Expand and reduce (2+√3)^2

Answers

Answer 1

Answer:

7 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a

Given

(2 + [tex]\sqrt{3}[/tex] )² = (2 + [tex]\sqrt{3}[/tex] )(2 + [tex]\sqrt{3}[/tex] )

Each term in the second factor is multiplied by each term in the first factor, that is

2(2 + [tex]\sqrt{3}[/tex] ) + [tex]\sqrt{3}[/tex](2 + [tex]\sqrt{3}[/tex] ) ← distribute both parenthesis

= 4 + 2[tex]\sqrt{3}[/tex] + 2[tex]\sqrt{3}[/tex] + 3 ← collect like terms

= 7 + 4[tex]\sqrt{3}[/tex]


Related Questions

find the missing value in the ratio table

Answers

The missing ratio is 20

The cost of a vacation package is ​249$ per person for the Smith family. If there are 6 family​ members, what is the total cost of the vacation​ package?

Answers

Answer:

$1,494

Step-by-step explanation:

the total cost multiplied by the number of family members

xoxo,your highness...

Step-by-step explanation:

249 x 6 = 1,494

Answer: $1,494

which function describes -1,1,3,5,7,9,11,13

Answers

Answer:

+2

Step-by-step explanation:

First person to get it right gets brainliest

Answers

Answer:

4

Step-by-step explanation:

Algebra
S.4 Find the slope from two points M05
Learn with an example
Find the slope of the line that passes through (5, 6) and (7, 7).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Submit

Answers

7-6/7-5= 1/2= 0.50.

Your answer could be written as 1/2 or 0.50
1/2 is the slope


Explanation:


You use the slope formula

Y2-y1/x2-x1

7-6/7-5

1/2

I NEED THIS ANSWER ASAP THIS IS WORTH A LOT OF POINTS PLEASE​

Answers

Answer:

Step-by-step explanation:

the slope is 1/1

HELPP ✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨

Brad already has $50 but needs a total of at least $250 per day for delivering
papers. What is the least number of days he must work to get enough money for
his vacation? Write the inequality an solve

Answers

Answer:

he needs to work 3 more days in order to make 250 dollars for his vacation

Step-by-step explanation:

Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.

q + d = 19

0.25q + 0.1d = 4


How many quarters does she have?

4

5

14

15

Answers

Answer:

I'm terrible at explaining so here's a screenshot

- Ripper

Step-by-step explanation:

The number of the quarters coins are 14. Then the correct option is C.

What is the solution of the equation?

The solution of the equation means the value of the unknown or variable.

Kat has 19 coins, all quarters and dimes, that are worth a total of $4.

The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.

           q + d = 19

                 d = 19 – q ...1

0.25q + 0.1d = 4        ...2

Solve the equation, we have

0.25q + 0.1(19 – q) = 4

0.25q – 0.1q + 1.9 = 4

                     0.15q = 2.1

                           q = 14

Then the correct option is C.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

URGENT! WILL MARK BRANLIEST
Draw the shape made by slicing the CUBE (THINK: A CUBE HAS 6 SIDES THAT ARE THE SAME MEASURE) parallel to its bases.
A) Square
B) Rectangle
C) Trapezoid
D) Rhombus

Answers

Answer:

B. Ractangle

Step-by-step explanation:

Technically rectangular prism but I guess B, rectangle

Choose one answer is math

Answers

The correct answer is D

the answer is d which is x=.5x=-4

Item 5 Which list shows the absolute values in order from least to greatest? Select each correct answer. |−17.12| , |−17.08| , ∣∣17.06∣∣ ∣∣21.95∣∣ , |−22.02| , |−22.11| |−7.38| , ∣∣7.39∣∣ , |−7.41| |−3.07| , ∣∣−3.25∣∣ , |3.31|

Answers

Lets go over some stuff before we answer this absolute values make anything positive or make you count down from zero so then just imagine those numbers as positive.

ill put them as positives and then sort them here

3.07 3.25 3.31    |3.07 3.25 3.31 (Correct)

7.38, 7.39 , 7.41 | 7.38, 7.39 , 7.41  (Correct)

17.12, 17.08 17.06 | 17.06 ,17.08 ,17.12 (Wrong)

21.95 , 22.02 , 22.11 | 21.96 , 22.02 , 22.11 (Correct)

Answer:

|−17.12| , |−17.08| , ∣∣17.06∣wrong∣ ∣∣21.95∣∣ , |−22.02| , |−22.11| correct |−7.38| , ∣∣7.39∣∣ , |−7.41|correct |−3.07| , ∣∣−3.25∣∣ , |3.31|:correct

Cynthia is training to run the 100 yard dash. The first week she ran it is 14.0 seconds. The third week she ran it in 13.1 seconds. What is the percent change from week 1 to week 3 rounded to the nearest tenth of a percent?



Answers

Answer:

We assign the older value to variable A and the newer value to variable B. Units, in this case the dollars, are always stripped or canceled out in percent change problems since we’re looking for increases or decreases in percentage.

Step-by-step explanation:

solve for w and simplify this fraction 3/2w=-20 ​

Answers

Answer:

4 2/3

Step-by-step explanation:

Answer:

w = -1.3 (.3 repeating)

Step-by-step explanation:

3/2w = -20

3/2w time 2/3 (flip to get rid of fraction)

- 20 time 2/3 (what you do to one side, you must do to the other side)

w = 1.3 (.3 repeating)

1.3 as a fraction is 4/3

write the slope-intercept form of the equation

6x-3y-12=0

Answers

Answer:

y=2x-4

Step-by-step explanation:

Please help with geometry!
Find x

Answers

Answer:6x-5+2x+5+3x+22 and u get your answer

Step-by-step explanation:

PLEASE HELP ILL MARK BRAINLIEST !!!

The following tables describe arithmetic sequences

(a) what is the common difference of the sequence xn?

(b) what is x8? what is x12?

(c) what is the common difference of the sequence am?

(d) what is a12? what is a15?

Answers

Answer:

a) the common difference is 20

b) [tex]x_8=115 , x_{12}=195[/tex]

c) the common difference is -13

d) [tex]a_{12}=52, a_{15}=13[/tex]

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: [tex]x_n=x_1+(n-1)d[/tex]

We know common difference d= 20, we need to find [tex]x_1[/tex]

Using [tex]x_3=16[/tex] we can find [tex]x_1[/tex]

[tex]x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25[/tex]

So, We have [tex]x_1 = -25[/tex]

Now finding [tex]x_8[/tex]

[tex]x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115[/tex]

So, [tex]\mathbf{x_8=115}[/tex]

Now finding [tex]x_{12}[/tex]

[tex]x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195[/tex]

So, [tex]\mathbf{x_{12}=195}[/tex]

c) what is the common difference of the sequence [tex]a_m[/tex]

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: [tex]a_n=a_1+(n-1)d[/tex]

We know common difference d= -13, we need to find [tex]a_1[/tex]

Using [tex]a_7=104[/tex] we can find [tex]x_1[/tex]

[tex]a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195[/tex]

So, We have [tex]a_1 = 195[/tex]

Now finding [tex]a_{12}[/tex] , put n=12

[tex]a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52[/tex]

So, [tex]\mathbf{a_{12}=52}[/tex]

Now finding [tex]a_{15}[/tex] , put n=15

[tex]a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13[/tex]

So, [tex]\mathbf{a_{15}=13}[/tex]

Will the answer to this expression be POSITIVE or NEGATIVE?

12 - 22

Answers

Answer:

the answer is -10

Step-by-step explanation:

the steps are in the picture

Answer:

The answer to this expression would be negative.

Step-by-step explanation:

-10

Write the equation in slope intercept form from the graph below​

Answers

Answer:

y=[tex]-\frac{1}{3}[/tex]+2

Step-by-step explanation:   m=slope, b= y-intercept

y=mx+b             how to find the slope=  [tex]\frac{3-0}{1-2}[/tex]

y=m(x)+b

1=m(3)+b

1=[tex]-\frac{1}{3}(3)[/tex]+2

solve the equation by taking square roots

(x-3)^2 +8 = -10​

Answers

Answer:

x = 3 ± 3i√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Vertex Form: f(x) = a(bx - c)ⁿ + dCompleting the SquareSolving roots

Algebra II

Imaginary Roots: √-1 = i

Step-by-step explanation:

Step 1: Define equation

(x - 3)² + 8 = -10

Step 2: Solve for x

Subtract 8 on both sides:                    (x - 3)² = -18Square root both sides:                       x - 3 = ±√-18Factor:                                                   x - 3 = √-1 · ±√18Simplify:                                                x - 3 = ±3i√2Add 3 to both sides:                            x = 3 ± 3i√2

what fraction is equal to 0.2​

Answers

Answer:

Fraction Decimal Percent

2/3 0.666… 66.666…%

1/4 0.25 25%

3/4 0.75 75%

1/5 0.2 20%

Geometry! Find the length of a-b. Give answer in simplest radical form.

Answers

Answer:

Length of AB is [tex]\sqrt{106}[/tex]

Step-by-step explanation:

Let us use the rule of the distance To find the length of AB

∵ A = (9, -3)

∵ B = (0, 2)

x1 = 9 and y1 = -3

x2 = 0 and y2 = 2

∵ AB = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

→ Substitute the values of x1, x2, y1, and y2 in the rule to find AB

∴ AB = [tex]\sqrt{(0-9)^{2}+(2--3)^{2}}[/tex]

∴ AB = [tex]\sqrt{(-9)^{2}+(2+3)^{2}}[/tex]

∴ AB = [tex]\sqrt{81+(5)^{2}}[/tex]

∴ AB = [tex]\sqrt{81+25}[/tex]

∴ AB = [tex]\sqrt{106}[/tex]

→ The square root of 106 is the simplest radical form

Length of AB is  [tex]\sqrt{106}[/tex]

4 divided by 2/9 in fraction form( whoever sees this I hope you have a wonderful day! )

Answers

36/2. Sklshsjsmsbsjsbsb

Answer:

4x9/2

4x9/2

36/2

18

UwU

18 is your answer

Will each student get more than or less than 1 cup of broth? Explain.

Answers

Answer:

1

Step-by-step explanation:

because every cup has to be equal and if is not then every cup will be less then a cup eather way it will be the same

What is an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4

Answers

Answer:

The equation of required line is: [tex]\mathbf{x+y=5}[/tex]

Step-by-step explanation:

We need to find an equation of the line that passes through the point (2,3) and is parallel to the line x+y=4

For finding an equation of line, we need to find slope and y-intercept of the line.

Finding slope:

If the lines are parallel their slope is same

We are given: x+y=4

Writing in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept

[tex]x+y=4\\y=-x+4[/tex]

Comparing [tex]y=-x+4[/tex] with [tex]y=mx+b[/tex] the slope m is -1

So, slope of given line is -1

It is parallel with required line, so they have same slope.

The slope of required line is m=-1

Finding y-intercept

Using slope m=-1 and point(2,3) we can find y-intercept

Using slope-intercept form: [tex]y=mx+b[/tex]

[tex]y=mx+b\\3=-1(2)+b\\3=-2+b\\b=3+2\\b=5[/tex]

So, y-intercept is: b=5

The equation of required line having slope m=-1 and y-intercept b = 5 is

[tex]y=mx+b\\y=-1x+5\\y=-x+5\\x+y=5[/tex]

So, equation of required line is: [tex]\mathbf{x+y=5}[/tex]

The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y  =  -x  +  5

Two equations are parallel if they have equal slope

For the equation x + y = 4

Rewrite the equation in the form y = mx + c

y  =  -x  +  4

Compare y = -x + 4 with y = mx + c

The slope, m = -1

The equation parallel to x + y = 4 will also have a slope, m = -1

The line passes through the point (2, 3)

That is, x₁ = 2, y₁ = 3

The point-slope form of the equation of a line is:

y - y₁  =  m(x  -  x₁)

Substitute x₁ = 2, y₁ = 3 into y - y₁  =  m(x  -  x₁)

y - 3 = -1(x  - 2)

y - 3 = -x + 2

y  =  -x  +  2  +  3

y  =  -x  +  5

The equation of the line that passes through the point (2,3) and is parallel to the line x+y=4 is y  =  -x  +  5

Learn more here: https://brainly.com/question/19484034

Identify the parent function that can be used to graph the function f(x) =4|x|-3
c. F(x) = x
b. F(x) = [x]
d. f(x) = |x|

Answers

Answer:

d

Step-by-step explanation:

f(x) = |x| will always be parent function unless told otherwise.

Will give Brainliest!!!
Ella is going to drive from her house to City A without stopping. Ella's house is 100 miles from City A and after driving for 3 hours, she will be 25 miles away from City A. Write an equation for D,D, in terms of t,t, representing Ella's distance from City A tt hours after leaving her house.

Answers

Answer:

d = 100 - 25t

Step-by-step explanation:

Mai has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can she buy?

Answers

Answer: 8

Step-by-step explanation: 36/4.50

Answer:

8tickets

Step-by-step explanation:

she has $36

1rickeet costs $4.50

hence,

$36/$4.50

=$8.0

=8tickets.

hope was helpful!

can someone make my day and explain this to me​

Answers

Answer:

Step-by-step explanation:

Remark

The first step is the critical one. Take the base and raise it to x. Then take the log of the base and the number whose log you need. x (the power)is brought down and the logs divided.

2^x = 1024

log 2^x = log(1024)

x log(2) = log(1024)

x * 0.30102 = 3.0102

x = 30102/0.30102

x = 10

You could use the e system to solve this as well

2^x = 1024

ln(2^x) = ln(1024)

x * ln(2) = ln(1024)

x 0.6931 = 6.9315

x = 6.9315/0.69315

x = 9.999959

x = 10

Is the answer right?

Answers

Answer:

yes I think...........

Solve the system using elimination

Answers

Answer:

(3, 2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define systems

2x + 5y = 16

3x - 5y = -1

Step 2: Solve for x

Eliminate y (add equations):                   5x = 15Divide 5 on both sides:                           x = 3

Step 3: Solve for y

Define equation:                          2x + 5y = 16Substitute in x:                             2(3) + 5y = 16Multiply:                                        6 + 5y = 16Subtract 6 on both sides:            5y = 10Divide 5 on both sides:               y = 2

Answer:

(3, 2)

Step-by-step explanation:

2x + 5y = 16 ........ (1)

3x - 5y = - 1 ......... (2)

(1) + (2)

( 2x + 3x ) + [ 5y + ( - 5y)] = 16 + (- 1)

5x = 15 ⇒ x = 3

2(3) + 5y = 16 ⇒ y = 2

(3, 2)

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