The function f(x) = x² +16x - 36 can be factored into the form
ƒ(x) = (x + B) (x − C).
-
What are the values for B and C?
NOTE: Enter your answers as positive integer values.
B =
C=

Answer: For both 3x+1 and 7x-1 is There are no like terms.

I don’t know if you want me to solve because I did “Answer: There are no like terms.” or how you want it because the picture you show it confusing

Step-by-step explanation: Hope this help :D

The final cost is lie between the amount $46.00 and $92.00.

What is an equation?

When two expressions are connected with both the equals sign (=) in a mathematical formula, it expresses this same equality of the two expressions. The meanings of the word equation as well as its cognates in those other languages can vary slightly. For instance, an equation in French is defined as having one or maybe more variables, whereas in English, an equation is any properly formed formula that consists of two expressions linked by the equals sign.

The coupon is given = 15% off

New price = Cost of meal (1 - coupon)

Now Substitute the known values in the equation;

New price = between 55(1 - 15%) and 100.00 (1 - 15%)

Evaluate;

The final cost of the meal is between $40.00 and $80.00

Tip = 22%

Thus Final cost = New price (1 + tip)

Now Substitute the known values in the equation

Final cost = Between 40.00 (1 + 22%) and 80.00 (1 + 22%)

The Final cost is Between $46.00 and $92.00

Hence, the final cost is lie between the amount $46.00 and $92.00

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5 people out of 100 will receive a free cookie and free coffee.

Given,

Every 4th person gets a free cookie and every 5th person gets a free coffee .

Now,

Compute the data in the form of equations,

Thus,

In every 20 people 1 person will get both cookie and coffee.

So,

In the group of 100 people 5 persons will be there those who will get both cookie and coffee.

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To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:

10 cups of red paint

Step-by-step explanation:

the painter will use 10 cups of red paint

Answer:

true

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

convert the mixed number to a improper fraction..then multiply both sides of the equation by 6...collect like terms..then divide both sides by 37..then you should get your answer...

Answer:

164

Step-by-step explanation:

B for brackets

O for of

D for division

M for multiplication

A for addition

S for subtraction

You first start with the brackets (20) and multiply with 4 which is equal to 80 and then add it to 84 which makes 164

I hope this helps

The scale factor of 0.75 would ensure that the new fence has a smaller area

The total cost of fencing the smaller area is $1610.28

From the complete question, we have the following parameters:

Start by calculating the perimeter of the smaller area using:

Smaller Area = Perimeter * Scale factor * k

Where k represents the number of units on the smaller area

So, we have:

Smaller Area = 28 yards * 0.75 * 12

Evaluate the product

Smaller Area = 252 yards

The total cost is then calculated as:

Total cost = Unit cost * Smaller Area

This gives

Total cost = 6.39 * 252

Total cost = $1610.28

Hence, the total cost of fencing is $1610.28

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Answer:

yehshjdjejrdjjej3u Rudd ixjje

The equation of the line in slope-intercept form that represents this situation is y = 1 / 4 x + 6

where

m = slope

b = y-intercept

Let's find slope using the two points on the graph(0, 6)(8, 8).

m = 8 - 6 / 8 - 0

m = 2 / 8

m = 1 / 4

let's find b using (0, 6)

y = mx + b

6 = 1 / 4(0) + b

b = 6

Therefore, the equation is as follows:

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This scenario represents an observational study because the clothing manufacturer is observing and measuring the number of returns versus the number of items sold without actively intervening or manipulating any variables

In an observational study, researchers gather data by observing and recording natural behaviors or phenomena without directly influencing them. In this case, the manufacturer is passively observing the level of satisfaction people have with the merchandise by comparing the number of returns (indicating dissatisfaction) to the number of items sold. They are not implementing any interventions or controlling variables, but simply collecting data on the existing patterns of returns and sales to assess customer satisfaction. versus the number of items sold without actively intervening or manipulating any variables.

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The first step to factorizing a polynomial is taking the Highest Common Factors.

Like Algebraic expressions, polynomials are expressions that consist of both coefficients and variables are called Polynomials.

The factors that are multiplied to obtain the original expressions are known as factors of the given polynomial.

Factorization is the method used to determine the factors of a given polynomial or mathematical expression.  

To factorize a given polynomial first we need to take the Highest common factors from the 4 terms of the polynomial.

Example:

x²-5x -10x +50    

To factorize the polynomial

Take common Highest Common Factors  

=> x(x - 5) -10(x - 5)        

=> (x - 5) (x - 10)

∴ Factors of given polynomial is (x - 5) and (x - 10)

Therefore,

The first step to factorizing a polynomial is taking the Highest Common Factors.

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Answer:

d

Step-by-step explanation:

the answer is d because we learned about this everyday

The area of the irregular figure will be equal to the sum of area of triangle and the area of the rectangle.

The required area can be determined as,

Thus, the required area of the irregular figure is 426 square feet.

Number combination can be used to find the number of selecting n  items from m items

The known parameters are;

Number of days the six friends play a game of tennis = Every day = 7 days

Number of weeks the six friends the friends play for = 7 weeks

Therefore the total number of days = 7 × 7 days = 49 days

Required:

(a) The number of ways the friends can play with each other once is given as follows;

\(The \ number \ of \ 2 \ combinations \ in \ 6 \ options, C_6^2 = \dfrac{6!}{2!\times (6-2)!} = 15\)

The number of ways the six friends can play with each other once is 15 ways

Therefore, minimum number of singles games that will be between the same friends playing each other is given as follows;

\(\mathbf{Number \ of \ games = \dfrac{7 \times 7}{C_6^2} }=3.2\overline 6\)

Therefore, more than 3 of the games or four games will be between pairs playing the game more than four times together, and when at least four of the games of singles are counted it will be between friends playing each other for the fourth time

(b) The number of ways the friends can play game of doubles is given as follows;

\(C_6^4 = \dfrac{6!}{4! \times (6 - 4)!} = 15\)

The number of pairs = ₆C₂ = 15

The number of games of doubles = 49

In 49 games, we have;

The number of times the same opposing  will play a game of doubles where a member of the pair can be on either side of the court will given as follows;

\(\mathbf{Number \ of \ games \ of \ doubles \ between \ same \ pair} = \dfrac{7 \times 7}{15 } =3.2\overline 6\)

Therefore, at least four of the of the games of doubles will be between the same set of four friends playing for the 4th time, which gives; at least four games of doubles between the same set of four friends, two of which are playing (as a pair) the same opposing pair for the 4/2 = second time

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Answer:

3m - 5

Step-by-step explanation:

First distribute the 3.

3(m - 3 ) = 3m - 9

= 3m - 9 + 4

Add the numbers.

= 3m - 5

Answer 2. Hope this helps, please mark brainliest if possible :)

Probability to choose an even numbered squares is 2/3.

Given that there are 6 squares in the bag.

They are numbered as 255, 256, 260, 263, 264, 270.

Even numbered squares are 256, 260, 264, 270

Here number of even numbered squares is = 4

So the according to definition the probability to choose an even numbered squares from the bag is = 4/6 = 2/3.

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Answer:

a

Step-by-step explanation:

the two lines intercept at 1,-2

Answer: it is b(4,2)

Step-by-step explanation: nice

The sum of the first three terms in the series is -557.921 and a bound for the error is approximately 865.474.

What is series?

In mathematics, a series is the sum of the terms of a sequence. It is represented by the sigma notation (∑), which indicates that a sequence of terms is being added together.

To calculate the sum of the series and find the bounds for the error, let's break down the problem step by step.

The series can be represented as:

\(\sum_{n=1}^{\infty} [(-1)^n * 400*n^{0.6}]\)

To find the sum of the first three terms, S3, we need to calculate the values for n = 1, 2, and 3 and then sum them up.

For n = 1:

\((-1)^1 * 400 * 1^{0.6\) = -400

For n = 2:

\((-1)^2 * 400 * 2^{0.6\) = 564.189...

For n = 3:

\((-1)^3 * 400 * 3^{0.6\) = -721.110...

Now, let's calculate the sum of the first three terms, S3:

S3 = -400 + 564.189 + (-721.110) = -557.921

The sum of the first three terms, S3, is approximately -557.921.

To find a bound for the error, we can use the Alternating Series Estimation Theorem. The theorem states that the error in approximating an alternating series is less than or equal to the absolute value of the next term.

In this case, the next term of the series would be for n = 4:

\((-1)^4 * 400 * 4^{0.6\) = 865.474...

The bound for the error is given by the absolute value of this term:

|Next Term| = |865.474...| ≈ 865.474

Therefore, a bound for the error is approximately 865.474.

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The mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is   and   .

For Discrete Uniform Distribution the probability mass function (pmf) is denoted by P(x)=1/n , where x=1,2,3,...,n.

in the given question

The mean of the Discrete Uniform Distribution is given by \(E(x)=\[\sum_{x=1}^{n}p(x)*x\]\)

By substituting the value of P(x)=1/n

\(E(x)=\[\sum_{x=1}^{n}\frac{1}{n} *x\]\)

\(=\frac{1}{n}\[\sum_{x=1}^{n}x\]\)

\(=\frac{1}{n} (1+2+3+4+...n)\)

\(=\frac{1}{n} *\frac{n(n+1)}{2}\)    ( as we know that sum of n terms is \(\frac{n(n+1)}{2}\)  )

=\(\frac{n+1}{2}\)

hence , \(\mu=\frac{n+1}{2}\) ....(i)

The Variance of the Discrete Uniform Distribution is denoted by Var(x) and is given by \(Var(x)=E[(x-\mu)^{2}]\)

As we know that \(E(x)=\[\sum_{x=1}^{n}p(x)*x\]\)   similarly for E[(x-μ)²] we get

\(E[(x-\mu)^{2}]=E[x^{2} ]-\mu^{2}\)

\(=E[x^{2}]-(\frac{n+1}{2} ) ^{2}\)        ( we have found \(\mu=\frac{n+1}{2}\) )  ....(ii)

For E[x²]

\(E(x^{2} )=\[\sum_{x=1}^{n}\frac{1}{n} *x^{2} \]\)

\(=\frac{1}{n}\[\sum_{x=1}^{n} x^{2} \]\)

\(=\frac{1}{n} (1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} )\)

We know that \(1^{2} +2^{2} +3^{2} +4^{2} +...+n^{2} =\frac{n(n+1)(2n+1)}{6}\)

Substituting the value in above equation we get we get

\(E[x^{2} ]=\frac{1}{n} *\frac{n(n+1)(2n+1)}{6}\)

\(E[x^{2} ]=\frac{(n+1)(2n+1)}{6}\)

Substituting the value of E[x²] back in equation (ii)

We get

\(Var[x]=\frac{(n+1)(2n+1)}{6} -( \frac{n+1}{2})^{2}\)

\(=\frac{(n+1)(2n+1)}{6} -\frac{(n+1)^{2} }{4}\)

\(=(n+1)(\frac{(2n+1)}{6} -\frac{(n+1) }{4})\)

taking LCM as 12 and solving further we get

\(=(n+1)(\frac{4n+2-3n-3}{12} )\)

\(=\frac{(n+1)(n-1)}{12}\)

\(=\frac{n^{2}-1 }{12}\)     (using identity of (a+b)(a-b)   )

Therefore , the mean and variance of the uniform discrete random variable x that takes values from the set {1, 2, . . . n} is \(\frac{n+1}{2}\)  and \(\frac{n^{2}-1 }{12}\)  .

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Answer: If a lawyer charges $120 an hour (or any fraction of an hour), how much is a bill for 3 hours and 20 minutes? What is the equation for this problem? answer choices l (x) = 120x l (x) = 120 [x-1] l (x) = 120 [x] l (x) = 120 [x+1]

Thank me later.

The inequalities that could be used to solve for x; the number of school buses still needed to transport all of the students is x > 3

The number of students still needing transportation is: 400 - 265 = 135

The number of school buses still needed to transport all of the students:

135 ÷ 45 = 3

Therefore, the principal still needs 3 more school buses to transport all of the students.

The inequality that could be used to solve for x: x > 3

This inequality represents the number of buses needed (x) as being greater than 3

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Answer:

Mizuki is here to help you! The volume of the figure above is 176\(in^2\), but since you can only put numbers you need to put in 176.

Step-by-step explanation:

11 x 4 x 8 ÷ 2 =

44 x 8 ÷ 2 =

352 ÷ 2 =

176

Answer:

$1,134 + $926 + $562 + $333 + $55 + $130

+ $1,500 + $313 = $4,953

The (f + g)(x) = 15x - 2 is represent the total round trip time.

According to the statement

we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.

And we have to find the total round trip time.

So, For this purpose, the given information is:

f(x) = 3x − 10 and g(x) = 12x + 8

And

The total round trip time is represented by the term (f + g)(x)

We know that the

(f + g)(x) = f(x) + g(x)

Substitute the given values in it

So, (f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x - 10) + (12x + 8)

(f + g)(x) = 15x - 2

Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.

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To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

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Answer:

Step-by-step explanation:

Therefore,

NOTE: n can't be equal to a negative number

hence n=20

The solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

To simplify the equation 3(x-6) - 1/2(8x+10) = -25, we can start by applying the distributive property and then combining like terms.

First, let's distribute the 3 and the -1/2 to the terms inside the parentheses:

3(x-6) - 1/2(8x+10) = 3x - 18 - (4x + 5)

Now, let's simplify further by combining like terms:

3x - 18 - 4x - 5 = -x - 23

So, the simplified equation is -x - 23 = -25.

To solve for x, we can isolate the variable by adding 23 to both sides of the equation:

-x - 23 + 23 = -25 + 23

This simplifies to:

-x = -2

Finally, we can solve for x by multiplying both sides of the equation by -1:

(-1)(-x) = (-1)(-2)

This gives us:

x = 2

Therefore, the solution to the equation 3(x-6) - 1/2(8x+10) = -25 is x = 2.

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