The square root of m^6 is always positive.
The square root of m^6 can be calculated by dividing the exponent 6 by 2, since taking the square root is equivalent to raising a number to the power of 1/2.
In this case, m^6 divided by 2 gives us m^3.
Thus, the square root of m^6 is m^3.
This means that if we square m^3, the result will be m^6.
It is important to understand that the square root operation yields the positive root, so the square root of m^6 is always positive.
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(-14)+x=14[/tex] what is the answer
The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.
To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:
Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.
(-14) + x + 14 = 14 + 14
x = 28
The solution to the equation (-14) + x = 14 is x = 28.
In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.
Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:
(-14) + 28 = 14
14 = 14
The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.
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Find the indefinite integral. (Use C for the constant of integration.)
1. v + 1/
(2v − 20)^5dv
2. x^2/
x − 5 dx
3. x cos 8x2 dx
4. 176/e^−x + 1 dx
5.
1. The indefinite integral of (v + 1) / (2v - 20)^5 dv is -1 / (8(2v - 20)^4) + C.
2. The indefinite integral of x^2 / (x - 5) dx is (1/2) x^2 + 5x + 25 ln|x - 5| + C.
3. The indefinite integral of x cos(8x^2) dx is (1/16) sin(8x^2) + C.
4. The indefinite integral of 176 / e^(-x) + 1 dx is 176 ln|1 + e^x| + C.
1. To find the indefinite integral of (v + 1) / (2v - 20)^5 dv:
Let u = 2v - 20. Then du = 2 dv.
The integral becomes:
(1/2) ∫ (1/u^5) du
Now we can integrate using the power rule:
(1/2) ∫ u^(-5) du
Applying the power rule, we get:
(1/2) * (u^(-4) / -4) + C
= -1 / (8u^4) + C
Substituting back u = 2v - 20:
= -1 / (8(2v - 20)^4) + C
Therefore, the indefinite integral of (v + 1) / (2v - 20)^5 dv is -1 / (8(2v - 20)^4) + C.
2. To find the indefinite integral of x^2 / (x - 5) dx:
We can use polynomial long division to simplify the integrand:
x^2 / (x - 5) = x + 5 + 25 / (x - 5)
Now we can integrate each term separately:
∫ x dx + ∫ (5 dx) + ∫ (25 / (x - 5) dx)
Using the power rule, we get:
(1/2) x^2 + 5x + 25 ln|x - 5| + C
Therefore, the indefinite integral of x^2 / (x - 5) dx is (1/2) x^2 + 5x + 25 ln|x - 5| + C.
3. To find the indefinite integral of x cos(8x^2) dx:
We can use the substitution method. Let u = 8x^2, then du = 16x dx.
The integral becomes:
(1/16) ∫ cos(u) du
Integrating cos(u), we get:
(1/16) sin(u) + C
Substituting back u = 8x^2:
(1/16) sin(8x^2) + C
Therefore, the indefinite integral of x cos(8x^2) dx is (1/16) sin(8x^2) + C.
4. To find the indefinite integral of 176 / e^(-x) + 1 dx:
We can simplify the integrand by multiplying the numerator and denominator by e^x:
176 / e^(-x) + 1 = 176e^x / 1 + e^x
Now we can integrate:
∫ (176e^x / 1 + e^x) dx
Using u-substitution, let u = 1 + e^x, then du = e^x dx:
∫ (176 du / u)
Integrating 176/u, we get:
176 ln|u| + C
Substituting back u = 1 + e^x:
176 ln|1 + e^x| + C
Therefore, the indefinite integral of 176 / e^(-x) + 1 dx is 176 ln|1 + e^x| + C.
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9497 ÷ 16 _R_ please
Please awnser asap i
Will brainlist
The row operation on the matrix [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
How to perform the row operation on the matrixFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
The row operation is given as
1/2R₁
This means that we divide the entries on the first row by 2
Using the above as a guide, we have the following:
[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
Hence, the row operation on the matrix is [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
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What is the radius of a circle that has a circumference of 68 cm
Step-by-step explanation:
The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.
In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):
68 = 2πr
To find the radius, we can divide both sides of the equation by 2π:
r = 68 / (2π)
Using an approximate value of π ≈ 3.14159, we can calculate the radius:
r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm
Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.
Therefore, The Radius of the Circle is 10.8 cm.
(08.01 MC)
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table
x h(x)
-6 12
-57
-4 4
-3 3
-24
-1 7
What are the vertex and range of h(x)?
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
To find the vertex of the quadratic function h(x), we can use the formula x = -b/2a, where the quadratic function is in the form [tex]ax^2 + bx + c[/tex].
From the given table, we can observe that the x-values of the vertex correspond to the minimum points of the function.
The minimum point occurs between -4 and -3, which suggests that the x-coordinate of the vertex is -3. Therefore, x = -3.
To find the corresponding y-coordinate of the vertex, we look at the corresponding h(x) value in the table, which is 3. Hence, the vertex of the function h(x) is (-3, 3).
To determine the range of h(x), we need to consider the y-values attained by the function.
From the table, we see that the lowest y-value is 3 (the y-coordinate of the vertex), and there are no other y-values lower than 3. Therefore, the range of h(x) is all real numbers greater than or equal to 3.
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
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The vertex of the quadratic function is (-4, 12).
The range of h(x) is [3, ∞).
To find the vertex and range of the quadratic function h(x) based on the given table, we can use the properties of quadratic functions.
The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be determined using the formula:
x = -b / (2a)
The domain of h(x) is all real numbers, we can assume that the quadratic function is of the form h(x) = ax² + bx + c.
Looking at the table, we can see that the x-values are increasing from left to right.
Additionally, the y-values (h(x)) are increasing from -6 to -4, then decreasing from -4 to -1.
This indicates that the vertex of the quadratic function lies between x = -4 and x = -3.
To find the exact x-coordinate of the vertex, we can use the formula mentioned earlier:
x = -b / (2a)
Based on the table, we can choose two points (-4, 4) and (-3, 3).
The difference in x-coordinates is 1, so we can assume that a = 1.
Plugging in the values of (-4, 4) and a = 1 into the formula, we can solve for b:
-4 = -b / (2 × 1)
-4 = -b / 2
-8 = -b
b = 8
The equation of the quadratic function h(x) can be written as h(x) = x² + 8x + c.
Now, let's find the y-coordinate of the vertex.
We can substitute the x-coordinate of the vertex, which we found as -4, into the equation:
h(-4) = (-4)² + 8(-4) + c
12 = 16 - 32 + c
12 = -16 + c
c = 28
The equation of the quadratic function h(x) is h(x) = x² + 8x + 28.
The range of the quadratic function can be determined by observing the y-values in the table.
From the table, we can see that the minimum y-value is 3.
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For g(x,y) = [tex]sin^{-1}[/tex](x² + y² — 3),
the domain of the function is the area between two circles.
The larger circle has a radius of
The smaller circle has a radius of
We conclude that there is no valid domain for the given function g(x, y) = sin^-1(x² + y² - 3). Thus, the concept of circles with radii does not apply in this case.
To determine the domain of the function g(x, y) = sin^-1(x² + y² - 3), we need to examine the range of the arcsine function. The arcsine function, [tex]sin^{(-1)[/tex](z), is defined for values of z between -1 and 1, inclusive. Therefore, for the given function, we have:
-1 ≤ x² + y² - 3 ≤ 1
Rearranging the inequality, we get:
-4 ≤ x² + y² ≤ -2
Now, let's analyze the inequalities separately:
x² + y² ≤ -2:
This inequality is not possible since the sum of squares of two non-negative numbers (x² and y²) cannot be negative. Therefore, there are no points that satisfy this inequality.
x² + y² ≤ -4:
Similarly, this inequality is also not possible since the sum of squares of two non-negative numbers cannot be less than or equal to -4. Therefore, there are no points that satisfy this inequality either.
Based on the analysis, we conclude that there is no valid domain for the given function g(x, y) = sin^-1(x² + y² - 3). Thus, the concept of circles with radii does not apply in this case.
It's important to note that the arcsine function has a restricted range of -π/2 to π/2, and for a valid domain, the input of the arcsine function must be within the range of -1 to 1. In this particular case, the given expression x² + y² - 3 exceeds the range of the arcsine function, resulting in no valid domain.
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A bacteria culture triples every 5 minutes. At 4:27 P.M. the population is . Determine what the population was 27 minutes earlier, at 4:00 P.M.
The population at 4:00 P.M., 27 minutes earlier, is[tex]3^3[/tex] times the initial population P.
To determine the population of a bacteria culture 27 minutes earlier, we need to calculate the population growth from 4:00 P.M. to 4:27 P.M. given that the bacteria culture triples every 5 minutes.
Let's break down the time period into intervals of 5 minutes:
From 4:00 P.M. to 4:05 P.M., the population triples once.
From 4:05 P.M. to 4:10 P.M., the population triples again.
From 4:10 P.M. to 4:15 P.M., the population triples for the third time.
From 4:15 P.M. to 4:20 P.M., the population triples for the fourth time.
From 4:20 P.M. to 4:25 P.M., the population triples for the fifth time.
From 4:25 P.M. to 4:27 P.M., the population undergoes partial growth.
Since the population triples every 5 minutes, we can express the population at 4:27 P.M. as 3^5 times the initial population at 4:00 P.M.
Let's denote the initial population at 4:00 P.M. as P. Then, the population at 4:27 P.M. is [tex]3^5[/tex] * P.
To find the population 27 minutes earlier, we need to reverse the growth from 4:27 P.M. to 4:00 P.M. Since the population triples every 5 minutes, we need to divide the population at 4:27 P.M. by [tex]3^{(27/5).[/tex]
Therefore, the population at 4:00 P.M., 27 minutes earlier, can be calculated as:
Population at 4:00 P.M. = (Population at 4:27 P.M.) / [tex]3^{(27/5)[/tex]
[tex]= (3^{5} * P) / 3^{(27/5)\\\\\\\\= 3^{(25/5)} * P\\= 3^5 * P / 3^2\\= 3^3 * P[/tex]
Hence, the population at 4:00 P.M., 27 minutes earlier, is 3^3 times the initial population P.
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A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation?
T1, –9(x, y)
T–1, –9(x, y)
T–9, 1(x, y)
T–9, –1(x, y)
The function rule that describes the given translation is T-9, 1(x, y).
The first value in the function rule represents the horizontal translation, while the second value represents the vertical translation. In this case, the square is translated 1 unit to the right, indicating a positive horizontal translation.
Additionally, the square is translated 9 units down, indicating a negative vertical translation. Therefore, the correct function rule is T-9, 1(x, y).
In the coordinate plane, the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position. When we apply the function rule T-9, 1 to the coordinates of the square, we subtract 9 from the y-coordinate and add 1 to the x-coordinate.
This results in the square being moved 9 units down and 1 unit to the right from its original position.
The negative sign in front of the 9 indicates a downward movement, and the positive sign in front of the 1 indicates a rightward movement. Hence, the translation is accurately described by the function rule T-9, 1(x, y).
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Answer:
C
Step-by-step explanation:
(−x² − 1) ÷ (x + 1)
Help
what is the midpoint of 70 and 90
Answer:
80
Step-by-step explanation:
Just average the two numbers to get (70+90)/2 = 160/2 = 80
Answer:
Step-by-step explanation:
To find the midpoint between two numbers, you add them together and divide the sum by 2.
In this case, the midpoint between 70 and 90 would be:
(70 + 90) / 2 = 160 / 2 = 80.
Therefore, the midpoint between 70 and 90 is 80.
pls help !!!!!! geometry
Solve the quadratic by taking square roots.
32=25x^2-4
Hello!
[tex]32 = 25x^2 - 4\\\\32 + 4 = 25x^2\\\\36 = 25x^2\\\\25x^2 - 36 = 0\\\\x = \dfrac{-b \±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-0 \±\sqrt{0^2 - 4 \times 25 \times (-36) } }{2 \times 25} \\\\\\x = \dfrac{\±60}{50} \\\\\boxed{x = \±\frac{6}{5} }[/tex]
NO LINKS!! URGENT HELP PLEASE!!
Answer:
a. 5π cm
b. 144π in²
c. 6 ft
Step-by-step explanation:
a.
The circumference of a circle is given by:
Circumference pf circle= πd
where d is the diameter.
In this case, d = 5 cm,
Therefore, Circumference of circle = π*5=5π cm
b.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, the diameter is d = 24 in,
so, the radius is r = d/2 = 24/2=12in
Therefore, Area of circle=π*12²=144π in²
c.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, Area is 36π ft²
Now substituting value
36π=πr²
dividing both side by π, we get
36=r²
[tex]r=\sqrt{36}=6[/tex]
r=6 ft.
Therefore, Radius is 6 ft.
PLS HELP ACTUAL ANSWERS
A random survey was conducted to gather information about age and employment status. The table shows the data collected.
0-17 years old 18+ years old Total
607
Has a Job
Does Not Have a Job
Total
A
B
C
240
679
What is the probability that a randomly selected student does NOT have a job, given that they are 18+ years old?
97
337
97
679
240
240
265
97
679
337
P
look at photo for reference
Answer: 337
Step-by-step explanation: it is 337 because if you subtract it all you get that
Pls help I’m stuck Tysm I can’t thank any more
Using the concept of perimeter of polygon, the perimeter of figure C is 27cm shorter than total perimeter of A and B
How much shorter is the perimeter of C than the total perimeter of A and B?To solve this problem, we have to know the perimeter of the polygon C.
The perimeter of a polygon is the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The perimeter of the figures are;
Using the concept of perimeter of a rectangle;
a. figure A = 2(4 + 11) = 30cm
b. figure B = 2(8 + 4) = 24cm
c figure C = 11 + 4 + 8 + 4 = 27cm
Now, we can add A and B and then subtract c from it.
30 + 24 - 27 = 27cm
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A sixth-grade class recorded the number of letters in each student's first name.
The results are shown in the dot plot.
A dot plot titled lengths of student names show the number of students with a certain number of letters in their name. The data is as follows. 1 dot above 3, 2 dots above 4, 4 dots above 5, 7 dots above 6 and 7, 3 dots above 8, 1 dot above 9, 2 dots above 10, and 3 dots above 11.
Which is the best representation of the center of this data set?
A. 8
B. 5
C. 7
D. 6
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with x-axis labeled study time in hours and y-axis labeled grade percent. Points are plotted at 1 comma 50, 2 comma 50, 2 comma 60, 2 comma 70, 3 comma 70, 3 comma 80, 4 comma 85, and 4 comma 90, and a line of fit drawn passing through the points 0 comma 30 and 2 comma 60
Determine the equation of the line of fit.
y = 15x + 60
y = 15x + 30
y = 30x + 60
y = 30x + 30
The equation of the line of fit is y = 15x + 30.
To determine the equation of the line of fit, we can use the given data points (0,30) and (2,60). We can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Using the two data points, we can calculate the slope (m) as the change in y divided by the change in x:
m = (60 - 30) / (2 - 0) = 30 / 2 = 15
Now that we have the slope, we can substitute one of the data points into the equation to solve for the y-intercept (b). Let's use the point (0,30):
30 = 15(0) + b
30 = 0 + b
b = 30
Therefore, the equation of the line of fit is y = 15x + 30. This means that for every additional hour of study time (x), the grade percent (y) increases by 15, and the line intersects the y-axis at 30.
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The graph of line I is shown below. Which of the following represents the slope of a line parallel to line P
Answer:
C) -1/3
Step-by-step explanation:
Slope=rise/run
Slope=-1/3
determine the surface area and volume
The surface area and the volume of the rectangular prism are 280 and 300
How to determine the surface area and volumeFrom the question, we have the following parameters that can be used in our computation:
The rectangular prism
The surface area is caculated as
Surface area = 2 * (10 * 5 + 10 * 6 + 5 * 6)
Evaluate
Surface area = 280
For the volume, we have
Volume = 10 * 5 * 6
Evaluate
Volume = 300
Hence, the surface area and the volume are 280 and 300
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Find the measure of the indicated angle.
20°
161°
61°
73°
H
G
F
73 ° E
195 °
Answer:
(c) 61°
Step-by-step explanation:
You want the measure of the external angle formed by a tangent and secant that intercept arcs of 73° and 195° of a circle.
External angleThe measure of the angle at F is half the difference of intercepted arcs HE and EG.
(195° -73°)/2 = 122°/2 = 61°
The measure of angle F is 61°.
<95141404393>
Find the local and absolute maximum and minimum points in (x, y) format for the
function f(x) = 3/5x^5 - 9x^3 + 2 on the closed interval [-4,5]. Answer the following
questions.
a) Find all critical numbers (x- coordinates only)
b) Find the intervals on which the graph is increasing Mark critical numbers
recursive formula for an=1/8(2)n-1
Answer:
The recursive formula for an=1/8(2)n-1 is:
a1=1/8 an+1=1/8(2)(n)
This formula defines a sequence where each term is equal to 1/8 of the previous term multiplied by 2.
Step-by-step explanation:
Given cos=
a.
b.
sin 8
4
and csc <0, find sine and tan
9
-4
9
A
B
tan =
csc0= 4√√9, tane=
9
4
65
9
C.
d.
sin = 4, tan 9 =
sin =
Please select the best answer from the choices provided
65
19
-4√65
9
tan 9 =
The best answer that matches the calculated values is C. sin θ = -1/3, tan θ = -3/(2√2)
Let's break down the given values and find the values of sine and tangent.
We are given:
cos θ = √(8/9)
csc θ < 0
Using the Pythagorean identity, sin^2θ + cos^2θ = 1, we can find the value of sin θ.
sin^2θ + (√(8/9))^2 = 1
sin^2θ + 8/9 = 1
sin^2θ = 1 - 8/9
sin^2θ = 1/9
Taking the square root of both sides, we get:
sin θ = ±1/3
Since csc θ is negative (csc θ < 0), we can conclude that sin θ is negative. Therefore, sin θ = -1/3.
Next, let's find the value of tan θ.
tan θ = sin θ / cos θ
tan θ = (-1/3) / (√(8/9))
tan θ = -√9/√8
tan θ = -√9/√(4*2)
tan θ = -√9/(2√2)
tan θ = -3/(2√2)
So, the values are:
sin θ = -1/3
tan θ = -3/(2√2)
The best selection from the available options that matches the calculated values is:
C. sin θ = -1/3, tan θ = -3/(2√2)
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Yesterday, Janie walked 3
5
mile to a friend’s house, 1
4
mile to the store, and 3
8
mile to another friend’s house. Which is the best estimate of the distance Janie walked?
Answer:
be more clear of what u mean edit the question so we can tell what u mean and answer correctly
Step-by-step explanation:
no explanation
The equation 4x – 4 – 5x = 7 – x + 5 has what type of solution set? Question 3 options: A) No solutions B) Two solutions C) One solution D) Infinitely many solutions
Answer:
A) No solutions
Step-by-step explanation:
First of all, we know that option B will always be incorrect. You cannot have two solutions. To illustrate this, try drawing two lines. You will find that they will either intersect once (one solution), or they will not intersect, (no solutions, parallel lines), or they are the same line and thus they will always intersect (infinitely many solutions).
With that in mind, let's solve the equation.
4x-4-5x=7-x+5
First, combine all like terms.
-x-4=12-x
Now add 4 to both sides to leave x by itself.
-x=16-x
This statement cannot be true. Therefore, this equation has no solutions (parallel lines. One line starts from 0, or the origin. That line is -x. The other line starts from 16. That line is -x+16.)
Hope this helps!
The first three steps in determining the solution set of
the system of equations algebraically are shown.
y=x²-x-3
y=-3x + 5
Step
1
2
3
Equation
x²-x-3=-3x+5
0=x²+
+2x-8
0=(x-2)(x+4)
What are the solutions of this system of equations?
O (-2,-1) and (4, 17)
O (-2, 11) and (4, -7)
O (2, -1) and (-4, 17)
(2, 11) and (-4,-7)
The solutions of the system of equations are (2, -1) and (-4, 17)
The given system of equations is:
y = x² - x - 3
y = -3x + 5
To find the solutions, we need to solve these equations simultaneously.
Set the equations equal to each other:
x² - x - 3 = -3x + 5
Simplify and rewrite the equation in standard form:
x² - x + 3x - 3 - 5 = 0
x² + 2x - 8 = 0
Factor the quadratic equation:
(x - 2)(x + 4) = 0
Now we can solve for x by setting each factor equal to zero:
x - 2 = 0 or x + 4 = 0
Solving for x, we get:
x = 2 or x = -4
To find the corresponding y-values, we substitute these x-values into either of the original equations. Let's use equation 1):
For x = 2:
y = (2)² - 2 - 3 = 4 - 2 - 3 = -1
For x = -4:
y = (-4)² - (-4) - 3 = 16 + 4 - 3 = 17
As a result, the system of equations has two solutions: (2, -1) and (-4, 17).
The right responses are therefore (2, -1) and (-4, 17).
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Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is |
%.
The percentile of 6.2 in the given data set is 40%.
To determine the percentile of 6.2 in the given data set, we can use the following steps:
Arrange the data set in ascending order:
4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2
Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.
Calculate the percentile using the formula:
Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100
In this case, the percentile of 6.2 can be calculated as:
Percentile = (4 / 10) × 100 = 40%
The percentile of 6.2 in the sample data set is therefore 40%.
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How much fencing is required to enclose a circular garden whose radius is 21 m
Answer:182.12 meters of fencing required.
Step-by-step explanation:
Select the correct answer. Which fraction converts to a terminating decimal number? A. 1\6 B. 2\9 C. 3\8 D. 4\7
The fraction that converts to a terminating decimal number is C. 3/8.
To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.
Let's examine each option:
A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.
D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.
Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.
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