Answers
[tex]\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
Answer :[tex]\displaystyle{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}[/tex]
Step-by-step-explanation:
We have given an expression.
We have to simplify the expression.
The given expression is
[tex]\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\sqrt{16\:\times\:3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
We know that,[tex]\displaystyle{\boxed{\pink{\sf\:\sqrt{a\:\times\:b}\:=\:\sqrt{a}\:\times\:\sqrt{b}\:}}\:\cdots\sf\:a\:,\:b\:\geq\:0}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\sqrt{16}\:\times\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\times\:4\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
We know that,[tex]\displaystyle{\boxed{\blue{\sf\:\sqrt{\dfrac{a}{b}}\:=\:\dfrac{\sqrt{a}}{\sqrt{b}}\:}}\:\cdots\sf\:b\: > \:0}[/tex]
[tex]\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{\sqrt{1}}{\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{1}{\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{16\:\sqrt{3}\:\times\:2\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{16\:\times\:2\:\sqrt{3}\:\times\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}} \\ \\\displaystyle{\implies\sf\:\dfrac{32\:\times\:3\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{8\:\times\:4\:\times\:3\:-\:5\:+\:(\:6\:\sqrt{3}\:\times\:2\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:6\:\times\:2\:\times\:\sqrt{3}\:\times\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:12\:\times\:3\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:12\:\times\:3}{2\:\sqrt{3}}} \\ \\ \\ \displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:+\:12\:\times\:3\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{12\:(\:8\:+\:3\:)\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{12\:\times\:11\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{132\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}} \\ \\ \\ \displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}\:\times\:\dfrac{\sqrt{3}}{\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{2\:\times\:3}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{6}} \\ \\ \\ \displaystyle{\therefore\:\underline{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}}[/tex]
Related Questions
The position of a large fish relative to the water surface was −17 1/3 feet. It suddenly dove straight down and increased its depth by 6 1/2 feet. What is the position of the fish now relative to the water surface? Enter your answer as a mixed number, in simplified form, in the box.
Answers
-17 1/3 - 6 1/2
Now, let’s subtract the two integers by finding the least common denominator of 2 and 3 so it can be easier to solve in this case it’s 6…then let’s set up our new equation:
-17 2/6 - 6 3/6
We know it’s a negative number since we are subtracting a negative number and our final answer is -23 5/6
A map scale indicates that .5 inches represents 13 miles. What is the actual distance of two cities that are measured on the map to be 4.5 inches apart?
Round your answer to the nearest integer.
Answers
Answer:
9 is the answer, wanna know how?
Step by Step explanation : So you do this and that equals 9.
Help me plzzzzzzzzzzzzz
Answers
Answer: It is D
Step-by-step explanation:
a farmer is creating a budget for planting soybeans and whet. planting soybessns cost $200 an acre and planting wheat cost $500 per acre. he wants to spend no more than $100000 planting soybeans and wheat.
Answers
Which graph shows a function and it’s inverse?
HELP PLEASE
Answers
Answer:
C
Step-by-step explanation:
A function and its inverse are obtained by reflecting in the line y = x
Under a reflection in the line y = x
a point (x, y ) → (y, x )
In graph C
the red line has a point (0, 2 )
the blue line has a point (2, 0 )
Then graph C shows a function and its inverse
A car travels a total distance of 380 miles in a total of 5 hours. The rate the car was traveling during
that time was
Answers
Three boxes are stacked one on top of the other. One box is 4 feet 8 inches tall, one is 3 feet 10 inches tall, and one is 2 feet 7 inches tall. How high is the stack?
Write your answer in feet and inches. Use a number less than 12 for inches.
Answers
Determine the period of the function g(x) = (cos ;)
Answers
Answer:
6[tex]\pi[/tex]
Step-by-step explanation:
The period of a sinusoidal function in the form a * cos (b (x + h)) + m is [tex]\frac{2\pi }{|b|}[/tex]. Therefore, we can see that "b" in g(x) is 1/3 and 1/3 substituted into [tex]\frac{2\pi }{|b|}[/tex] is 2[tex]\pi[/tex]/1/3 which is 6[tex]\pi[/tex].
What is the slope of the line. ?
Answers
Answer:
-1
Step-by-step explanation:
rise/run
rise=-1
run=1
-1/1=-1
When Hugo puts a book and a candle on a scale, the scale reads 8.705 lbs. When he removes the book, the scale reads 4.93 lbs. How much does the book weigh?
Answers
Answer:
8.705-4.93=3.775
Hope This Helps!!!
The perimeter of the equilateral triangle drawn below is 9b + 12.
The shape below is made of four of these triangles.
Find a simplified expression for its perimeter.
Answers
If the perimeter of a triangle is 9b+12 then one side equals 3b+4 (divide by 3 because there are 3 sides
In the big triangle there are 6 sides so multiply 3b+4 by 6
=18b+24
I need help find the value of x
Answers
x+100+x=180
x=the base angle measures since they are congruent.
100+x+x=180
Community Property of Addition
100+2x=180.
Added x+x as like terms to = 2x.
100-100+2x=180-100
Subtraction of 100 from both sides to cancel it out and move it.
2x=80
Subtraction operation
2x/2=80/2
Divided by 2 to cancel it out on both sides and move it.
x=40°.
Therefore, the two base angles (angles opposite of the two congruent sides) are 40°.
2(40)+100=80+100=180.
So x=40
During a sale, a store offered a 10% discount on a stereo system that originally sold for $810. After the sale, the discounted price of the stereo system was marked up by 10%. What was the price of the stereo system after the markup? Round to the nearest cent.
Answers
"Viewer discretion advised
Answer:
$801.9
Step-by-step explanation:
10% of 810 is 81
810-81 = 729
10% of 729 is 72.9, so add that back to get the extra 10%
729+72.9 = 801.9
Please give brainliest if I helped! :)
5x²-11x +6 . factories the expression
Answers
Answer:
5
x
2
−
11
(
x
)
+
6
Step-by-step explanation:
[tex]5x^2-11x+6\\\\=5x^2-5x-6x+6\\\\=5x(x-1) - 6(x-1)\\\\=(x-1)(5x-6)[/tex]
Help help help help math math
Answers
Answer:
y = -2x - 1
See image
Step-by-step explanation:
The "slope-intercept" form of the equation is the
y = mx + b form
So you need to find the slope (m) and the y-intercept (b), which you are able to find on the image in the question.
Slope (m) tells how steep a line is and whether it goes up or down from left to right. It also works just like directions, from any point on the line to any other point on the line.
The y-intercept (b) is the point on the line where the line crosses the y-axis.
The slope is -2 and the y-intercept is -1
So the equation is
y = -2x - 1
See image
The diagonal of an isosceles trapezoid with angle to the base is equal to 30. Find the length of the height of the trapezoid if it is known that the midline of this trapezoid is equal to 8 cm.
Answers
Answer:
4.62 cm to nearest hundredth.
Step-by-step explanation:
If the parallel sides are x and y then:
x + y = 2*8 = 16
x + y = 16
If we drop a perpendicular line from one of the upper points on the trapezoid we have the height. Let the upper point be C and the point on the base be A. Let the point on right of the base be B.
AC is the height of the trapezoid. AB is the baseline of the triangle CAB.
In triangle CAB the angle B is 30 degrees.
As this is a 30-60-90 degree triangle
AC/AB = 1/√3 so AC = AB/ √3.
As the trapezoid is isosceles:
AB = x + 0.5(y - x)
AB = 0.5x + 0.5y
So AC = 1 /√3 (0.5x + 0.5y)
= 1 /√3 (0.5x + 0.5(16 - x)) (Substituting for x)
= 1 /√3 (0.5x + 8 - 0.5x)
=8 / √3
. = 4.6188 cm
find the equivalent fraction 2/6= __ 2/5= ___
Answers
The equivalent fraction of 2/5 is 4/10
Please help me!!!! I will try to give brainliest!!!
Marcus is buying 10 gift bags for his birthday party. He will choose items to put in the bags and then pay an additional charge of $0.75 for the actual bag. Marcus cannot spend more than $50. Write and solve an inequality to find the most Marcus can spend on the items for each bag.
Starting inequality:
Ending inequality:
Answers
Answers:
Starting inequality: [tex]10(x+0.75) \le 50[/tex]
Ending inequality: [tex]x \le 4.25[/tex]
==================================================
Work Shown:
x = amount spent per bag, ignoring the bag fee
x+0.75 = amount per bag including bag fee
10(x+0.75) = total amount spent on the ten bags
This amount cannot be more than $50. This means 50 dollars is the highest we can go, aka the ceiling value.
That means we'd write [tex]10(x+0.75) \le 50[/tex] as one possible starting inequality.
Let's solve for x
[tex]10(x+0.75) \le 50\\\\10x+7.5 \le 50\\\\10x \le 50-7.5\\\\10x \le 42.5\\\\x \le 42.5/10\\\\x \le 4.25[/tex]
The most he can spend on the items for any single bag is $4.25, which is ignoring the $0.75 fee
If we tack that fee on, then he spends 4.25+0.75 = 5 dollars per bag and ten of such bags leads to 5*10 = 50 dollars total. The answer is confirmed.
Help help help help help
Answers
Answer:
x=18
Step-by-step explanation:
x - 3 = 15
+3
x=18
Help help math math math
Answers
Answer:
x = 16
Step-by-step explanation:
The two marked angles are supplementary:
(7x -2) +(4x +6) = 180
11x +4 = 180
11x = 176
x = 176/11 = 16
The value of x is 16.
_____
Additional comment
The angle on the left is 110°; the one on the right is 70°, so that answer checks.
These marked angles are called "consecutive exterior" angles. Just as "consecutive interior" angles are supplementary, so are consecutive exterior angles.
Essentially, all of the obtuse angles are congruent, as are all of the acute angles. The obtuse angles are supplementary to the acute angles.
Answer: x=1 6
Step-by-step explanation:
What is the range of the relation below?
Answers
A choir teacher is dividing 48 sopranos and 32 altos into singing groups. He wants each
group to have the same combination of sopranos and altos, with no singers left over. What is
the area
Answers
Answer:
32
Step-by-step explanation:
x(48 - 2x) = 32
Hope it helps.
factorize completly Mn + np + or + rt
Answers
Answer:
n (m + p) + r (o + t)
Step-by-step explanation:
You have to split the expression in half.
First, focus on mn + np, the common factor would be n.
So the first part of the answer would be mn ÷ n and np ÷ n.
Leading to it being n(m + p).
Then you focus on the second half or + rt.
You find the common factor, which is r.
You divide both sides by r.
Hence why you get r(o + t).
Lastly, you put them together, n(m + p) + r(o + t).
Hope this helps :)
when the height of a rectangular prism was halved, the volume was 168 cubic cm. if the original prism had a length, width, and height of consecutive integers, increasing in that order,
(a) write and equation to solve for the length, x, of the original figure,
(b) solve length, x,
(c) show that the equation is unique
show all work.
Answers
a) The equation is therefore; x³ + 3x² + 2x = 336
b) Solving for the length, we get the length to be; x = 6.
c) All workings are as shown below;
According to the question;
When the height of a rectangular prism was halved, the volume was 168 cubic cm.In essence, the volume of the original prism is;
Volume = 168 × 2.Volume = 336cm³Since, the original prism had a length, width, and height of consecutive integers, increasing in that order.
Therefore, length = xwidth = (x +1)height = (x +2)Volume = x (x+1) (x+2) = 336a) The equation is therefore;
x³ + 3x² + 2x = 336b) Solving for the length, x is as follows;
(x-6) (x² + 9x + 56) = 0By testing values and checking;
Upon solving the polynomial, x = 6.c) All workings are as shown above.
Read more on cubic equation:
https://brainly.com/question/8878887
The variables x and y vary directly. Given the model y = -2x , find the value of x when
y = -16.
a. 8
32
b. 16
d. 64
C.
Answers
Hope this helped
Answer:
a.8
Step-by-step explanation:
y=-16
-16=-2x
16=2x
x=16/2=8
A 4-card hand is dealt from a standard 52-card deck, and then one of the 4 cards is chosen at random. If only two of the cards in the hand are hearts, what is the probability that the chosen card is a heart?
Answers
Explanation:
There are two hearts out of four cards in this particular hand. The probability of picking a heart card is 2/4 = 1/2
In other words, we have a 50% chance of getting a heart. The prior stuff dealing with the 52 card deck is just extra unneeded info.
Simplify -6
1
4.
8
3
00w
8
1
A
8
00
00 W
3
8
8
Answers
Answer:
4th on should be the correct
What is the answer to this : Simplify 4 4128
Answers
Answer:
1032/1
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 4128 and 4 is 4
Divide both the numerator and denominator by the GCD
4128 ÷ 4
4 ÷ 4
Reduced fraction:
1032
1
Therefore, 4128/4 simplified to lowest terms is 1032/1.
pls help me . Eleven family members are going on a trip together. They have cars that fit only 4
people. How many cars will they need to take? help
Answers
Answer:
3.
Step-by-step explanation:
Since there are 11 family members and only 4 people fit in a car, they will have to take 3 cars.
4 x 3 = 12,
Also, even though there is going to be 1 seat extra you cannot squeeze 3 people in. Ps. (Just a safety note) In real life it is illegal to drive with extra passengers in a vehicle.
Hope that helps. x
Answer:
3
Step-by-step explanation:
3×4=12 so will still have one vacant seat on one of the cars
Help please
(1/5 x 5) to the 5th power =
Answers
Answer:
(1/5 x 5) to the 5th power = 1