Answers
Answer: Choice C) [tex]2-\sqrt{3}-2\sqrt{2}+\sqrt{6}\\\\\\[/tex]
====================================
Work Shown:
Part 1
[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}\\\\\\\frac{(2-\sqrt{8})(4-\sqrt{12})}{(4+\sqrt{12})(4-\sqrt{12})}\\\\\\\frac{2(4-\sqrt{12})-\sqrt{8}(4-\sqrt{12})}{(4)^2-(\sqrt{12})^2}\\\\\\\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{8}*\sqrt{12}}{16-12}\\\\\\\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{8*12}}{4}\\\\\\[/tex]
Part 2
[tex]\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{96}}{4}\\\\\\\frac{8-2\sqrt{4*3}-4\sqrt{4*2}+\sqrt{16*6}}{4}\\\\\\\frac{8-2\sqrt{4}*\sqrt{3}-4\sqrt{4}*\sqrt{2}+\sqrt{16}*\sqrt{6}}{4}\\\\\\\frac{8-2*2*\sqrt{3}-4*2*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{8-4*\sqrt{3}-8*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\[/tex]
Part 3
[tex]\frac{8-4*\sqrt{3}-8*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{4*2-4*1*\sqrt{3}-4*2*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{4(2-\sqrt{3}-2\sqrt{2}+\sqrt{6})}{4}\\\\\\2-\sqrt{3}-2\sqrt{2}+\sqrt{6}\\\\\\[/tex]
This shows the answer is choice C.
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Explanation:
There are a lot of steps, so I broke things up into 3 sections or parts. The idea I'm applying is if the denominator is of the form [tex]a+\sqrt{b}[/tex], then multiplying top and bottom by [tex]a-\sqrt{b}[/tex] will rationalize the denominator. This is due to the difference of squares rule (step 3 of part 1). The following step shows squaring a square root has the two cancel out.
From that point, I simplified each square root and factored to cancel out a pair of '4's.
To expand out [tex](2-\sqrt{8})(4-\sqrt{12})[/tex], we can use either the FOIL method, the box method, or the distribution property. I used the distribution property.
Related Questions
Look at the black points on the graph. Fill in the
missing coordinates for y = 2^x.
(0,_) and (_,32)
Answers
Answer:
(0,1) and (5,32)
Step-by-step explanation:
Edg.2020
Answer:
Step-by-step explanation:
Please simplify: 5x + 2 (x - 3) = -2 (x - 1)
Answers
Answer:
x= 8/9
Step-by-step explanation:
Open everything up to get 5x+2x-6=-2x+2. Move numbers with an x to the left side and without to the right to have 5x+2x+2x=2+6. Simplify to have 9x=8. Divide by 9 which leaves you with x= 8/9
Triangle XYZ is reflected across the x-axis, and X = (–11, 8). What are the coordinates of X’ ?
Here are your choices:
A) (11,–8)
A) (–8, 11)
A) (11, 8)
A) (–11, –8)
I hope this question isn't confusing you guys∪ω∪
Answers
9514 1404 393
Answer:
(-11, -8)
Step-by-step explanation:
Reflection across the x-axis changes the sign of the y-coordinate.
For X(-11, 8), the reflected point is X'(-11, -8). (matches the last choice)
Answer:
IS THIS REALLY FOR HIGH SCHOOL
Step-by-step explanation:
IF NOT I WILL ANSWER
Can someone check this thanks
Answers
Answer:
That is correct! Good boy, you get a treat. :)
Step-by-step explanation:
A runner leaves his house at 7:45 for a morning run. If he travels at an average speed of 6 mph and gets back home at 10:00, how many miles did he run
Answers
Answer:
13.5
Step-by-step explanation:
no explenation needed
Find the slope and Y intercept from the equation 12x+3y=6
Answers
Answer:
slope = -4 y-intercept = (0, 2)
Step-by-step explanation:
12x + 3y = 6
-12x -12x
-----------------------------------------------
3y = -12x + 6
3y/3 = -12x/3 + 6/3
-----------------------------------------------
y = -4x + 2 ( this is in y = mx + b form, m representing the solpe and b representing the y-intercept)
This being said, the slope = -4 and the y-intercept = (0, 2).
What are some of the more significant limitations of mathematical models as imitators/predictors of natural phenomena
Answers
Answer:
See explanation
Step-by-step explanation:
A mathematical model refers to a mathematical function that describes natural phenomena.
Models are used to approximate natural phenomena hence they are not really exact representations of reality. Thus mathematical models are inherently imperfect and so is our understanding of natural phenomena represented by these mathematical models.
The mathematical parameters used in models to represent real processes are uncertain since they are determined from experiment or represent more than one process.
Lastly, the initial and the boundary conditions in a model may not be explicitly established.
y'all i need help immediately
Answers
Answer:
Option B
Step-by-step explanation:
Don't trust answers teachers don't bother to spell correctly. Plus, finding the 100th term is very easy.
However, the explicit formula will take a long time to use, because it's explicit.
Option C is just wrong. You're supposed to multiply in the recursive formula.
Option D might be correct, but never trust those answers. Teachers do that to trip you up
A lab scale weighs 3 pounds, 5 ounces. Which of the following is the scale weight in (oz)?
a. 35 oz
b. 53oz
c. 41
d. 29oz
Answers
Answer:
53 ounces
Step-by-step explanation:
We know that,
1 pound = 16 ounce
3 pounds = 48 ounces
We need to find the weight in 3 pounds, 5 ounces.
3 pounds, 5 ounces = 48 ounces+ 5 ounce
= 53 ounces
So, the scale weight is 53 ounces. Hence, the correct option is (b).
500 - 237 in subtraction standard algorithm
Answers
Answer:
is 267 the answer your looking for
Answer:263
Step-by-step explanation:
Start from the ones place and subtract.
Please help me answer this!
Answers
Answer:
the answer is c
Step-by-step explanation:
4x = 4 x 2=8
8+12=20
which is equal to or greater than 8
Hope this helps plz mark brainliest
time in hours which is greater 5 1/3, 5 3/5, 5 2/3, 5 2/5
Answers
2 circle graphs. One circle graph is titled Freshmen Movie Preference. 38 percent is comedy, 27 percent is horror, 23 percent is drama, 9 percent is romance, 3 percent is documentary. Circle graph 2 is titled Senior Movie Preference. 19 percent is comedy, 4 percent is horror, 71 percent is drama, 1 percent is romance, 6 percent is documentary. The freshman and senior classes were surveyed on movie preference. Each class has 100 students. Which statements are true? Check all that apply. More seniors like drama than freshmen. More freshmen like comedy than seniors. Only 4 seniors prefer horror movies. Twice as many seniors like horror than freshmen. Twice as many freshmen like comedy than seniors.
Answers
Answer:
you probably got the answer already but its a, b, c, and e
Step-by-step explanation:
i just got the answer
Answer:
abce
Step-by-step explanation:
A minor arc will have a measure that is
OA. more than 180°
O B. equal to 180°
OC. less than 180°
Answers
Hope this helps
A fair charges a $15 entry fee plus $3 for every
ride. Write an expression to represent the total
cost of the fair? HELLPP
Answers
Answer:
15 + 3r
Step-by-step explanation:
$15 entry fee plus $3 for every
ride.
The average person that weighs 150 pounds has approximately 4.5 liters of blood in their body. Based on that same scale, supposedly how many liters of blood would a 250 pound person have?
Answers
Answer:
First you find how many pounds for 1 litre of blood. Trick is if you divide x by y, the answer you get will follow the unit of x. So if you divide 150 pounds by 4.5 litres, the answer will be 33.33 pounds per litre. So how many 33.33... is there in 250? Just divide 250 by 33.333 or (150/4.5), you'd get 7.5. That means for there's 7.5 parts of 33.333 pounds in 250 pounds. And if 33.333 pounds is equal to 1 litre of blood, you get 7.5 liter!
Need help ASAP :)
Question on the picture:)
Answers
Answer:
a. No
b. Yes
Step-by-step explanation:
a.
x - 4 = 12
x - 4 + 4 = 12 + 4
x = 16
16 ≠ 8
Therefore, the following value given for problem a is not a solution to the given equation.
b. (3 + x)/4 = 3
(3 + x)/4 * 4 = 3 * 4
3 + x = 12
3 + x - 3 = 12 - 3
x = 9
9 = 9
Therefore, the following value given for problem b is a solution to the given equation.
Pls help I need it don’t understand
Answers
Answer: one solution.
Chris can type 490 words in 7 min how many works can he type PER min
You get 14 points
Answers
Find the value of the x in the equation 4(6x-9.5)=46
Answers
Answer:
3.5
Step-by-step explanation:
First you distribute. 24x-38=46.
Then add 38 to both sides
24x=84
Then divide both sides by 24
x=3.5
Answer:
x= 3.5
Step-by-step explanation:
[tex]4(6x-9.5)=46\\24x-38=46\\ +38 +38\\\\frac{24x}{24} = \frac{84}{24} \\ x=3.5[/tex]When a numerator equals zero, a ratio is what?
Answers
Answer:
A numerator is allowed to take on the value of zero in a fraction. Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of zero. all have a fraction value of zero because the numerators are equal to zero.
What is the factored form of the expression 9x2 + 6x + 1?
Answers
Answer:
(3x+1)^2
Step-by-step explanation:
Cole’s backyard is rectangular an has a perimeter of 104 meters. The ratio of its length to its width is 6:2. What length is the long side of Cole’s backyard?
Help Me To Find The Answer Please !!!!!!!
Answers
Answer:
[tex]39\ m[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\Perimeter\ of\ Cole's\ backyard=104\ meters\\Now,\\Let\ the\ constant\ of\ proportionality\ between\ the\ length\ and\ the\ width\ of\\ Cole's\ backyard\ be\ x.\\Hence,\\Length\ of\ Cole's\ backyard=6x\\Breadth\ of\ Cole's\ backyard=2x\\Hence,\\As\ we\ know\ that,\\Perimeter\ of\ a\ rectangle=2(l+w)\\Hence,\\Here,\\Perimeter\ of\ Cole's\ backyard=2(6x+2x)=2(8x)=16x\\Hence,\\As\ the\ perimeter\ of\ Cole's\ backyard=104\ m,\\104=16x\\x=\frac{104}{16}=6.5\\Hence,\\[/tex][tex]Length\ of\ Cole's\ backyard=6x=6*6.5=39\ m\\Width\ of\ Cole's\ backyard=2x=2*6.5=13\ m\\Here,\\We\ are\ asked\ Length,\\Hence,\\Length\ of\ Cole's\ backyard=39\ m[/tex]
.
If the value of x is -4, which inequality is true?
Answers
The sides of an equilateral triangle are reduced by 12 units, 13 units and 14 units respectively and a right-angle triangle is formed. Find the length of each side of the equilateral triangle?
Answers
Answer:
the length of each side of the equilateral triangle = 17
Step-by-step explanation:
suppose the side length of equilateral triangle = x
The 3 side of right triangle formed (by side length): x-12 , x-13, x-14
(x-13)² + (x-14)² = (x-12)² .... Pythagorean theorem
x² -26x + 169 + x² -28x + 196 = x² -24x + 144
x² - 30x +221 = 0
(x- 17) (x - 13) = 0
x = 17 or x = 13
if x = 13 the right triangle will have a side length of 13-13=0 ... not solution
x = 17
check: 17-12=5 17-13=4 17-14=3
3²+4² = 25 = 5²
Bamboo grows at a rate of 3 inches every month. Gina planted Bamboo when it was initially only 11 inches. -Create an explicit formula for this situation. -How tall will the plant be after 6 months?
I’ll give brainliest if you are correct.
Please answerrrrr
Answers
Answer:
Step-by-step explanation:
initial growth = 11
growth in 6 months= 3*6= 18
Final growth = 29 inches (11+18)
Joseph paid $10 for six avocado at a grocery mart he wants to know what the price will be buying different numbers of avocado what is the price of 9 out of avocado
Answers
The answer is going to be 5.00 because the price of it for the avocados are 3 because 6 are 10 which all you had to do was divide 10 by 2 so that the answer would be 5.
Answer: $15
9 avocados = $15
Step-by-step explanation:
1 x 3 = 9
5 x 3 = 15
Our Data:
Avocados Price (dollars)
3 5
6 10
9 15
So, our answer is $15
How many degrees are in a 29 sided figure?
Answers
Answer:
4860 degrees
Step-by-step explanation:
Triangle=180
Square=360.
The pattern: increase by 180.
Triangle=3 sides.
29-3 is 26.
26*180+180
4860.
Hope this helps :D
make a math card game
Answers
Answer:
Use Close Call to practice two-digit addition or subtraction. The best math card games are simple at heart. To play Close Call, each player deals themselves four cards then determines how to arrange them so they make two two-digit numbers that add up as close as possible to 100 without going over.
An on-demand printing company has monthly overhead costs of $1,900 in rent, $450 in electricity, $80 for phone service, and $230 for advertising and marketing. The printing cost is $40 per thousand pages for paper and ink. The average cost for printing x thousand pages can be represented by the function C(x)= 2660+40x/x
For a given month, if the printing company could print unlimited number of pages, what value would the average cost per thousand pages approach? What does this mean in the context of the problem?
Answers
Answer:
$40
It means that when an infinite number of pages are printed in a month then the fixed cost will be negligible.
Step-by-step explanation:
Given that:
Monthly overhead costs in rent = $1900
Costs in electricity = $450
Costs for phone service = $80
Costs for advertising and marketing = $230
Printing cost per thousand pages = $40
If number of pages printed are [tex]x[/tex] thousand then cost of printing for [tex]x[/tex] thousand pages = $40[tex]x[/tex]
Average cost to print [tex]x[/tex] thousand pages can be given as:
(Total fixed cost + Total cost of printing [tex]x[/tex] thousand pages) divided by [tex]x[/tex]
[tex]\dfrac{2660+40x}{x}[/tex]
Now, it is given that an infinite number of pages are printed in a month, and we have to find the value that average cost would approach to.
[tex]\lim_{x \to \infty} (\dfrac{2660+40x}{x})[/tex]
Let us solve the above limits.
[tex]\Rightarrow \lim_{x \to \infty} (\dfrac{2660}x+\dfrac{40x}{x})\\\Rightarrow \lim_{x \to \infty} (\dfrac{2660}x)+40\\\Rightarrow 40+\lim_{x \to \infty} (\dfrac{2660}x)[/tex]
When
[tex]x\rightarrow \infty\Rightarrow \frac{2660}{x} \rightarrow 0[/tex]
Putting the value in the limits, we get:
Average cost per thousand pages month would approach to [tex]\rightarrow \$40[/tex]
It means that when an infinite number of pages are printed in a month then the fixed cost will be negligible.