Expand and simplify
(4 + 2)(6-12)
Give your answer in the form b+cV2

Answers

Answer 1

Note: Consider the expression is [tex](4+\sqrt{2})(6-\sqrt{2})[/tex].

Given:

[tex](4+\sqrt{2})(6-\sqrt{2})[/tex]

To find:

The value of given expression in the form of [tex]b+c\sqrt{2}[/tex].

Solution:

We have,

[tex](4+\sqrt{2})(6-\sqrt{2})[/tex]

Using distributive property, we get

[tex]=4(6-\sqrt{2})+\sqrt{2}(6-\sqrt{2})[/tex]

[tex]=4(6)+4(-\sqrt{2})+\sqrt{2}(6)+\sqrt{2}(-\sqrt{2})[/tex]

[tex]=24-4\sqrt{2}+6\sqrt{2}-2[/tex]

On combining like terms, we get

[tex]=(24-2)+(6\sqrt{2}-4\sqrt{2})[/tex]

[tex]=22+2\sqrt{2}[/tex]

On comparing with [tex]b+c\sqrt{2}[/tex], we get

[tex]a=22,b=2[/tex]

Therefore, the required form is [tex]22+2\sqrt{2}[/tex].


Related Questions

Mr. Martinez is buying food for a party. Hamburger patties are sold in packages of 6 and hamburger buns are sold in packages of 8. If he wants to have an equal number of each, what is the LEAST number of hamburger patties and buns that Mr. Martinez will have to buy?

Enter the correct answer in the box.

Answers

Answer:

24 is the least number of hamburger patties and buns Mr. Martinez will have to buy.

Step-by-step explanation:

You need to find the LCM of 6 and 8. The number they have first have common is 24

How many 1/5s are there in 8/10?

Please answer right away helpers!!!
The time is ticking by now.

Answers

4/5=8/10, therefore the answer is 4

help pls!!!!!!!!!!!!!

Answers

The percentages, from left to right, are:

1) 56.25%

2) 18.75%

3) 18.75%

4) 6.25%

How to get the percentages?

In this case, the 100% is 16.

We know that there are 9 individuals with black fur and black eyes, so we can write the equations:

100% = 16

X% = 9

We want to find the percentage X%. By combining these equations we get:

X% = (9/16)*100% = 56.25%

Now we can use the same equations for the other genotypes.

There are 3 units with black fur and red eyes, here the percentage is:

p = (3/16)*100% = 18.75%

There are 3 units with white fur and black eyes, so the percentage is:

p = (3/16)*100% = 18.75%

There is 1 unit with white fur and red eyes, so the percentage is:

p = (1/16)*100% = 6.25%

If you want to learn more about percentages:

https://brainly.com/question/843074

#SPJ1

What property should you use first to solve 14+c=39

Answers

Answer:

Subtraction

Step-by-step explanation:

what’s the value of x in the solution to this system of equitations:
3x + 4y =-3
x= -2y- 1

Answers

Answer:

x = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

3x + 4y = -3

x = -2y - 1

Step 2: Solve for y

Substitution

Substitute in x:                    3(-2y - 1) + 4y = -3Distribute 3:                         -6y - 3 + 4y = -3Combine like terms:           -2y - 3 = -3Isolate y term:                     -2y = 0Isolate y:                              y = 0

Step 3: Solve for x

Define equation:                   x = -2y - 1Substitute in y:                      x = -2(0) - 1Multiply:                                 x = 0 - 1Subtract:                                x = -1

480/____=80
what does ____=???

Answers

The answer is 6. 480 divided by 80 gives you the answer 6.

A student had 500 milliliters of water in a water bottle. She drank 25% of the water before soccer practice. After practice, she drank the remaining water. How much water, to the nearest ten 3 1milliliters does the student have left in the bottle?

Answers

Answer:

25\100*500=125

1/3*125=41.66

41.66 millilites is left in the bottle

Step-by-step explanation:

True or False. Horizontal translations move a graph up and down.

Answers

Answer:

false

Step-by-step explanation:

horizontal is left and right

Fill in the blank pls

Answers

Step-by-step explanation:

Factors

hope it helpful

HELP!!!! I have never seen this. I will award big brain.​

Answers

Step-by-step explanation:

Angles APD, DPC and CPB are supplementary. (Angles on a straight line)

Therefore Angle APD + Angle DPC + Angle CPB = 180°.

Since Angle DPC = 90° (Right angle),

Angle APD + Angle CPB = 180° - 90° = 90°.

=> (7x + 1) + (9x - 7) = 90

=> 16x - 6 = 90

=> x = 6

Hence arc measure of minor arc AD

= (7x + 1)° = [7(6) + 1]° = 43°.

Find x such that f(x) = 10 given f(x) = 4x+2

Answers

Answer:

x=2

Step-by-step explanation:

So you make the equation equal. f(x)=10 so you would put it as 10=4x+2, than you subtract two from both sides making it 8=4x and than divide both sides by 4 making it 2=x.

Answer:

[tex]\boxed {\boxed {\sf x=2}}[/tex]

Step-by-step explanation:

We know that:

[tex]f(x)=4x+2 \\f(x)= 10[/tex]

Both 4x+2 and 10 are equal to f(x). We can use substitution and set 4x+2 and 10 equal to each other.

[tex]4x+2=10[/tex]

Now, solve for x. Perform the inverse operations to isolate x on one side of the equation.

2 is being added to 4x. The inverse of addition is subtraction. Subtract 2 from both sides of the equation.

[tex]4x+2-2=10-2[/tex]

[tex]4x=10-2 \\[/tex]

[tex]4x=8[/tex]

x is being multiplied by 4. The inverse of multiplication is division. Divide both sides of the equation by 4.

[tex]\frac{4x}{4} =\frac{8}{4}[/tex]

[tex]x=\frac{8}{4}[/tex]

[tex]x=2[/tex]

For the function f(x)= 4x+2, when f(x)=20, x=2

Which of the sets of ordered pairs represents a function? (1 point)

P = {(6, −7), (3, −2), (−9, 2), (−5, −7)}

Q = {(−7, 8), (4, −6), (−3, 1), (1, 5)}

Answers

Answer:

Conclusion:

Both sets represent the function.

Step-by-step explanation:

We know that a function relates an input to an output.

For example, a certain plant grows 10 cm each year. Thus, the height of the plant is associated with its age using the function

h (age) = age × 10

Thus, if the age of the plant is 2 years, the height is:

h(10) = 2 × 10 = 20 cm

Set P

P = {(6, −7), (3, −2), (−9, 2), (−5, −7)}

The set P represents the function because the function relates an input to an output. In other words, here each input is related to exactly one output.

The x-values are 6, 3, -9, and -5.

Thus, there are no duplicated inputs or x-values.

Therefore, the set P  of ordered pairs represents a function.

Set Q

Q = {(−7, 8), (4, −6), (−3, 1), (1, 5)}

The set P represents the function because the function relates an input to an output. In other words, here each input is related to exactly one output.

The x-values are -7, 4, -3, and 1.

Thus, there are no duplicated inputs or x-values.

Therefore, the set Q  of ordered pairs also represents a function.

Conclusion:

Both sets represent the function.

z=32+41.9i
What are the real and imaginary parts of z?
--------------------------------------------------------------
A. Re(z) = 32 and Im(z) = 41.9
B. Re(z) = 32 and Im(z) = 41.9i
C. Re(z) = 41.9i and Im(z) = 32
D. Re(z) = 41.9 and Im(z) = 32

Answers

A. Re(z)= 32 and Im(z)= 41.9

The real part of a complex number z=a+bi is ‘a’, and the imaginary part is ‘b’

Darnell created a scale drawing of the community garden in his town. The actual garden is 20 feet long. Darnell's scale drawing of
the community garden is 4 inches long
What scale did Darnell use to draw the garden?
O 2 inches equal 5 feet
o 1 inch equals 5 feet
o inch equals 1 foot
O 1 inch equals foot

Answers

The scale that Darnell used is required.

The scale that Darnell used is 1 inch equals 5 feet.

Scale diagrams

The length of the actual garden is 20 feet.

The scale drawing is 4 inches long

[tex]20\ \text{feet}=4\ \text{inches}[/tex]

Since, we are finding the inches to feet we divide the expression by [tex]4[/tex]

[tex]\dfrac{20}{4}\ \text{feet}=1\ \text{inch}[/tex]

[tex]1\ \text{inch}=5\ \text{feet}[/tex]

Learn more about scale diagrams:

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At a bus station, buses depart at a rate of 4 every 10 minutes. At this rate, how many buses would depart in 1 hour?

Answers

Answer:

24 buses.

Step-by-step explanation:

10 minutes equals 4 buses.

There is a total of 60 minutes, so 60 ÷ 10 = 6.

Then 4 × 6 = 24 buses.

Pls help it timed!!!!

Answers

Answer:

its subtraction property of equality

Step-by-step explanation:

it shows that the 3/4 next to the 16 was subtracted on both sides to cancel out on of the other 3/4 on the other side...

i uploaded a pic just incase u didnt understand

Hope this helps!!!

For the solution to the inequality in the previous problem, list all integers from -10 through 10 that will make the
inequality a true statement when substituted for "n"? (The integers for -10 through 10 are shown below.)
{-10,-9,-8, -7,-6, -5, -4,-3,-2,-1,0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
HELP PLEASE HURRY
ILL GIVE 30 POINTS AND MOST BRAINLIEST

Answers

Answer: -10, -7, -5, -2, -1, 3, 4, 8, 9

Step-by-step explanation:

Considerando las siguientes variables a = ancho y l = longitud, determina su valor, si se sabe que se cuenta con un rectángulo que tiene como perímetro 35 metros, y se sabe que el doble de su ancho es igual a 3 veces su longitud.

Answers

Answer:

La longitud = 7 metros

La anchor = 10.5 metros

Step-by-step explanation:

La fórmula para el perímetro de un rectángulo es

P = 2L + 2W

L = longitud

A = ancho

P = 35 metros

se sabe que el doble de su ancho es igual a 3 veces su largo.

2A = 3L

Ancho = 3L / 2 = 1.5L

Sustituimos 1.5L por W

35 = 2 L + 2 (1.5 L)

35 = 2L + 3L

35 = 5 litros

L = 35/5

L = 7 metros

Por lo tanto, la longitud = 7 metros

Recuerda

A = 1.5 L

A = 1.5 × 7

A = 10.5 metros

La anchor = 10.5 metros

I need the value of X

Answers

Answer:

x=36

Step-by-step explanation:

By vertical angles we know that

[tex]72 = 2x\\\\x=\frac{72}{2}\\\\x=36[/tex]

Answer:

x = 36

Step-by-step explanation:

72 and 2x are vertical angles, so they are equal.

2x = 72

2x/2 = 72/2

x = 36

if the scientific notation is 9.63x10^-3 what would it look like in standard form? MARKING BRAINLIEST!!!!

Answers

Answer:

.00963

Step-by-step explanation:

Since its 10^-3, the decimal point moves to the left 3 times. hope this helped :)

Lin found the area of a rectangle with a of length 5 in and a width of 3 inches, to be 15 square inches. Lin creates another rectangle that is a scaled copy with a scale factor of 2. What is the area of the new rectangle? How did you find it?

Answers

Answer:

60in^2

Step-by-step explanation:

Step one:

given data

lenght L= 5in

width W= 3 in

area= L*W

area= 5*3= 15in^2

Step two:

The rectangle was scaled by 2, this means that the dimensions were doubled

therefore the lenght and width will be

L=5*2= 10

W=3*2= 6

hence the area is

Area= 10*6= 60in^2

Tyler converted 0.0000783 to scientific notation.

0.0000783 = 78.3 x 10-6

is he correct?

Answers

Let's convert your number to scientific notation.

0.0000783

Move the decimal point 5 places to the right.

7.83*10−5

Answer:

7.83 * [tex]10^{5}[/tex]

Answer: No , the coefficient should be 7.83

Step-by-step explanation:

Find the value of X and Y

Answers

Answer:

Answer: x=4, y=10

Step-by-step explanation:

Lines and Angles

When lines cross, the angles formed in the intersections meet certain properties that help us to solve some geometry problems.

We must recall the so-called linear angles, defined as the adjacent angles formed in the point where two lines cross.

Linear angles always add up to 180°

We can see line m intersects with the horizontal (unnamed) line forming two pair of linear angles, thus:

29x - 3 + 15x + 7 = 180

Simplifying:

44x +4 = 180

Subtracting 4:

44x = 176

Dividing by 44:

x = 176/44

x = 4

Now below the horizontal line, we find other pair of linear angles, thus:

13y - 17 + 15x + 7 = 180

Substituting x=4:

13y - 17 + 60 + 7 = 180

Simplifying:

13y + 50 = 180

Subtracting 50:

13y = 180 - 50 = 130

Dividing by 13:

y = 130/13 = 10

y = 10

Answer: x=4, y=10

true Or false

1.inequalities are similar to equations

2.you never isolate the variable in an inequality '

Answers

True and false you can do that on #2

7÷7/11=
Please explain for me

Answers

Answer:

11

Step-by-step explanation:

You have to first make the 7 into a fraction (7/1) then keep, change, flip.

You keep the 7/1 as it is, you change the division sign into a multiplication sign, and you flip the 7/11 to 11/7. You then just multiply straight across to get 77/7 which is the same thing as 11/1 which is the same thing as 11!

Final answer:11


f) Cosec2A + Cot4A = CotA – Cosec4A

Answers

Answer:

True (the sides are equal)

I hope this helps!

how do u do this im confused

Answers

Answer:

Line one answers: -x^2.  2x^2.  0.  5x^2

Line two answers: -x^2.  12x^2.   -2x^2.   8x^2

Line three answers: 4x^2.  8x^2.   -x^2.   x^2

Step-by-step explanation:

Answer:

-x^2.  2x^2.  0.  5x^2

-x^2.  12x^2.   -2x^2.   8x^2

4x^2.  8x^2.   -x^2.   x^2

Step-by-step explanation:

Mariana is choosing a beverage to drink. She wants a beverage with no more than 3 grams of sugar per ounce. Which beverages meet Mariana's requirements?

Answers

Answer:

Step-by-step explanation:

The main beverage that would easily meet Mariana's requirements would be water as it contains no sugar. Other than these two flavored options that she can choose from would be to make home-made Ice-tea or lemonade. Therefore, she can choose the amount of sugar to add without going over her own requirements, but still having a delicious beverage to drink.

Please help me thank you

Answers

i’m pretty sure the answer is A. ( i also use my hrw too lol)

Answer:

the answer is A

Step-by-step explanation:

they are 3 sets of 2.3. the 5 at the top represents the number of 2.3s that r there. so the answer is A

A recipe for shepherd's pie uses 3 cups potatoes, 2 cups carrots, 1 cup onions, 1 ½ cups ground round to create enough for 6 people. If you need to feel 16 people, how many cups of carrots do you need? Use scale factors and ratios to solve this problem. Remember to show your work.

Answers

Answer:

[tex]5\frac{1}{3}[/tex] cups of carrot.

Step-by-step explanation:

Let's set up proportional equation.

6 people need 2 cups of carrots

Let 16 people need x cups of carrots.

We could form ratio for number of people to cups of carrot used as

6:2

16:x

So, proportional equation would be

[tex]\frac{2}{6} =\frac{x}{16}[/tex]

Cross multiply

32=6 x

Divide both sides by 6.

x=[tex]\frac{32}{6}[/tex]

Divide to get mixed number

x=5[tex]\frac{2}{6}[/tex]

Simplify the fraction

x=[tex]5\frac{1}{3}[/tex] cups of carrot.

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