1. Solve for x. Show your work.

2x-1/2=3-x

Final answer:

Parametric equations for a sphere centered at the origin with radius 3 are x = 3 sin(t) cos(s), y = 3 sin(t) sin(s), and z = 3 cos(t), where t is the angle from the vertical and s is the angle from the x-axis on the xy-plane.

Explanation:

To find parametric equations for a sphere centered at the origin with radius 3 using parameters s and t, we make use of spherical coordinates. In spherical coordinates, a point on the sphere can be expressed as:

x = r sin(t) cos(s)

y = r sin(t) sin(s)

z = r cos(t)

Where r is the radius of the sphere, t is the angle with the vertical (ranging from 0 to π), and s is the angle on the xy-plane from the x-axis (ranging from 0 to 2π). Given that the radius r is 3, the parametric equations become:

x( s, t) = 3 sin(t) cos(s)

y( s, t) = 3 sin(t) sin(s)

z( s, t) = 3 cos(t)

Final answer:

To find the parametric equations for a sphere with radius 3 centered at the origin, we use spherical coordinates with parameters s and t to define the x, y, and z components in terms of trigonometric functions. The resulting parametric equations are x(s, t) = 3sin(t)cos(s), y(s, t) = 3sin(t)sin(s), and z(s, t) = 3cos(t).

Explanation:

Finding Parametric Equations for a Sphere

To find the parametric equations for a sphere centered at the origin with radius 3 using the parameters s and t, we use spherical coordinates. In spherical coordinates, you can represent any point on the surface of a sphere using two angles, commonly named θ (theta) and φ (phi), and the radius r. Since we're given a radius of 3, we can set r to be 3.

The standard spherical coordinates in terms of s and t can be expressed as:

Here, t represents the polar angle, measured from the positive z-axis, and s is the azimuthal angle in the xy-plane from the positive x-axis. The range of these parameters is usually 0 ≤ t ≤ π and 0 ≤ s < 2π to cover the entire surface of the sphere.

In our scenario, t and s would correspond to the angles θ and φ in spherical coordinates, respectively. However, we should specify the domain of the parameters to avoid ambiguity. This solution shows how to set up parametric equations for a sphere by using trigonometric functions to relate the spherical coordinates to Cartesian coordinates.

we know that

the statement

[tex]1=3[/tex] -----> is not true

so

The system has no solutions

For example

two parallel lines

[tex]y=5x+1[/tex] -----> equation A

[tex]y=5x+3[/tex] -----> equation B

The system has no solution. because the lines are parallel

If you equate equation A and equation B

[tex]5x+1=5x+3[/tex]

[tex]1=3[/tex] ------> is not true

therefore

the answer is the option

There is no solution

Answer:

There is no solution

Step-by-step explanation:

1 doesn't equal 3 so it can't have a solution

The polynomial function of minimum degree with real coefficients that has the zeros 7, -11, and 2 + 6i is obtained by also including the conjugate zero 2 - 6i and multiplying the corresponding factors. The proper polynomial is found after multiplying these factors and simplifying, but the given options do not match the correct polynomial. There may be an error in the given options.

To write a polynomial function of minimum degree with real coefficients given the zeros 7, -11, and 2 + 6i, we must remember that complex zeros in polynomials with real coefficients always come in conjugate pairs. Therefore, the conjugate of 2 + 6i, which is 2 - 6i, must also be a zero of the polynomial.

First, we write a factor for each zero: (x - 7), (x + 11), (x - (2 + 6i)), and (x - (2 - 6i)). Multiplying these factors together will give us the required polynomial:

After multiplying and simplifying these factors, and combining like terms, the polynomial function in standard form with these zeros and with real coefficients is:

f(x) = x´ - 9x³ + 42x² - 154x + 3080

However, none of the given options match the correct polynomial derived from the provided zeros. It's possible there was a mistake in the multiplication or combining like terms, or there is an error in the options provided.

In an arithmetic sequence, the common difference is constant. In a geometric sequence, the terms are obtained by multiplying the previous term by a constant ratio. In this case, the value of y in the sequence is 3 for an arithmetic sequence and 9 for a geometric sequence.

In an arithmetic sequence, the difference between consecutive terms is constant. To find the value of y in the sequence 2, 8, 3y + 5, we observe that the common difference is 8 - 2 = 6. Therefore, we can set up the equation 8 - 2 = 3y + 5 - 8 to solve for y. Simplifying, we get 6 = 3y - 3. Solving for y, we have y = 3.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. To find the value of y in the sequence 2, 8, 3y + 5, we need to determine the common ratio. We can see that the ratio between 8 and 2 is 8/2 = 4. Therefore, we can set up the equation 8/2 = (3y + 5)/8 to solve for y. Simplifying, we get 4 = (3y + 5)/8. Multiplying both sides by 8, we have 32 = 3y + 5. Solving for y, we get y = 9.

Answer:

27 blue balloons

Step-by-step explanation:

Salina was at a party and she noticed that the room had 54 balloons.

For every red balloon there were 2 yellow and 3 blue balloons.

This is written in the form of ratio as = 1 : 2 : 3

First we calculate the number of red balloon.

54 / (1 + 2 + 3)

= 54 / 6 = 9 red balloons

For every red balloons there were 3 blue balloons.

Therefore, Blue balloons = 9 × 3 = 27 blue balloons

27 blue balloons were in the room.

Final answer:

To find the total height of Stephan's sculpture with the base, we add the heights represented by fractions with a common denominator to get an overall height of 11/12 feet.

Explanation:

To determine the overall height of Stephan's sculpture with the base, we simply need to add the height of the sculpture to the height of the base. The sculpture is 7/12 foot tall and the base is 1/3 foot tall. To add these two fractions together, we need to find a common denominator, which is 12 in this case. So, we convert 1/3 foot into 4/12 foot. Now we can add the two fractions:

7/12 + 4/12 = 11/12 feet

Therefore, the combined height of the sculpture and the base is 11/12 feet.

The ordered pairs lie on the graph of the exponential function is (3, 16).

The formula f(x) = [tex]a^x[/tex]defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x.

We have,

f(x) = 180 (0.5[tex])^x[/tex]

Now, for x = 0,

So, f(x) = 128(0.5[tex])^0[/tex]

= 128(1)

= 128

Now, for x = 1,

f(x) = 128(0.5[tex])^1[/tex]

= 128(0.5)

= 256

Now, for x = 3,

f(x) = 128(0.5[tex])^3[/tex]

= 128(1/8)

= 16

So, the correct ordered pair is (3, 16).

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The slope between points (-2, 5) and (1, 4) is -1/3. The pair of points (16, 15) and (13, 10) could lie on a line with a slope of -5/3. For a line with slope 1/4 passing through (6, y) and (10, -1), the value of y is 2. The slope of a vertical line is undefined. The rate of change in the charter boat cost is $55 per additional person.

The slope of a line passing through two points can be found using the formula slope = (y2 - y1) / (x2 - x1). For the points (-2, 5) and (1, 4), the slope is (4 - 5) / (1 - (-2)) = -1 / 3, which is choice c, -1/3. For a line with a slope of -5/3, we can pick two points and use the slope formula to verify that the slope between them is -5/3. For example, using points (16, 15) and (13, 10), the slope would be (10 - 15) / (13 - 16) = -5 / -3, which is indeed 5/3, making choice b, (16, 15) (13, 10), correct.

For a pair of points (6, y) and (10, -1) lying on a line with slope 1/4, we can set up the equation 1/4 = (-1 - y) / (10 - 6) and solve for y to find that y = 2, so the answer is choice c, 2. The slope of a vertical line is undefined because the change in x is zero, hence choice d, Undefined, is the correct answer.

For the fishing charter boat cost problem, the rate of change or the cost per additional person is the difference in cost divided by the difference in the number of people. For example, for 3 and 2 people, the rate is (165 - 110) / (3 - 2) = 55, so the rate of change is 55 dollars per additional person, which is choice d, 55/1. This rate of change represents the additional cost for each extra person joining the fishing charter.

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The number 4.4354 correct to 2 decimal places is 4.44. The third digit, 5, indicates that the second decimal place is rounded up.

The question is asking to write the number 4.4354 correct to 2 decimal places. When you're rounding a number to a certain number of decimal places, you look at the digit in the next spot decimal place. In this case, for two decimal places, we look at the third decimal. If this number is 5 or above, we 'round up' the second decimal place by one digit. If it is less than 5, we leave it as is. The third digit in this case is 5, so we 'round up' meaning the number 4.4354 written correct to 2 decimal places is 4.44.

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The number 0.7008 rounded to the greatest non zero place is 1.

Rounding is a process to estimate a particular number in a context.

To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, roundup.

Now the given number is,

0.7008

To round the number to the greatest non zero place.

The greatest non zero digit in the number 0.7008 is 0.

The digit '0' in the given number is at ones place.

So, we will round the number 0.7008 to the nearest ones place.

Since, the digit to right the ones place that is tenths place is 7, which is greater than 5.

So, the digit will roundup to 1.

Thus, the number 0.7008 rounded to the greatest non zero place is 1.

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Answer:

always

I just did it on my  website

Answer:

d

Step-by-step explanation:

edge 2020

The result of the division is:

[tex]\[\boxed{4x^2 - 10x + 11 + \frac{6}{2x + 5}}\][/tex]

To find [tex]\( \frac{f(x)}{g(x)} \)[/tex] where [tex]\( f(x) = 8x^3 - 28x + 61 \)[/tex] and [tex]\( g(x) = 2x + 5 \)[/tex], we need to perform polynomial division.

Polynomial Division

1. Divide the leading term of the dividend by the leading term of the divisor:

 [tex]\[ \frac{8x^3}{2x} = 4x^2 \][/tex]

2. Multiply the entire divisor by this result and subtract from the dividend:

[tex]\[ 8x^3 - 28x + 61 - (4x^2 \cdot (2x + 5)) = 8x^3 - 28x + 61 - (8x^3 + 20x^2) \][/tex]

  Simplifying, we get:

[tex]\[ -20x^2 - 28x + 61 \][/tex]

3. Repeat the process with the new polynomial:

 [tex]\[ \frac{-20x^2}{2x} = -10x \][/tex]

4. Multiply the entire divisor by this result and subtract:

[tex]\[ -20x^2 - 28x + 61 - (-10x \cdot (2x + 5)) = -20x^2 - 28x + 61 - (-20x^2 - 50x) \][/tex]

  Simplifying, we get:

[tex]\[ 22x + 61 \][/tex]

5. Repeat the process again:

  [tex]\[ \frac{22x}{2x} = 11 \][/tex]

6. Multiply the entire divisor by this result and subtract:

[tex]\[ 22x + 61 - (11 \cdot (2x + 5)) = 22x + 61 - (22x + 55) \][/tex]

  Simplifying, we get:

 [tex]\[ 6 \][/tex]

Putting it all together, we have:

[tex]\[\frac{f(x)}{g(x)} = 4x^2 - 10x + 11 + \frac{6}{2x+5}\][/tex]

So, the result of the division is:

[tex]\[\boxed{4x^2 - 10x + 11 + \frac{6}{2x + 5}}\][/tex]

Let x be a time in hours and y be an amount of remaining entries. You have that:

Find the slope of the line that is passing through the points [tex] (x_1,y_1)[/tex] and [tex] (x_2,y_2)[/tex]  by formula

[tex] \dfrac{y_2-y_1}{x_2-x_1}.[/tex]

Thus, the slope is

[tex] \dfrac{5-2}{2-4}=-1.5.[/tex]

Answer: graph of line going through (0, 8) with a slope of -1.5

Answer:

Step-by-step explanation:

Use proportions to figure this out.  On the top you'll have miles and on the bottom you'll have minutes.  I am going to change 3/4 to .75 and 1/8 to .125:

[tex]\frac{miles}{minute}:\frac{.75}{.125}[/tex]

We want to know how many miles per 1 minute that is.  So we have the unknown on top in a new ratio, with 1 on the bottom:

[tex]\frac{miles}{minute}:\frac{.75}{.125}=\frac{x}{1}[/tex]

This second ratio is allowing us to calculate what the decimal ratio is in miles per 1 minute.  Cross multiply to get

.125x = .75 so

x = 6 miles

That tells us that the decimal ratio is equivalent to 6 miles per minute

Answer: $110

Step-by-step explanation: $110 is the correct approximation. The easiest way is to divide the total by 4, since 25% represents  1 /4 .

In a regular pentagon with equal sides and angles, the sum of the inside angles is 540 degrees. The third polygon P has 6 sides.

In a regular pentagon with equal sides and angles, the sum of the inside angles is 540 degrees, and each angle is 108 degrees. Some actual items, including stars, soccer balls, and even street signs, contain pentagons.

Since P has a vertex at B, we can assume that its other sides emanate from B. Let's call the length of one of these sides x. Since the angle formed by AB and BC is a right angle, we can use the Pythagorean theorem to find the length of AC, which is the hypotenuse of the right triangle ABC:

AC² = AB^²+ BC²= s² + s² = 2s²

AC = √(2s²) = s x √(2)

Now, we can use the fact that AB and BC are sides of a regular pentagon and a square, respectively, to find the value of x. Since a regular pentagon has five sides of equal length, we know that AB is also a side of the Pentagon. Therefore:

AB = s

Similarly, since a square has all sides of equal length, we know that BC is also a side of the square. Therefore:

BC = s

Now, we can use the fact that the sum of the interior angles of a polygon with n sides is (n-2) x 180 degrees to find the value of n for polygon P. Since P has one right angle at B and two angles of 108 degrees (since a regular pentagon has interior angles of 108 degrees),

Set up the following equation:

90 + 108 + 108 + (n-3)180 = 180n

Simplifying, we get:

n = (540-90-108-108)/(180-180) + 3

n = 6

Therefore, the third polygon P has 6 sides.

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Answer: she needs to complete 8 more paintings

Step-by-step explanation:every month she completes 5 paintings

it has beeen 6 months

6*5=30 paintings

needs 38

38-30=8 paintings more

Talia took approximately 0.8 hours, or 48 minutes, to walk home.

To determine the time it took Talia to walk home, we can solve the equation

40(0.9 – x) = 5x.

First, distribute the 40 to get 36 - 40x = 5x.

Combine like terms to get 36 = 45x.

Divide both sides by 45 to solve for x.

Therefore, Talia took approximately 0.8 hours, or 48 minutes, to walk home.

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To solve the equation 40(0.9 – x) = 5x, distribute 40, combine like terms, and solve for x. Talia took 0.8 hours or 48 minutes to walk home.

The subject of this question is Mathematics and the grade level is High School.

To solve the equation 40(0.9 – x) = 5x, we can start by distributing 40 to the terms inside the parentheses: 36 – 40x = 5x.

Then, we combine like terms by adding 40x to both sides: 36 = 45x.

Finally, we divide both sides by 45 to find that x = 36/45 = 0.8.

Therefore, it took Talia 0.8 hours, or 48 minutes, to walk home.

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Answer:

The system of inequalities is equal to

[tex]x+y\geq 9[/tex]

[tex]4x+6y\leq 55[/tex]

The graph in the attached figure

Step-by-step explanation:

Let

x------> the number of gallons of iced tea

y-----> the number of gallons of lemonade

we know that

[tex]x+y\geq 9[/tex] -----> inequality A

[tex]4x+6y\leq 55[/tex] -----> inequality B

using a graphing tool

the solution is the shaded area

see the graph in the attached figure

The answer is 10,1

The explanation is below. The graph is correct and the point 10,1 is in the shaded area that is covered by both equations.