The polynomial of degree 3, p(x),has a root of multiplicity 2 at x=2 and root of multiplicity 1 at x=-4 the y intercept is -3.2

The required algebraic expression is: 9n - (6n +1)

What is an algebraic expression and how is it formed?
Variables and constants are used to create algebraic expressions using a variety of techniques. It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions. An algebraic expression (or variable expression) is a grouping of terms that have undergone operations like addition, subtraction, multiplication, division, etc.

Let the given number be = n
Therefore, nine times the number = 9n
Also, six times the number = 6n
Again, one more than six times the number = 6n + 1
Given, difference between nine times a number and one more than six times the number.
Using all of the expressions derived above, we curate the algebraic expression as:
Algebraic expression: 9n - (6n +1)

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Answer:

y(1,6) x(-4,6) z(1,1)

Step-by-step explanation:

Answer:

X(-8,6)Y(-3,6)Z(-3,1)

Step-by-step explanation:

just moving the coordinate over to the left 4 times

Answer: 156480 feet in 3 laps?

Step-by-step explanation:

320x163=52160 square feet as area

52160x3=156480

1. The price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.

2. Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.

1. Let's assume the price of a pair of gloves is represented by 'x' and the price of a hat is represented by 'y'.

From the given information, we can establish the following equations based on Cody and Tor's purchases:

Equation 1: 2x + 4y = 43.00 (Cody's purchase)

Equation 2: 2x + 2y = 30.00 (Tor's purchase)

To solve this system of equations, we can use a method like substitution or elimination.

Using the substitution method, we can rearrange Equation 2 to express x in terms of y:

2x = 30.00 - 2y

x = 15.00 - y

Now, we substitute this value of x into Equation 1:

2(15.00 - y) + 4y = 43.00

30.00 - 2y + 4y = 43.00

2y = 43.00 - 30.00

2y = 13.00

y = 6.50

Substituting this value of y back into Equation 2 to find x:

2x + 2(6.50) = 30.00

2x + 13.00 = 30.00

2x = 30.00 - 13.00

2x = 17.00

x = 8.50

Therefore, the price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.

2. Let's assume Aaliyah invested an amount represented by 'x' in the mutual fund that rose 6% and an amount represented by 'y' in the mutual fund that rose 9%.

From the given information, we can establish the following equations based on the rise in investment:

Equation 1: 0.06x + 0.09y = 684 (rise in investment)

Equation 2: x + y = 10,000 (total investment)

To solve this system of equations, we can use a method like substitution or elimination.

Using the substitution method, we can rearrange Equation 2 to express x in terms of y:

x = 10,000 - y

Now, we substitute this value of x into Equation 1:

0.06(10,000 - y) + 0.09y = 684

600 - 0.06y + 0.09y = 684

0.03y = 84

y = 2800

Substituting this value of y back into Equation 2 to find x:

x + 2800 = 10,000

x = 10,000 - 2800

x = 7200

Therefore, Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.

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Answer:

There are 9 arms.

Step-by-step explanation:

Answer:

Answer 1008

Step-by-step explanation:

To solve this problem, we need to apply the formula for the equation of a straight line.

One of the forms of this formula, which is appropriate for this problem, is as follows:

Where (x1 , y1) and (x2 , y2), are the coordinates of any two points that lie on the line.

In this case, the coordinates are: ( -5,-2), and (3, -4)

Now:

Answer: 3/25

Step-by-step explanation:

E/total = 6/50 = 3/25

Answer:

Step-by-step explanation:

1. j

2. k

3. L

4. Lj

5. kL

6. jk

The values of x are 7 and -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

\(log_{10}\) (x - 6) + \(log_{10}\) (x + 3) = 1

This can be written as,

log (ab) = log a + log b

So,

log (x - 6)(x + 3) = 1

And,

log 10 = 1

So,

log (x - 6)(x + 3) = log 10

The log gets canceled

(x - 6) (x + 3) = 10

x² + 3x - 6x - 18 = 10

x² - 3x - 18 = 10

x² - 3x - 18 - 10 = 0

x² - 3x - 28 = 0

x² - (7 - 4)x - 28 = 0

x² - 7x + 4x - 28 = 0

x(x - 7) + 4(x - 7) = 0

(x - 7) (x + 4) = 0

x - 7 = 0 and x + 4 = 0

x = 7 and x = -4

Thus,

x values are 7 and -4.

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Answer:

  d

Step-by-step explanation:

Answer: The answer is D

The probability that a student plays basketball or soccer (or both) is 1/5.

Option A is the correct answer.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

To find P(A or B), we need to add the probabilities of event A and event B and then subtract the probability of their intersection (A and B), since it has been counted twice:

P(A or B) = P(A) + P(B) - P(A and B)

We are given that:

P(A) = 3 (out of 10 students)

P(B) = 2 (out of 10 students)

P(A and B) = 3 (out of 10 students)

Plugging these values into the formula, we get:

P(A or B) = 3/10 + 2/10 - 3/10

P(A or B) = 2/10 = 1/5

Therefore,

The probability that a student plays basketball or soccer (or both) is 1/5 or 0.2.

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The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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They need to sell at least 13 cups to gain profits.

Here, we have,

Givens

The initial cost is $1.20.

Each cup of lemonade costs 6 cents to make.

May's children sell 10 cents a cup.

First, we need to represents the cost of their investment.

0.06x = 1.20, because each cup costs 6 cents, and the initial costs of all is $1.20.

That means,

x= 20

They can produced 20 cups.

However, they already sell a cup for 10 cents. So, how many cups they need to sell to gain profits? We need to establish a similar relation,

0.10 x = 1.20

 x = 12

This means if they sell 12 cups, they will just cover the investment, that is, zero profits.

Therefore, they need to sell at least 13 cups to gain profits.

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complete question

Mary's children decide to run a lemonade stand to earn some extra money.The cost to start the business is $1.20 and each cup of lemonade costs 6 cents to make. If lemonade sells for 10 cents a cup,how many cups must Mary's children sell to make a profit?----Apply systems of equations

Answer:

-11.8684210526

Step-by-step explanation:

The true statement is if k = - 1 there are solutions, but if k = - 3 there are no solutions

Given: |x+3|-2=k

Below are rules for solving absolute value equations:

1. If p is positive and |y| = p, then

x = p   OR    y = -p

(two equations are set up)

2. If p is negative and |y| = p, then

No solution

3. If p is zero  and |y| = p, then

One solution

Using the rules:

|x+3|-2=k

when k = -1

|x+3|-2= -1    

|x+3| = 1

Rule 1 is applicable here. Thus, there are solutions  

when k = -3

|x+3|-2 = -3

|x+3| = -1

Rule 3 is applicable here. Thus, no solution

Therefore, if k = - 1 there are solutions, but if k = - 3 there are no solutions.     The 2nd option is the true statement

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Answer:

Step-by-step explanation:

The angle on the interior of the triangle with an exterior angle of 130 degrees is 60 degrees.

All the angle of the triangle added up should equal 180 degrees, so:

x = 180 - 60 - 113 = 7 degrees

so x is 7 degrees

Answer:

8

Step-by-step explanation:

Step 1:

4x - 3 = 2x + 13        Equation

Step 2:

4x = 2x + 16     Add 3 on both sides

Step 3:

2x = 16     Subtract 2x on both sides

Step 4:

x = 16 ÷ 2     Divide

Answer:

x = 8

Hope This Helps :)

Answer:

x=8

Step-by-step explanation:

4X-3=2x+13

   +3.      +3

4X=2x+16

-2x.  -2x

2x=16

/2.   /2

x=8

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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The maturity value due on January 16 is $34,320.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that,

Principal amount ( Starting amount) = $33,000

Rate of interest = 6% = 0.06

The loan is taken in May 17.

There is a time of 8 months in between May 17 and January 16.

Time in years = 8/12 years = 2/3 years

Amount of simple interest = Principal amount × Interest rate × Time

                                            = 33,000 × 0.06 × 2/3

                                            = 1320

Maturity value = Principal amount + Amount of simple interest

                        = $33,000 + $1320

                        = $34,320

Hence the maturity value is $34,320.

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Using the binomial distribution, we have that:

a) There is a 0.2111 = 21.11% probability that a six will occur exactly twice.

b) The expected number of sixes is of 3.2.

c) The variance of the number of sixes is of 2.35.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

For this problem, the parameters are given by:

p = 8/30 = 0.2667, n = 12.

Item a:

The probability is P(X = 2), hence;

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{12,2}.(0.2667)^{2}.(1-0.2667)^{10} = 0.2111\)

Item b:

The expected number of the binomial distribution is:

E(X) = np.

Hence:

E(X) = 12 x 8/30 = 3.2.

Item c:

The variance of the binomial distribution is:

V(X) = np(1-p).

Hence:

E(X) = 12 x 8/30 x 22/30 = 2.35.

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Answer:

y=381

Step-by-step explanation:

given: y=45  x=225

y=kx

45=k√(225)

45=k(15)

45=15k

45/15=15k/15

3=k

given: x=127  k=3

y=kx

y=3(127)

y=381

The expression for total cost per month is 30(100000+2000f).

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

The standard deviation formula is σ = √∑(xi-μ)²/N

A) The expression for total cost per month

Let the number of flites be f.

Total cost = 30(100000+2000f)

B) The expression for total revenue per month

Rise airlines has the current capacity to fly a mean of 15 flites a day with a standard deviation of 12.

So, total revenue per month

= 30(100000+2000×15)

= $3,900,000

C) Here, σ=12, μ=15, N=60

σ = √∑(xi-μ)²/N

12= √∑(xi-15)²/60

144=(xi-15)²/60

8640=(xi-15)²

xi-15=92.95

xi=108

Therefore, the expression for total cost per month is 30(100000+2000f).

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Answer: T'=(-1,-1), U'=(-3,-1), V'=(-1,-4)

Step-by-step explanation:

The True statements are:

Each element of X is given exactly one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

For D (x) = 2 x:

- x is the independent variable,

- D ( 6 ) = 2 · 6 = 12.

10 = 2 · 5,     12 = 2 · 9,     - 4 = 2 · ( - 2 ).

True statements are:

A ) D ( x ) is a function.

D ) D ( x ) is a direct variation.

E ) D ( x ) is a rule for the set of points ( 5, 10), ( 6, 12 ) and ( -2, - 4 ).

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The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

d

Step-by-step explanation:

The total cost of the installation units that was purchased is calculated as: $288.

To calculate the total cost when given the unit price, the formula to use is:

Total cost = number of units × cost of each unit (unit price).

We are given the following information:

Cost of each unit that is on sale (unit price) = $18

Number of unit that was purchased 16 units.

To calculate the total cost of the solar lighting units that you purchased for installation along the driveway for your house, multiply the cost of each unit by the number of units to be bought.

Total cost = 16 units × $18.

Total cost = $288

Therefore, the total cost of the installation units that was purchased is calculated as: $288.

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a) Numerical Expression

b) Variable Expression (c)

c) Variable Expression (x)

d) Numerical Expression

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