15 points!!! please help me figure this out I am so confused

Answer:

The width = 16 yards and the length = 25 yards.

Step-by-step explanation:

Let x yards be the original width, then the original length is 2x - 7 yards.

Therefore the original area = x(2x - 7) yd^2.

The new area =  (2x - 7 + 11)(x - 6)

= (2x + 4)(x - 6) yd^2.

So we have the equation

x(2x - 7) - (2x + 4)(x - 6) = 40

2x^2 - 7x - (2x^2 - 12x + 4x - 24) = 40

2x^2 - 7x - 2x^2 + 8x + 24 - 40 = 0

x - 16 = 0

x = 16 yards = the width.

The length = 2(16) - 7 = 25 yards.

To find the original dimensions of the lot, assume the width is 'w', then solve an equation using the information given.

To find the original dimensions of the lot, let's assume that the width is 'w' yards. The length of the lot is then '2w-7' yards, since it is 7 yards less than twice the width.

If we increase the length by 11 yards and decrease the width by 6 yards, the new dimensions would be '2w-7+11' yards for the length and 'w-6' yards for the width.

The area of the lot is given by length multiplied by width, so we can set up the equation:

(2w-7+11)(w-6) = (2w)(w) - 40

Simplifying this equation and solving for 'w', we find that the original width of the lot is 12 yards. The length is then 2(12) - 7 = 17 yards.

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Answer:

  √3

Step-by-step explanation:

  cot²(θ) = csc²(θ) -1 . . . . . a relevant identity

  = 1/sin²(θ) -1

  = (1/(1/2))² -1 = 2² -1 = 3

Then ...

  cot(θ) = √3 . . . . . . . . take the square root

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

It just is

Answer:

The area of a triangle is given by the formula:

A = bh/2

If the height of the triangle is 3 units more than the base we can say that:

h = b + 3

Therefore, the area of the triangle will be:

A= b(b+3)/2

Where 'b' comes to be the base of the triangle.

Answer:

A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]

Step-by-step explanation:

Given: Height of the triangle is 3 units more than the base.

Let "b" be the base of the triangle.

So, h = b + 3

Area of a triangle A = [tex]\frac{1}{2} base * height[/tex]

Now plug in h = b +3 in the above area of formula, we get

A(b) = [tex]\frac{1}{2} b*(b + 3)[/tex]

Now we can multiply b and (b + 3), we get

A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]

Therefore, the answer is A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]

Answer:

The correct graph is D (Compare to the graph above)

Answer:

D.

Step-by-step explanation:

You can see it calculating the vertex. the formula of the vertex is

[tex](\frac{-b}{2a}, y(\frac{-b}{2a}))[/tex]

where a = 1/2 and b=2.

[tex](\frac{-2}{1}, \frac{1}{2}(-2)^2+2(-2)-6)[/tex]

[tex](-2, \frac{1}{2}*4-4-6)[/tex]

[tex](-2, 2-4-6)[/tex]

[tex](-2, -8)[/tex]

The only option of graph that has vertex in (-2,-8) is option D.

Answer:

4 donuts and 2 brownies

Step-by-step explanation:

Guess and check

2 donuts --> $2.50

1 brownie -->$2.50

Since the amount of donuts is double,

we try :

4 donuts -->$1.25(4) = $5

2 brownies --> $2.50(2) = $5

Answer:

she bought 4 donuts and 2 brownies.

Step-by-step explanation:

This is a question on simultaneous equations where two variable are given with two or more relational equations. if she bought $10 worth of donuts and brownies, and each donut costs $1.25 and each brownie costs $2.50.

Then,

1.25d + 2.50b = 10 where d and b are the numbers of donuts and brownies purchased respectively.

if She bought twice as many donuts as brownies, then

d = 2b

Therefore,

1.25(2b) + 2.50b = 10

5b = 10

b = 2

d = 2 × 2 = 4

Hence she bought 4 donuts and 2 brownies.

Answer:

Step-by-step explanation:

____

Good evening ,

_______________

2(7) + 5(1) + 3(-3) = 10

3(7) ­ - (1) + 4(-3) = 8

5(7) - ­ 2(1) + 7(-3) = 12

Then (7,1,-3) is a solution to system

____

:)

Answer:

He should prepare 260 pounds of first mixture and 0 pounds of second mixture

Step-by-step explanation:

Let x be the total quantity ( in pounds ) of cherries and mints in the first mixture and y be the total quantity in second mixture,

Since, first mixture will contain half cherries and half mints by weight,

That is, in first mixture,

Cherries = [tex]\frac{x}{2}[/tex]

Mints = [tex]\frac{x}{2}[/tex],

While, second mixture will contain one-third cherries and two-thirds mints by weight,

That is, in second mixture,

Cherries = [tex]\frac{y}{3}[/tex]

Mints = [tex]\frac{2y}{3}[/tex]

According to the question,

The manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock,

That is,

[tex]\frac{x}{2}+\frac{y}{3} \leq 130[/tex]

[tex]\frac{x}{2}+\frac{2y}{3}\leq 170[/tex]

Also, pounds can not be negative,

x ≥ 0, y ≥ 0,

Since, the first and second mixture must be sell at the rate of $2.00 per pound and $1.25 per pound respectively,

Hence, the total revenue,

Z = 2.00x + 1.25y

Which is the function that have to maximise,

By plotting the above inequalities,

Vertex of feasible regions are,

(0,255), (180, 120) and (260, 0),

Also, at (260, 0), Z is maximum,

Hence, he should prepare 260 pounds of first mixture and 0 pounds of second mixture in order to maximize his sales revenue.

To maximize sales revenue, the candy manufacturer should prepare one-third cherries and two-thirds mints mixture.

To maximize sales revenue, the candy manufacturer should prepare a mixture that contains one-third cherries and two-thirds mints by weight. Let's assume that he prepares x pounds of this mixture. To calculate the amount of the other mixture, we subtract x from the total weight of the ingredients in stock. So, the amount of the other mixture will be (130 + 170) - x pounds. The candy manufacturer should prepare x pounds of the one-third cherries and two-thirds mints mixture and (130 + 170) - x pounds of the other mixture to maximize his sales revenue.

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Answer:

B= 32.11

A= 52.82

C= 95.07

Step-by-step explanation:

To find these angles, since you have all sides, you will need to use the law of cosines.

Answer:

(-2,3)

Step-by-step explanation:

7x+8y=10

5x+y=-7

To solve this by elimination, we need both equations in the same form.  There are.  They are both in form ax+by=c.

Now we also need for one of the columns with the variables to be opposite or same terms.

I like the way the column with the y's are looking because if I multiply that second y by 8 or -8 I will have sames or opposites.

I'm going to multiply the second equation by -8.

This will give me:

  7x+8y=10

-40x-8y=56

--------------------Add the equations!

-33x+0=66

 -33x   =66

      x    =66/-33

       x  =-2

Now we need to find the other variable. It doesn't matter which equation you use.

I'm going to use 5x+y=-7 where x=-2 to find y.

5(-2)+y=-7

-10+y=-7

Add 10 on both sides

     y=3

The solution is (-2,3)

Answer:

The solution is x = -2, y = 3. As an ordered pair it is (-2, 3).

Step-by-step explanation:

7x +  8y = 10

5x +   y = −7

Multiply the second equation by -8:

-40x - 8y = 56

Add this to the first equation, we get:

-33x = 66

x = -2

Now substitute for x in the second equation:

5(-2) + y = -7

y = -7 + 10

y = 3.

Check these results in the first equation:

7(-2) + 8(3) = -14 + 24 = 10 - so correct.

Multiply the first bracket by -2

Multiply the second bracket by 2

x-3-12+4x= 4x-10

- negative number times + positive number= - negative number

- negative number times -negative number = + positive number

x+ 4x-3-12= 4x-10

5x-15= 4x-10

Move 4x to the other side

5x-4x-15= 4x-4x-10

x-15= -10

Move -15 to the other side

x-15+15= -10+15

x= 5

Answer : x= 5

Answer: X = 5

Step-by-step explanation:

x - 3 - 2(6-2x) = 2(2x-5)

x - 3 - (12-4x) = (4x-10)

Simplify

5x - 15 = 4x - 10

Then move to common sides giving you the answer

X = 5

Answer:

mean of sample is 55.7

sample standard deviation is  0.2375

Step-by-step explanation:

given data

population mean  = 55.7

population standard deviation = 3.8

n = 256

to find out

the mean and standard deviation

solution

we know directly mean of sample is mean of population

i.e. mean of sample = 55.7

and standard deviation will be calculate by this formula

sample standard deviation = population standard deviation / [tex]\sqrt{n}[/tex]

sample standard deviation =  3.8 / [tex]\sqrt{256}[/tex]

sample standard deviation =  3.8/ 16

sample standard deviation =  0.2375

so last option is right

(E) μ = 55.7 , σ = 0.2375.

Answer:

Step-by-step explanation:

Let the time taken by the john to get to his uncle be x.

Let the time taken by the john to get back from his uncle be y.

So,

x+y=12 ------ equation 1

According to the given velocities:

20x=30y

x=3/2y

Put the value x=3/2y in equation 1

3/2y+y =12

3y+2y/2=12

3y+2y=12*2

5y=24

y=24/5

y=4.8h

Now put the value of y in x=3/2y

x=3/2*4.8

x=14.4/2

x=7.2h ....

Answer:

V = 1 1/4 m³

M = 3000.0  kg

Step-by-step explanation:

Volume = Length × Width ×  Height

2 1/2 x 3/4 x 2/3

V = 1 1/4

M=  2.5m ⋅ 0.75m ⋅ 0.666666666666m ⋅ 2400kg/m³

Answer:

(a) 1.25 m^3

(b) 3000 kg

Step-by-step explanation:

(a) The volume of a rectangular prism is L*W*H.

So volume = [tex](2\frac{1}{2})(\frac{3}{4})(\frac{2}{3})=1.25 m^3[/tex]

(b) The mass=density*volume.

So mass = [tex]2400 \frac{kg}{m^3} \cdot 1.25 m^3=3000 kg[/tex].

Answer:

  4 and 13

Step-by-step explanation:

You want integer solutions to ...

  15 ≤ n(n+1) ≤ 200

If we let the limits be represented by "a", then the equality is represented by ...

  n² +n -a = 0

  (n² +n +1/4) -a -1/4 = 0

  (n +1/2)^2 = (a +1/4)

  n = -1/2 + √(a +1/4)

For a=15, we have

  n ≥ -1/2 + √15.25 ≈ 3.4 . . . . . minimum n is 4

For a=200, we have

  n ≤ -1/2 + √200.25 ≈ 13.7 . . . maximum n is 13

The least and greatest integers on the cards are 4 and 13.

Answer:

Step-by-step explanation:

A non-directed graph will have an Euler circuit if all vertices have even degree. It will have an Euler path if it has an Euler circuit or if it has two vertices with odd degree (where the path can start and end).

Graph A

  4 of the 5 vertices have odd degree. No Euler path, no Euler circuit.

Graph B

  All 6 vertices have degree 4. This graph has an Euler path and an Euler circuit.

Graph C

  5 of 6 vertices have degree 4, the remaining one has degree 2. This graph has an Euler path and an Euler circuit.

Graph A: neither an Euler path nor an Euler circuit

   Graph B: both an Euler path and an Euler circuit

   Graph C: both an Euler path and an Euler circuit

An Euler Paths and Circuits visits every edge in a graph once, while an Euler circuit also starts and ends at the same vertex.

To determine which, if any, a graph has, count the vertices - even-degree vertices indicate an Euler circuit, while exactly two odd-degree vertices indicate only an Euler path.

A non-directed graph will have an Euler circuit if all vertices have even degree. It will have an Euler path if it has an Euler circuit or if it has two vertices with odd degree (where the path can start and end).

  Graph A: neither an Euler path nor an Euler circuit

   Graph B: both an Euler path and an Euler circuit

   Graph C: both an Euler path and an Euler circuit

Graph A

 4 of the 5 vertices have odd degree. No Euler path, no Euler circuit.

Graph B

 All 6 vertices have degree 4. This graph has an Euler path and an Euler circuit.

Graph C

 5 of 6 vertices have degree 4, the remaining one has degree 2. This graph has an Euler path and an Euler circuit.

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Answer:

D. 5x2 is the GCF

The greatest common factor of the terms of the given polynomial is 5x². So, option D is correct

To find the GCF of a polynomial,

Given that,

the polynomial is [tex]20x^4-10x^3 + 15x^2[/tex]

Finding factors for all the terms:

[tex]20x^4[/tex] = 2 × 2 × 5 × x × x × x × x

[tex]10x^3[/tex] = 2 × 5 × x × x × x    

[tex]15x^2[/tex] = 3 × 5 × x × x

So, from these three terms, the common factors are 5, x, x

On multiplying them,

⇒ 5 × x × x

∴ GCF = 5x²

Therefore, the greatest common factor of the given polynomial is 5x². So, option D is correct.

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Answer:

a) The portfolio will be at maximum after 12 months (1 year)

b) The maximum value of the portfolio is $5432

Step-by-step explanation:

The function that models Jennifer's stock portfolio (in dollars) is [tex]f(t)=-3t^2+72t+5000[/tex], where t is the time in months since she opened the account.

We complete the square to obtain this function in vertex form:

Factor -3 from the first two terms

[tex]f(t)=-3(t^2-24t)+5000[/tex].

Add the zero pairs -3(+144),-3(-144)

[tex]f(t)=-3(t^2-24t+144)+5000+-3(-144)[/tex].

Factor the perfect square trinomial and simplify.

[tex]f(t)=-3(t-12)^2+5432[/tex].

The vertex of this function is (h,k)=(12,5432)

a) The portfolio will be at maximum when t=12, the h-value of the vertex

b) The maximum value of the portfolio is the k-value of the vertex which is 5432

Jennifer's stock portfolio reaches its maximum value after 12 months, with the maximum value being $5432.

The given function is a quadratic equation in the form f(t) = -3t² + 72t + 5000. This function opens downwards because the coefficient of t2 is negative.

To find the time t when the portfolio is at its maximum, we use the vertex formula for a parabola

t = -b / (2a), where a = -3 and b = 72.

t = -72 / (2 * -3) = 72 / 6 = 12.

So, the portfolio reaches its maximum value at t = 12 months.

To find the maximum value of the portfolio, substitute t = 12 back into the function:

f(12) = -3(12)² + 72 * 12 + 5000.

f(12) = -432 + 864 + 5000 = 5432.

Therefore, Jennifer's stock portfolio will be at its maximum value after 12 months, and the maximum value of the portfolio will be $5432.

Complete Question:

The value of Jennifer's stock portfolio (in dollars) is given by the function f(t) = -3t² +72t + 5000, where t is the time in months since she opened the account. After how many months will her portfolio be at a maximum? What is the maximum value of the portfolio?

Answer:

108 yards

Step-by-step explanation:

Let circle A be the circle with the 62 yard diameter

Let circle B be the circle whose diameter we are trying to solve for.

Answer:

1) 68%

2) 68%

Step-by-step explanation:

We know the mean and the standard deviation.

The mean is:

[tex]\mu=25[/tex]

The standard deviation is:

[tex]\sigma=5[/tex]

The Z-score formula is:

[tex]Z = \frac{x-\mu}{\sigma}[/tex]

For x=20 the Z-score is:

[tex]Z_{20}=\frac{20-25}{5}=-1[/tex]

For x=30 the Z-score is:

[tex]Z_{30}=\frac{30-25}{5}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of the trees are between 20 and 30 years old

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=27[/tex]

The standard deviation is:

[tex]\sigma=3[/tex]

The z-score formula is:

[tex]Z = \frac{x-\mu}{\sigma}[/tex]

For x=24 the Z-score is:

[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]

For x=30 the Z-score is:

[tex]Z_{30}=\frac{30-27}{3}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of pizzas are delivered between 24 and 30 minutes

Answer:

She will use:

3 tablespoons of pepper

7 tablespoons of garlic powder

[tex]\frac{1}{4}[/tex] tablespoon of thyme

8 tablespoons of onion powder

Explanation:

To double the amount, Stephanie will need to double the amount of each ingredient used. This means that she will multiply each amount by 2

Therefore:

New amount of any ingredient = old amount of that ingredient x 2

This means that:

New amount of pepper = [tex]1\frac{1}{2}*2= 3[/tex] tablespoons

New amount of garlic powder = [tex]3\frac{2}{4}*2=7[/tex] tablespoons

New amount of thyme = [tex]\frac{1}{8}*2=\frac{1}{4}[/tex] tablespoons

New amount of onion powder = [tex]4*2=8[/tex] tablespoons

Hope this helps :)

Stephanie will need double the original amounts: 3 teaspoons of pepper, 7 1/2 teaspoons of garlic powder, 1/4 teaspoon of thyme, and 8 teaspoons of onion powder when doubling her recipe for the party.

When Stephanie needs to double the recipe for a party, the amount of each ingredient will be doubled as well. Here's the doubled amount for each ingredient:

Pepper: 1 1/2 teaspoons doubled is 3 teaspoons.

Garlic powder: 3 2/4 teaspoons doubled is 7 1/2 teaspoons (since 3 2/4 is equivalent to 3.75 and doubling it gives 7.5).

Thyme: 1/8 teaspoon doubled is 1/4 teaspoon.

Onion powder: 4 teaspoons doubled is 8 teaspoons.

To calculate this, each original amount is multiplied by two. For example, to double 3 2/4 teaspoons of garlic powder, you can first convert the mixed number to a decimal (3 + 2/4 = 3.75) and then multiply by 2 to find that you will need 7.5, which is the same as 7 1/2 teaspoons.

Answer:

The probability that the sample mean will be between 80.54 and 88.9 is 0.951

Step-by-step explanation:

* Lets revise some definition to solve the problem

- The mean of the distribution of sample means is called M

- The standard deviation of the distribution of sample means is

 called σM

- σM = σ/√n , where σ is the standard deviation and n is the sample size

- z-score = (M - μ)/σM, where μ is the mean of the population  

* Lets solve the problem

∵ The sample size n = 36

∵ The sample mean M is between 80.54 and 88.9

∵ The mean of population μ = 84

∵ The standard deviation σ = 12

- Lets find σM to find z-score  

∵ σM = σ/√n

∴ σM = 12/√36 = 12/6 = 2

- Lets find z-score

∵ z-score = (M - μ)/σM

∴ z-score = (80.54 - 84)/2 = -3.46/2 = -1.73

∴ z-score = (88.9 - 84)/2 = 4.9/2 = 2.45

- Use the normal distribution table to find the probability

∵ P(-1.73 < z < 2.45) = P(2.45) - P(-1.73)

∴ P(-1.73 < z < 2.45) = 0.99286 - 0.04182 = 0.95104

∴ P(-1.73 < z < 2.45) = 0.951

* The probability that the sample mean will be between 80.54 and 88.9

  is 0.951

The probability that the sample mean lies between 80.54 and 88.9 is calculated using the Central Limit Theorem and z-scores. The standard error is calculated to convert the measure into a standard normal distribution where probability can be determined.

In order to solve this problem, we use the concept of the Central Limit Theorem in statistics. According to the theorem, as the sample size increases, the sampling distribution tends towards a normal distribution. In this case, the population mean (μ) is 84 and the standard deviation (σ) is 12. If you take a sample of 36 observations, the mean of this sample should theoretically be close to the population mean. The standard deviation of the sampling distribution of the means (also known as Standard Error) is given by σ/√N (√36 in this case).

Now, to find the probability that the sample mean lies between 80.54 and 88.9, you'd first convert these into z-scores, using the formula z = (X - μ)/standard error. Thus, you get two z-scores corresponding to 80.54 and 88.9. The probability that the sample mean lies between these two points is the area under the standard normal distribution between these two z-values, which can be found using standard statistical tables or software.

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Answer:

The cost of the telegram was 1,270 shilling

Step-by-step explanation:

we know that

The total words-----> 44

The first ten words ----> 10

Extra words----> 44-10=34

so

The total cost is equal to

25(10)+30(34)=1,270 shilling

Answer:

The probability is 2 out of 9 chances to pull a green card.

Step-by-step explanation:

Because your original probability was 3/9 but you removed one so that makes it 2/9 chances to draw one.

If im right may i get brainliest?

Answer: 1/15

Step-by-step explanation:

The odds would be 1/15.

To find these odds, you first have to find the total number of cards.

2 + 3 + 1 + 4 = 10 cards

Then you can find the first set of odd for pulling a green card by placing the goal amount over the total amount.

3 green / 10 total = 3/10

Now, with that green card not being replaced, we have one less green and one less total. This gives us 2 green and 9 total, which helps us find the odds of pulling one again.

2 green / 9 total = 2/9

Now to find the odds of doing both, you need to multiply the two odds together.

3/10 * 2/9 = 6/90 or simplified 1/15

Answer:

  D.  y = 3/5x + 13/5

Step-by-step explanation:

The slope of the desired line is the ratio of the difference in y-values to the difference in x-values:

  m = Δy/Δx = (2 -5)/(-1 -4) = -3/-5 = 3/5 . . . . . . eliminates choices B and C

The slope-intercept equation will then be ...

  y = mx + b . . . . . . . generic slope-intercept form

  y = 3/5x + b . . . . . . put in m; true for some b that puts the given points on the line

Using the first point, we have ...

  5 = 3/5×4 + b

  25/5 = 12/5 + b

  13/5 = b . . . . . . . . . subtract 12/5

Then the equation is ...

  y = 3/5x + 13/5

_____

You know as soon as you consider putting a point value in the equation ...

  y = 3/5x + b

that the equation of choice A cannot work. That only leaves choice D.

Answer:

Step-by-step explanation:

No, the relationship is not linear. It is "roughly" an "inversely proportional" relationship, not a linear relationship. (Read the problem statement: "the product of the number sold and the price in dollars is roughly constant".)

__

The points, when graphed, are not on a straight line.

Answer:

b

Step-by-step explanation:

just took the test

Answer:

A.)  Slope of function B = 2 * the slope of Function A.

Step-by-step explanation:

The slope of Function A is 1  ( because of the x  ( = 1x) in the equation).

From the graph, the slope of Function B = 5 / 2.5 = 2.

Answer:

The correct option is A.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]               .... (1)

where, m is slope and b is y-intercept.

The equation of Function A is

[tex]f(x)=x-9[/tex]      .... (2)

From (1) and (2) we get

[tex]m=1[/tex]

It means slope of Function A is 1.

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that the line passes through two points (0,-1) and (1,1).

[tex]m=\frac{1-(-1)}{1-0}=2[/tex]

The slope of Function B is 2.

We can say that

Slope of Function B = 2 x Slope of Function A

Therefore the correct option is A.

The first step in simplifying a mathematical expression, especially those with parentheses, is to eliminate and simplify terms within the parentheses. This involves combining like terms or performing operations according to the order of operations. Subsequent steps may involve factoring and applying algebraic rules to further simplify.

The question is asking for the first step in simplifying a mathematical expression. To begin simplifying any expression, especially when involving parentheses, the first step typically involves eliminating terms within the parentheses wherever possible. This process often involves combining like terms or simplifying the algebraic expression by performing any operations inside the parentheses first, according to the order of operations (PEMDAS/BODMAS).

After simplifying the expression inside the parentheses, you can then apply other algebraic techniques, such as factoring, combining like terms outside the parentheses, and explicit multiplication of terms across the parentheses if needed. Always remember to check the answer to see if it is reasonable and to ensure that no simplification step has been missed.

If the expression involves complex denominators or numerators, applying algebraic rules such as the power rule or the chain rule can further simplify the expression. In cases involving equations, isolating the variable on one side can help in solving for the unknown value.

In the figure based on proportions of triangle, the value of variable "x" is : (a) 7.5.

Proportions of a triangle based on its sides refer to the ratios between the lengths of different sides within the triangle. Common proportions include the Pythagorean theorem, where the square of the hypotenuse equals the sum of the squares of the other two sides in a right triangle.

In similar triangles, corresponding sides are in proportion, meaning they have the same ratio.

We observe that the figure is based on the property of proportions of triangle, so, the equation of proportion can be written as :

⇒ 4/6 = 5/x,

⇒ 2/3 = 5/x,

⇒ 2x = 15,

⇒ x = 15/2,

⇒ x = 7.5.

Therefore, the correct option is (a) 7.5.

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A, it's not fair because the chance to lose points far outweighs the chance to gain points

Answer with explanation:

→Total faces on the dice and marked numbers =6={1,2,3,4,5,6}

If you are rolling the dice and getting number 1 and 5 , you win 4 and 6 points respectively.

And, If you roll the dice and getting number 2,3,4 and 6 , you loose -5  points .

→→So,suppose the dice is rolled 6 times, and considering each outcome to be equally likely

         then you loose more points than gaining which is equal to

   = 4+(-5)+(-5)+(-5)+6+(-5)

   =10-20

   = -10

And, Average

[tex]=\frac{-10}{5}\\\\= -2[/tex]

So, if number of outcomes are equally likely, you can't accumulate 20 points.

Option B:→ It is not a fair game because weighted average is Negative.

Answer:

Step-by-step explanation:

Here are some facts you can mention:

1. Parabola.

The equation of a parabola is one where x^2 is the term  of the highest degree. ( the degree being '2' in x^2).  For example y = x^2, y = 2x^2 - 5x,

y = -x^2 + 1 are all parabolas. Also we have the type x = f(y)  - for example

4x = y^2.

The graph looks like a U ( which maybe on its side or upside down The graph of a parabola where  the term coefficient of x^2 is positive opens upwards while if it is negative it open downwards.

It is also a 'conic section' .  A parabola is formed when we  intersect a right cone with a plane surface through the side wall and through the base.

When a projectile  is fired from  a gun at  an angle,  the path it follows is close to a parabola. If fired in a vacuum the path we would be exactly parabolic.

2. Ellipse.

This is another conic section formed when we intersect the cone with a plane surface at an angle  to the base ( not 90 degrees) and the plane passes through both sides walls of the cone.

It is oval shaped.  The path of the planets around our sun form an ellipse.

You can draw an ellipse by fixing 2 pins at a distance apart on a sheet of paper, and tie the ends of a piece of string, longer in length than the distance between the pins, to each pin. We then press a pen or pencil to the string at some point and draw around the 2 pins.

3.   Parametric equations.

A third variable is introduced in a parametric equation. Both x and y  are written in terms of this third variable. This variable is called a parameter , hence the name parametric equation.

Many functions can be written in the form y = f(x) or x = f(y) but there are some that cannot be written this way.  An example is  the circle

x^2 + y^2 = r^2. There are many other such functions. By introducing another variable we are able to identify any point on the graph  and it also makes the calculus work  easier.

The variable used is usually t or  the Greek letter theta (for angles). An example of  parametric equations are the ones for a parabola:   x= at^2, y = 2at,

which are the parametric equation for the parabola y^2 = 4ax.

I hope this helps.

Answer:

Step-by-step explanation:

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