Answers
the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
Which statement explains why 6^(1/2) is equal to √6?Well, this is just a notation thing.
We know the following property for exponents:
(a^n)^m = a^(n*m)
And we know that the square rooth is the inverse of the square power (exponent equal to 2) such that:
√x^2 = 2
Then if we define the square root as an exponent, let's say that is an exponent "a" we will have:
√x = x^a
Rewritting the above relation again, we can write:
√(x^2) = (x^2)^a = x^(2*a)
And we know that it must be equal to x, so we get:
x^(2*a) = x
This means that 2*a = 1
then a = 1/2
√x = x(1/2)
Then the correct statement is the first one.
The inverse of 6^2 is 6^(1/2), then 6^(1/2) is the square root of 6.
If you want to learn more about exponents:
https://brainly.com/question/11464095
#SPJ1
Related Questions
Here are five number cards.
2
5
7
8
One of the cards is removed and the mean aver
of the remaining four number cards is 6
Which card was removed?
Answers
The card with the number 7 was removed.
What are equations?An equation, in its most basic form, is a mathematical statement that shows that two mathematical expressions are equal.For example, 3x + 5 = 14 is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So,
The sum of all the numbers on the cards is 2+5+7+8+9=31.One card is removed, for example, with the number x.Now the sum new would be =31-x. ... (1)6 is the average of the remaining four cards.So the sum of the remaining four cards is 6(4) = 24. ...(2)The sum of the remaining four cards is represented by(1) and (2). As a result, they should be equal to 31 - x = 24.Subtraction 31 from both sides yields -x = -7 or x = 7.Therefore, the card with the number 7 was removed.
Know more about equations here:
brainly.com/question/2972832
#SPJ9
Which expression is equivalent to sum of quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity? negative twenty nine sixths times n minus one twelfth negative twenty nine sixths times n plus one twelfth negative eleven sixths times n minus one twelfth negative eleven sixths times n plus five twelfths
Answers
The expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or (-3 1/3n + 1/6) + (1 3/6n - 3/12) is equivalent to "negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or simply (-3 1/3n + 1/6) + (1 3/6n - 3/12), combine all like terms and perform necessary operations.
(-3 1/3n + 1/6) + (1 3/6n - 3/12)
⇒ -3 1/3n + 1 3/6n + 1/6 - 3/12
⇒ (-3 1/3 + 1 3/6)n + 1/6 - 3/12
⇒ (-10/3 + 9/6)n + 2/12 - 3/12
⇒ (-20/6 + 9/6)n - 1/12
⇒ -11/6n - 1/12
Hence, the equivalent expression is negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.
Learn more about algebraic expression here: https://brainly.com/question/723406
#SPJ4
help me please i need math
Answers
Based on the information given, the area of the trapezoid will be 89.7cm².
How to calculate the area?It should be noted that the formula for calculating the area of a trapezoid will be:
= (a + b)/2 × h
where a = 8
b = 13
h = 7.8
Area = (13 + 8)/2 × 7.8
= 21/2 × 7.8
= 11.5 × 7.8
= 89.7cm²
Therefore, based on the information given, the area of the trapezoid will be 89.7cm².
Learn more about area on:
brainly.com/question/25292087
#SPJ1
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
0
2
8
10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter
Answers
Answer:
$3.90
Step-by-step explanation:
Expected Value formula
[tex]\boxed{\displaystytle E(x)=\sum x_iP(x_i)}[/tex]
where:
[tex]x_i[/tex] is an outcome.[tex]P(x_i)[/tex] is the probability of the outcome.Given table:
[tex]\begin{array}{l | ccccc}\sf Payout\:(\$) & 0 & 2 & 4 & 8 & 10\\\cline{1-6} \sf Probability & 0.35 & 0.2 & 0.1 & 0.2 & 0.15\end{array}[/tex]
Substitute the given values into the Expected Value formula:
[tex]\begin{aligned}\implies E(x) & = 0(0.35) + 2(0.2)+4(0.1)+8(0.2)+10(0.15)\\& = 0+0.4+0.4+1.6+1.5\\& = 3.9\end{aligned}[/tex]
Therefore, the expected value is $3.90.
So, on average, you would expect to receive $3.90 in winnings per game.
2(7x-7)=14x-20
with work plss and ty :)
Answers
Answer:
0=-6 (No solution)
Step-by-step explanation:
2(7x-7)=14x-20 - Distribute the 2 to 7x-7
14x -14 = 14x -20 - Subtract +14 from both sides
+ 14 +14
14x = 14x -6
-14x -14x
0=-6
Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|.
h(x) =_____
Answers
To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10).
So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|
We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph.
To know more about Cartesian coordinates
Visit:. brainly.com/question/6444755
#SPJ9
In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations or permutations? explain.
Answers
In horse racing, a trifecta, which is a bet that the first three finishers in a race are selected, and they are selected in the correct order, involves selection done in permutation.
Permutation is the method of selecting or arranging objects or numbers in order. It is used when the order or sequence of the elements selected is important. The number of permutations of n objects taken r at a time is determined by the following formula: P(n , r) = n!
On the other hand, combination is the method of selecting or arranging objects or numbers from a group of objects or numbers where order does not matter. The number of combinations of n objects taken r at a time is determined by the following formula: C(n , r) = n!/[r!(n - r)!]
Learn more about permutation here: https://brainly.com/question/1216161
#SPJ4
Answer:
Step-by-step explanation:
Because the order of the first three finishers does not make a difference, the trifecta involves permutations
What's 704 divided by 24? Make sure to give an explanation for Brainliest!
Answers
Answer:29.3 repeating
Step-by-step explanation:Just use
calculator
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
A scalene triangle has at least two congruent sides.
Answers
A scalene triangle has at least two congruent sides is a FALSE statement.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
A scalene triangle is a triangle whose all sides are unequal.
Since congruent sides are the sides that are equal in length but in a scalene triangle, none of the sides are equal to each other.
Hence "A scalene triangle has at least two congruent sides is a FALSE statement".
For more information about the triangle,
https://brainly.com/question/2773823
#SPJ4
Use the Distance Formula to calculate the distance between points A (-4, 2) and D (1, 7). Round your answer to 1 decimal place.
Answers
Step-by-step explanation: I hope this helps.
Answer: 7.07 units
I don’t really understand this can someone please help me I have to find the tangent ratios for
Answers
The tangent ratio for the ΔABC is tanФ = 1.
What is defined as the trigonometric ratios?The values of all trigonometric functions derived from the ratio of sides inside a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of such a right-angled triangle with respect to that acute angle.Some of the trigonometric ratios are-
sin = perpendicular/hypotenusescos = base/hypotenusestan = perpendicular/basecosec = 1/sinsec = 1/coscot = 1/tanFor the given right angles triangle ABC.
The sides AC = CB = 15
As, the angle ACB is the right angle i.e, ∠ACB = 90°, so, AB is the hypotenuses of the triangle.
For finding the value of tangent ratio;
tan = perpendicular/base
tan B = AB/ CB
tan B = 15/15
tan B = 1/1
tan B = 1
Thus, the value of tangent ratio = 1.
To know more about the trigonometric ratios, here
https://brainly.com/question/24349828
#SPJ9
Ethan burns 650 calories when he runs for 1 hour. Suppose he runs 5 hours in one week and is the answer going to be negative or positive
Answers
Answer:
Negative. Because he should run all seven weeks to get positive result.
Copy and complete the proof.
Given: MN ≅ PQ, PQ ≅RS
Prove: MN ≅ RS
Proof:
Answers
We conclude that MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.
What clearly does "triangle congruency" imply?Two triangles are said to be congruent if all three corresponding angles are equal and all three corresponding angles are equal in measure.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.If two triangles gratify the five congruence conditions, they are congruent.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: MN ≅ PQ, PQ ≅RS
To Prove: MN ≅ RS
There is a rule that states that:If a = b, and b = c; then automatically a = c.This rule satisfies the above condition.
If MN ≅ PQ and PQ ≅RS, then MN ≅ RS automatically.Therefore, MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.
Know more about the congruency of a triangle here:
brainly.com/question/2938476
#SPJ4
Each sequence has eight terms. Evaluate each related series. -3.5,-1.25,1,. . . . . . , 12.25
Answers
An arithmetic progression (AP) is a sequence of numbers ordered such that the difference between any two consecutive numbers is a constant value. Also called arithmetic sequence. For example, the sequence of natural numbers: 1, 2, 3, 4, 5, 6, … is an arithmetic sequence in which the common difference between two consecutive terms (e.g., 1 and 2) is 1 (2 - 1) ... It can be seen that the tolerance of two consecutive terms is equal to 2, even for odd and even numbers.
First term a=-3.5,
Common difference d=2.25,
Number of terms n=8
Solution:
Here first term a=-3.5,
Common difference d=2.25
We know that,
f(n)=a+(n-1) d
f (8)=-3.5+(8-1)(2.25)
=-3.5+(15.75)
=12.25
We know that,
Sn=n2[2a+(n-1)d]
∴S8=82⋅[2(-3.5)+(8-1)(2.25)]
=4⋅[-7+(15.75)]
=4⋅[8.75]
=35
Hence, 8th term of the given series is 12.25 and sum of first 8th term is 35.
More similar question are solved in the link below.
https://brainly.com/question/21961097?referrer=searchResults
#SPJ4
What is the x intercept of the line x = 3.5
Answers
Answer:
x=3.5
Y=None
Step-by-step explanation:
If P(A | B) is the same as P(A) , and P(B \mid A) is the same as P(B) , what can be said about the relationship between events A and B ?
Answers
When P(A | B) = P(A) and P(B ∩ A) = P(B). Then, the given events A and B are independent events.
What is defined as the independent events?Independent events are those where the occurrence is unrelated to any other event.
For example, suppose we toss a coin as in air and the result Head, then we throw the coin again and get the result Tail. Both events occur independently of one another in both cases.Now, as for the given question.
There are two events given as A and B.
The probability of occurrence of event A is P(A).
The probability of occurrence of event B is P(B).
The occurrence of the event A when B is already happened is denoted by P(A | B).
The intersection of events A and B are given as; P(B ∩ A).
Now, it is given in the question that;
P(A | B) = P(A) and P(B ∩ A) = P(B)
And, we already know that, the formula of the conditional probability for event A when event B has already occurred is;
P(A | B) = P(B ∩ A)/P(B)
This can also be written as;
P(B ∩ A) = P(A | B).P(B)
Now, P(A | B) = P(A), replace in the obtained equation.
P(B ∩ A) = P(A).P(B)
The obtained result is the condition for independent events.
Therefore, the events A and B are found to be independent events.
To know more about the independent events, here
https://brainly.com/question/1374659
#SPJ4
if caleb pick 2 grapes in 15 minutes how many would he pick in 2 hours
Answers
Answer:16
Step-by-step explanation:
Choose the letter of the correct answer.Write the chosen letter on a separate sheet of paper.
1.A number is divisible by 4 if the last_____.
A.digit of a number is divisible by 4
B.digit is even
C.two digit formed is divisible by 4
D.digit is zero
Answers
Answer:
C
Step-by-step explanation:
a number is only divisible by 4, if the number formed by the last 2 digits is divisible by 4.
please help asap (true or false question)
Answers
Answer:
The statement is true.
Step-by-step explanation:
Let us plug[tex]24=-4(8)-8[/tex] in 8 for [tex]x[/tex] and 24 for [tex]y[/tex] in our equation: [tex]24 =-4 (8) - 8[/tex].
Now we will solve in the order described by PEMDAS.
-4(8)=32
32-8=24
24=24
Thus, our statement is true.
Which equation models the line that passes through points (2, 5) and (3, 1)?
Answers
Answer: y = -4x + 13
Step-by-step explanation:
Given points (2, 5) and (3, 1)
First Step find the slope given the two points:
Use the slope formula [tex]m=\frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{1-5}{3-2} = -4[/tex] (Result)
Slope is equal to -4
Second step plug into y - y1 = m(x - x1) formula (Point Slope Formula)
For this I am using the first coordinate pair given (2, 5)
y - 5 = -4(x-2)
y - 5 = -4x + 8
y = -4x + 13
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Perimeter: 2(7+12), 2*7+2*12, 7+12+7+12
Area: 7*12, 7*10 + 7*2
neither: 7+12
Step-by-step explanation:
perimeter is like if you want a fence all the way around your property and your yard is 7x12 feet. In that case you could use the first option because you have to count the sides and add them up. If it’s a rectangle then there are 2 12’s and 2 7’s so the first one would work. The fourth one also uses distribution. The Fourth and first one are pretty much the same and have the same answer so the fourth one would work for perimeter.
Another way to do perimeter is to instead of multiplying, is to add the sides. 7+12+7+12 is basically 7 times 2 plus 12 times 2 (the fourth ne) and the answer is still correct so this one works too,
For area you times one of the dimensions by the other so 7*12 would work for area.
7*10 + 7*2 would also work because that uses the distributive property and that’s 70 + 14 which is 84 which is still the same answer.
The only one that falls under neither is the fifth one. 7+12 is half of the perimeter because it only adds two of the sides together and has n multiplying so it’s not area either.
The length of a rectangle is four more than double the width. If the perimeter is 80 inches, find the dimensions.
The width is inches.
The length is inches.
Answers
Answer: width = 12 inches
length = 28 inches
Step-by-step explanation:
l = 4 + 2w
Perimeter = 2 ( l + w )
80 = 2 ( 4 + 2w + w )
80 = 2 ( 4 + 3w )
80 = 8 + 6w
80 - 8 = 6w
72 = 6w
w = 72 / 6
width = 12 inches
length = 4 + 2 (12)
= 4 + 24
= 28 inches
checking
Perimeter = 2 ( 28 + 12 )
= 2 (40)
= 80 inches
correct
Caroline walks Nine and a half inches per second. Rou d to the nearest tenth.
Answers
The speed of Caroline in miles per hour is 0.5 miles/hour.
Given that, Caroline walks 9 1/2 inches per second.
How do you convert the inches to miles formula?How to convert inches to miles. To convert an inch measurement to a mile measurement, divide the length by the conversion ratio. The length in miles is equal to the inches divided by 63,360.
Now, 9.5 inches/second
We know that 1 inch/second=0.0568182 miles/hours
So, 9.5 × 0.0568182=0.5397729 miles/hours
≈0.5 miles/hours
Therefore, the speed of Caroline in miles per hour is 0.5 miles/hour.
To learn more about the speed visit:
https://brainly.com/question/7359669.
#SPJ1
Your question is incomplete, probably the complete question/missing part is:
Give the rate in miles per hour. Round to the nearest tenth. Caroline walks 9 1/2 inches per second.
Solve without graphing. Find the slope and the y-intercept for the graph of each equation in the given system. Use this information (and not the equations' graphs) to determine if the system has no solution, one solution, or an infinite number of solutions.
Answers
For equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.
We are given 2 equations:
y = 3 / 4 x - 9 ...(1)
and y = 3 / 4 x - 4 ... (2)
Slope for equation (1) will be
slope = m1 = 3 / 4
Slope for equation (2) will be
Slope = m2 = 3 / 4
Y intercept for equation (1) will be:
= - 9
Y intercept for equation (2) will be:
= - 4
Also, since the Slope of equation are equal, so, it has no solutions as they are parallel to each other.
Therefore, for equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.
Learn more about equation here:
https://brainly.com/question/1214333
#SPJ9
Below are the graphs of functions over the interval [-4,4]. Find the following for each function:
The domain
Zeroes of the function(the values of x where the value of the function is 0)
Intervals where the function is positive and intervals where it is negative
Answers
For the given function, we have that:
The domain is [-4,4].The function has no zeros.The function is positive for x <= 0.The function is negative for x > 0.What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.
Hence, the domain is [-4,4] for the given function.
What are the zeros of a function?The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.
For this problem, the function does not cross the x-axis, hence it has no zeros.
When a function is negative and when it is positive?Looking at a graph, we have that:
It is positive if it is above the x-axis.It is negative if it is below the x-axis.Hence, for the given function:
The function is positive for x <= 0.The function is negative for x > 0.More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
What is the image point of (1,4)(1,4) after a translation left 5 units and down 5 units?
Answers
The image of the point after the translation is (-4, -1)
How to determine the image point after the translation?The point is given as
(1,4)
The translation is given as
Left 5 units and down 5 units
This is represented as
(x, y) = (x - 5, y - 5)
So, we have
(x, y) = (1 - 5, 4 - 5)
Evaluate
(x, y) = (-4, -1)
Hence, the image of the point after the translation is (-4, -1)
Read more about transformation at:
https://brainly.com/question/4289712
#SPJ1
(- 3/4x - 8) - (- 17 + 2/8x)
Answers
Answer:
9-x
Step-by-step explanation:
Use each recursive definition to write an explicit formula for the sequence. a₋₁ = 1, a n =a n ₋₁ +4
Answers
The explicit formula for the given sequence is a(n) = 1 + 4(n - 1).
What is termed as recursive definition?A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.
The recursive formula for an arithmetic sequence is as follows.
a(1) = 1 and a(n) = a(n - 1) + 4.
Remember that this formula provides us with two types of data.
1 is the first term.Add 4 to obtain any term out of its previous term. To put it another way, this same common difference is 4.Let's look for a formal formula again for sequence.
Remember that we can use the standard explicit form to represent a sequence in which the first term is A & common difference is B: A + B(n - 1).As a result, the sequence's explicit formula is a(n) = 1 + 4(n - 1).Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) = 1 + 4(n - 1).
To know more about the explicit formula, here
https://brainly.com/question/22691266
#SPJ4
Sarah paid for 6 bags of sand to be delivered. Each bag of sand costs $114.95. Sarah paid $54.55 for delivery. What is the total amount Sarah paid?
Answers
Answer: $744.25
Step-by-step explanation:
6 * 114.95 = 689.7
689.7 + 54.55 = 744.25
find the value of (8x^6)^2/3
Answers
Answer: 4x^4
Step-by-step explanation:
from the law of indices,
( a^x)^y = a^xy
Now from the question
( 8x^6)^2/3
8^2/3X^6x2/3
From another law of indices,
a^x/y = ( y cube root of a)^x
8^2/3 = 2^2 = 4 ——— 1
Now X^6*2/3
= X^4 ——————-2
Now combine 1 & 2 together gives the answer
= 4x^4
