Rewrite the expression with a rational exponent as a radical expression.
(4^2/5)^1/4
a.)^10sqrt4
b.)^4sqrt4
c.)^5sqrt4^2
d.)sqrt4^10
sqrt=square root
Answers
Answer:
First option is correct.
[tex]\sqrt[10]{4}[/tex]
Step-by-step explanation:
Given:
The given expression is [tex](4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]
We write the given expression with a rational exponent as a radical expression such as.
[tex]=(4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]
Simplify the above equation by multiplication of powers.
[tex]=(4^{\frac{2}{5}\times \frac{1}{4}})[/tex]
[tex]=(4^{\frac{1}{5}\times \frac{1}{2}})[/tex]
[tex]=(4^{\frac{1}{5\times 2}})[/tex]
[tex]=(4^{\frac{1}{10}})[/tex]
[tex]=\sqrt[10]{4}[/tex]
Therefore, The answer is [tex]=\sqrt[10]{4}[/tex].
Related Questions
I need help trying to find out what is 73% of 83?
Answers
Answer:
60.59
Step-by-step explanation:
73%=0.73
0.73*83=60.59
60.59 is the number you're looking for.
Hope this helps, if not, comment below please!!!!
What is the equation of the line that passes through the point (-1, -3) and has a slope of -5?
answers y = -5x -16
y = -5x -8
y = -5x +8
y = -5x + 16
Answers
Answer:
y = -5x -8
Explanation:
Find b in equation y = mx + b
Insert numbers to find b
-3 = -5· -1 + b
Step 1: Simplify both sides of the equation.
−3=(−5)(−1)+b
−3=5+b
−3=b+5
Step 2: Flip the equation.
b+5=−3
Step 3: Subtract 5 from both sides.
b+5−5=−3−5
b=−8
Insert into equation
y = -5x - 8
Let’s start by writing out the model equation for slope-intercept
y=mx+b
M: Slope
X: Variable
B: Y-intercept
Now we know that m is slope. Let’s fill in the slope provided to us, which is -5
y=mx+b
y=-5x+b
Now let’s solve for b. We’ll do this by taking the point given to us and substituting it into the equation and solving.
y=-5x+b
*substitute the y and x of the point*
-3=-5(-1)+b
*multiply -5 and -1*
-3=5+b
*subtract 5 on both sides*
-8=b
Now you know b! Let’s put this into our equation
y=mx+b
y=-5x+b
y=-5x-8
This is your answer! Hope this helps comment below for more questions :)
What equation represents the proportional relationship displayed in the table? x=2,4,6,8 y=10,20,30,40 Enter your answer in the box to complete the equation. y = ? x
Answers
The answer is y = 5x.
⭐ Please consider brainliest! ⭐
✉️ If any further questions, inbox me! ✉️
Answer:
y=5x
Step-by-step explanation:
I did the test
The 3rd term of a geometric sequence is -2 and the 7th is -32. Find the common ratio,the first term, the explicit formula, and the 10th term.
Answers
Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Both a and r have to be found
Given a₃ = - 2, then
ar² = - 2 → (1)
Given a₇ = - 32, then
a[tex]r^{6}[/tex] = - 32 → (2)
Divide (2) by (1)
[tex]\frac{ar^6}{ar^2}[/tex] = [tex]\frac{-32}{-2}[/tex], that is
[tex]r^{4}[/tex] = 16 ( take the fourth root of both sides )
r = 2 ← common ratio
Substitute r = 2 into (1)
a × 2² = - 2, that is
4a = - 2 ( divide both sides by 4 )
a = - [tex]\frac{1}{2}[/tex] ← first term
Hence
[tex]a_{n}[/tex] = - [tex]\frac{1}{2}[/tex][tex](2)^{n-1}[/tex] ← explicit formula
and
[tex]a_{10}[/tex] = - [tex]\frac{1}{2}[/tex] × [tex]2^{9}[/tex] = - 0.5 × 512 = - 256
The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. [-5, 5] by [-5, 5]
a. r = 2 - 2 sin θ
b. r = 3 - 2 sin θ
c. r = 2 + 2 sin θ
d. r = 1 - 3 sin θ
Answers
Answer:
A
Step-by-step explanation:
A limacon curve passes trough the point [tex]\left(\dfrac{\pi}{2},0\right)[/tex], this means when [tex]\theta =\dfrac{\pi}{2},[/tex] the distance [tex]r=0.[/tex]
Note that
[tex]\sin \dfrac{\pi}{2} =1,[/tex]
so, if [tex]r=a+b\sin \theta,[/tex]
then
[tex]r\left(\dfrac{\pi}{2}\right)=a+b=0\\ \\a=-b[/tex]
The only option which shows a = -b is option A.
Answer:
b
Step-by-step explanation:
Simplify each expression, and then arrange them in increasing order based on the coefficient of n2. -5(n3 – n2 – 1) + n(n2 – n) (n2 – 1)(n + 2) – n2(n – 3) n2(n – 4) + 5n3 – 6 2n(n2 – 2n – 1) + 3n2
Answers
To simplify the expressions and arrange them based on the coefficient of n², combine like terms and perform necessary operations. The expressions, in increasing order, are: 3n + 2, 2n³ - n² + 2n, -5n³ + 6n² - n + 5, and 6n³ - n² + n - 6.
Explanation:To simplify each expression and arrange them in increasing order based on the coefficient of n², we need to combine like terms and perform any necessary operations. Let's go through each expression:
-5(n³ – n² – 1) + n(n² – n) = -5n³ + 6n² - n + 5(n² – 1)(n + 2) – n²(n – 3) = 3n + 2n²(n – 4) + 5n³ – 6 = 6n³ - n² + n - 62n(n² – 2n – 1) + 3n² = 2n³ - 4n² + 2n + 3n² = 2n³ - n² + 2nArranging them in increasing order based on the coefficient of n², we have:
3n + 22n³ - n² + 2n-5n³ + 6n² - n + 56n³ - n² + n - 6Learn more about Simplifying Expressions here:https://brainly.com/question/29003427
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o find the minimum value of the quadratic expression −4x2+8x−25,
−
4
x
2
+
8
x
−
25
,
Marla used the following steps to complete the square:
Step 1: −4(x2+8x)−25
−
4
(
x
2
+
8
x
)
−
25
Step 2: −4(x2+8x+16−16)−25
−
4
(
x
2
+
8
x
+
16
−
16
)
−
25
Step 3: −4(x2+8x+16)+64−25
−
4
(
x
2
+
8
x
+
16
)
+
64
−
25
Step 4: −4(x+4)2+39
−
4
(
x
+
4
)
2
+
39
Did Marla use the correct steps to complete the square?
Answers
Answer:
Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x
Step-by-step explanation:
we have
[tex]-4x^{2}+8x-25[/tex]
This is a vertical parabola open downward
The vertex is a maximum
Find the vertex
step 1
Factor the leading coefficient -4
[tex]-4(x^{2}-2x)-25[/tex]
step 2
Complete the square
[tex]-4(x^{2}-2x+1-1)-25[/tex]
step 3
[tex]-4(x^{2}-2x+1)-25+4[/tex]
[tex]-4(x^{2}-2x+1)-21[/tex]
step 4
Rewrite as perfect squares
[tex]-4(x-1)^{2}-21[/tex]
the vertex is the point (1,-21)
so
The maximum value of the quadratic equation is (1,-21)
therefore
Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x
Marla correctly completed the square for the expression −4x2+8x−25, arriving at the simplified form −4(x+4)2 + 39 to find the minimum value.
Explanation:To find the minimum value of the quadratic expression −4x2+8x−25, Marla completed the square. Her steps are as follows:
Factor out the coefficient of x2: −4(x2+∼2x−∼) -25Add and subtract (b/2a)2 inside the parentheses: −4(x2+8x+16−16) −25Combine the added 16 with the −4 outside and subtract from −25: −4(x2+8x+16) + 64 −25Factor the perfect square trinomial and simplify: −4(x+4)2 + 39
Marla used the correct steps to complete the square, which simplifies to −4(x+4)2 + 39.
[tex] {x}^{2} - 1 < 18[/tex]
Answers
[tex]
x^2-1 < 18 \\
x^2 < 19 \\
x < \sqrt{19}
[/tex]
Hope this helps.
How do you graph 4x+2y=10
Answers
Step-by-step explanation:
2x+y = 5 (divided by 2)
If x= 0, y=5
If x= 1, y=3
If x=-1, y=7
So, coordinate points are (0,5),(1,3),(1,7) and so on.
Continue above explanation.
After , draw a graph on x,y axis .
Answer: I used a graphing calculator.
Step-by-step explanation:
I need help on this problem
Answers
Answer: [tex]QR=4.04[/tex]
Step-by-step explanation:
For this exercise you must use the followinG Trigonometric Identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
In this case, given the right triangle PQR, you can identify that:
[tex]\alpha=60\°\\opposite=PR=7.0\\adjacent=QR[/tex]
Then, the next step is to substitute those values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]:
[tex]tan(60\°)=\frac{7.0}{QR}[/tex]
And the final step is to solve for "QR" in order to find its value.
So you get that this is:
[tex](QR)(tan(60\°))=7.0\\\\QR=\frac{7.0}{tan(60\°)}\\\\QR=4.04[/tex]
A survey of all beings on planet Tott found that 12 beings preferred
hab juice to all other juices. If 40 beings were surveyed altogether,
what percent of them preferred hab juice?
(step by step)
Answers
Answer:
30% of them preferred hab juice.
Step-by-step explanation:
Given:
A survey of all beings on planet Tott found that 12 beings preferred hab juice to all other juices.
40 beings were surveyed altogether.
Now, to find percent of them preferred hab juice.
Total beings surveyed = 40.
Number of beings preferred hab juice = 12.
So, to get the percent:
[tex]\frac{Total\ beings\ surveyed}{Number\ of\ beings\ preferred\ hab\ juice} \times 100.[/tex]
[tex]=\frac{12}{40} \times 100[/tex]
[tex]=0.3\times 100[/tex]
[tex]=30\%.[/tex]
Therefore, 30% of them preferred hab juice.
plz help in the attachment below
Answers
Answer:
M(t) = 741·(1/2)^(t/5730)
Step-by-step explanation:
One way to write an exponential function is this:
value at time t = (initial value) · (multiplier over period)^(t/period)
Here, the initial value is given as 741 grams, and the time period is 5730 years. The multiplier over that period is 1/2, since half of the quantity remains after that time. The problem statement tells us that "value at time t" is M(t), so we have ...
M(t) = 741·(1/2)^(t/5730) . . . . . t in years; M(t) in grams
Find the number, if d 12/13 of it is 24
Answers
Answer:
26 is the number
Step-by-step explanation:
12/13 x = 24
Multiply by 13 on both sides
12x = 24 * 13
12x = 312
Simplify
x = 26
26
Hope this helps :)
The area of a square is 144 square centimeters. Find the length of the diagonal. Write your answer in simplest radical form.
Answers
Answer:
[tex]12\sqrt{2}\ cm[/tex]
Step-by-step explanation:
step 1
Find the length side of the square
we know that
The area of a square is equal to
[tex]A=b^{2}[/tex]
where
b is the length side
we have
[tex]A=144\ cm^2[/tex]
substitute in the formula of area
[tex]144=b^{2}[/tex]
solve for b
square root both sides
[tex]b=12\ cm[/tex]
step 2
Find the length of the diagonal
Applying the Pythagorean Theorem
[tex]d^2=b^2+b^2[/tex]
see the attached figure to better understand the problem
substitute the given values
[tex]d^2=12^2+12^2[/tex]
[tex]d^2=288[/tex]
square root both sides
[tex]d=\sqrt{288}\ cm[/tex]
simplify
[tex]d=12\sqrt{2}\ cm[/tex]
Write an linear equation that passes through (5,2) and (6,4)
Answers
Answer:
2x-y=8
Step-by-step explanation:
(6,4)-(5,2)=(1,2)
L: 2x-y=k
(5,2) -> L, k=8
2x-y=8
Find the value of X and y?
Answers
Answer:
y = 12 ; x = 14
Step-by-step explanation:
2x + 7 =3x - 7 { corresponding angles}
7 + 7 = 3x - 2x
14 = x
x = 14
12y + 1 + 3x - 7 = 180 {co interior angles}
12y + 1 + 3 * 14 - 7 = 180
12y + 1 + 42 - 7 = 180
12y + 36 = 180
12y = 180 - 36
12y = 144
y = 12
What is the equation of the line that passes through the point
(
−
6
,
−
6
)
(−6,−6) and has a slope of
2
3
3
2
?
Answers
Answer:
y+6=2(x+6)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-6)=2(x-(-6))
y+6=2(x+6)
How do you graph x-y-3=0
Answers
Answer:
see explanation
Step-by-step explanation:
To graph the line, we require 2 points
Find the intercepts, that is where the graph crosses the x and y axes
To find the x- intercept let y = 0 in the equation and solve for x
x - 3 = 0 ( add 3 to both sides )
x = 3 ⇒ (3, 0 ) ← x- intercept
To find the y- intercept let x = 0 in the equation and solve for y
- y - 3 = 0 ( add 3 to both sides )
- y = 3 ( multiply both sides by - 1 )
y = - 3 ⇒ (0, - 3 ) ← y- intercept
Plot the points (3, 0) and (0, - 3) and draw a straight line through them
Mickey buys 5 lemons and 3 limes for 3.70.Minnie buys 15 lemons and 4 limes for 7.85. How much does one lime cost?
Answers
Answer:
The cost of one lime is $0.65
Step-by-step explanation:
Let
x ---> the cost of one lemon
y ---> the cost of one lime
we know that
Mickey
[tex]5x+3y=3.70[/tex] ----> equation A
Minnie
[tex]15x+4y=7.85[/tex] ---> equation B
Solve the system by elimination
Multiply by -3 both sides equation A
[tex]-3(5x+3y)=-3(3.70)[/tex]
[tex]-15x-9y=-11.10[/tex] ----> equation C
Adds equation C and equation B
[tex]-15x-9y=-11.10\\15x+4y=7.85\\--------\\-9y+4y=-11.10+7.85\\-5y=-3.25\\y=0.65[/tex]
therefore
The cost of one lime is $0.65
A credit card issuer charges an APR of 19.66%, and its billing cycle is 30 days
long. What is its periodic interest rate?
O
A. 21.72%
OB. 1.62%
O C. 21.53%
O D. 1.22%
SUBMIT
Answers
Answer:
The periodic interest rate is 1.62 %
Step-by-step explanation:
Given:
Annual percentage rate = 19.66%
Time period = 30 days
To Find:
Periodic interest rate =?
Solution:
The periodic interest rate r is calculated using the following formula:
r = (1 + \frac{i}{m})^{\frac{m}{n}} - 1
Where,
i = nominal annual rate
n = number of payments per year i.e., 12 for monthly payment, 1 for yearly payment and so on.
m = number of compounding periods per year
The period interest rate per payment is integral to the calculation of annuity instruments including loans and investments.
Now substituting the values we get
[tex]r = (1 + \frac{19.66}{12})^{\frac{12}{12}} - 1[/tex]
[tex]r = (1 + \frac{19.66}{12})^1 - 1[/tex]
r = (1 +1.638 ) - 1
r = (2.638 ) - 1
r = 1.638 %
What is a reasonable distance between two cities? A. 200 km B. 200 m C. 200 cm D. 200 mm
Answers
Answer:
A would be best
Step-by-step explanation:
200 km is roughly 124.2 miles
200 m is about 0.12 miles
200 cm and 200 mm is way too small to be distances between cities because 200 cm is like 78.7 inches
200 mm is like 7.8 inches
124.2 miles or 200 km would be a reasonable distances between two cities.
Answer:
A. 200km is your answer
Step-by-step explanation:
Dave's sister baked $3$ dozen pies of which a third contained chocolate, a quarter contained marshmallows, a sixth contained cayenne, and one twelfth contained salted soy nuts. What is the smallest possible number of pies that had none of these ingredients?
Answers
Step-by-step explanation:
As Dave's sister baked 3 dozen pies.
So, total number of pies = 3 × 12 = 36
Number of pies = 3×12 = 36
Pies which contained chocolate = 1/3×36 = 12
Pies which contained marshmallows = 1/4×36 = 9
Pies which contained cayenne = 1/6×36 = 6
Pies contained soy nut = 1/12×36 = 3
So,
Pies that had none of these ingredients = 36 - (12+9+6+3)
= 36 - 30
= 6 pies
So, total 6 pieces are left that had none of these ingredients.
i.e. 1, 2, 3, 4, 5, 6
Therefore,
The largest possible number of pies that had none of thees ingredients = 6 piecesThe smallest possible number of pies that had none of thees ingredients = 1 pieceKeywords: smallest possible number
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She baked 36 pies. Of these
1/3*36=12 contained chocolate
1/4*36=9 contained marshmallows
1/636=6 contained cayenne
1/12*36=3 contained salted soy nuts.
In order to make the number of pies with none of these ingredients as small as possible, Dave's sister should put all of these ingredients in different pies so that only one of the ingredients is in any pie. If she does this, then 12+9+6+3=30 of the pies will have one of these ingredients. The other 6 pies will have none of these ingredients. At least 6 pies have none of these ingredients.
-Alcumus AoPS Staff
Brainliest would be great!!!
HELP
Find the area of the semicircle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answers
Area of complete circle with radius of 2 is about 12.56
Divided by 2 is 6.28
The area of the semicircle if the radius is 2 in terms of π is 2π.
What is the area of the semicircle?Area of a circle = πr²
Where,
r = radius
A semicircle is half of a circle.
So,
Area of a semicircle = ½πr²
If r = 2
Area of a semicircle = ½ × π × 2²
= ½ × Π × 4
= 4/2π
= 2π
Hence, the area of the semicircle is 2π.
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Round 0.566 to the nearest tenth
Answers
Answer:
0.06
Step-by-step explanation:
If you round 0.566 to the nearest tenth it would be 0.06
pls rate and thank me
Answer:
To round 0.566 to the nearest tenth consider the hundredths' value of 0.566, which is 6 and equal or more than 5. Therefore, the tenths value of 0.566 increases by 1 to 6.
=0.6
Step-by-step explanation:
comment how this helps
Your second mortgage of $31,200 is at a rate of 10.7% compounded quarterly for 8 years. What total will you have paid for your second mortgage after 8 years?
Answers
Answer:
The Amount paid after 8 years is $72611.76
Step-by-step explanation:
Given as :
The principal mortgage = p = $31,200
The rate of interest = r = 10.7% compounded quarterly
The time period of mortgage = t = 8 years
Let The Amount paid after 8 years = $A
Now, According to question
From Compounded Interest method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{4\times 100})^{\textrm 4\times time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{4\times 100})^{\textrm 4\times t}[/tex]
Or, A = $31,200 × [tex](1+\dfrac{\textrm 10.7}{4\times 100})^{\textrm 4\times 8}[/tex]
Or, A = $31,200 × [tex](1.02675)^{32}[/tex]
Or, A = $31,200 × 2.3273
∴ A = $72611.76
So, The Amount paid after 8 years = A = $72611.76
Hence, The Amount paid after 8 years is $72611.76 Answer
Madison’s monthly salary is $1348. If her budget for rent is 32% of salary, then how much is budgeted for rent?
Answers
Answer:
$431.36 is budgeted for rent.
Step-by-step explanation:
Given:
Madison’s monthly salary is $1348.
Her budget for rent is 32% of salary.
Now, to find the amount budgeted for rent.
So, salary = $1348.
And, budget for rent = 32% of $1348.
Thus, the budgeted for rent is:
[tex]32\%\ of\ \$1348.[/tex]
[tex]=\frac{32}{100} \times 1348[/tex]
[tex]=0.32\times 1348[/tex]
[tex]=\$431.36.[/tex]
Therefore, $431.36 is budgeted for rent.
there are 13 items in a bakers dozen. If Natalie orders 9 bakers dozen of muffins, how many muffins did Matslie order?
Answers
Natalie ordered a total of 117 muffins.
Explanation:A bakers dozen is equal to 13 items. If Natalie orders 9 bakers dozen of muffins, we can calculate the total number of muffins by multiplying 13 by 9.
Number of muffins = 13 * 9 = 117
Therefore, Natalie ordered 117 muffins.
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Ron and Hermione are lifting feathers into the air with magic. Hermione can lift a feather 3,525
centimeters (cm) into the air. That is 5 times as high as Ron can lift a feather.
How high can Ron lift a feather with his magic?
Answers
Answer:705 cm
Step-by-step explanation:
3525 divided by 5
=705
Ron’s feather flew 705 cm
Ron’s feather flew 705 cm with his magic.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Hermione can lift a feather 3,525 centimeters (cm) into the air. 5 times as high as Ron can lift a feather.
So
We have to 3525 divided by 5;
3525 / 5
=705
Hence, Ron’s feather flew 705 cm with his magic.
Learn more about the unitary method;
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[tex](1 \times 10^{5)(6 \times {10}{4} [/tex]
Answers
Note that [tex]10^a\cdot10^b=10^{a+b}[/tex] or more general form, [tex]a^b\cdot a^c=a^{b+c}[/tex].
[tex]10^5\cdot6\cdot10^4=\boxed{6\cdot10^9}[/tex]
Hope this helps.
ILL GIVE BRAINLEST AND EXTRA POINTS
Answers
Answer:
it's (-3,9 i hope in prey so
Step-by-step explanation:
Answer:
(- 2, - 5 )
Step-by-step explanation:
Note that y = 1 is a horizontal line passing through all points with a y- coordinate of 1
The point (- 2, 7 ) is 6 units above y = 1 (7 - 1 = 6 ), thus
The reflection is 6 units below y = 1, (1 - 6 = - 5 ), hence
P(- 2, 7 ) → P'(- 2, - 5 )