option A.

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

arc BD = 2 x m∠BED

From the diagram, we have, m∠BED = 62⁰

The value of arc BD is calculated as follows;

arc BD = 2 x 62⁰

arc BD = 124⁰

arc BD = arc BC + arc CD

arc CD = 124 - 64

arc CD = 60⁰

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JKLMN is a regular polygon inscribed in a circle. The radius of the polygon is 5 units.

What is regular polygon?

Every polygon with equal side lengths and interior angles is said to be regular. A regular polygon's circumradius, also known as its radius, is the constant distance from the center to any of its vertices. It holds true for every vertex in the polygon. Therefore, PM = radius = 5 units.

As a result, the circumradius acts as a fundamental geometric characteristic of a regular polygon, describing both the size of the circle that completely encloses the polygon and the equal distance between its center and vertices. Therefore, the radius of the polygon is 5 units.

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The unit vector that has the same direction as v is u = v/|v| = (2i - 5j)/√(29)

To find the unit vector that has the same direction as the vector v, we need to divide the vector v by its magnitude. The magnitude of a vector is the square root of the sum of the squares of its components. In other words, if v = (a,b), then the magnitude of v is given by:

|v| = √(a² + b²)

Using this formula, we can find the magnitude of the vector v as:

|v| = √(2² + (-5)²) = √(29)

Now, to find the unit vector that has the same direction as v, we divide v by its magnitude:

u = v/|v| = (2i - 5j)/√(29)

This is the unit vector in the same direction as v. It has a magnitude of 1, which means that it is a vector of length 1. By dividing v by its magnitude, we have scaled v so that its length is 1, but its direction is still the same as the original vector v.

In summary, to find the unit vector that has the same direction as the vector v, we divide v by its magnitude. This gives us a vector of length 1 in the same direction as v.

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On average, per roll, he can expect to win: (1/36 * 50) - (35/36 * 5) = $1.39 - $4.86 = -$3.47.

Sammy has a 1/36 chance of rolling a sum of 2 (1+1), and a 35/36 chance of rolling any other sum.

On average, per roll, he can expect to win: (1/36 * 50) - (35/36 * 5) = $1.39 - $4.86 = -$3.47.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. It is stated as a number between 0 and 1, or, when using percentage notation, as a number between 0% and 100%.

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