Simplify the expression.
a. square root 6
b. square root 12
c. 9 square root 12
d. 9 square root 6
Answers
All you need to do is add both terms together since the square root in each is 6, and 6 has no perfect squares:
4√6 + 5√6 = 9√6
Answer: 9√6
I hope this helps!
The expression is d) [tex]9 \sqrt{6}[/tex]
To simplify the given expressions involving square roots, follow these steps:
a. Square root 6
Since 6 is not a perfect square and has no perfect square factors, [tex]\sqrt{6} i[/tex]s already in its simplest form.
b. Square root 12
Break down 12 into its prime factors: 12 = [tex]2 \times 2 \times 3[/tex]. Therefore,[tex]\sqrt{12}[/tex]can be simplified as follows:
[tex]\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}[/tex]
c. 9 square root 12
We already know that [tex]\sqrt{12} = 2\sqrt{3},[/tex] so we substitute it into the expression:
[tex]9 \sqrt{12} = 9 \times 2\sqrt{3} = 18\sqrt{3}[/tex]
d. 9 square root 6
Since [tex]\sqrt{6[/tex]} is already in its simplest form, the expression remains:
[tex]9 \sqrt{6}[/tex]
Related Questions
What is the correct name for this circle?
Answers
the circled is named for the letter in the center
so this one is named circle C
Find the product.
(-5a ^2)^3 · a ^5
-15a^10
-125a^11
15a^6
-125a^10
Answers
Hence, the answer is D.
The variable Z is directly proportional to X. When X is 3, Z has the value 54. Wha is the value of Z when X= 12
Answers
Z = kX (Where k is the constant of proportionality)
To find k
54 = k3
k = 54/3
k = 18
now find new Z
Z = 18X
Z = 18(12)
Z = 216
Simplify 12 to the 16th power over 12 to the 4th power
Answers
[tex] \frac{ 12^{16}}{12^{4} } [/tex]
Do solve for this, we actually just have to do one thing since our number is the same - subtract the exponents.
When you divide by exponents, you are subtracting them.
For example;
[tex] \frac{ x^{5} }{x^{2} } [/tex]
Subtract the exponents.
[tex] x^{3} [/tex] is your answer for this example.
Let's apply this to our current expression.
[tex] \frac{ 12^{16}}{12^{4} } [/tex]
Subtract the exponents.
[tex] 12^{12} [/tex] is your simplified expression with exponents.
I hope this helps!
Find the fifth roots of 243(cos 240° + i sin 240°)
Answers
zⁿ = rⁿ(cos.n.Ф + i.sinn.Ф).
The 5th root, that means that n = 1/5 ↔↔↔ rⁿ = r¹/₅ = ⁵√r
zⁿ = ⁵√(243) [cos (240+2kπ)/5 +i.sin(240+2kπ)/5]
with k = 1,2,3,..,n-1. Note that ⁵√(243) = 3
1st root : for k=0 → 3[cos(240/5)+isin(240/5) = 3(cos48°+isin48°)
2nd root : for k=1→3[cos(240+360)/5)+isin(240+360)/5]=3(cos120°+isin120°)
3rd root : for k=2 →→ 3(cos192 + isin192)
4th root : for k=3→→3(cos264+isin264)
5th root : for k =4↔↔3(cos336+isin336)
The next four batters on a baseball team have hitting percentages of 0.400,0.325, o.250, and 0.300, respectively The team currently has two outs. If any player gets an out, the next player or players will not get an opportunity to bat. What is the probability that the fourth player will have an opportunity to bat?
Answers
.4(.325)(.25)=0.0325
Which should be expressed as a fraction as this is probabilities :P
325/10000
13/400
(This of course is not true as we only know their hitting averages not the on-base averages...they can be walked or beaned for example and still get on base :P)
B for online school yuhp
A farmer kept 96 kilograme of animals feed inhis barn the barn leaked and 1/10 of the feed was waisted , how mych animal feed was left
Answers
Find P(organic | oranges)
Find P(Non-organic | oranges)
Answers
Answer to part B: 0.37
Answer to part C: organic oranges
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Work Shown:
Part A
P(Organic|Oranges) = P(Organic AND oranges)/P(Oranges)
P(Organic|Oranges) = 0.19/0.30
P(Organic|Oranges) = 0.63
Part B
P(Non-organic|Oranges) = P(non-organic AND oranges)/P(oranges)
P(Non-organic|Oranges) = 0.11/0.30
P(Non-organic|Oranges) = 0.37
Part C
The probability in part A is larger compared to the answer in part B, so it's more likely to have someone pick organic oranges rather than non-organic oranges. Melina should restock organic oranges for the next sale.
Determine whether the sequence converges or diverges. If it converges, give the limit. 60, 10, five divided by three, five divided by eighteen, ...
Answers
Using geometric sequence form, we can rewrite it as:
[tex]A_n = a_1 \cdot r^{n-1}[/tex]
[tex]A_n = 60 \cdot \frac{1}{6}^{n - 1}[/tex]
Since r < 1, there exists a limit, and thus, it is said to converge.
[tex]\lim_{n \to \infty} 60 \cdot (\frac{1}{6})^{n - 1}[/tex]
[tex] = 0[/tex]
Since the ratio is still positive, as n tends towards infinity, the graph of the sequence will never go below the horizontal. Thus, we say that the limit of the function is zero, which means that as we increase the size of n, eventually after the infinite-th time, it will hit zero.
Solve using perfect square factoring patterns. x2 – 8x + 16 = 25
Answers
-25 both sides
x^2-8x-9=0
(x-9)(x+1)
x=9,-1
What is the data path width for a dimm that supports ecc?
Answers
Normally, the data path width for DIMMs is 64 bits but for the DIMMs that support ECC, the data path is 72 bits.
To add, error checking uses the extra 8 bits. ECC memory is more reliable than non-ECC memory but it costs more than a non-ECC memory. Comprising the DIMMS are a series of dynamic random-access memory integrated circuits. Mounted on a printed circuit board, these modules are designed for use in personal computers, workstations and servers.
The most common kinds of internal data corruption are detected and corrected by a type of computer data storage called error-correcting code memory.
A committee consisting of 6 people is to be selected from eight parents and four teachers. find the probability of selecting three parents and three teachers.
Answers
n = 12C6 = 924
To choose, 3 parents out of the 8 parents, we use again the concept of combination.
x = 8C3 = 56
Similarly, we use the same concept for choosing 3 teachers out of 4 teachers.
y = 4C3 = 4
The probability required in this item can be solved through the equation,
P = xy/n
Substituting,
P = (56)(4) / 924 = 0.2424
Thus, the probability is 24.24%.
Answer with explanation:
→Total Number of People which are in the group =8 parents + 4 Teacher=12 People
→Probability of an Event
[tex]=\frac{\text{Total Favorable Outcome}}{\text{Total Possible Outcome}}[/tex]
→Probability of selecting three parents and three teachers
= Selecting 3 parents from 8 Parents +Selecting 3 teacher from 4 teacher
As order of Arrangement is not Important ,so we will use the concept of Combinatorics.
→→ Required Probability
[tex]=\frac{_{3}^{8}\textrm{C}\times _{3}^{4}\textrm{C}}{_{6}^{12}\textrm{C}}\\\\=\frac{\frac{8!}{3!\times 5!}\times \frac{4!}{3!\times 1!}}{\frac{12!}{6!\times 6!}}\\\\=\frac{56 \times 4}{7\times 4 \times 3\times 11}\\\\=\frac{8}{33}[/tex]
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply:
A.) 0 < x ≤ 6
B.) 0 < x ≤ 3
C.) 4 ≤ x ≤ 6
D.) x ≤ 6
E.) |x - 5| ≤ 1
F.) |x - 2| ≤ 6
Answers
By writing an inequality and then converting it to an absolute value equation, we will see that the correct options are C and E.
How to find an inequality?
To find the inequality, we need to find the lower and upper bounds.
First, we know that the machine fills the cups with 4 oz of yogurt, so this is the minimum value allowed, we will have:
4 ≤ x
Then we can add toppings to a maximum value of 6 ounces, this will be the maximum, then we have:
4 ≤ x ≤ 6
We can also write this an absolute value equation, we define:
m = half of the difference of the bounds.M = lower bound + mThen the absolute value equation is:
|x - M| ≤ m
By replacing what we found before, we have:
m = (6 - 4)/2 = 1M = 4 + 1 = 5So the absolute value equation is:
|x - 5| ≤ 1
Finally, we can conclude that the correct options are C and E.
If you want to learn more about inequalities, you can read:
https://brainly.com/question/11234618
Which is the slope of the line that connects points (3,17) and (7,25) ?
Answers
slope=(y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are any two points...
slope=(25-17)/(7-3)
slope=8/4
slope=2
8/4, reduced to 2/1.
2/1 is the correct answer.
What is the arc length when Θ = pi over 3 and the radius is 5 cm?
Answers
Answer:
Arc length = 5.23 cm
Step-by-step explanation:
Given : Radius = 5 cm
Angle = [tex]\theta=\frac{\pi}{3}[/tex]
To find : Arc length(A)
Solution: The formula of arc length is
A = radius × angle(in radian)
[tex]A= 5\times\frac{\pi}{3}[/tex]
⇒[tex]\frac{5\pi}{3}[/tex]
A ⇒15.70/3 = 5.23 cm
Given the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2
Answers
Domain and range are from negative infinity to positive infinity or all real numbers
There is a traffic light at the intersection of walnut street and Lawrence avenue. The traffic light in walnut street follows a cycle. It is green for 50 seconds, yellow for 10 seconds, and red for 30 seconds, as you travel along walnut and approach the intersection, what is the probability that the first color you see is red?
Answers
P(R)=30/90
P(R)=1/3
Answer: The probability that the first color we see is red is 0.34.
Step-by-step explanation:
Since we have given that
Time taken by green color on the traffic light = 50 seconds
Time taken by yellow color on the traffic light = 10 seconds
Time taken by red color on the traffic light = 30 seconds
Total number of seconds = 50+10+30=90
So, Probability that the first color we see is red is given by
[tex]\dfrac{\text{Time alloted for red color}}{\text{Total number of seconds}}\\\\=\dfrac{30}{90}\\\\=\dfrac{1}{3}\\\\=0.3333...\\\\\approx 0.34[/tex]
Hence, the probability that the first color we see is red is 0.34.
What is the problem to this
Answers
24:x
Set up a proportion
4/9=24/x
4x=216
x=54
a) 54 is your answer
hope this helps, and please give brainliest if it does!
__________________________
Given: "For every 4 people that made the team, 9 people did not make the team. 24 people made the team. How many did NOT make the team?
24 people made the team. How many groups of 4 people is that?
24 divided by 4 equals: "6".
__________________________
6 * 9 = 54 .
__________________________
The answer is: [A]: " 54 " .
__________________________
Write an equation of the line that passes through the given point and has the given slope. Write the equation in slope-intercept form.(–5, –6), m = –3 Show your work :)
Answers
What is the domain of y = tan x, where n is any integer?
Answers
so.. one can say the domain of tangent, is all angles EXCEPT those where cosine turns to 0
[tex]\bf \{x|x\in \mathbb{R}; x\ne \frac{\pi }{2}\pm\pi n\}\qquad \textit{\underline{n} being an integer}[/tex]
Answer:
x is not equal to pi/2 + n*pi
Step-by-step explanation:
just got it right on a pex
Find the sum of the arithmetic sequence. 15, 17, 19, 21, ..., 33
Answers
sum = [tex] n *\frac{ a_{1} + a_{n} }{2} [/tex]
in our case n = 10, a1 = 15 and An = 33 so the answer will be:
sum = 10 * (33 + 15)/2 = 10 * 48 / 2 = 10 * 24 = 240
Answer:
240
Step-by-step explanation:
Hope this helps! :)
Hosting a breakfast for 25 people you plan to serve scrambled eggs the grocery store sells eggs in cartons and each carton can feed people. how many cartoons of eggs must you buy to ensure each guest a serving
Answers
The number of egg cartons required to serve 25 people with scrambled eggs is 3 cartons, assuming each carton serves 12 people and we cannot purchase partial cartons.
To calculate the number of egg cartons needed to serve scrambled eggs to 25 people, we first need to know how many people each carton can serve. However, it appears there's a typo or missing information in the question regarding the number of people an egg carton can serve. Assuming that one egg carton can serve a certain number of people, we'd use that information to determine the total number of cartons required.
If we refer to the related information provided about pancakes - where one egg is needed for 8 pancakes - we can draw a parallel for eggs for scrambled eggs. If one egg serves one person in the case of scrambled eggs, and typically there are 12 eggs in a carton, then one carton would serve 12 people.
Using this assumption, since we have 25 people to serve, we can calculate the number of cartons needed as follows:
25 people
Since we cannot purchase a partial carton, we would need to round up to the nearest whole number. Therefore, we would need to purchase 3 cartons of eggs to ensure each guest has a serving.
please help!!!! question is/.........
Answers
1/2 circle = 113.04 / 2 = 56.52
Area of rectangle = 8 x 6 = 48
Area of figure = 48 + 56.52 = 104.52
answer
104.52 ft^2
What is recorded in section 24 of cms-1500?
Answers
A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) and (7, –13), and the center of the arch on the bridge is located at (0, 0). Find the equation of the arch of the bridge.
Answers
The equation of the arch is y = (-13/49)x².
The equation of an arch can be described by a parabola when one side of the arch mirrors the other side. This is the case for the bridge problem given.
The center of the bridge is at the origin (0, 0), and it is the vertex of the parabola. Since the arch is symmetrical and the x-coordinate of the vertex is 0, the parabola is a vertical one. Thus, the equation will be in the form y = ax². To find the value of a, we will use the fact that one end of the bridge is at (7, -13).
Since (7, -13) is a point on the parabola, by plugging these values into the equation y = ax², we get:
-13 = a(7²)
-13 = 49a
a = -13/49
Thus, the equation is y = (-13/49)x².
Teh width of a rectangle is 2 cm less than 7 times the length. the perimeter is 60 cm. determine the length and the width of the rectangle
Answers
60=P=2(L+W)
60=2(L+W)
divide by 2
30=L+W
given
W=-2+7L
subsitute
30=L+W
30=L-2+7L
30=8L-2
add 2
32=8L
divide by 8
4=L
sub back
W=-2+7L
W=-2+7(4)
W=-2+28
W=26
width is 26cm
length is 4cm
On a blueprint, the scale indicates that 7 cm represent 16 ft. What is the length of a room that is 9.8 cm long and 5 cm wide on the blueprint?
Answers
7/16 =9.8/ x =156.8/7 = 22.4 feet long
7/16 = 5/x = 80/7 = 11.428 feet wide round to 11.43 or 11.4 feet
Suppose a youth organization wants to choose a president, vice-president and secretary for the upcoming year from its 35 person membership. In complete sentences, explain why this is a permutation. Determine how many different ways the youth board can be chosen.
Answers
is the formula which gives the total number of permutations of r objects out of n.
A permutation means an arrangement in a list, be it horizontally, or vertically.
So there is a first place, a second and so on.
Example: a, b, c and a, c, b are 2 different permutations.
with these in mind:
the problem described is a permutation problem, because the order is important.
We do not only care whether a certain person is chosen among the 3, we also care what position he/she will hold.
The total number of permutations of 3 objects out of 35 is calculated by the formula:
[tex]P(35, 3)=\frac{35!}{(35-3)!}=\frac{35!}{(32)!}= \frac{35*34*33*32!}{32!}=35*34*33=39,270[/tex]
Answer: 39, 270
If EF = HG and HG = 16, find the diameter of K
Answers
Answer:
Diameter of the circle K = 20 units
Step-by-step explanation:
Given that : EF = HG
Also, HG = 16 units
⇒ EF = 16 units
Now, any line drawn perpendicular to the chord always bisects the chord
⇒ KI will bisect the chord EF
⇒ EI = 8 units
Now, in ΔEIK using Pythagoras theorem we have :
⇒ EK² = 8² + 6²
⇒ EK² = 100
⇒ EK = 10 units
So, Radius of the circle K = 10 units
Now, Diameter of the circle K = 2 × 10
= 20 units
Class a has x students and class b has y students. the average of class a is 85 and class b is 90. when the scores of class a and b are combine the average is 88, what is the ratio of x to y
Answers
In similar manner, we are able to find for the total scores of the students from Class B. That would be, 90y.
Combining the scores, the new average then becomes 88. This is equal to,
(85x + 90y) / (x + y ) = 88
Cross-multiplying,
85x + 90y = 88x + 88y
Combine all the x's and y's in each side of the equation.
85x - 88x = 88y - 90y
Combining terms,
-3x = -2y
The ratio is obtained through the step below,
-3x/-3y = -2y/-3y
x/y = 2/3
Thus, the ratio is 2/3.