ChallengE
See attachment and answer :)​

ChallengESee Attachment And Answer :)

Answers

Answer 1

QuestionSimplify:

[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

help me plssssssssssssss

Answers

multipley by 2, to get the answer

12 cars in 15 hours how many cars is in 10 hours

Answers

Answer:

8

Step-by-step explanation:

12 cars in 15 hours how many cars is in 10 hours

12 : 15 = x : 10

x = 12 * 10 : 15

x = 8

-------------------

check

12 : 15 = 8 : 10

0.8 = 0.8

the answer is good

Martina's fish tank has 15 liters of water in it. She plans to add 5 liters per minute until the tank has at least 60 liters. What are the possible numbers of minutes
. :
Martina could add water?
Use t for the number of minutes
Write your answer as an incqua ty solved fort

Answers

Answer:

9 minutes

Step-by-step explanation:

60=15+5t

45=5t : subtract 15 from both sides

9=t : divide by 5 for both side

This is Functions and Statistics Class:

Answers

[tex] \sqrt[6]{x} . \sqrt[4]{ {y}^{3} } \\ = {x}^{ \frac{1}{6} } . {y}^{ \frac{3}{4} } \\ = {x}^{ - 6} . {y}^{ \frac{3}{4} } [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Help help help math math

Answers

Answer: -1 = (-3/3)

Step-by-step explanation

You go from one point to another, i started from 3,1 and went to 3,0. I got down -3 which is my rise and right 3 for the run. Tell me if this is correct

What is the greatest common factor shared by 70 and 15?
Answer here
SUBMIT

Answers

The answer is 5
Step by step explaination

Answer:

The greatest common factor of 70 and 15 is 5.

Step-by-step explanation:

First, list the prime factors for each individual number

Next, circle each common prime factor. This means that you must find the prime factors that are the same as each other. For example, if it's 1 3 4 and 2 3 5, the common prime factor would be 3.

Finally, you must multiply all of the common prime factors. Your answer will be the greatest common factor!

So, the greatest common factor of 70 and 15 is 5.

Which inequality matches the graph?

Answers

Answer:

x < 2/3 y + 2 1/3

Step-by-step explanation:

put it in a graphing calculator and they matched, I do not know

Decomposition of 1,980

Answers

Answer:

2

990

2

495

3

165

3

55

5

11

Step-by-step explanation:

Help help help math math

Answers

Answer:

gradient M = 4

Step-by-step explanation:

pick any two pairs

M= change in Y / change in X

considering the last pairs

3--1/0--1=4✓

considering first pair

-1--5/-1--2 is also 4✓

I hope it helps

HELP
In \triangle JKL,△JKL, \angle J \cong \angle L,∠J≅∠L, LJ = 17LJ=17 and KL = 10KL=10. Find the length of JK.JK.

Answers

It's a isosceles right angled triangle

LJ=17KL=10

[tex]\\ \sf{:}\Rrightarrow JK^2=17^2+10^2[/tex]

[tex]\\ \sf{:}\Rrightarrow JK^2=289+100[/tex]

[tex]\\ \sf{:}\Rrightarrow JK^2=389[/tex]

[tex]\\ \sf{:}\Rrightarrow JK=19.72[/tex]

20 charecters lol pls solve

Answers

Answer:

-3x+12

Since we are adding like terms you add everything that has an "x" after it [(3.4x) + (-5.4x) + (-x)] it all that adds up to -3x and the you add the 12 to it. It could also be written 12-3x

Which TWO identify the same sequence?


A) f(x) = 6x + 4 for x = {1, 2, 3, ...}


B) f(x) = 10x + 4 for x = {1, 2, 3, ...}


C) a1 = 6 and an + 1 = an + 4 for n = {1, 2, 3, ...}


D) a1 = 10 and an + 1 = an + 4 for n = {1, 2, 3, ...}


E) a1 = 10 and an + 1 = an + 6 for n = {1, 2, 3, ...}

Answers

A and E are equivalent sequences

The sequences A and E are the same sequences.

What is Sequence?

Sequences are set of numbers where the numbers are arranged in a specific order. Some of the common types of sequences are Arithmetic sequences and Geometric sequences.

A) f(x) = 6x + 4 for x = {1, 2, 3, ....}

f(1) = 10, f(2) = 16, f(3) = 22, ....

B) f(x) = 10x + 4 for x = {1, 2, 3, ...}

f(1) = 14, f(2) = 24, f(3) = 34, ....

C) a₁ = 6 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}

a₁ = 6, a₂ = a₁ + 4 = 10, a₃ = a₂ + 4 = 14, ....

D) a₁ = 10 and aₙ₊₁ = aₙ + 4 for n = {1, 2, 3, ...}

a₁ = 10, a₂ = a₁ + 4 = 14, a₃ = a₂ + 4 = 18, .....

E) a₁ = 10 and aₙ₊₁ = aₙ + 6 for n = {1, 2, 3, ...}

a₁ = 10, a₂ = a₁ + 6 = 16, a₃ = a₂ + 1 = 22, ....

A and E are the same sequences with a common difference 6 and the first term 10.

Hence A and E have the same sequence 10, 16, 22, .....

To learn more about Sequences, click :

https://brainly.com/question/21961097

#SPJ5

Write the equation in standard form.
y + 7 = -3 (x + 1)

Answers

Answer:

Standard form = ax+by+c=0

= Writing the given eq. in standard form =

= y+7=-3x-3

= 3x+y+7+3=0

= 3x+y+10=0

Help help math math math

Answers

the answer is x = 8

thank u

Answer:

-3/7,0

Step-by-step explanation:

-PLEASE HURRY
8. Given: x2 – 2x + 5, find :
1.f(2)
2.f(-3)
3.f(0)
4.f(5) - f(-2)
5.f(1) + f(6)
-

Answers

Answer:

Step-by-step explanation:

     f(x) = x² - 2x + 5

1)   f(2) = (2)² - 2(2) + 5 = 5

2) f(-3) = (-3)² - 2(-3) + 5 = 20

3)  f(0) = (0)² - 2(0) + 5 = 5

4) f(5) - f(-2) = (5)² - 2(5) + 5 - [(-2)² - 2(-2) + 5 = 20 - 13 = 7

5) f(1) + f(6) = (1)² - 2(1) + 5 + [(6)² - 2(6) + 5 = 4 + 29 = 33

What is an equation of the line parallel to the line on the graph that passes
through (4, 15)?
Weight of Bucket of Sand
Total weight (ounces)

Answers

Answer:

Step-by-step explanation:

The existing line appears to pass through (0, 20) and (10, 50)

so the line slope is m = Δy/Δx = (50 - 20) / (10 - 0) = 3

parallel lines have identical slopes

y = 3x + b

15 = 3(4) + b

b = 3

D.  y = 3x + 3

(0,20)(2,25)

[tex]\\ \rm\Rrightarrow m=\dfrac{25-20}{2}=5/2[/tex]

Slope of parallel line=5/2

Equation of line in point slope form

[tex]\\ \rm\Rrightarrow y-y_1=m(x-x_1)[/tex]

[tex]\\ \rm\Rrightarrow y-15=5/2(x-4)[/tex]

[tex]\\ \rm\Rrightarrow 2y-30=5x-20[/tex]

[tex]\\ \rm\Rrightarrow 5x-2y+10=0[/tex]

This 3 by 3 grid shows nine 1 cm x 1cm squares and uses 24 cm of wire.
What length of wire is required for a similar 20 by 20 grid?
A 400 cm B 420 cm C 441 cm D 800 cm E 840 cm

Answers

Answer:

  E  840 cm

Step-by-step explanation:

For a 20×20 grid, there will be 21 strands in the vertical direction, and 21 in the horizontal direction. Each strand wil be 20 cm long. The total length is ...

  (20 cm)(2 × 21) = 840 cm

_____

Additional comment

In this case, we take "similar" to mean that the grid squares are 1 cm, and the wire encloses a larger array of those squares.

In geometry, the term "similar" would mean the larger grid is simply a scaled-up version of the smaller one, with squares that are 20/3 cm, instead of 1 cm. The length of wire required in that case is (4+4)(20 cm) = 160 cm = (20/3)×(24 cm).

i have a question yall

Even though you can take drivers ed at 14 but you cant get ur license till 15 would you take drivers ed at 14 or 15
answer asap

Answers

I’m driving in the road in the road
Drivers Ed differs from state to state so I’m not sure the rules exactly from wherever you are but I’d recommend to do it at 14 because once you pass, most state will then issue you a driving permit that you must have for a few months before giving you a license but if you get that at 14, you don’t have to wait as long to get an actual license.

I wish this was free ✋

Answers

Answer: It is tho ?

Step-by-step explanation:

Select the correct answer. This table represents the boiling point of water at different altitudes.Which equation represents water's boiling point (y) based on the change in altitude (x)? Altitude (thousands of feet) Boiling Point of Water (Fahrenheit) (sea level) 0 212 0.5 211.1 1.0 210 2.0 208.4 2.5 207.5 3.0 206.6 4.0 204.8 4.5 203.9

Answers

Answer:

Step-by-step explanation:

The net income reported on the income statement for the current year was $135,500 depreciation recorded on store equipment for the year amounted to $22,400 balances of the current asset and current libaility accounts at the beginning and end of the year are as follows

A watch band is 8 in long. What is its diameter when you wrap it around your wrist? Round your answer to the nearest
hundredths.
Please be accurate and explain.

Answers

Answer:

well, all you need to do is 8 x 3.14 so then you shall get your answer!

Step-by-step explanation:

Marsha is driving 630 otal miles on a trip. She has already driven 2/5 of the distance. How far has Marsha driven?

Answers

Answer:

Marsha has driven 252 miles

Step-by-step explanation:

In order to figure out the problem, you take the total distance and multiply it by the fraction she has gone. This would be 630*(2/5) which would equal 252. Thus, Masha has driven 252 total miles.

Hope this helps!     :)

Mandy spins a biased spinner 3 times. The probability that the spinner will land on blue on all 3 spins is 27/512 Calculate the probability that when the spinner is spun 3 times it does not land on blue on any of the spins​

Answers

Answer:

0.158203125

i think

Which situation can be represented by the expression 5.3d?
1. the total cost of an item that is d dollars more than $5.30
2.the total cost of d items that cost $5.30 each
3.the amount of change when $5.30 is used to pay for an item costing d dollars
4.the amount of change when $5.30 is used to pay for an item costing d dollars

Answers

Answer:

tang inamo ok please tell me

Sally gets $8.00 each week for allowance. She wants to purchase a used bicycle that costs $24.00. She also wants to donate $8.00 to the food kitchen. Label your drawings with bike.

1. How much money will she have to save for both?

2. How many weeks will it take her to save for both?

3.How many weeks will she have to save if she wants to buy a newer used bicycle
that costs $32.00 and still make her $8.00 donation?

Answers

Answer:

1: $32. 2: 4 weeks. 3: 5 weeks

Step-by-step explanation:

1: 8+24=32$

2: 32/8=4=4 weeks

3: 32+8=$40

    40/8=5=5 weeks

Find the value for x ​
(x+20) (4x-5)

Answers

Answer:

I think it x=33

Step-by-step explanation:

[tex]x+20+4x-5=180\\5x+15=180\\-15 -15\\5x = 165\\/5 /5\\x = 33[/tex]

Can someone help me out? Will mark brainiest

Answers

Ok done. Thank to me :>

3. Find the area of the trapezoid.
8 ft
4V3
10 ft

Answers

Answer:

[tex]32\sqrt3[/tex]

Step-by-step explanation:

We need first to find the measure of the red horizontal line, call it x. The triangle i filled is a right triangle, so we can apply pythagoras theorem,

[tex]8^2 = x^2+(4\sqrt3)^2 \rightarrow 64=x^2+(16\times3) \\x^2=64-48 \rightarrow x^2=16 \rightarrow x=4[/tex]

(we are talking lengths of segment so we take only the positive root!)

At this point we can find the length of the smaller base of the trapezoid (which is [tex]10-4=6[/tex]) and apply the formula, or split the figure in a rectangle of sides 6 and [tex]4\sqrt3[/tex] and a triangle of sides [tex]4\sqrt3[/tex] and 4.

With the trapezoid formula

[tex]A=\frac12(B+b)h = \frac12(10+6)4\sqrt3 = 32\sqrt3[/tex]

With the sum of figures:

[tex]A= bh+\frac12 xh=6\times4\sqrt3 +\frac12\times4\times4\sqrt3=24\sqrt3+8\sqrt3=32\sqrt3[/tex]

Write the word sentence as an equation. Then solve.

The difference of a number n and 3 is -7.

Answers

Answer:

n-3 = -7

n = -4

Step-by-step explanation:

(Meeting character limit)

Answer:

-4

Step-by-step explanation:

n - 3 = -7, n = -4

Which property explains why these two expressions are equal? 7 + q + 4 = 4 + 7 + q

Answers

Commutative property, the order in adding or multiplying does not matter
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