A local health club offers two membership plans. Under Plan A, you pa
flat rate of $201 a month and you get unlimited visits. Under Plan B, yo
pay only $33 per month, but must pay $8 for each visit to the club. At
what number of visits will both plans be the same?
The plans cost the same if you visit
times.

After diving the polynomials, the quotient and remainder is q(x)=-x^2+1 and r(x)=-1 respectively.

What are polynomials?

The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases." There is no limit to the number of terms that can exist in a polynomial.

The polynomials are -

a(x)=-x^4

b(x)=x^2+1

Divide a(x) by b(x).

-x^4/x^2+1 = -x^2+1 with remainder as -1.

The quotient is obtained as q(x)=-x^2+1 and the remainder is r(x)=-1.

The given equation is -

a(x)/b(x)=q(x)+[r(x)/b(x)]

Plugging in all the values -

-x^4/x^2+1=-x^2+1+[-1/x^2+1]

[-x^4/x^2+1]-[-1/x^2+1]=-x^2-1

-x^4+1/x^2+1=-x^2-1

-x^4+1=[-x^2+1][x^2+1]

-x^4+1=(-x)^2[x^2+1]+(1)[x^2+1]

-x^4+1=-x^4-x^2+x^2+1

-x^4+1=-x^4-1

So, LHS=RHS is proved using the equation.

Therefore, the quotient is q(x)=-x^2+1 and the remainder is r(x)=-1.

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Answer:

The ratio of the new area to the old area will be 16:1

Step-by-step explanation:

I remember learning this in class. The radius is quadrupled, which means the radius is 4 times bigger. This will make the new area 16 times bigger than the old area.

Let's check

Area of circle: 3.14 x r^2

Area of the circle when radius 6:

3.14 (6)^2 = 113.04 ft^2

Area of the new circle when the radius is quadrupled:

3.14 (24)^2 = 1808.64 ft^2

1808.64 divided by 113.04 = 16

So, the ratio of the new area to the old area will be 16:1

We would need to multiply the first equation by -4 to eliminate the y variable when solving the system of equations by elimination.

The first equation is: 3x + 4y = 5

To eliminate the y variable when solving the system of equations by elimination, we need to multiply the first equation by -4. This is because when two equations are multiplied by the same number, any terms that have the same variable will be eliminated when the equations are added together.

Formula:

3x + 4y = 5

-4(3x + 4y = 5)

3x + 4y = 5

-12x - 16y = -20

Thus, we would need to multiply the first equation by -4 to eliminate the y variable when solving the system of equations by elimination.

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The value of x is 15 units and the value of y is 12 units from the given figure.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the figure, AB is parallel to CD.

∠AOB=∠COD (Vertically opposite angles)

∠OAB=∠ODC (Alternate angles)

By AA similarity ΔAOB similar to ΔCOD

Now, 9/x =y/20 =3/5

9/x=3/5

x=15 units

y/20=3/5

y/4=3/1

y=12 units

Therefore, the value of x is 15 units and the value of y is 12 units from the given figure.

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4.68

find unit rate by dividing 208 cents by 16 which is 13 than multiply by 36

Answer:

16 inches of ribbon cost- $2.08

36 inches of ribbon cost- ?

36*$2.08/ 16

$74.88/16

= $4.68

Thus, 36 inches of ribbon would cost $4.68

Answer:

Step-by-step explanation:

25×80%=20

so she need to get 20 questions right

Answer:

20

Step-by-step explanation:

total question: 25

marks need to pass: 80%

25-20% = 20

The four names of an angle are acute angle, right angle, obtuse angle, and reflex angle.

An acute angle measures less than 90 degrees.

A right angle measures exactly 90 degrees.

An obtuse angle measures greater than 90 degrees but less than 180 degrees.

A reflex angle measures greater than 180 degrees but less than 360 degrees.

It's worth noting that these names are based on the measure of the angle, an acute angle is less than 90 degrees, a right angle is exactly 90 degrees, an obtuse angle is greater than 90 degrees but less than 180 degrees, and a reflex angle is greater than 180 degrees but less than 360 degrees.

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2a³b⁻⁴/3a⁵b⁻² =  2/3(ab)²

The exponent of a number shows how many times the number is multiplied by itself.

Example: 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power."

In general, xⁿ means that x is multiplied by itself for n times.

Properties of exponents:

Law of Product: a ^m × a ^n = a ^(m + n)

Law of Quotient: a ^m/a ^n = a ^(m - n)

Law of Negative Exponent: a^-m = 1/a ^m

Law of Power of a Product: (ab)^m = a ^m . b ^m

Law of Power of a Quotient: (a/b) ^m = a ^m/b ^m

Given expression

2a³b⁻⁴/3a⁵b⁻²

= 2/3 . a³/a⁵ . b⁻⁴/b⁻²

Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]

= 2/3 . a³/a⁵ . b²/b⁴

Law of Quotient: [tex]a^{m} /a^{n} = a^{m-n}[/tex]

= 2/3 . a³⁻⁵ . b²⁻⁴

= 2/3 . a⁻² .b⁻²

Law of Power of a Product: [tex]a^{m} .b^{m}= (ab)^{m}[/tex]

= 2/3 . (ab)⁻²

Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]

= 2/3 . 1/(ab)²

= 2/3(ab)²

Hence the simplified expression of 2a³b⁻⁴/3a⁵b⁻² is  2/3(ab)².

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Vivian and her dad travelled for a total distance of 12 miles

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

Time taken = 4 hours

Rate of travel = 3 miles per hour

The distance travelled can be calculated using the following equation

Distance = Rate of travel * Time taken

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

Distance = 3 miles per hour * 4 hours

Evaluate the product

So, we have the following representation

Distance = 12 miles

Hence, the distance is 12 miles

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Complete question

Vivian and her dad drive 4 hours to the rock and roll hall of fame in Cleveland, Ohio. if they drive at the same rate how far do they travel if the rate is 3 miles per hour

Answer:

D) 7.5%

Step-by-step explanation:

We can solve this through guessing and checking, or we can do this mathematically. We will try both approaches.

Mathematically:

We know that to get the extra $30 if we have $100, is a 30% interest. Now, since we have 4x 100, and these numbers are inversely proportional, we will need to divide 30 by 4. Doing this gives us 30/4 = 7.5, so the answer is 7.5%.

Guess and Check:

This way is a bit slower, but we will go through each answer and find how much money we would get from them. So, we would take our percent, change it to a number of that percent, considering we are taking it from 100, and multiply it by 4 since we have $400. We will get each of these respectively:

A) 3% = 3 * 4 = $12

B) 4.5% = 4.5 * 4 = $18

C) 6% = 6 * 4 = $24

D) 7.5% = 7.5 * 4 = $30

As you can see, D) gives us that extra $30, so the answer is D) 7.5%.

Hope this helped!

x>9 perfectly describes the situation.

In mathematics, inequalities characterise the connection between two non-equal numbers. Inequality implies being unequal. If two values are not equal, we use the "not equal symbol ()". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.

Let x be the amount of hot cocoa in fluid ounces that each mug contains.

Since each mug has more than 9 fluid ounces of hot cocoa, we can write the inequality as:

x > 9

We also know that the total amount of hot cocoa made is 8 mugs * the amount of hot cocoa in each mug = 8x.

So the inequality can be written as:

8x > 9*8 = 72

or

x>9

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When the two lines makes angle of 90 degree , then the lines are known as Perpendicular Lines .

What are Perpendicular Lines ?

Two lines are said to be perpendicular to each other if the straight line  makes an angle of 90 degree with another line. 90 degree is also called a Right Angle and is represented by a little square between two perpendicular lines .

when the two lines intersect at a right angle, they are said to be perpendicular to each other.

For Example : In a football field all the four corners of a football field are perpendicular to each other.

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Answer:

Step-by-step explanation:Select any two random points on the graph of the line (preferably with integer coordinates).

Label them as A and B (in any order).

Calculate the "rise" from A to B. While going vertically from A to B, if we have to go

"up", then the rise is positive;

"down", then the rise is negative.

Calculate the "run" from A to B. While going horizontally from A to B, if we have to go

"right", then the run is positive;

"left", then the run is negative.

Now, use the formula: slope = rise/run.

Answer:y=1.19x

Step-by-step explanation: Since each pound of tomato costs 1.19, you multiple the price by the amount of pounds to get the total cost.

The missing values in the table can be calculated by multiplying the given weights by 0.92 and 0.88 to get the maximum and minimum weights for each size.

Small egg:

Minimum weight = 1.2 * 0.92 = 1.104 ounces;

Maximum weight = 1.2 * 1.08 = 1.296 ounces

Medium egg:

Minimum weight = 1.6 * 0.92 = 1.472 ounces;

Maximum weight = 1.6 * 1.08 = 1.728 ounces

Large egg: Minimum weight = 2 * 0.92 = 1.84 ounces; Maximum weight = 2 * 1.08 = 2.16 ounces

Extra Large egg: Minimum weight = 2.4 * 0.92 = 2.208 ounces; Maximum weight = 2.4 * 1.08 = 2.592 ounces

Yes, it is possible for an egg to be both large and extra large, as long as the weight of the egg is between 1.84 and 2.592 ounces.

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The probability to draw a green bead is 1/3 and the probability to draw a green or yellow bead is 2/3

It is given that the bag contains 1 red bead, 2 yellow beads, 2 green beads, and 1 blue bead.

Hence the total no. of beads in the bag = no. of red + yellow + green + blue beads

= 1 + 2 + 2 + 1 beads

= 6 beads.

Let the event to draw a green bead be A

Let the event to draw a yellow bead be B

Probability of any event = no. of outcomes favorable to that event/ total number of outcomes

Hence P(A) = no. of green beads/ total no. of beads

= 2/6

= 1/3

Hence the probability that a green bead is drawn is 1/3

P(B) = no. of yellow beads/ total no. of beads

2/6 = 1/3

We need to find P(A or B)

= P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A ∩ B) = P(A and B)

Since no bead is of 2 colors, P(A ∩ B) = 0

Hence we get

P(A U B) = 1/3 + 1/3

= 2/3

Hence the probability to draw a green or yellow bead is 2/3

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On solving the provided question, we can say that - the both triangle similar triangle ABC and triangle DEF

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

AB = DE

BC = EF

AC = DF

so, by SSS both triangles are similar

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FG is not a defined term, so there is no way to determine its value.

FG is not a defined term, so there is no way to determine its value. This means that we cannot assign a numerical or other value to it. In order to determine the value of FG, we would first need to identify the context in which it is being used, as different contexts may assign different meanings to the same term. Once the context has been established, we can then look up the definition of FG in order to understand what it means in that particular context, and then assign a value to it accordingly. For example, if FG stands for "Frequency Generator" in a physics context, then it would likely have a numerical value associated with it.

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The probability that the sum of the 2 dice rolls will not be greater than 8 are 8 : 13.

When the probability of an event occurring is know, it is easy to calculate the probability that the event does not occur. Hence, If P(A) is the probability of event A, then 1 - P(A) is the probability that the event does not occur.

the probability that the sum of the 2 dice rolls being greater than 8 are expressed in the ratio 5:13 and expressed in fraction as 5/13

then;

probability that the sum of the 2 dice rolls will not be greater than 8 = 1 - 5/13

probability that the sum of the 2 dice rolls will not be greater than 8 = (13 - 5)/13

probability that the sum of the 2 dice rolls will not be greater than 8 = 8/13

Therefore probability that the sum of the 2 dice rolls will not be greater than 8 can be expression as the ratio 8 : 13

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So I have 5 and 3 notes each

You need to use simultaneous equations to solve this problem since there are 2 variables.

50x + 100y = 550 (value of the notes x the number of each note)

x + y = 8 (the number of each note added).

Multiply the second equation by 50 so that it the x variables are the same in both equations. Thus, 50x + 50y = 400.

Subtract 50x + 50y = 400 from 50x + 100y = 550.

The subtraction results in 50y = 150.

Divide by 50. y = 3, so x must equal 5.

So I have 5 and 3 notes each

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[tex]( x - 4 ) + ( 2x - 7 )[/tex]

Combine Like Terms:

[tex](x+2x)+(-4+-7)[/tex]

[tex](3x)+(-11)[/tex]

[tex]\fbox{3x - 11}[/tex]

Answer:3x-11

Step-by-step explanation:

(x-4)+( 2x-7)

x-4+2x-7

3x-11

Answer: it is the 4 one which is 3(5-n)=2n+16

There are [tex]7\frac{1}2}[/tex] grams on the scale in all once she added 2 5/6 grams to the scale.

The International System of Units (SI) is the modern form of the metric system and is the most widely used measurement system in the world. It consists of seven basic units of seven basic quantities.

Length is the meter, mass is the kilogram, time is the second, electric current is the ampere, temperature is the kelvin, amount of matter is the mole, and luminosity is the cand. SI also includes derived units such as Newton (force) and Pascal (pressure), which are combinations of base units. SI is the standard measurement system in most countries around the world and is used in scientific, engineering, and commercial applications.

Given,

initial weight = [tex]4\frac{2}{3} = \frac{14}{3}[/tex]

Final weight = [tex]2\frac{5}{6} = \frac{17}{6}[/tex]

Final weight = [tex]\frac{14}{3} + \frac{17}{6} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}[/tex]

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Answer:

Center: = (-1,-3)

Radius: = 1

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

In geometry, triangular polygons are ones that have three vertices and a right side. This object in two dimensions has three straight sides. Triangles are examples of three-sided polygons. The sum of a triangle's three angles is 180 degrees. The triangle lies on one plane.

Here,

Given : side = 12cm

Area of an equilateral triangle

=> √3/4 * side²

Side of triangle =12 cm

Area of an equilateral triangle

= >  √3/4 * 12²

=>√3/4 * 12*12

=> 62.28 cm²

Therefore , the solution of the given problem of triangle comes out to be  the equilateral triangle are is 62.28 cm².

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The linear relation y = |2x - 5| is a function which has it's domain along     (-∞, ∞) and it's range at [0, ∞)

A linear relation is a relationship between two variables (x and y) in which the points, when plotted on a graph, form a straight line. This means that for a given change in the independent variable (x), there will be a corresponding, predictable change in the dependent variable (y).

In this given relation, we can graph the absolute function and determine it's range and domain.

Using a graphing calculator;

y = |2x - 5|

The x-intercept of the relation is 2.5 and it's y-intercept is 5

The domain of the relation is (-∞, ∞)

The range of the relation is [0, ∞)

The relation y = |2x  5| is a function which is known as an absolute function

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Answer: Choice 2

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

y < -2x -2 Substitute in -1 for x and 0 for y and see if the statement is true.

0 < -2(-1) - 2

0 < 2-2

0 < 0  

This is a false statement.                                                                                                                                                                                                                                                                  

Answer: A / No.

Step-by-step explanation:

     We will substitute the point given, (-1, 0) and see if the inequality is true after simplifying.

     Given:

y < -2x - 2

     Substitue:

0 < -2(-1) - 2

     Multiply:

0 < 2 - 2

     Subtract:

0 < 0 ✗

     0 is not less than 0, so this point is not a solution.