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

what is 53829-(-538)7902(6)=?

Answers

Answer:

25561485

Step-by-step explanation:

What number is 25% of 160? (worth lots of points because why not lol) help me-

Answers

Answer:

40

Step-by-step explanation:

This can be solved by changing the percentage to a decimal number, then multiplying by 160.

0.25×160=40

Mr. M has a recipe for sourdough bread. He uses 8/3 cups of flour to make 2 loaves of sourdough bread. If you were to follow the same recipe, which equation would work for making y loaves of bread with x cups of flour?

Answers

Answer:

2y=8/3x

Step-by-step explanation:

PLEASE HELP FAST I WILL GVIE BRAINLIST AND EXTRA MARKS FOR CORRECT ANSWER! THANKS

Answers

Answer:

f(-2) = 2

Step-by-step explanation:

Look at the graph and find -2 on the x-axis and see what the y-coordinate is on the line where x is -2. When you do this, you can see that where x is -2, y is 2.

So basically it wants the y-value :)

Answer:

1.25

Step-by-step explanation:

the answer is 1.25. To get that, I found the slope, wrote the equation in point slope form, and then I calculated when the f(x) function hits the line

what does x equal and what are the angle measures?? help Asap

Answers

all triangles are 180 always. make a equation 2x+x+x+8 then combine like terms so it will be 4x+8 then divide by 4 on bith sides x=2

1/5(x-2)=1/10(x+6) and
0.35(x+4)=0.25(x-6) please

Answers

Answer:

1) x=10   2) x= -7.25

Step-by-step explanation:

Im not sure

81/11 as a mixed number

Answers

Answer:

7 4/11

Step-by-step explanation:

this is the answer

Answer:

7  4/11

Step-by-step explanation:

81/11= 7  4/11

parallel lines, transversal, and algebra really need help

Answers

Answer:

1. 58 = 5x-2, 60 = 5x, x = 12

2. 134 = 16x+22, 112 = 16x, x = 7

3. 125 = 7x-1, 126 = 7x, x = 18

4. 133+9x+2 = 180, 9x=45, x=6

5. 8x-77 = 3x+38, 5x = 115, x=23

6. 11x-47 = 6x-2, 5x = 45, x=9

7. 13x-21 = 5x+75, 8x = 96, x=12

8. 5x+3+9x-33 = 180, 14x = 210, x=15

9. 8x-31 = 6x+3, 2x = 34, x=17

5y+35+6(17)+3 = 180, 5y = 40, y = 8

10. 29x-3+15x+7 = 180, 44x = 176, x=4

13y-17+15(4)+7 = 180, 13y = 130, y=10

1. x = 12

2. x = 7

3. x = 18

4. x = 5

5. x = 23

6. x = 9

7. x = 12

8. x = 15

9. x = 17; y = 8

10. x = 4; y = 10

To find the value of each missing variable(s), we would need to apply our knowledge of algebra. However, recall the following rules of angles in parallel lines:

corresponding angles are congruent (i.e. equal to each other)vertically opposite angles are congruent alternate angles are congruent same-side interior angles are supplementary (i.e. sum up to give 180°alternate exterior angles are congruent.

Let's solve the given problems as shown below given that line l is parallel to line m:

1. [tex]58 = (5x - 2)[/tex] (corresponding angles)

solve for x

[tex]58 = 5x - 2\\58 + 2 = 5x - 2 +2[/tex] (addition property of equality)

[tex]60 = 5x \\\frac{60}{5} = \frac{5x}{5}[/tex](division property of equality)

[tex]12 = x\\x = 12[/tex]

2. [tex]134 = 16x+22[/tex] (alternate exterior angles)

[tex]\\134 - 22 = 16x +22-22[/tex] (subtraction property of equality)

[tex]134 - 22 = 16x +22-22\\112 = 16x\\\frac{112}{16} = \frac{16x}{16}[/tex](division property of equality)

[tex]7 = x\\x = 7[/tex]

3. [tex]7x - 1 = 125[/tex] (alternate angles)

[tex]7x - 1 + 1 = 125 + 1\\7x = 126\\\frac{7x}{7} = \frac{126}{7} \\x = 18[/tex]

4. [tex](9x+2) + 133 = 180[/tex] (same-side interior angles)

[tex]9x+2 + 133 = 180\\9x + 135 = 180\\9x + 135 - 135 = 180 - 135\\9x = 45\\\frac{9x}{9} = \frac{45}{9} \\x = 5[/tex]

5. [tex]3x+38 = 8x-77[/tex] (alternate exterior angles)

[tex]77 + 38 = 8x - 3x\\115 = 5x\\\frac{115}{5} = \frac{5x}{5} \\23 = x\\x = 23[/tex]

6. [tex]6x-2 = 11x-47[/tex] (corresponding angles)

[tex]6x-2 = 11x-47\\47 - 2 = 11x - 6x\\45 = 5x\\x = 9[/tex]

7. [tex]5x+75 = 13x - 21[/tex] (alternate angles)

[tex]5x+75 = 13x - 21\\21 + 75 = 13x - 5x\\96 = 8x\\12 = x\\x = 12[/tex]

8. [tex](5x+3)+(9x-33)= 180[/tex] (same-side interior angles)

[tex]5x+3+9x-33= 180\\14x - 30 = 180\\14x - 30 + 30 = 180 + 30\\14x = 210\\x = 15[/tex]

9. [tex]8x-31 = 6x+3[/tex] (alternate angles)

[tex]8x - 6x = 31 + 3\\2x = 34\\x = 17[/tex]

Solve for y

[tex](5y + 35) + (6x + 3) = 180[/tex] (same-side interior angles)

[tex]5y + 35 + 6x + 3 = 180\\[/tex]

Plug in the value of x

[tex]5y + 35 + 6(17) + 3 = 180\\5y + 35 + 102 + 3 = 180\\5y + 140 = 180\\5y = 180 - 140\\5y = 40\\y = 8[/tex]

10. [tex](29x-3)+(15x+7) = 180[/tex](supplementary angles)

Solve for y

[tex]13y - 17 = 29x - 3[/tex] (alternate exterior angles)

Plug in the value of x

[tex]13y - 17 = 29(4) - 3\\13y - 17 = 116 - 3\\13y - 17 = 113\\13y = 113 + 17\\13y = 130\\y = 10\\[/tex]

Learn more about parallel lines here:

https://brainly.com/question/16227989

I need help with this geometry problem please​

Answers

Answer:

A. 29

Step-by-step explanation:

Set 5x - 11 = to 3x + 5, and then solve for X, and substitute the x value (8) back into the equation to get 29.

~theLocoCoco

The answer for A. Is 29 sorry for late responses

The Science Club went on a two-day field trip. The first day the members paid $70 for transportation plus $19 per ticket to the planetarium. The second day they paid $100 for transportation plus $16 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.

Answers

Answer:

$170 + $35n

Step-by-step explanation:

Given that:

First day:

Transport fare = $70

Fee per ticket = $19

2nd day:

Transport fare = $100

Fee per ticket = $16

Total cost in dollars for the two days for n members

Number of members = n

First day:

70 + 19n

Second day :

100 + 16n

Totak cost :

(70 + 19n) + (100 + 16n)

70 + 100 + 19n + 16n

170 + 35n

$170 + $35n

hello can anyone help me ? here the question

Answers

Answer:

A. 1/5k - 2/3j and -2/3j +1/5k

Step-by-step explanation:

A. 1/5k - 2/3j and -2/3j +1/5k

B. 1/5k - 2/3j and -1/5k +2/3j

There is a change in the signs of each term

1/5k changed to -1/5k

-2/3j changed to +2/3j

Not equivalent

C. 1/5k - 2/3j and 1/5j - 2/3k

There is a change in the variables

1/5k changed to 1/5j

-2/3j changed to -2/3k

D. 1/5k - 2/3j and 2/3j - 1/5k

The is a change in the signs of each term

1/5k changed to -1/5k

-2/3j changed to +2/3j

The only equivalent expression is

A. 1/5k - 2/3j and -2/3j +1/5k

Please help me will be much appreciated <3

Answers

Answer:

She earned 300 dollars by selling 100 headbands.

please help me answer this!! geometry

Answers

Answer:

-2x+7(10+18)

Step-by-step explanation:

Hope this helps

4. What is the value of -24 + 6?

Answers

Answer:-18

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

Please give brainliest!

Please help me solve this.

Answers

Answer:

9

Step-by-step explanation:

13*3=39

48-39=9

Answer:

48-39=9

        ^

(13 x 3=39)

what isvequivalent to y=23x−6?

Answers

Answer:

Slope = 46.000/2.000 = 23.000

x-intercept = 6/23 = 0.26087

y-intercept = -6/1 = -6.00000

ANSWER PLEASE 40 POINTS!

Answers

Answer: |10 - (-8)|  

The absolute value is 18

Step-by-step explanation:

The distance between two numbers is a subtraction equation.

10 - (-8)  Subtracting a negative is like adding a positive

10 + 8 = 18

If you look at it as the first negative sign means -1 multiplied by the next negative number, "Remember that a negative times a negative is a positive!"

Answer:

|-10 - (-8)|

Step-by-step explanation:

Distance from 10 to 0: 10Distance from 0 to -8: 8Put them together (with absolute value): |-10 - (-8)|

I hope this helps!

What is the quotation (-3)^0/(-3)^2

Answers

Hey there!

(-3)^0 / (-3)^2

(-3)^0 = 1 ⬅️ Numerator

(-3)^2 = (-3)(-3) = 9 ⬅️ Denominator

Answer: 1/9 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

What is it will mark Brainliest

Answers

the absolute minimum of this graph is y=-10

The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
(3x-9)°
(x+15)

Answers

Answer:

318.6

Step-by-step explanation:

(3x-9) + (x+15) = 180

3x (x+15) -9 (x+15)

4x + 45x - 9x + 6 = 180

40x + 6 = 180

40x = 180 - 6

40x = 174

x = 4.34

(3x-9) = 4.34 * 3x-9 = 4.02

(x+15) = 4.34 + 15 = 19.34

180 - (4.02 + 19.34)

= 180 - 23.36

= 156.64

hope this answer helps!!

The graph of f (x) = x + 5 is a vertical translation 5 units
up of the graph of f(x) = x. How can you obtain the graph of
f(x) = x + 5 from the graph of f (x) = x using a horizontal
translation?

Answers

Answer:

A horizontal translation of 5 units to the left.

Step-by-step explanation:

Given the parent linear function:

[tex]\displaystyle f(x)=x[/tex]

To shift vertically n units, we can simply add n to our function. Hence:

[tex]f(x)=x+n[/tex]

So, a vertical shift of 5 units up implies that n=5. So:

[tex]f(x)=x+5[/tex]

As given.

However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:

[tex]f(x-n)=(x-n)[/tex]

Where n is the horizontal shift.

For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:

[tex]f(x-1)=(x-1)[/tex]

Or:

[tex]f(x)=x-1[/tex]

We notice that this is also a vertical shift of 1 unit downwards.

Therefore, we want a number n such that -n=5.

So, n=-5.

Therefore, it we shift our function 5 units to the left, then n=-5.

Then, our function will be:

[tex]f(x-(-5))=(x+5)\text{ or } f(x)=x+5[/tex]

Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.

someone answer please:)
I think its saying to find out what a means

Answers

It should be 7.5 rounded up

can someone help me. Arithmetic Sequences
Your bucket of Halloween candy has 125 pieces of candy in it. You decide that to ration yourself, you’re going to only eat 5 pieces per day.

What is the common difference?

Answers

Answer:

-5

Step-by-step explanation:

when you eat 5 pieces of candy per day then the sequence will be

125, 120, 115, 110, 105......

And Then, the common difference will be -5

uhh.i dumb the screenshot is here

Answers

Answer:

40

Step-by-step explanation:

Just use a calculator. I didn´t need to. My brother helped me a little

The answer is 40 I believe

A line passes through the points (-8,-4) and has a slope of 5/4.​

Answers

The answer is y=5/4x+6

Is it scaling isosceles or equilateral and what is the answer

Answers

Answer:

[tex]scalene[/tex]

Step-by-step explanation:

[tex]\textsf{Sum of internal angles;}[/tex]

  [tex]71+50+6x-1=180[/tex]

 [tex]6x-1=180-71-50[/tex]

  [tex]6x-1=59[/tex]

the answer is scalene. please mark me brainliest^^^!

The amount of tax is $3.40, which is 5% of the food bill. How much was the food bill not including the tax?
If Simon wants to leave a 20% tip on the amount of the food bill before tax, how much should he leave for a tip?
What is Simon’s total bill including tax and tip? What percent of the food bill is this?

Answers

Answer:

You are told tax is $3.40 which is 5% of the total priceWe want to find the original food bill not including the tax of $3.40We also want to find the tip quantity based on the original food billSo X * 0.05= 3.40 Gives us X= 68 Hence the original bill was $68Now $68* .20 = $13.6I'm confident you can answer the rest with the information I've provided.

help please i’ll give brainlest and lots of points

Answers

Answer:

1+1=2 so that's the answer

A rectangle has an area of 135 ft 2 . What is the length, if the width is 9 ft?

Answers

Answer:

15 ft

Step-by-step explanation:

A=LxW

135 ft2 =m X 9ft

Divide 135 by 9

& that equals 15ft.

To check your answer, you multiply 15X9 and that equals 135. So the length of the rectangle is 15ft.

The equation f = V + at represents the final velocity of an object, f, with an initial velocity, w, and an acceleration rate,
a, over time, t. Which is an equivalent equation solved for a?
Of-v=a
Of-vra
1
Of+V = a
o+v=a

Answers

Answer:

hey

Step-by-step explanation:

the answer is 5

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