Rational exponents
I need help ASAP!! Can someone solve and explain step by step how to do it???
Answers
Answer:
a . x = 512
b. x^1/2•y•z^5/4
Step-by-step explanation:
a. Here in this question, we want to find the value of x, given the equation.
x^2/3 = 64
Now, to find the value of x, we shall raising both powers to the reciprocal of 2/3
When we talk of reciprocal, we mean a number such that when we multiply this number by that particular number, our result is 1.
So for 2/3, the reciprocal is 3/2
So let’s raise the power of both sides to 3/2
Thus;
x^2/3(3/2) = 64^3/2
Kindly recall that 2/3(3/2) = 2/3 * 3/2 = 1
Thus ;
x = 64^3/2
So what this mean is that we will find the square root of 64 and cube our answer.
Thus;
x = {√(64)}^3
x = 8^3
x = 512
b. According to laws of indices, kindly note that
b√(a) = a^1/b
Thus;
4 √(x^2•y^4•z^5) = (x^2•y^4•z^5)^1/4
So what we do is to multiply each of the powers in the bracket by 1/4
Thus, we have the following;
x^2(1/4) • y^4(1/4) • z^5(1/4)
= x^1/2•y•z^5/4
where • simply refers to multiplication between the terms
Related Questions
help asap will give 10 points
Answers
Answer:
FALSE
Step-by-step explanation:
The properties of exponents tells us that
[tex]9^9\ \ *\,\,9^{-20}\,=\,9^{9-20}\,=9^{-11}[/tex]
Answer:
False
Step-by-step explanation:
[tex](9 {}^{9} ) \times (9 {}^{ - 20}) = 9 {}^{9 + ( - 20)} = 9 {}^{9 - 20} = 9 {}^{ - 11} [/tex]
Hope this helps ;) ❤❤❤
please help i beg plsssssssssz
Answers
Answer:
5/2=20/8=35/14=125/50
Answer:
8, 14, 50
Step-by-step explanation:
5 x 4 = 20
2 x 4 = 8
5 x 7 = 35
2 x 7 = 14
5 x 25 = 125
2 x 25 = 50
Find the median of the following frequency distribution
Answers
Answer:
3
Step-by-step explanation:
First right out all the data in numerical order from left to right.
2, 2, 2, 3, 4, 5, 7
The median is the middle number in the set. If there is an even amount of data points, find the average of the two middle numbers. If there is an odd number of data points, like in this data set, just take the middle number as you median.
There are 7 data points in this set so the fourth number in the set written in numerical order would be your median.
When writing this set out in numerical order, repeated numbers must be repeated, we find that the fourth, or middle, number is 3. Therefore, 3 is the median of this data set.
interpret the parts of the expression 9x + 4y – 5. Rewrite the expression as a sum: _______________
Answers
Answer:
9x + 4y +(-5)
Step-by-step explanation:
Given
9x + 4y - 5
Required
Interpret
Write as a sum
The parts of an expression can be interpreted in the following ways; Terms, Variables, Constant, Coefficient, etc.
The terms are the expression being added together and they are 9x, 4y and -5
The variables are the represented with alphabets they change in values; the two variables in the given question are x and y
Constant are numbers standing alone; This is 5
Coefficient are numbers in front of variables; In this case, the coefficient are 9 and 4
Writing 9x + 4y - 5 as a sum
The -5 can be written as +(-5); So, we have
9x + 4y +(-5)
What is the name of the property illustrated in the equation below?
5+(3x+0)=5+3x
Answers
Answer:
Step-by-step explanation:
Additive identity property.
The sum of any number and zero is the original number
3x + 0 = 3x
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Hope this helps!
Answer:
x<10
Step-by-step explanation:
On the number line it shows that the dot is at 10. Since the dot is not colored in, we know it's not greater/less than or equal to. Greater/less than or equal to is where it shows the symbol, but it's underlined, like this: ≤. Only when the dot is colored in, is there a possibility it is greater/less than or equal to. So it can be greater than or less than something. Since it starts at 10 and is decreasing, it is going to be less than.
X will be less than something. And because the dot is at 10, it means 10 was the start. X is less than 10 since the arrow is pointing to where the numbers are decreasing. So, x<10.
On Tuesday, Dec. 3, I began drinking a glass of cola every day except Saturday and Sunday. I drank my 22nd glass of cold on A) Dec. 24 B) Dec. 25 C) Dec. 31 D) Jan. 1
Answers
Answer:
The correct option is;
D) Jan. 1
Step-by-step explanation:
The given information are;
The date at which drinking a glass of cola a day of cola began = Dec 3
The days in which to drink cols = Every day of the week except Saturday and Sunday
The number of glasses of drinking cola = 22
In the fires week, number of days in which to drink cola = Tuesday, Wednesday, Thursday, and Friday which is 4 days
On the week commencing Dec 9, 5 glasses drank
On the week commencing Dec 16, 5 glasses drank
On the week commencing Dec 23, 5 glasses drank
On the week commencing Dec 30, 3 glasses drank
Therefore on the week commencing Dec 30, cola was drank on the 30th, 31st and the 22nd glass was drank on Jan. 1
The correct option is Jan. 1.
Is a 118 supplementary or complementary?pls ASAP!!
Answers
Answer:
[tex]\huge\boxed{Supplementary \ Angle}[/tex]
Step-by-step explanation:
118 is a supplementary angle. It is not a complementary angle because complementary angles add up to 90 and 118 is greater than 90 degrees. So, 118 is a supplementary angle and it is an angle adding up to 180 degrees with any other angle measuring 62 degrees.
Answer:Supplementary
Step-by-step explanation:You should remember that complementary refers to any number from 0-90 and supplementary refers to any number from 90 onwards..
Hereby giving the answer as ''Supplementary''
Tom ate 3/8 of a pizza, and his brother ate 2/5 of the remainder. What fraction of the pizza was left?
Answers
Answer:
3/8 is left
Step-by-step explanation:
Tom ate 3/8 of the pizza
Take 1 - 3/8
8/8 - 3/8 = 5/8
5/8 of the pizza is left
The brother at 2/5 of the remainder
5/8 * 2/5
2/8
1/4
His brother at 1/4 of the of the pizza
5/8 - 1/4
5/8 - 2/8
3/8 is left
(-6x)(½y)(-⅓z) what is the product?
Answers
Answer:
xyz
Step-by-step explanation:
[tex](-6x)(\frac{1}{2}y)(-\frac{1}{3}z) = (-6)*\frac{1}{2}*(-\frac{1}{3}) * xyz = \frac{6}{6} xyz = xyz[/tex]
There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true? I. db III. c3
Answers
Complete question is;
There are three different hoses used to fill a pool: hose x, hose y, and hose z. Hose x can fill the pool in a days, hose y in b days, and hose z in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d < c
II. d > b
III. c/3 < d <a/3
A) I only
B) III only
C) I and III only
D) II only
E) I, II and III
Answer:
The correct option is C
Step-by-step explanation:
From the question, the 3 hoses combined together will fill the pool faster than the time for the hoses to accomplish it individually. Therefore, the time "d" will be lesser than any of the individual times used by each hose.
Hence, statement I is true and II is false.
Now, we know that if each of the three hoses took c days to complete the job, then together they would take c/3 days. However, in reality, two of the three hoses even took more than c days. So, in a nutshell together they would take more than "c/3" days, and therefore d > c/3.
Likewise, if each of the three hoses took "a" days to finish the job, then when combined together, they would take "a/3" days. Now, two of the three hoses used fewer than "a" days and so when combined together they would take less than "a/3" days and therefore d < a/3.
If we combine the last 2 paragraphs, we will arrive at c/3 < d < a/3 and that is same as statement III.
Thus, statement I and III are true. The correct option is C
Please help me I promise I will mark you brainliest if you are correct!!!!!!!!!!!!!!!!!!!!!!!!!! Use the graph of f to estimate the local maximum and local minimum. A quadratic graph is shown. The graph intercepts the x axis at approximately -2.8 and 1.2. A). No local maximum; local minimum: approx. (1,-7.67) B). Local maximum: (-2,8); local minima: (-3,0) and (3,3) C). Local maximum: approx. (1,8.08); local minima: approx. (-2,-7.67) and (3,2.75) D). Local maximum: ∞ local minima: (-3,0) and (3,3)
Answers
Answer:
Local Maximum Approx.: (1,8.08)
Local Minima Approx.: (-2,-7.67) and (3,2.75)
Step-by-step explanation:
Local maximums and minima there the highest and lowest points, respectively, on a graph in a specific region. (This is different from absolute maximum and minimum, which are the highest and lowest points overall.)
These are pretty clear to see on a curve, as they are the "turns" or the points where the curve switches direction from up to down or down to up.
On your graph, we have two local minima and one local maximum. The local minima are at x= -2 and x=3. The local maximum is at x=8. Because of the way the graph is, we have to approximate the y-values of each point.
The answer option which best describes this is the third option, so that is your answer.
Please help.. very confused
Answers
Answer:
D { -1,0,3,5}
R { -3,-1,1,7}
Step-by-step explanation:
The domain is the input values
3,-1,5,0
We normally put them from smallest to largest
D { -1,0,3,5}
The range is the output values
1,-3,7, -1
We normally put them from smallest to largest
R { -3,-1,1,7}
A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.5 minutes and the standard deviation was 0.70 minutes. What is the probability that calls last between 3.5 and 4.0 minutes? (Round your z value to 2 decimal places and final answer to 4 decimal places.)
Answers
Answer:
0.2611
Step-by-step explanation:
Given the following information :
Normal distribution:
Mean (m) length of time per call = 3.5 minutes
Standard deviation (sd) = 0.7 minutes
Probability that length of calls last between 3.5 and 4.0 minutes :
P(3.5 < x < 4):
Find z- score of 3.5:
z = (x - m) / sd
x = 3.5
z = (3.5 - 3.5) / 0.7 = 0
x = 4
z = (4.0 - 3.5) / 0.7 = 0.5 / 0.7 = 0.71
P(3.5 < x < 4) = P( 0 < z < 0.714)
From the z - distribution table :
0 = 0.500
0.71 = very close to 0.7611
(0.7611 - 0.5000) = 0.2611
P(3.5 < x < 4) = P( 0 < z < 0.714) = 0.2611
Which of these is a ratio table?
A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 5, 6, 7.
A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 4, 5, 7.
A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 1, 4, 9.
A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 2, 4, 6.
Answers
Answer:
A 2-column table has 3 rows. Column 1 is labeled A with entries 1, 2, 3. Column 2 is labeled B with entries 2, 4, 6.
Step-by-step explanation:
The table with a constant ratio between A and B is the one with entries ...
B/A = 2/1 = 4/2 = 6/3
The ratio is 2. The table is the last one described here.
Answer:
b
Step-by-step explanation:
hope this helps
What is the value of this expression when c = -4 and d = 10?
Answers
Answer:
[tex]\Large \boxed{\mathrm{\bold{B. \ 9}}}[/tex]
Step-by-step explanation:
Plug in c = -4 and d = 10 for the expression.
1/4(-4³ + 10²)
Evaluate the expression.
1/4(-64 + 100)
1/4(36)
36/4 = 9
Answer:
[tex]\huge\boxed{B. \ \ 9}[/tex]
Step-by-step explanation:
1/4 (c³ + d²)
Given that c = -4 and d = 10
1/4 ( -4³ + 10²)
1/4 ( -64+100)
1/4 ( 36 )
=> 9
Evaluate the expression when c = 4 and x = -2.
-C+ 6x
Answers
Answer:
-16
Step-by-step explanation:
We are given the expression:
-c+6x
and asked to evaluate when c=4 and x=-2. Therefore, we must substitute 4 in for c and -2 in for x.
-(4)+6(-2)
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, Subtraction.
First, multiply 6 and -2.
6 * -2= -12
-(4)+ -12
-(4) -12
Distribute the negative sign.
-4 -12
Subtract 12 from -4.
-16
The expression -c+6x when c=4 and x= -2 is -16.
Answer:
-16
Step-by-step explanation:
Start with -C+ 6x. Replace C with '4' and x with '-2'
This comes out to -(4) + 6(-2) = -4 - 12 = - 16
Which of the following is an irrational number?
5 / 4
√5 / 7
1/ 8
3 / 5
Answers
Answer: [tex]\sqrt{5} /7[/tex]
Step-by-step explanation:
5/4 is not an irrational number because it is already in a fraction the same as 1/8 and 3/5.
The square root of 5 is not rational because it cannot be converted to a fraction or in other words is not a perfect square.
Answer:√5 / 7
Step-by-step explanation:
PLEASE HELP ME I GIVE 5 STARS !
Answers
Answer:
It's the 2nd option 2*2*3*3*5
Step-by-step explanation:
Answer:
b.
Step-by-step explanation:
you find a square root that goes into 180. i did 4 times 45. when you break apart 4 you get two times two. when you break apart 45 to get another square root, you get 9 times 5. when you break down 9 you get 3 and 3. so it is 2 times 2 times 3 times 3 times 5
We can calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation e=17/20d. How many U.S. dollars have the same value as 1 euro?
Answers
Answer: 1.18 dollars
Step-by-step explanation:
Given that:
E = Euros
D = US dollars
If the equation showing the relationship between Euros and Dollar
is E = 17/20D
To find the equivalent amount of dollars for 1 euros, substitute E for 1 in the formula and make D the subject of formula
1 = 17/20 D
Cross multiply
17D = 20
D = 20/17
D = 1.18 dollars approximately
Therefore, 1.18 dollars have the same value as 1 euro.
sinθ/(1-〖cos〗^2 θ)=cosecθ
Answers
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
cosec x = [tex]\frac{1}{sinx}[/tex]
Consider the left side
[tex]\frac{sin0}{1-cos^20}[/tex]
= [tex]\frac{sin0}{sin^20}[/tex] ← cancel sinΘ on numerator/denominator
= [tex]\frac{1}{sin0}[/tex]
= cosecΘ = right side
Four students are verifying that x2 + x– 12 = (x – 3)(x + 4). Their conclusions are presented in the table. A 4-column table with 1 row. First column is labeled Damien with entry 3(negative 4) = negative 12, so the factors are correct. Second column is labeled Lauryn with entry negative 4 + 3 = negative 1, so the factors are correct. Third column is labeled Rico with entry negative 4(3) = negative 12 and negative 4 + 3 = negative 1, so the factors are correct. Fourth column is labeled Latisha with entry 4(negative 3) = negative 12 and negative 3 + 4 =1, so the factors are correct. Which student correctly verified that x2 + x – 12 = (x – 3)(x + 4)? Damien Lauryn Rico Latisha
Answers
Answer:
Latisha correctly verified that x² + x - 12 = (x - 3)(x + 4)
Step-by-step explanation:
In the problem, each student was to give their explanation of why the statement above is correct. In order to know if this statement is correct, you can also simply multiply the terms after the equal sign.
(x - 3)(x + 4)
Use foil method to multiply.
x² - 3x + 4x - 12
Combine like terms.
x² + x - 12
You can also find out if the statement is correct is multiplying and adding the numbers together.
-3 * 4 = -12
-3 + 4 = 1
So, Latisha is correct because her explanation verified the statement above.
Answer:
Latisha
Step-by-step explanation:
Correct on edg
0.21212121 as a fraction
Answers
Answer:
21212121/100000000
Step-by-step explanation:
21212121/100000000 cannot be simplified
Hope this helps!
Answer:
0.21212121 Cannot be converted into a fraction
f(x) = x^2. What is g(x)?
pls help
Answers
Answer:
A. g(x)= 1/3x²
Step-by-step explanation:
The graph of the function g(x) has a point (3,3) on it.
So
g(3) = 3Let's check which of the answer choices is correct:
A. g(x)= 1/3x²g(3) = 1/3*3² = 3g(3) = 3This is correctB. g(x)= (1/3x)²
g(3) = (1/3*3)² = 1g(3) = 1 ≠ 3IncorrectC. g(x) = 1/9*x²
g(3)= 1/9*3²= 1g(3) = 1 ≠ 3IncorrectD. g(x)= 3x²
g(3)= 3*3²= 27g(3) = 27 ≠ 3IncorrectCorrect choice is A. g(x)= 1/3x²
Will give brainliest
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50 a plus 3.75 b equals 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold? ___adult tickets
Answers
Answer: The number of the adult tickets is 168
Step-by-step explanation: * Lets explain how to solve the problem
- The adults ticket costs $10.50
- The students ticket costs $3.75
- The total money of the opening night is $2071.50
- The equation of the total money earned in the opening night is:
10.50 a + 3.75 b = 2071.50, where a is the number of the adult ticket
and b is the number of the student ticket
- There were 82 students attended
* Lets solve the problem
∵ 10.50 a + 3.75 b = 2071.50
∵ The number of the students attended is 82
∵ b is the number of the students
∴ b = 82
- Substitute the value of b in the equation
∴ 10.50 a + 3.75(82) = 2071.50
∴ 10.50 a + 307.5 = 2071.50
- Subtract 307.5 from both sides
∴ 10.50 a = 1764
- Divide both sides by 10.50
∴ a = 168
∵ a is the number of the adult tickets
∴ The number of the adult tickets is 168
Give credit to ashraf 82
Answer:
The answer is 168
Step-by-step explanation:
Directions: Using the digits 0 to 9, fill in the boxes so that the chart is accurate. Use each digit only once per blue box and once per red box. Logs are base 10. Please help me out with this would really appreciate it, thanks.
Answers
Step-by-step explanation:
log 10 = 1. So if log x < 1, then x < 10. And if log x > 1, then x > 10.
The upper left number is the smallest, and can't be smaller than 1. If the exponent is 0, we can put any number in the red box.
The fractions in the upper right and lower left need to be as large as possible. The denominators will be small, and the numerators will be large.
From there, a little trial and error does the rest. The are many possible answers. I've included one.
What are all of the properties of kites? This is an inquiry comprised within the means of 'high school' 'geometry'.
Answers
[tex] \Large{ \boxed{ \rm{ \red{Refer \: to \: the \: attachment}}}}[/tex]
It is a quadrilateral in which two pairs of adjacent sides are equal in measure.➤ Like Here, AB = BC and AD = CD
The diagonals intersect at right angles. Here, OA = OC and angle A = angle CDiagonals bisect the touching angles. Like here, Diagonal BD intersects angle B and angle D.Diagonal BD divides the kite into two congurent triangles of equal area. So, these triangles can overlap each other.━━━━━━━━━━━━━━━━━━━━
3. E, F and G are collinear points. E is between F and G.
If FE = 3 in., and FG = 7 in., what is the length of EG?
a. 4
c. 3
I
b. 10
d. 21
Answers
Answer:
A. 4 inStep-by-step explanation:
Collinear points are points that lies on the same straight line. If the points E, F and G are collinear points, then the three points lies on the same straight line.
If E is between F and G, the FE+EG = FG
EG = FG - FE
Given FE = 3 in and FG = 7 in
On substituting into the expression above to get EG;
EG = 7in - 3in
EG = 4in
Hence the length of EG is 4in
QUICK IT IS FOR, NOW!!! I WILL GIVE BRAINLIESTS AND 10 POINTS
When p2 – 4p is subtracted from p2 + p – 6, the result is: -3p-6, 5p-6 or 4p+6. To get p – 9, subtract: 4p+3, 4p-15 or 4p+12 from this result.
Answers
Step-by-step explanation:
p² - 4p is subtracted from p² + p - 6 is written as
p² + p - 6 - (p² - 4p)
Remove the bracket and simplify
That's
p² + p - 6 - p² + 4p
p² - p² + 4p + p - 6
We have the answer as
5p - 6Let the unknown expression be x
Subtract x from the expression to get p - 9
That's
5p - 6 - x = p - 9
x = 5p - p - 6 + 9
x = 4p + 3
The expression is
4p + 3Hope this helps you
Find the area of the following shape. Show all work
Answers
Best way to solve this is by using
[tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex]where \: s = \frac{a + b + c}{2} [/tex]
s=(12+8+17)/2
=18.5
using the formulae
area =43.5
