Mathematics College

Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
method. Which method is most efficient? Explain.

Answers

Answer 1
Foil method:
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8

Distributive property:

(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8

Both methods are efficient, it all depends with the users preference
Answer 2

Final answer:

To simplify (3x+8)(x+1), we can use the FOIL method, the Distributive Property, or a multiplication table, all leading to the same simplified expression: 3x² + 11x + 8. The FOIL method is typically the most efficient for binomials.

Explanation:

The question asks to simplify the expression (3x+8)(x+1) using a table, the Distributive Property, and the FOIL method and to determine which method is most efficient.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last and represents a quick way to multiply two binomials:

First: Multiply the first terms in each binomial (3x×x = 3x²).

Outer: Multiply the outer terms (3x×1 = 3x).

Inner: Multiply the inner terms (8×x = 8x).

Last: Multiply the last terms in each binomial (8×1 = 8).

Adding these products together, we get 3x² + 3x + 8x + 8, which simplifies to 3x² + 11x + 8.

Using the Distributive Property

This involves expanding the expression by multiplying each term in the first polynomial by each term in the second: (3x+8)(x) + (3x+8)(1), which also simplifies to 3x² + 11x + 8.

Using a Table

Create a table where you list each term of the first polynomial in the first row and the terms of the second polynomial in the first column, and then fill in the table with the products of the intersecting terms. The sum of these products will also yield 3x² + 11x + 8.

While all three methods will give the correct answer, the FOIL method is generally seen as the most efficient for this particular problem, as it provides a straightforward, step-by-step process that is easy to follow and remember for multiplying two binomials.

Related Questions

Find the intervals on which f is increasing and decreasing, find the local maximum and minimum values of f, find the intervals of cocavity and inflection f(x) 2x^3 + 3x^2 -36x

Answers

A graphing calculator can be helpful.

Increasing: x ∈ (-∞, -3) ∪ (2, ∞)
Decreasing: x ∈ (-3, 2)
Local maximum: (-3, 81)
Local minimum: (2, -44)
Concave downward: x ∈ (-∞, -0.5)
Concave upward: x ∈ (-0.5, ∞)
Point of inflection: (-0.5, 18.5)

One side of a cube has an area of 25 centimeters squared. What is the surface area of the cube?

Answers

a cube has all equal sides, so every face in the cube is just a square, if the area of one of those square is 25 cm², that simple means,

[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=length~of\\ \qquad a~side\\ ------\\ A=25 \end{cases}\implies 25=s^2\implies \sqrt{25}=s\implies 5=s[/tex]

now, look at the picture below, a cube is really just 6 squares stacked up to each other at the edges, in this case, all 6 squares are 5x5.

so, simply get the area of all of them, and sum them up, and that's the surface area of the cube.

(5*5)+(5*5)+(5*5)+(5*5)+(5*5)+(5*5).

how to Solve for the Missing Side

Answers

Here you would need to use trigonometry. 
Remember SOHCAHTOA
You need to find the hypotenuse, and you are given the opposite side to the given angle. Which means you will be solving Sine.
Now just plug the numbers in.
[tex]Sin 67 = \frac{15}{x} \\Sin 67 (x) = 15 \\\frac{sin67(x)}{sin 67} = \frac{15}{sin67} \\x = 16.2954[/tex]

I need help

Circle P is below

Answers

1. remember all of them add up equal to 360 degree.
2. add all of them up together
[tex](4y + 6) + (7y - 7) + (20y - 11) = 360[/tex]
3. combine like term then solve for Y
4. you will figure the arc measure of BC when you get answer for Y.
20y-11+4y+6+7y-7=360
31y-12=360
31y=360+12
31y=372
y=372/31=12

BC=BA+AC=4y+6+7y-7=11y-1
BC=11*12-1=131⁰

Emily got a newjob that guarantees her a 6% raise every year. If she started out making 25,000, how long will it be before she doubles her current salary

Answers

It would take about 17 years for her to double her salary, since the salary is increasing 1,500 dollars a year. This means we divide 25,000/1,500 to get 16.66666 which we can round to 17.

What is the answer for 5 3/4+3 1/3 =?

Answers

[tex] 5 \frac{3}{4} + 3 \frac{1}{3} [/tex]

Let's start by adding the whole numbers.
5+3=8
Set it to the side.
Now let's rewrite the problem without the whole numbers.
[tex] \frac{3}{4} + \frac{1}{3} [/tex]
We must find the least common denominator.
The LCD is 12.
In order to get 12 we must multiply by 3 on the left and 4 on the right.
[tex] \frac{3*3}{4*3} + \frac{1*4}{3*4} [/tex]
[tex]\frac{9}{12} + \frac{4}{12} [/tex]
Now just add them together since they have a common denominator.
[tex] \frac{13}{12} [/tex]
Now we need to simplify
[tex]1 \frac{1}{12} [/tex]
Now it is time to add that 8 back 
8+[tex] 1 \frac{1}{12} [/tex]
Add the whole numbers
8+1=9
Answer: [tex] 9 \frac{1}{12} [/tex]
The answer is 9 1/12

In RST , RS=11 ,RT=9 and ST=6 which angle of RST has the smallest measure ?

Answers

The angle opposite the shortest side has the smallest measure. That is the angle opposite side ST, ...
   C. ∠R

<R angle of RST has the smallest measure.

The correct option is C.

We have,

RS=11 ,RT=9 and ST=6

Now, from the given lengths it can be seen that the length of ST is shortest and length of RS is longest.

By the definition which states that,

The angle opposite to longest side is largest and the angle oppsite to shortest side is smallest.

From given, <R is opposite to shortest side ST.

Thus, the smallest angle is R.

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Which statistic is used to test a global hypothesis about a multiple regression equation?

Answers

Answer:  an " F-statistic " .
_____________________________________________________

Suppose you choose two families at random. what is the chance that family a owns exactly one car and family b owns exactly one car?

Answers

the chances or possibility would be 50/50

hey can you please help me posted picture of question

Answers

The correct answer is option C

(4 - 6i)(6 - 8i)

= 4(6-8i) - 6i(6-8i)

= 24 - 32i - 36i + 48i²

= 24 - 68i + 48(-1)

= 24 -  68i - 48

= - 24 - 68i

show this fraction as a decimal 1 1/4

Answers

1 = 1

1/4 is the same as 25/100 (if you multiply 25 top and bottom). 25/100 = 0.25

1 + 0.25 = 1.25

1.25 is your answer

hope this helps
Fraction: 1 1/4
Decimal: 1.25
Think about like this: kinda like money
1/4: 25 (cents)
2/4 50 (cents)
3/4 75 (cents)
4/4 100 (cents) or 1 (a dollar bill)
Hope that could help out!

what is the answer to the problem above?

Answers

4 × 25 = 100
5 × 18 = 90
100/90 = 10/9 = 1 1/9

-845 degree coterminal angle

Answers

check the picture below.

with negative angles, we go "clockwise", the same direction a clock hands move.

so -360-360-125 = -845.

so as you see in the picture, you go around twice, and then a little bit more, an extra 125°, landing you at -125°, or its positive counterpart, 235°.

A cross-section​ of a light reflector is a parabola. The bulb is located at the focus. Suppose the bulb is located 11 in from the vertex of the reflector.

Use this information to make the following determinations.
Model a cross section of the reflector by writing an equation of a parabola that opens upward and has its vertex at the origin.

Answers

An equation of a parabola that opens upward and has its vertex at the origin,

⇒ y² = - 8 x

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now,

The equation of the parabola turned to the left is to the negative side of the coordinate system is:

⇒ y² = - 2 p x  

where, p is the parameter of the parabola

The relationship between the parameter and the focus is.

⇒ p = 2 f  

=> p = 2 × 2

⇒ p =  4 cm  

Then, the equation of the parabola is:

y² = - 2 p x

    = - 2 × 4 x

     = - 8 x

Therefore, An equation of a parabola that opens upward and has its vertex at the origin,

⇒ y² = - 8 x

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the local weather forecast has been accurate for 17 of the past 33 days based on this fact what is the relative frequency probability that the forecast for tomorrow will be accurate

Answers

P(accurate)  = 17/33 

Answer: 17/33

[tex] \frac{17}{33} [/tex]

What is the inequality for this verbal description?Sam has d dollars to spend on grapes and carrots. He wants to buy one bag of grapes for $4.00 and c pounds of carrots that cost $2.00 per pound. Which inequality represents this situation?

Answers

4+2c<=d
this tells us that $4 for grapes plus c bags of carrots that are $2 per pound will give us his total. he wants this to be less than or equal to d.

if able please vote brainliest if you like my response! thanks

Final answer:

The inequality for Sam's expenditures on grapes and carrots, with grapes costing $4 and carrots costing $2 per pound, is 4 + 2c <= d.

Explanation:

The inequality that represents Sam's spending on grapes and carrots, given that he has d dollars to spend, is 4 + 2c ≤ d. This inequality is derived from the cost of one bag of grapes, which is $4, and the cost of carrots, which is $2 per pound. The variable c represents the number of pounds of carrots Sam wants to buy. The total cost of grapes and carrots must be less than or equal to the amount of money Sam has, which is d dollars.

What is the y-intercept of the quadratic y=-2x^2-4x-5 ?
(-5,0)
(0,-2)
(-1,3)
(0,-5)

Answers

y - intercept is f(0) then (0; m)

We have:

[tex]y=-2x^2-4x-5\to f(0)=-2(0)^2-4(0)-5=-5[/tex]

Answer: (0; -5)

In the linear equation y = 2x + 1, if x increases by 4 points, how much will y increase?

Answers

If [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.

In the linear equation [tex]\(y = 2x + 1\)[/tex], the coefficient of [tex]\(x\)[/tex] is 2. This means that the slope of the line is 2, and for every one unit increase in [tex]\(x\), \(y\)[/tex] will increase by 2 units.

Given that [tex]\(x\)[/tex] increases by 4 points, the corresponding increase in [tex]\(y\)[/tex] can be found by multiplying the change in [tex]\(x\)[/tex] by the slope:

[tex]\[\Delta y = \text{Slope} \times \Delta x\][/tex]

[tex]\[ \Delta y = 2 \times 4 = 8\][/tex]

Therefore, if [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.

Example:

Let's use the given linear equation [tex]\(y = 2x + 1\)[/tex] and demonstrate how an increase in [tex]\(x\)[/tex] by 4 points results in an increase in [tex]\(y\)[/tex] by 8 units.

Given Linear Equation:

[tex]\[y = 2x + 1\][/tex]

Let's consider an initial point on the line where [tex]\(x = 3\)[/tex]. Find the corresponding [tex]\(y\)[/tex]:

[tex]\[y = 2(3) + 1 = 7\][/tex]

So, when [tex]\(x = 3\), \(y = 7\)[/tex].

Now, if [tex]\(x\)[/tex] increases by 4 points, new [tex]\(x\)[/tex] value will be [tex]\(3 + 4 = 7\)[/tex].

Using the same linear equation to find the new [tex]\(y\)[/tex]:

[tex]\[y_{\text{new}} = 2(7) + 1 = 15\][/tex]

Now, calculate the increase in [tex]\(y\)[/tex]:

[tex]\[\Delta y = y_{\text{new}} - y_{\text{initial}} = 15 - 7 = 8\][/tex]

So, in this example, when [tex]\(x\)[/tex] increases by 4 points (from 3 to 7), [tex]\(y\)[/tex] increases by 8 units (from 7 to 15), confirming that the increase in [tex]\(y\)[/tex] is proportional to the increase in [tex]\(x\)[/tex] with a slope of 2.

Sergio runs 2 1/4 miles in 30 minutes. Write the ratio in fractional form and determine Sergio's speed in miles per hour.

Answers

[tex] \dfrac{ 2\dfrac{1}{4} }{ \dfrac{30}{60} } \\ \\ = \dfrac{9}{4} \div \dfrac{30}{60} \\ \\ = \dfrac{9}{4} \times \frac{60}{30} \\ \\ = 4.5[/tex]

4.5 miles per hour.

Hope this helps. - M
Final answer:

Sergio runs at a speed of 4.5 miles per hour. The ratio of his running distance to time is 9/2.

Explanation:

To determine Sergio's speed in miles per hour (mph), we use the equation: speed = distance/time. Sergio runs 2 1/4 miles in 30 minutes. First, we need to convert the fractional distance to a decimal and the time to hours. 2 1/4 miles is equal to 2.25 miles and 30 minutes is equal to 0.5 hours.

Substitute these values into the equation:

speed = 2.25 miles/0.5 hour = 4.5 mph.

Therefore, Sergio's running speed is 4.5 miles per hour. The ratio of distance to time in fractional form would be 9/2.

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What is 134,500 rounded to the nearest ten thousand

Answers

130,000 because when you round 1-4 is rounded down and 5-9 is rounded up. If you were to round to the nearest ten thousand then you would look at the 134 and round down
130,000 because it is lower than 5 grand so you would round down because it is less than halfway to 140,00. Hope this helps

need help fast don't understand both A and B show work please

Answers

Problem A
Usually the number of bits in a byte is 8 or 16 or 32 and recently 64. You don't have to write a formula to restrict it to this number of bits. You are not asked to do so. The general formula is 2^n - 1 for the problem of Millie and her golden keys. Somehow the system can be made to choose the right number of bits. Apple IIe s for example, used 8 bits and there was a location that told the processor that fact.

2^n - 1 <<<<< Answer

Problem B
In this case n = 4
2^n - 1 = 2^4 - 1 = 16 - 1 = 15


Millie can collect 15 keys <<<<<< Answer

What is the total future value six years from now of $80 received in one year?

Answers

UGH MY CLOSEST ANSWER 13.3   :( sorry if the answer wasn't right

giovanni justifies what is expression -4x - 8 is equivalent to -2( x + 1) - 2 ( x + 3 ) by letting x equal 3 in both expressions what is the value of each expression when x equals 3

Answers

Hello!

You put 3 in for x in both equations

Equation 1
-4(3) - 8 = 

Multiply

-12 - 8 = -20

The answer is one of the ones with -20
------------------------------------------------------------------------------------------------------
Equation 2
-2(3 + 1) - 2(3 + 3)

Do what is in paraenthesis

-2(4) - 2(6)

Multiply

-8 - 12 = -20
------------------------------------------------------------------------------------------------------
The answer is C) -20 and -20

Hope this helps!

Answer:

C. -20 & -20

Step-by-step explanation:

If you substitute x for 3 in the expressions, they will both evaluate to -20.

Thus, the answer is -20

Write an equation to solve each problem and then solve it. There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?

Answers

let
x------> larger number
y------> smaller number

we know that
x+y=53------> y=53-x-----> equation 1
3y=x+19-----> equation 2

substitute equation 1 in equation 2
3*[53-x]=x+19------> 159-3x=x+19----> 3x+x=159-19-----> 4x=140
x=140/4-----> x=35
y=53-x----> 53-35-----> y=18

the numbers are
35 and 18

hey can you please help me posted picture of question

Answers

We have the following function:
 N (k):
 Where, the indepent variable is k
 The dependent variable is N
 For the function:
 k (n):
 the independent variable is n
 The dependent variable is k
 Thus,
 N (12) = 4
 k (4) = 12
 Answer:
 TRUE
 option A

MpRashawn recently spent $100 to open a store selling tee-shirts. At his business, he purchases plain tee-shirts for $11 each, prints graphics on them, and then sells them for $26 each. What is the minimum number of tee-shirts that Rashawn would need to sell in order to make a profit (total income minus total expenses) of at least $400?

Answers

26-11=15
400÷15=26,(6)
He would need to sell 27 T-shirts

Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.

What is profit percentage?

SP-CP divided by CP multiplying with 100 we get profit percentage.

P= [(SP-CP)/CP ] × 100

Given the following details about Mr. Rashawn.

Mr. Rashawn recently spent = $100 to open a store selling tee-shirts

He purchases plain tee-shirts for = $11 each

Then sells them for = $26 each

Profit on each shirt = $26 - $11 = $15

Profit = $400 -$100= $ 300

Number of t- shirts= $300/15 = 20 T -shirts.

Thus, Rashawn would need to sell 20 T-Shirts in order to make a profit of at least $400.

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You roll a standard number cube. Find P(number is not 2).
Select one:
a. 2/3
b. 1/2
c. 5/6
d. 1/6

Answers

A standard number cube has 6 sides, and so the numbers are:

1,2,3,4,5,6

P, is any of those numbers that are not 2.

2 is one of the numbers in 6, and so it is 1/6 of the die.

6/6 - 1/6 = 5/6

C) 5/6 is your chance of getting a number that is not 2


hope this helps
Its 5/6 since we are excluding the number two (6-5=1)

Find F'(x) for F(x) = [x^3,1] integral cos(t^4)dt

A. cos(1)-cos(x^12)
B. -3x^2cos(x^12)
C. cos(x^7)
D. -cos(x^12)

Answers

The upper limit is constant, so the derivative of the integral evaluated there is 0. The derivative of the integral evaluated at the lower limit is the product of the integrand evaluated at the lower limit and the derivative of the lower limit. 
  F'(x) = 0 -cos((x^3)^4)·3x^2
Simplifying, ...
  F'(x) = -3x^2·cos(x^12)

The appropriate choice is ...
  B. -3x^2cos(x^12)

please help me out i will reward brainliest

Answers

I can not see the picture so i caN NOT HELP SORRY

The American flag is customarily made with its width and length in the ratio of 10 to 19. Which of the following dimensions is in the correct ratio for the flag?

Answers

Final answer:

The given dimensions do not match the American flag's customary ratio of 10 to 19. To find the correct dimensions, the numbers must divide to equal approximately 0.5263. None of the provided options are correct.

Explanation:

The American flag is customarily made with its width and length in the ratio of 10 to 19. To ensure the dimensions are correct, we must find a pair of numbers that, when divided, are in the same proportion as 10/19 (approximately 0.5263). Looking at the listed dimensions:

51 H (Height is not a width or length measurement, so we cannot confirm the ratio)

53 x 38 (53/38 = 1.3947 which is not equal to 10/19)

55 x 0.025 (55/0.025 = 2200 which is not equal to 10/19)

57 x (2.93, 3.59) (This does not provide a pair of length and width measurements)

59 (This is not a dimension)

Since none of the provided options has numbers that mirror the 10 to 19 ratio of the flag, none of these dimensions would be correct for an American flag. If we want to find dimensions that are proportional, we have to look for any two numbers that, when divided, equal approximately 0.5263. Hence, an example of a correct dimension following the flag's ratio would be 10 inches by 19 inches or any multiple thereof.

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