Simplify the expression by first transforming the radical to exponential form. Leave the answer in exact form as a radical or a power, not as a decimal approximation.
Answers
Answer:
[tex]\textsf{Radical form}: \quad \sqrt[4]{2}\\\\\textsf{Exponent form}: \quad 2^{\frac{1}{4}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{8} \div \sqrt[4]{32}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies 8^{\frac{1}{2}} \div 32^{\frac{1}{4}}[/tex]
Rewrite 8 as 2³ and 32 as 2⁵:
[tex]\implies (2^3)^{\frac{1}{2}} \div (2^5)^{\frac{1}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 2^{\frac{3}{2}} \div 2^{\frac{5}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^b \div a^c=a^{b-c}:[/tex]
[tex]\implies 2^{\frac{3}{2}-\frac{5}{4}}[/tex]
[tex]\implies 2^{\frac{6}{4}-\frac{5}{4}}[/tex]
[tex]\implies 2^{\frac{1}{4}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies \sqrt[4]{2}[/tex]
Related Questions
If 2x+y=4 and 2x-y=8, then what does 3x-y equal?
Answers
THE TRICK IS TO FIND THE VALUE OF X AND Y FIRST.
I WILL USE SUBSTITUTION TO SOLVE THIS SYSTEM OF EQUATIONS.
[tex]y = 4 - 2x......(3)equation[/tex]
[tex]2x - (4 - 2x) = 8 \\ 2x - 4 + 2x = 8 \\ 2x + 2x = 8 + 4 \\ 4x = 12 \\ \frac{4x}{4} = \frac{12}{4} \\ x = 3[/tex]
[tex]y = 4 - 2(3) \\ y = 4 - 6 \\ y = - 2[/tex]
THEN FOR 3X-Y PLUG IN THE VALUES YOU FOUND FOR X AND Y
[tex] = 3(3) - ( - 2) \\ = 9 + 2 \\ = 11 \\ 3x - y = 11[/tex]
ATTACHED IS THE SOLUTION
The weight M of an object on the moon varies directly as its weight E on earth. A person who weighs 162.71lb on earth weighs 27.66lb on the moon. How much would a 220lb person weigh on the moon?
Answers
A 220lb person on earth would weigh 23.81lb on moon
Given
Weight of an object on moon varies same as that on the planet earth
This means the weights are directly proportional
Weight of person on earth = 162.7lb
Weight of person on moon = 27.66lb
Also,
Weight of person on earth = 220lb
We need to find weight of this person on moon.
Let weight of person on moon be x
According to the data equation can be formed as
27.66 x 220 = 162.71x
3885.2 = 162.71x
x= 23.81
Hence the weight of the person on moon is 23.lb
Learn more about weights at
https://brainly.com/question/10069252?referrer=searchResults
#SPJ1
Vă rog,Am nevoie urgent
Mulțumesc
Answers
Step-by-step explanation:
The Answer
I hope you are doing well and I don't want to be a part of this the only reason why you would want this
Consider the function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree. Is this a one-to-one function? Explain why or why not.
Answers
No, a function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree is not a one-to-one function.
What is a one-to-one function?A one-to-one function is also referred to as an injective function and it can be defined as special type of function in which every element of the range is mapped to exactly a single element of its domain. This ultimately implies that, the output values (y-values) of a one-to-one function never repeat themselves.
Additionally, a one-to-one function maps distinct elements of its domain (y-values) to distinct elements of the range (x-values) and as such, it connotes the mapping of two (2) sets.
In this context, we can reasonably and logically deduce that this function is not a one-to-one function because it fails the horizontal line test as there could be the same temperature at different times of the day.
Read more on one-to-one function here: https://brainly.com/question/24144999
#SPJ1
A toy store would like to open a new store in the city of Thousand Oaks, and they would like to know what proportion of households have kids. Out of 100 households sampled, 28 had kids. Based on this, to construct a 90% confidence interval for the true population proportion of Thousand Oaks households with kids, you need to use which one of the following calculators?
Answers
Answer: 55
Step-by-step explanation: It makes sense
URGENT HELP PLEASE SOLVE QUESTIONS FIVE AND SIX USING THE INSTRUCTIONS IN THE PIC VERY URGENT PLEASE HELP ME!!!!!!
Answers
Answer:
4.number 1
5.number 2
Step-by-step explanation:
4.Because the the expression tan can be written as sin divided by cos it will be beneficial to write the square of cos as cos multiplied by cos so that after canceling out we are left with cos multiplied by sin of the left hand side.
5.because transforming cos squared to 1-sin squared will allow us to to have a fraction where both the numerator and denominator are the same which equals one.
Determine algebraically ifthe function is even, odd, or neither.f(x)=3x-2
Answers
A function is even if
[tex]f(-x)=f(x)[/tex]A function is odd if
[tex]f(x)=-f(x)[/tex]For the given question, we will test for both even and odd conditions
Step 1: Test for an even condition
[tex]\begin{gathered} f(-x)=3(-x)-2 \\ f(-x)=-3x-2 \\ \sin ce \\ f(-x)\ne f(x) \\ it\text{ is not an even function} \end{gathered}[/tex]Step 2: Test for an odd function
[tex]undefined[/tex]will give brainlist
Which graph represents the solution to one half m is greater than or equal to negative seven elevenths?
number line with closed circle on point negative 14 over 11 and arrow shaded to the right
number line with closed circle on point negative 7 over 22 and arrow shaded to the right
number line with closed circle on point negative 14 over 11 and arrow shaded to the left
number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Answers
The solution to the inequality is m ≤ -14/11 which is the correct answer would be option (C).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
If it is "> or," the shaded arrow is drawn to the right of the inequality graph; if it is "or," it is drawn to the left.
Given the inequality, -1/2m ≥ 7/11,
Which represents the solution to one-half m is greater than or equal to negative seven elevenths
Solve for m:
⇒ -1/2m(-2) ≥ 7/11(-2)
m ≤ -14/11 [Because we are multiplying both sides by a negative value, the sign shifts]
The solution to the inequality is m ≤ -14/11 which the graph is attached below for m ≤ -14/11.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ1
Which inequality represents the compound inequality x > 3 and x < 5
Answers
Given:
x > 3 and x < 5
The inequality compound is:
[tex]3Answer: 3 < x < 5Karl earned $188 last month doing chores after school. If 68% of the money he earned was from doing yard work, about how much did Karl earn doing yard work?
Answers
188 x 68% = $127.84
Graph the line with the given slope that passes through the given point.
(a) slope:
3
4
,
point:
(1, 5)
Answers
The linear equation can be written as:
y = (3/4)*x + 17/4
And the graph can be seen at the end.
How to graph the linear equation?
A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we have the slope m = 3/4, so we get:
y = (3/4)*x + b
And the line passes through (1, 5), replacing these values in the equation we get:
5 = (3/4)*1 + b
5 - 3/4 = b
20/4 - 3/4 = b
17/4 = b
So the linear equation is:
y = (3/4)*x + 17/4
To graph the line we need other point, if we use x = 0 we get:
y = (3/4)*0 + 17/4 = 17/4
Then we have the points (1, 5) and (0, 17/4).
To graph the line, we just need to find these two points and connect them with a line, the graph can be seen below.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Evaluate without a calculator.[tex] log_{4}(16) + log_{3}(27) [/tex]please show your work..!
Answers
Answer:
The value of the given expression is;
[tex]5[/tex]Explanation:
Given the logarithmic expression;
[tex]\log _416+\log _327[/tex]To solve, Recall the rules of logarithm;
[tex]\begin{gathered} \log _ax^y=y\times\log _ax\text{ ------1} \\ \log _aa=1\text{ -------2} \end{gathered}[/tex]Apply the above rules;
[tex]\begin{gathered} \log _416+\log _327 \\ \log _44^2+\log _33^3 \\ \text{Applying rule 1;} \\ 2\log _44+3\log _33 \end{gathered}[/tex]Aplplying rule 2;
[tex]\begin{gathered} 2\log _44+3\log _33 \\ =2(1)+3(1) \\ =2+3 \\ =5 \\ \log _416+\log _327=5 \end{gathered}[/tex][tex]\begin{gathered} \text{Note that from the rule 2;} \\ \log _aa=1 \\ so\text{ when a logarithm has the same number as the base it will equal to 1;} \\ \text{for example;} \\ \log _44=1 \\ \log _33=1 \\ \log _55=1 \end{gathered}[/tex]Therefore, the value of the given expression is;
[tex]5[/tex]A wealthy businessman invests $10,000 and expects a 6.75% rate of return annually. How many years will it take the investment to reach $15,000 in value?Round your answer to the nearest number of years.
Answers
Answer
7 years
Explanation
Given:
Principal, P = $10,000
Rate, R = 6.75%
Amount, A = $15,000
What to find:
The years will it take the investment to reach $15,000 in value.
Step-by-step solution:
You need to first calculate the total interest on the investment using;
Interest, I = Amount, A - Principal, P
Interest, I = $15,000 - $10,000
Interest, I = $5,000
The final step is to find the years it takes the investment to reach $15,000 in value using simple interest formula.
[tex]\begin{gathered} S.I=\frac{T\times P\times R}{100} \\ \\ \Rightarrow T=\frac{S.I\times100}{P\times R} \end{gathered}[/tex]Putting the values of the parameters into the formula, we have;
[tex]\begin{gathered} T=\frac{5000\times100}{10000\times6.75}=\frac{500,000}{67,500}=7.407\text{ }years \\ \\ To\text{ }the\text{ }nearest\text{ }number\text{ }of\text{ }years, \\ \\ T=7\text{ }years \end{gathered}[/tex]Therefore, it will take 7 years for the investment to reach $15,000 in value.
can someone please help me with this angle puzzle?!
Answers
Answer:
See below
Step-by-step explanation:
If I did the math numbers correctly : ( a = 51° too)
Factor this polynomial. The image is attached here. Need help!
Answers
Answer:
[tex]4x^2+11xy-3y^2=(x+3y)(4x-y)[/tex]Step-by-step explanation:
To factor the following polynomial, break the expression into groups:
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings. Just find families easier-to-factor groups that we can better approach the problem.
[tex]\begin{gathered} 4x^2+11xy-3y^2 \\ (4x^2-xy)+(12xy-3y^2) \end{gathered}[/tex]Then, factor it using factor by grouping:
[tex]\begin{gathered} x(4x-y)+3y(4x-y) \\ \text{ Since the two terms have (4x-y) as a common factor:} \\ (x+3y)(4x-y) \end{gathered}[/tex]15. Which of the following is true about the relationship in the table shown? Х 7 11 20 25 100 8.4 13.2 24 30 120 A. The table is non-proportional because it does not include the point (0,0). B. The table is non-proportional because the x-values do not increase at a constant interval. C. The table is proportional because all of the x and y-values are positive and increasing, D. The table is proportional because the ratio between y and x is constant.
Answers
Explanation:
To determine if the table is proportional or not, we need to find the ratio between x and y for each of the data. if it is constant, then it is proportional
Proportional relationship:
y = kx
k = constant of proportionality
k = y/x
for the x = 7, y = 8.4
k = 8.4/7 = 1.2
for x = 11, y = 13.2
k = 13.2/11 = 1.2
for x = 20, y = 24
k = 24/20 = 1.2
for x = 25, y = 30
k = 30/25
k = 1.2
when x = 100, y = 120
k = 120/100
k = 1.2
Since the ratio between y and x is the same for all, the table is proportional
The correct option:
The
Find the area of the figure.
Answers
Based on the given figure, the area of the figure can be found to be 126.50 cm²
How to find the area?The figure given is a mix of a triangle and a rectangle. The area of the figure can then be found by finding the area of the triangle and the rectangle individually, and then summing them up.
The area of a rectangle is:
= Length x Width
= 8 x 11
= 88 cm²
The area of the triangle is:
= 1/2 x base x height
= 1/2 x 11 x 7
= 38.5 cm²
The area of the figure is:
= 88 + 38.5
= 126.50 cm²
Find out more on area at https://brainly.com/question/25292087
#SPJ1
Question 94 ptsONLY write your answer as a number. You do not needto write the unit measurement.Round you answer to the nearest tenth.15. A fireman leaned a 42-foot ladder against a building. If he placed the ladder 8.5 feetfrom the base of the building, what angle is formed between the ladder and the ground
Answers
The length of ladder is L = 42 foot.
The distance between base of building and ladder is b = 8.5.
Determine the measure of angle by using the trigonometry.
[tex]\begin{gathered} \cos \theta=\frac{8.5}{42} \\ \theta=\cos ^{-1}(0.20238) \\ =78.323 \\ \approx78.3 \end{gathered}[/tex]So measure of angle is 78.3 degree.
Sarah got a $60 gift card to Walmart. She uses the gift card to buy orange juice for $4.50. She also wants to use the gift card to buy shirts. Each shirt costs $2.29. Write an inequality to describe this situation, where n is the number of shirts Sarah wants to buy?Please answer quick, will give 18 points
Answers
ANSWER
[tex]4.50+2.29n\le60[/tex]EXPLANATION
We have that Sarah got a $60 gift card to use in Walmart.
This means that everything she can buy cannot be worth more than $60 (i.e. less than or equal to $60).
She buys orange juice for $4.50 and she wants to buy shirts (which cost $2.29 each)
Let n be the number of shirts Sarah wants to buy.
This means that the cost of n shirts is $2.29n.
Recall that she can only spend less than or equal to $60. This means that the sum of the cost of the orange juice and n shirts is less than or equal to $60.
That is:
[tex]4.50+2.29n\le60[/tex]That is the inequality that represents the situation.
Question A maritime flag is shown. What is the area of the shaded part of the flag
Answers
Answer:
There is no picture.
Step-by-step explanation:
If you ask a question, be mindful that people cannot read each other minds.
What is the actual distance between these two cities in kilometers?
Answers
1) Whenever we have problems that deal with the real distance and distance on the map, we can write out the following formula:
[tex]\begin{gathered} Scale=\frac{distance\: on\: the \: map}{real\: distance} \\ S=\frac{3.5}{R} \end{gathered}[/tex]So, let's call the Real distance "R". Note that in this question, 1 centimeter represents 20 kilometers
2) So, in order to plug that as the scale we need to convert kilometers to centimeters:
[tex]\begin{gathered} 1km--100000cm \\ 20km---x \\ x=2000000cm \end{gathered}[/tex]3) Finally, we can plug that into the formula and cross multiply the ratios this way:
[tex]\begin{gathered} \frac{3.5}{r}=\frac{1}{2000000} \\ r=2000000\times3.5 \\ r=7000000cm \end{gathered}[/tex]Converting it back to kilometers we can write:
[tex]\frac{7000000}{100000}=70km[/tex]Quadrilateral ABCD has coordinated a(-4,3) b(-3,6) c(0,8) d(-2,5). Prove that quadrilateral ABCD is a parallelogram and explain whether quadrilateral ABCD is a rectangle or not.
Answers
Quadrilateral ABCD has coordinate
A(-4, 3) , B(-3, 6) C(0,8) & D(-2,5)
so we will find the length of the sides
[tex]AB=\sqrt[]{(6-3)^2+(-3-(-4))}^2=\sqrt[]{9+1}=\sqrt[]{10}[/tex]for CD
[tex]CD=\sqrt[]{(5-8)^2+(-2-0)^2}=\sqrt[]{9+4}=\sqrt[]{13}[/tex]as we can see AB and CD is not equal to Quadrilateral is not equal.
now we compute the midpoint of the diagonals
midpoint of
[tex](x,y)=(\frac{-4-3}{2},\frac{3+6}{2})=(-\frac{7}{2},\frac{9}{2})[/tex]The measure of the angle 6 = _____
Answers
I need help with please!!!
Answers
or each ordered pair, determine whety=5x-315x-3y=9(2,7)(-1,– 8)(3,4)(0,-9)
Answers
Question 2 (4 points)y = x|d: {-8, -3, 4,7} {Blank 1:Blank 2:Blank 3:Blank 4
Answers
r: {8, 3, 4, 7}
Explanation:
y = |x|
domain = -8, -3, 4, 7
domain are the x values or input
r = range
Range are the y values or output
when x = -8
y = |-8| = 8
when x = -3
y = |-3| = 3
when x = 4
y = |4| = 4
when x = 7
y = |7| = 7
r: {8, 3, 4, 7}
blank 1 = 8
blank 2 = 3
blank 3 = 4
blank 4 = 7
Four friends use a spinner to decide the luckiest person. Who is more likely to be the luckiest person?
Answers
The luckiest person is Clinton because it is more likely.
Answer: Clinton
Write your answer as a fraction or as a whole or mixed number 3 7/10 * 4 5/6
Answers
Answer:
17 53/60
Step-by-step explanation:
The table below shows the number of house calls three different plumbers made on three different days.
Number of House Calls
Plumber A
Plumber B
Plumber C
Monday
2
8
8
Tuesday
4
7
10
Wednesday
3
9
9
The total amount of money earned by all three plumbers on Monday was $1,400. On Tuesday they earned a total of $1,660, and on Wednesday, they earned a total of $1,650. On Thursday, Plumber A made four house calls, Plumber B made six house calls, and Plumber C made three house calls. How much total money is earned on Thursday?
$250
$1,060
$1,090
$1,130
Answers
The total money that is earned on Thursday is $1090
How to determine the total money that is earned on Thursday?From the question, we have the following table of values
Monday Tuesday Wednesday
Plumber A 2 8 8
Plumber B 4 7 10
Plumber C 3 9 9
Using the given parameters in the question, we have the following system of equations
2a + 8b + 8c = 1400 --- (1)
4a + 7b + 10c = 1660--- (2)
3a + 9b + 9c = 1650 --- (3)
Subtract equation (2) from twice equation (1)
So, we have
(4a + 16b + 16c = 2,800) - (4a + 7b + 10c = 1,660)
This gives
9b + 6c = 1140 --- (4)
Subtract four times equation (3) from three times equation (2)
So, we have
12a+ 21b +30c = 4,980 -(12a + 36B + 36c = 6,600)
This gives
-15b - 6c = -1,620 --- (5)
Add equations (4) and (5)
(9b + 6c = 1140) + (-15b - 6c = -1620)
So, we have
-6B = -480
Divide by -6
b = 80
Substitute b = 80 in -15b - 6c = -1,620
-15 x 80 - 6c = -1,620
Evaluate
-1200 - 6c = -1,620
So, we have
-6c = -420
Divide
c = 70
In (2), we have
4a + 7b + 10c = 1660
This gives
4a + 7 * 80 + 10 * 70 = 1660
Evaluate
4a = 400
Divide
a = 100
On Thursday, we have
a = 4, b = 6 and c = 3
So, we have
Total = 4 * 100 + 6*80 + 3*70
Evaluate
Total = 1090
Hence, the total earnings is 1090
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
Which is true about investments and risk?
Answers
Answer:
Every investment carries some degree of risk, All investments carry some degree of risk. Stocks, bonds, mutual funds, and exchange-traded funds can lose value, even all their value, if market conditions sour. Even conservative, insured investments, such as certificates of deposit (CDs) issued by a bank or credit union, come with inflation risk. They may not earn enough over time to keep pace with the increasing cost of living.
Step-by-step explanation: