Answer:
Step-by-step explanation:
they are prime to eachother.
There is only one common factor .i.e.,1
45=1×3×3×5
272=1×2×2×2×2×17
ChallengE
See attachment and answer :)
[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]
How is 8/15 written as a mixed number?
Answer:
8/15 is already a proper fraction, therefore it cannot be converted to a mixed number. Hope this helps!
Step-by-step explanation:
I need Help Asapp
Please!!!!!!!!!!!!!!!!!!
Answer:
i know it is C last year i took that quiz and well i studied /j
Step-by-step explanation:
1. What is the value of x that satisfies the equation? Must show all proper work/steps!
32^2x = 16^2x+8
Student's Work
Student's Answer
A. x = 4
B. x =- 4
C. x = 16
D. x = 1
Please explain all steps
[tex] {32}^{2x} = 16 ^{2x + 8} \\ = > {2}^{5(2x)} = {2}^{4(2x + 8)} \\ = > {2}^{10x} = {2}^{8x + 32} \\ = > 10x = 8x + 32 \\ = > 10x - 8x = 32 \\ = > 2x = 32 \\ = > x = \frac{32}{2} \\ = > x = 16[/tex]
Answer:
x = 16
Hope you could get an idea from here.
Doubt clarification - use comment section.
Which equation describes the line shown in the graph?
Answer:
D
Step-by-step explanation:
:)
Simplify the ratio:
42 : 28 : 21
Please explain step by step to get marked as brainliest!
Answer:
6:4:3
Step-by-step explanation:
Use 7 to simplify
Help bell bell help help help
Answer:
answer is ‐10
Step-by-step explanation:
(x+14) =(5x-74)pick like terms together (x+5x)=(+14‐74)(6x)=(‐60)divide by 6answer is ‐10cant seem to figure this out
Answer:
log14=1.146
log18=1.255
Step-by-step explanation:
Use log rules to break up the given logs, to be able to use the information give
Using the product rule, log14 = log(7 x 2) = log7 + log2
Substitute .845 + .301 = 1.146
Using the quotient rule, log18 = log(2 x 3 x 3) = log2 + log3 + log 3
Substite .301 + .477 + .477 = 1.255
A metric drawing scale of 1:100 typically depicts units in
Answer:
This usual depicts units in centi-metre
Usually Centi-(and the unit you have)
Step-by-step explanation:
Because it is 1 in 100
100 is what centi means, so centi-metre
Like centipede, an insect with 100 legs
1:100 means 1 in 100
or one centi-metre
Hope this helps!
14.9 x 100 PLS HELP
Answer:
just move the decimal to the right two place, for two zeroes. The answer is 1490.
Step-by-step explanation: Just simply multiply 14.9 by 100.
Answer:
1490.Step-by-step explanation:multiply 14.9 by 100
A calf weighs 18 lbs. when it is 2 months old, and after 8 months it weighs 36 lbs.
Let x be the calf's age and y be the weight.
a. Write an equation in slope-intercept form that represents the situation.
The equation in slope-intercept form that represents the situation is y = 3x + 12
A linear equation is on the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let x be the calf's age in month and y be the weight.
A calf weighs 18 lbs. when it is 2 months old, and after 8 months it weighs 36 lbs. Hence it can be represented by:
(2, 18) and (8, 36). The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-18=\frac{36-18}{8-2}(x-2) \\\\y=3x+12[/tex]
The equation in slope-intercept form that represents the situation is y = 3x + 12
Find out more on linear equation at: brainly.com/question/14323743
Determine which of the values is a solution of 4t+6 is less than or equal to 10.
Values:
1, -8, -4, 3, 0, 7
Answer:
1, 3, 7
Step-by-step explanation:
4t + 6≤10
4t≤4
t≤1
Therefore, t can either be equal to or greater than 1.
__________________________________________________________
Hope this helps!!
If I am wrong, please tell me, I enjoy learning from my mistakes:)
Rewrite this equation in Slope-intercept form
(PLEASE SHOW ALL WORK)
PLEASE HELP WILL MARK BRAINLIEST!
Answer:
Step-by-step explanation:
[tex]12000(1+\frac{.12}{4})^{4*45}=2454040.31463\\=2454040[/tex]
write a quadratic equation in standard form.
1. -6 and 4 are solutions
2. 2 and 5 are solutions
1 and 2 are two different problems
Answer:
1. x^2 +2x -24 = 0
2. x^2 -7x +10 = 0
Step-by-step explanation:
If you look at the factored and expanded forms of a quadratic with solutions p and q, you see ...
(x -p)(x -q) = x^2 -(p+q) +pq
The x-term coefficient is the opposite of the sum of solutions.
The constant is the product of solutions.
This knowledge lets you write down the standard form equation with no particular effort.
1. x^2 +2x -24 = 0
2. x^2 -7x +10 = 0
The scale of a blueprint is 3 inches : 10 feet. On the blueprint, a house is 9 inches
a
long. What is the length in feet of the actual house?
Answer:
30/5=68x6=48 feet
Step-by-step explanation:
divide the demesions
What is the slope of the linear equation that has the values shown in the table
Answer:We noted above that a linear function has the form f(x)= mx+b, f ( x) = m x + b, where m m is the slope of the line, and b b is the y y -intercept. Since m m and b b can take on various values
Step-by-step explanation:
What kind of taxes are likely to pay for universities and police?
а
local taxes
b. state taxes
C federal taxes
d income taxes
Answer: I'd say the best answer is b.
Step-by-step explanation:
Define the following sequence recursively: 96, 48, 24, 12, ....
Select one:
a. f(1)=12 f(n−1)=2⋅f(n) n≥2
b. f(1)=12 f(n−1)=−12⋅f(n) n≥2
c. f(1)=96 f(n)=12⋅f(n−1) n≥2
d. f(1)=96 f(n)=2⋅f(n−1) n≥2
Answer:
I do not see that any of your options will work.
Step-by-step explanation:
a) and b) have a false first statement because f(1) = 96, not 12
c) would create the sequence 96, 1152, 13824
d.) would create the sequence 96, 192, 384. 768...
I believe the correct answer would be
f(1) = 96 f(n) = ½f(n-1) n ≥ 2
which could be either c) or d) if taking potential typographic errors into account. Recording a "2" or "12" where a "½" ought to be.
You can walk 1/34 miles in 1/2 hour. What is your average speed?
State if the triangles in each pair are similar. If so, state how you know they are similar and complete the
similarity statement.
Answer:
the answer is in the site faith mate is the same question and in that site have the response np
Graph the system. Use the graph to approximate
the solution of the equation.
Answer:
2.09
Step-by-step explanation:
And set them up as a function. We could set y equals to each side of it. So if we set y equals to the left-hand. Side we get Y is equal to three has to the X power.
Answer:
Plot a graph of the function y = log (x) and move it by 1 unit to the left.
Plot the graph of the function y = x ^ 2, reflect over the x-axis, and move it 10 units up.
The coordinates of the intersection of the graphs are the solution.
Solution: x=3
I think this your answer you did not really say your answer?????
In the number 777.77 how does the value of 7 in the tenths place compare to the value of 7 in the hundredths place
Answer:
630
Step-by-step explanation:
the value of 7 in the tenths place is 70
the value of 7 in the hundredths place is 700
compare 700 and 70
So 700-70 = 630
Examine the figure. What is the measure of angle a?
Answer:
59Step-by-step explanation:
90+31=121
180-121=59
Answer:
a=59
basic fact:
angles on a straight line add up to 180
Step-by-step explanation:
we can ignore b for a start
31+90+a=180
121+a=180
121+59=180
a=59
Help help help math math help
Hello, would be very nice if someone could help me ! :)
A finite geometric series is the sum of a sequence of numbers. Take the sequence
1, 2, 4, 8, ..., for example. Notice that each number is twice the value of the
previous number. So, a number in the sequence can be represented by the
function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th
number in the sequence is ∑^5 n-1 2^n-1.
This equation can also be written as S5 = 2^0+2^1+ 2^2+ 2^3+ 2^4. If we multiply this equation by 2. the equation becomes 2(S5) = 2^1+ 2^2+ 2^3+ 2^4+ 2^5
What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the
form ∑^a n-1 b^n-1 ?
Answer:
Step-by-step explanation:
2S₅ - S₅ = 2⁵ - 2⁰
S₅ = 2⁵ - 1
Sₙ = (bᵃ - 1) / (b - 1)
If you sleep 30% of the day. how many hours did you sleep?
answer fast please
Answer:
7.2 hours
Step-by-step explanation:
24 · 0.3 = 7.2
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Pythagorean theorem )
Answer:
5 sqrt(6) = x
Step-by-step explanation:
The pythagorean theorem states
a^2 + b^2 = c^2
Where a and b are the legs and c is the hypotenuse
7^2 + (sqrt(101))^2 = x^2
49+101 = x^2
150 = x^2
Take the square root of each side
sqrt(150) = sqrt(x^2)
sqrt(25*6) = x
5 sqrt(6) = x
x+18-3x=20 help me out
the bbc lenth is 19 which i like in my mouth an deven my throayt
ms. valdez is preparing dinner for 6 people she bought an 8 pund tukey to rost for dinner and plans to distribute it evenly to each of the 6 people how many pounds of turkey should each person get
a- 1 1/3
b- 1 1/6
c 3/4
1/2
1/4
Answer:
A
Step-by-step explanation:
8/6 is also 1 1/3.
(assuming she doesn't include herself in the distribution).