PLEASE PLEASE PLEASE HELP MEEEEEE!!!!!!!!!!!!!!!!!!!!

The calculated volume of the figure is 761.97 cubic inches

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

The volume of the figure is calculated as

Volume = Cylinder + Cone - Hollow cylinder

So, we have

Volume = 3.14 * (8/2)^2 * 18 + 1/3 * 3.14 * (8/2)^2 * 5 - 3.14 * (2)^2 * 18

Evaluate

Volume = 761.97

Hence, the volume is 761.97 cubic inches

Read more about volume at

https://brainly.com/question/463363

#SPJ1

1. The numeric values of the function are given as follows:

2. As x approaches negative infinity, y approaches zero.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The numeric values for this problem are given as follows:

Increasing the negative exponent, the number gets closer to zero.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Answer:

y = (1/25)x^2 - 1

Step-by-step explanation:

To begin, we can use the fact that the x-intercepts of the parabola are at (5, 0) and (-6, 0) to determine the x-intercepts form of the equation. The x-intercepts form of a parabola is given by:

(x - r)(x - s) = 0,

where r and s are the x-coordinates of the x-intercepts.

Using this form, we can write:

(x - 5)(x + 6) = 0

Expanding this equation gives:

x^2 + x - 30 = 0

Next, we use the fact that the vertex of the parabola is at (0, -1) to determine the y-intercept form of the equation. The y-intercept form of a parabola is given by:

y = a(x - h)^2 + k,

where (h, k) is the vertex.

Substituting (0, -1) into this equation gives:

y = a(x - 0)^2 - 1

Simplifying gives:

y = ax^2 - 1

Now we can use the fact that the parabola passes through the point (5, 30) to determine the value of a. Substituting x = 5 and y = 0 into the equation above gives:

0 = a(5)^2 - 1

Solving for a gives:

a = 1/25

Substituting this value of a into the equation above gives the final equation of the parabola:

y = (1/25)x^2 - 1

5/0-6/0-41=

hope that helps okay :) if not really really sorry

Matching of the equation will be:

A) x= -7

B) x= 3

C) x= 9

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

A) 3(x-5) = 2(x-11) has x= -7 as the solution.

B) 4(3x+7) -5 = 12x +8 has x= 3 as the solution.

C) 3(x+1) -2x = x+3 has x= 9 as the solution.

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

There are 46 students don't drink soda.

Let's use a Venn diagram to represent the information given in the problem:

                         Athletes

                          /        \

                         /          \

          Soda     /            \    No Soda

                       /              \

                      /                \

                     /                  \

       ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

Drink                                      No Drink

      |                                              |

      |                                              |

      |                                              |

       ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

     19                                            24

      |                                              |

      |                                              |

      |                                              

    ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

     33                                             10

      |                                              |

      |                                              |

      |                                              |

    ----------------------------------------------

      |                                              |

      |                                              |

      |                                              |

     24                                             22

      |                                              |

      |                                              |

      |                                              |

       ----------------------------------------------

The diagram, we can see that there are 24 students who drink soda and are athletes, 19 who drink soda but are not athletes, 33 who are not athletes but drink soda, and 22 who are neither athletes nor soda drinkers.

The number of students do not drink soda, we need to add the number of students who are athletes but do not drink soda to the number of students who are neither athletes nor soda drinkers:

Number of students who don't drink soda

= Number of athletes who don't drink soda + Number of students who are neither athletes nor soda drinkers

Number of athletes who don't drink soda = Total number of athletes - Number of athletes who drink soda = 43 - 19 = 24

Number of students who are neither athletes nor soda drinkers = 22

The number of students who don't drink soda is:

Number of students who don't drink soda = 24 + 22 = 46.

For similar questions on Student

https://brainly.com/question/28521601

#SPJ11

Answer:

10 cm

Step-by-step explanation:

V =1/3 x π x r² x h

94.25 =1/3 x π x 3² x h

94.25 ÷ 3π =h

so, h= 10 cm

Therefore, can b and c are the same better deal since they have the same price per cubic inch using the volume of a cylinder.

To compare which can of beans is a better deal, we need to calculate the volume of each can and divide it by the price. The can with the highest volume per dollar is the better deal.

a) The volume of the can is V=πr²h=(3.14)(3²)(9)=254.34 cubic inches. The price per cubic inch is $39.95/254.34 = $0.157, rounded to three decimal places.

b) The volume of the can is V=πr²h=(3.14)(2²)(3)=37.68 cubic inches. The price per cubic inch is $5.96/37.68 = $0.158, rounded to three decimal places.

c) The volume of the can is V=πr²h=(3.14)(3²)(3)=84.78 cubic inches. The price per cubic inch is $13.41/84.78 = $0.158, rounded to three decimal places.

Therefore, can b and c are the same better deal since they have the same price per cubic inch.

Learn more about volume of a cylinder below.

https://brainly.com/question/9554871

#SPJ1

The expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.

In mathematics, an expression is a combination of variables, numbers, and mathematical operations that can be evaluated to produce a value. It can be as simple as a single number or variable, or it can be more complex and involve multiple variables and operations. Expressions can be used to represent a wide variety of mathematical concepts and relationships, and are an essential part of algebra, calculus, and other branches of mathematics.

The number of sundaes that can be made by one student is 3 x 3 = 9 (since each student chooses one of 3 syrups and one of 3 candy toppings).

Since there are 22 students in each class, the total number of sundaes made by one class is 22 x 9 = 198. Since there are 3 classes, the total number of sundaes made by all the students is 3 x 198 = 594.

Therefore, the expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.

To know more about expression visit:

https://brainly.com/question/1859113

#SPJ1

The correct statements  to conclude that a parallelogram is a rhombus are:  a.)  Segment AD ≅  Segment AB  e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

In two dimensions, a parallelogram is a geometric figure with parallel sides. It has two parallel sides that are  the same length, making it a four-sided polygon (sometimes called a quadrilateral). The sum of the adjacent angles of a parallelogram is 180 degrees. Parallelograms are a unique class of polygons.  

To conclude that a parallelogram is a rhombus, we must show that all four sides are congruent (of equal length). Therefore, statements that provide information about the sides of a parallelogram can help us make this conclusion.  

The correct statements  to conclude that a parallelogram is a rhombus are:

a.)  Segment AD ≅  Segment AB

e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

These statements tell us that opposite sides are congruent and opposite angles are congruent, which are properties of a rhombus. However, the expressions b, c and d do not give information about the sides, so it cannot be concluded from them that the parallelogram is a rhombus.

Learn more about parallelogram here

https://brainly.com/question/29147156?referrer=searchResults

p-value of 0.028 is considered statistically significant at a significance level of 0.05. This suggests that we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis that the true proportion exceeds 0.75.

To calculate the p-value for this test, we need to use the standard normal distribution table or a statistical software.

First, we need to find the area under the standard normal distribution curve to the right of the test statistic of 1.91.

Using a standard normal distribution table, we can find that the area to the right of 1.91 is 0.0287 (rounded to four decimal places).

Since this is a one-tailed test (the alternative hypothesis is that the true proportion is greater than 0.75), the p-value is equal to the area to the right of the test statistic, which is 0.0287.

Therefore, the p-value for this test is 0.028 (rounded to three decimal places). This means that if the null hypothesis (that the true proportion is less than or equal to 0.75) were true, we would expect to see a test statistic as extreme as 1.91 or more extreme in only 0.028 of all possible samples.

Learn more about p-value

https://brainly.com/question/30078820

#SPJ4

The p-value for the test when the test statistic is 1.91 and we are testing if the true proportion exceeds 0.75 is

approximately 0.028, rounded to 3 decimal places.

Given that the test statistic for testing, if the true proportion exceeds 0.75, is 1.91, we need to find the p-value for this

test and round it to 3 decimal places.

Identify the test statistic

The test statistic provided is 1.91.

Determine the tail of the test

Since we are testing if the true proportion exceeds 0.75, it is a right-tailed test.

Find the p-value

Using a Z-table or statistical software, find the area to the right of the test statistic (1.91) under the standard normal

distribution. This area corresponds to the p-value.

The area to the right of 1.91 in the Z-table is approximately 0.028. Therefore, the p-value for this test is approximately

0.028.

for such more question on  p-value

https://brainly.com/question/13786078

#SPJ11

Answer:

48

Step-by-step explanation:

50 (total green apples)  - 2 (green apples eaten) = 48 (green apples left)

The electrician needs approximately 296.26 feet of wire.

The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).

The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.

Using trigonometry, we can write:

sin(17°) = opposite / hypotenuse

where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:

hypotenuse = opposite / sin(17°)

To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:

tan(17°) = opposite / 85

Solving for the opposite side, we get:

opposite = 85 tan(17°)

Substituting this into the formula for the hypotenuse, we get:

hypotenuse = (85 tan(17°)) / sin(17°)

hypotenuse ≈ 296.26 feet

Therefore, the electrician needs approximately 296.26 feet of wire.

To know more about trigonometry visit:

https://brainly.com/question/22698523

#SPJ1

By using slope intercept , These were the two points on the line: (0,-2) and (7,2).

A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.

We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.

These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.

We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).

So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.

Graph given below:

To know more about slope intercept visit:

brainly.com/question/30216543

#SPJ1

The missing measure of the square pyramid and the net would be 11.18 units.

The amount of wood that Dee needs to make the doghouse is 98 square feet of wood.

The missing measure is the side of the pyramid and this can be found using the Pythagorean Theorem with 11 ft being the height of the triangle and 4/ 2 = 2 being one of the sides and the missing measure being the hypotenuse.

The side length is:

= √ (2 ² + 11²)

= √ ( 4 + 121)

= 11.18 units

To determine the amount of wood needed for Dee's doghouse, we need to calculate the surface area of the square pyramid using its net.

Calculate the area of all four triangular faces:

Total area of triangular faces = 4 x area of one triangular face = 4 x 20.5 = 82 square feet

Calculate the total surface area of the pyramid (net):

Total surface area = area of base + total area of triangular faces = 16 + 82 = 98 square feet

Find out more on square pyramids at https://brainly.com/question/27350043

#SPJ1

An equation that expresses the relationship between the lengths of the three sides is a^2 + b^2 = c^2.

In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

The relationship between the lengths of the three sides in a right triangle is described by the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

Mathematically, this can be represented as:

a^2 + b^2 = c^2

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

For the given right triangle with lengths 5, 2.2360679775, and 5.47722557505, we can plug in the values of a, b, and c to get:

5^2 + 2.2360679775^2 = 5.47722557505^2

which simplifies to:

25 + 5 = 30

This equation is true, indicating that the given lengths do indeed form a right triangle according to the Pythagorean Theorem.

To learn more about lengths click on,

https://brainly.com/question/17839185

#SPJ4

The vertex of the quadratic functions are (-3, -6), (7, 2) and  (4, 0).

The vertex of a quadratic function in the form y = a(x - h)² + k is given by the point (h, k).

To find the vertex, we need to rewrite the quadratic function in this form by completing the square.

a) y = (x + 3)² - 6:

We can rewrite this equation as y = (x - (-3))² - 6, which is in the form y = a(x - h)² + k.

Therefore, the vertex is (h, k) = (-3, -6).

b) y = (x-7)² + 2:

We can rewrite this equation as y = (x - 7)² + 2, which is in the form y = a(x - h)² + k.

Therefore, the vertex is (h, k) = (7, 2).

c) y = (x-4)²:

We can rewrite this equation as y = (x - 4)² + 0, which is in the form y = a(x - h)² + k.

Therefore, the vertex is (h, k) = (4, 0).

Read more about vertex at

https://brainly.com/question/20303598

#SPJ1

The curve xy²=2+xy has two horizontal or vertical tangent lines, namely x = 2/3 and y = -1/3, and x = -1/3 and y = 1/3.

To find the horizontal or vertical tangent lines of the curve xy²=2+xy, we need to take the derivative with respect to x and y and solve for when the derivative equals zero.

Taking the derivative with respect to x, we get:

y^2 + 2xy(dy/dx) = y(dy/dx) + 2x

Simplifying, we get

(dy/dx)(y^2 - y) = 2x - y^2

Taking the derivative with respect to y, we get

2xy + x(dy/dy)(2y) = dy/dy + x

Simplifying, we get

(dy/dy)(x-2y) = 1-x

Setting both derivatives equal to zero, we have

(dy/dx)(y^2 - y) = 2x - y^2 ...(1)

(dy/dy)(x-2y) = 1-x ...(2)

From (2), we get

dy/dy = (1-x)/(x-2y)

Substituting into (1), we get

(1-x)/(x-2y)(y^2 - y) = 2x - y^2

Simplifying, we get

y^3 - 3xy^2 + (2x^2-1)y + x = 0

This is a cubic equation in y, which can have up to three solutions. To find the horizontal or vertical tangent lines, we need to set dy/dx = 0 or dy/dy = 0.

Setting dy/dx = 0, we get

2x - y^2 = 0

Setting dy/dy = 0, we get

x - 2y = 1

Solving these equations simultaneously, we get

x = 2/3 and y = -1/3 or x = -1/3 and y = 1/3

Learn more about tangent lines here

brainly.com/question/13634178

#SPJ4

The given question is incomplete, the complete question is:

In the xy-plane, how many horizontal or vertical tangent lines does the curve xy²=2+xy have?

Answer:

P = 11 + (1/2)π(11) = 11 + 5.5π = 28.279 cm

Letting π = 3.142:

P = 11 + (1/2)(3.142)(11) = 28.281 cm

Answer: To find the average change in temperature per hour, we need to divide the total change in temperature by the number of hours.

The temperature dropped 25 degrees over 8 hours, so the average change per hour is:

25 degrees / 8 hours = 3.125 degrees per hour

Therefore, the temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.

Step-by-step explanation: The temperature on top of Mt. Katahdin dropped by an average of 3.125 degrees per hour.

The two data sets that meet the given conditions for in centers, and variability is in the explanations.

Data Set 1 - Heights of Adults in a City:

Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62

Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.

Data Set 2 - Salaries of Employees in a Corporation:

Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55

Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.

Learn more about data set here: https://brainly.com/question/28168026

#SPJ1

1)  The lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.

2)  CD = 2AD.

1) To prove that BMED is a trapezoid, we need to show that BM || ED.

Since O is the midpoint of AM, we have OB || MD (as OB and MD are both perpendicular to AM).

Also, since E is the midpoint of DC, we have DE || AC (as DE and AC are both perpendicular to BC).

Therefore, to show that BM || ED, it is enough to show that AC || OB.

We know that OB is a transversal to the parallel lines BM and AM, so we have:

∠OBD = ∠MBC (corresponding angles)

Similarly, we have:

∠OAD = ∠ABC (corresponding angles)

Since ∠MBC = ∠ABC (because [AM] is the median), we have:

∠OBD = ∠OAD

Therefore, the lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.

2) To prove that D is the midpoint of [AE], we need to show that AD = DE.

Since [AM] is the median, we have:

AD = MC

Also, since E is the midpoint of DC, we have:

DE = EC

So it is enough to show that MC = EC.

Since O is the midpoint of AM, we have:

OM = MA/2

But MA = MC + AC/2 (because [AM] is the median), so we have:

OM = (MC + AC/2)/2

= MC/2 + AC/4

Also, since E is the midpoint of DC, we have:

OE = EC/2

But AC = 2DC (because [AM] is the median), so we have:

OE = EC/2 = AC/4

Therefore, we have:

OM = OE

So triangle OME is isosceles, and we have:

∠OEM = ∠OME

But ∠OED = ∠OEM (because DE || AC), so we have:

∠OED = ∠OME

Therefore, triangles ODE and OME are similar, so we have:

OD/OM = OE/OE

= 1

Therefore, OD = OM.

But we also have:

OM = MA/2 = MC/2 + AC/4

= AD/2 + AC/4 (because [AM] is the median)

So we have:

OD = OM = AD/2 + AC/4

= AD/2 + DC/2 (because AC = 2DC)

= (AD + DC)/2

= AE/2 (because E is the midpoint of DC)

Therefore, we have shown that D is the midpoint of [AE].

Moreover, we have:

CD = AE/2 = AD + DC/2 = AD + AC/4 (because AC = 2DC)

= AD + MC/2 (because [AM] is the median)

= AD + AD/2 (because AD = MC)

= 3AD/2

So we have CD = 2AD.

3) To prove that OD = 4BD, we need to show that BD = (1/4)OM.

Since [AM] is the median, we have:

BM = MC

Also, since O is the midpoint of AM, we have:

OM = BM/2 + AM/2

= BM/2 + 2BM/2 (because [AM] is the median)

= 3BM/2

Therefore, we have:

BD = BM - MD

= MC - MD

Learn more on trapezoids here https://brainly.com/question/1410008

#SPJ1

a. The difference between the high and the low prices on October 20 was $3.33.

b. The actual volume of Discovery Group shares posted on October 27 was 23,600.

c. The closing price for Discovery Group on October 19 was $38.50

The percentage decrease is calculated below as follows:

closing price on October 19 = $38.50

the opening price on October 20 = $37.22

the percentage decrease in prices = (37.22 - 38.50) / 38.50

the percentage decrease in prices = -3.33% to the nearest hundredth

e. The net change =  $32.00 - $38.50

The net change = -$6.50.

The percentage change = (-6.50 / 38.50) * 100

The percentage change  = -16.9% to the nearest tenth percent

Learn more about percentages at: https://brainly.com/question/24877689

#SPJ1

The table for the function f(x) = 2ˣ should be completed as follows;

x         -4      -3     -2    -1    0

f(x)      1/16   1/8    1/4   1/2  1

As x approaches negative infinity, f(x) decreases.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the negative power rule to the function based on each of the x-values, we have the following:

f(x) = 2⁰ = 1

f(x) = 2⁻¹ = 1/2

f(x) = 2⁻² = 1/2² = 1/4

f(x) = 2⁻³ = 1/2³ = 1/8

f(x) = 2⁻⁴ = 1/2⁴ = 1/16

Read more on exponent here: https://brainly.com/question/27858496

#SPJ1

The perimeter of rectangle JKLM which has vertices J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2) On the coordinate plane is 30 units.

By applying the Pythagorean distance formula we calculate the length of each side of the rectangle as,

Distance, d = √{(x₁ - x₂)² + (y₁ - y₂)²}  (units)

where  (x₁, y₁ ) and ( x₂, y₂) are the coordinates of both the end of a side of the rectangle.

The coordinates of the rectangle JKLM are given as J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2).

Thus,

| JK | = √{(-2 - 6)² + (2 +4)²} = 10 units

| JM | = √{( -2 +5)² + (2 +2)²} = 5 units

| KL | =√{(6-3 )² + (-4+8 )²} = 5 units

| LM | = √{(3+5)² + (-8+2)²} = 10 units

Therefore,  JK and LM are sides opposite to each other (and let it be length) and JM and Kl are the other pair (and let it be the breadth) in the rectangle.

Thus, perimeter of a rectangle can be found with the formula,

Perimeter of JKLM = 2( length + breadth) in units

= 2(10+ 5) units

= 30 units

To know more about perimeter of rectangle here

https://brainly.com/question/29595517

#SPJ4

Answer: the answer is d) 0.3466.

Step-by-step explanation:

Starting with the equation:

6e^(4x) - 3 = 21

Add 3 to both sides:

6e^(4x) = 24

Divide both sides by 6:

e^(4x) = 4

Take the natural logarithm of both sides:

ln(e^(4x)) = ln(4)

Use the property of logarithms that ln(e^y) = y:

4x ln(e) = ln(4)

Simplify:

4x = ln(4)

Solve for x by dividing both sides by 4:

x = (1/4) ln(4)

Using a calculator, we get:

x ≈ 0.3466

Therefore, the answer is d) 0.3466.

After comparing the data, a measure of variability for both sets of data to  be utilised to find the place with the most stable temperature: C. Range, because Sunny Town is skewed.

Skewness is a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram in mathematics, and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.

We may rationally establish that Sunny Town's box plot (box-and-whisker plot) is distorted by closely inspecting it.

Conversely, the Desert Landing box plot (box-and-whisker plot) is symmetrical (vertical line dividing the box into two equal halves), which simply means that both whiskers on either side of the box plot (box-and-whisker plot) are roughly equal and symmetric.

Learn more about range here:

brainly.com/question/17083142

#SPJ1

The simplified form of the expression is written as 11x³ - 39x -2x²/(x²- 9)(x+ 3)

Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, factors and coefficients.

These expressions are also made up of arithmetic operations such as addition, multiplication, division, subtraction, etc

From the information given, we have that;

x -2/x + 3 + 10x/x² - 9

Find the lowest common denominator and simplify

(x-2)(x² - 9) + (x-3)(10x)  /(x²- 9)(x+ 3)

Now, expand the bracket, we get;

x³ - 9x - 2x² + 10x³ - 30x/(x²- 9)(x+ 3)

collect the like terms of the denominator and that of the numerator, we get;

11x³ - 39x -2x²/(x²- 9)(x+ 3)

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.

How to solve the question?

In polar coordinates, a graph of a function passes through the origin if and only if the function's value at θ=0 is equal to zero. This is because the origin in polar coordinates represents the point (r=0, θ), where r is the distance from the origin and θ is the angle of the point with respect to the positive x-axis. When a function's value at θ=0 is equal to zero, it means that the point on the graph at θ=0 lies on the positive x-axis and has a distance of r=0 from the origin, which is the origin itself.

In contrast, a graph of a function in rectangular coordinates passes through the origin if and only if the function's value at (0,0) is equal to zero. This is because the origin in rectangular coordinates represents the point where the x and y axes intersect, and a point on the graph with coordinates (x,y) passes through the origin if and only if x=0 and y=0, which means the function's value at (0,0) is equal to zero.

In summary, the condition for a function's graph to pass through the origin in polar coordinates is that the function's value at θ=0 is equal to zero, while the condition for a function's graph to pass through the origin in rectangular coordinates is that the function's value at (0,0) is equal to zero.

To know more about graph visit :-

https://brainly.com/question/19040584

#SPJ1