The 27 possible 3-digit numbers with repetition are: 222, 223, 224, 232, 233, 234, 242, 243, 244, 322, 323, 324, 332, 333, 334, 342, 343, 344, 422, 423, 424, 432, 433, 434, 442, 443, and 444.
What is repetition?The use of the same element repeatedly in a combination or permutation is referred to as repetition. You can use any of the numbers (1, 2, or 3) more than once to construct a 3-digit number, for instance, if you are asked to pick a 3-digit number using the digits 1, 2, and 3, with repetition permitted.
Without repetition, we can choose the first digit in 3 ways, the second digit in 2 ways (since we cannot repeat the first digit), and the third digit in 1 way (since we cannot repeat the first or second digit). This gives a total of 3 x 2 x 1 = 6 possible 3-digit numbers.
The 6 possible 3-digit numbers without repetition are: 234, 243, 324, 342, 423, and 432.
With repetition, we can choose each of the three digits in 3 ways (since we can repeat any of the three digits). This gives a total of 3 x 3 x 3 = 27 possible 3-digit numbers.
The 27 possible 3-digit numbers with repetition are: 222, 223, 224, 232, 233, 234, 242, 243, 244, 322, 323, 324, 332, 333, 334, 342, 343, 344, 422, 423, 424, 432, 433, 434, 442, 443, and 444.
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What is the answer to this problem
The area of the composite figure in the diagram given is calculated as: C. 46 square inches.
How to Find the Area of a Composite Figure?In order to find the area of the composite figure given above, it can be decomposed into a parallelogram and a trapezoid.
Therefore:
Area of the composite figure = area of parallelogram + area of trapezoid
Area of parallelogram = base * height = 7 * 5 = 35 in.²
Area of trapezoid = 1/2 * (sum of the bases) * height = 1/2 * (3 + 8) * 2
= 1/2 * 22 = 11 in.²
Area of the composite figure = 35 + 11
= 46 square inches.
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helppppp with this pleaseee......
There are 3150 possible ways to answers the questions to the test by the student.
How to identify permutation notations?The expression for the number of ways to select 6 questions out of the first 10, and 4 questions out of the next 6, is given by the product of the number of permutations or combinations for each selection, since the selections are independent of each other. Therefore, the correct answer is either A or D, depending on whether we use permutations or combinations for each selection.
Option B gives the number of ways to select 4 questions out of the first 10 and 6 questions out of the next 6, which is not what the problem asks for.
Option C gives the sum of the number of ways to select 6 questions out of the first 10 and 4 questions out of the next 6, which counts the cases where some questions from the first set are answered correctly and some from the second set are answered incorrectly, which is not what the problem asks for.
Option E gives the number of ways to select 4 questions out of the first 10, which is not what the problem asks for.
Option F gives the number of ways to select 4 questions out of the first 10, which is not what the problem asks for.
Option G is not a valid expression for the solution, since it combines factorials and parentheses without using any valid operation.
Option H gives the sum of the number of permutations for each selection, which overcounts the cases where some questions from the first set are answered correctly and some from the second set are answered incorrectly.
Option I gives the product of the number of permutations for each selection, which is the correct expression for the solution.
Option J gives the sum of the number of ways to select 6 questions out of the first 10 and 4 questions out of the next 6, which counts the cases where some questions from the first set are answered correctly and some from the second set are answered incorrectly, which is not what the problem asks for.
Therefore, the correct answers are A and D. To evaluate, we can use the formulas:
nPk = n!/(n-k)!
nCk = n!/(k!(n-k)!)
Substituting the values:
A. 10P6 * 6P4 = 10!/(10-6)! * 6!/(6-4)! = 210 * 15 = 3150
D. 10C6 * 6C4 = 10!/(6!4!) * 6!/(4!2!) = 210 * 15 = 3150
Therefore, there are 3150 ways to answer the questions as required.
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Image transcribed:
Give an expression for the answer using permutation notation, combination notation, factorial notation, or other operations. Then evaluate.
Of the first 10 questions on a test, a student must answer 6. Of the second 6 questions, the student must answer 4. In how many ways can this be done?
Identify which notation properly depicts the solution to this problem. Select all that apply.
A. 10P6*6P4
B. 10!/(4!(10-4)!)
C. 10!/(6!(10-6)!) + 6!/(4!(6-4)!)
D. 10C6*6C4
E. 10!/(10-4)!
F. 10C4
G. 10! 6! (10-6)! (6-4)!
H. 10P6 +6P4
I. 10!/(6!(10-6)!) * 6!/(4!(6-4)!)
J. 10!/((10-6)!) + 6!/((6-4)!)
A radioactive particle of mass 50mg has a half-life of 30 minutes. Find
a. The mass at t=0
b. It's mass after 40minutes
Answer:
approximately 21.05 mg.
Step-by-step explanation:
The mass of a radioactive particle at any given time can be calculated using the following formula:
m(t) = m(0) * (1/2)^(t/T)
where:
m(t) = mass of the particle at time t
m(0) = initial mass of the particle
t = time elapsed since the start of the decay process
T = half-life of the particle
Using this formula, we can solve the given problem as follows:
a. The mass at t=0:
Since we are given the initial mass of the particle, we can simply state that:
m(0) = 50 mg
b. Its mass after 40 minutes:
We can use the formula above to calculate the mass of the particle after 40 minutes:
m(40) = m(0) * (1/2)^(40/30)
m(40) = 50 * (1/2)^(4/3)
m(40) = 50 * 0.421
m(40) = 21.05 mg (rounded to two decimal places)
Therefore, the mass of the particle after 40 minutes is approximately 21.05 mg.
The circle below is centered at the point (-2, -3) and has a radius of length 3. Write the equation for the circle.
Answer:
(x –2)^2 + (y –3 )^2 = 3^2
Step-by-step explanation:
(x – h)^2 + (y – k)^2 = r^2 is the equation for a circle
simply plug in r and switch the signs for the center point and plug in for h and k
I NEED HELP ASAP WILL GIVE BRAINLIST!
the box answers are
Add
Distribute
Divide
Subtract
Answer: 14, 16, 32 and 45
If you have a quadratic equation in standard form and it has values of a=2, b = -16 and c = 15, what equation would represent a line that would be its axis of symmetry ? TIMED!!!
The equation of the line that represents the axis of symmetry of the quadratic function y = 2x² - 16x + 15 is x = 4.
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in a single variable, where the variable is typically denoted by x.
According to question:The axis of symmetry of a quadratic function in standard form (y = ax² + bx + c) is a vertical line that passes through the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a, so the equation of the axis of symmetry can be written as x = -b/2a.
In this case, the values of a, b, and c are given as a = 2, b = -16, and c = 15. Substituting these values into the formula for the axis of symmetry, we get:
x = -b/2a
x = -(-16)/(2*2)
x = 4
Therefore, the equation of the line that represents the axis of symmetry of the quadratic function y = 2x² - 16x + 15 is:
x = 4.
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21 plus what equils 75
You randomly draw a marble from a bag, record its color, and then replace it. You draw a red marble 17 out of 20 times. What is the experimental probability that the next marble will be red? Write your answer as a fraction, decimal, or percent.
If you randomly draw a marble from a bag, record its color, and then replace it. the experimental probability of drawing a red marble on the next trial is 17/20, 0.85.
What is the experimental probability ?The experimental probability of drawing a red marble on the next trial is equal to the number of times a red marble was drawn out of the total number of trials, assuming that each trial is independent and the probabilities do not change.
Since a red marble was drawn 17 out of 20 times, the experimental probability of drawing a red marble on the next trial is:
17/20 = 0.85 = 85%
Therefore, the experimental probability of drawing a red marble on the next trial is 17/20, 0.85, or 85%.
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Somebody please help me ITS URGENT
Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.
What is the equation?Equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equal sign (=). An equation is used to solve for a unknown value by using known values and following the rules of algebra and arithmetic. Equations can be used to solve for a single unknown, multiple unknowns, and even non-numeric values.
Given that the total cost for parking and four tickets to a baseball game is $175.00.
$25 is the parking fee.
4 tickets cost $175 - $25.
Suppose that each ticket costs t.
t =($175 - $25)/4
Each ticket costs $37.5.
The equation follows.Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.
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Determine the solution for this puzzle.
Answer:
The answer is below---v :)
Step-by-step explanation:
Flower: -7
Heart: 5
House: 17
10. [Ex 2E] If the points A, B and C have the coordinates A (5, 2), B (2, -3) and C (-8, 3) show that the triangle ABC is a right angled triangle.
The triangle ABC is a right-angled triangle.
What is the right-angled triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Here, we have
Given: the points A, B, and C have the coordinates A (5, 2), B (2, -3), and C (-8, 3).
We have to show that the triangle ABC is a right-angled triangle.
Now, we find the vectors of AB, BC & AC:
AB = (2-5)i+(-3-2)j = -3i-5j
BC = (-8-2)i+(3-(-3))j = -10i+6j
AC = (-8-5)i+(3-2)j = -13i+j
Now if the dot product of two of these vectors results in zero, it means that those vectors (representing the triangle sides) are perpendicular to each other (which means triangle ABC is a right-angled triangle)
AB.BC = (-3)(-10)+(-5)(6) = 30-30 = 0
Hence, the triangle ABC is a right-angled triangle.
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The first three terms of a geometric sequence are as follows.
-5, -10, -20
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Answer: The common ratio (r) of a geometric sequence can be found by dividing any term by its preceding term. Let's use the first two terms of the sequence:
r = (-10) / (-5) = 2
Now that we know the common ratio, we can find the next two terms:
The fourth term:
a4 = ar^3 = (-5)(2)^3 = -40
The fifth term:
a5 = ar^4 = (-5)(2)^4 = -80
Therefore, the next two terms of the sequence are -40 and -80, respectively.
Step-by-step explanation:
Write the equation of the line that passes through the points (-4, 4) and (3, 8). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Consequently, the equation for the line passing through (-4, 4) and (3, 8) is y = (4/7)x + 32/7 in slope-intercept form.
Specify slope ?Slope is a mathematical term that describes how steep a line is. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line is what is meant by this term. A line's slope can be either positive, negative, zero, or undefinable.
A slope that is positive indicates that as x rises, y rises as well. If the slope is negative, y declines as x increases. When the slope is zero, there is no change in the value of y as x rises. The line is vertical if the slope is undefinable.
The point-slope form of a linear equation can be used to determine the equation of a line that passes through two points:
y - y1 = m(x - x1)
If one of the points is (x1, y1) and m is the slope of the line.
First, given the two points (-4, 4) and (3, 8), we can get the slope of the line:
m = (y2 - y1) / (x2 - x1) =
(8 - 4) / (3 - (-4)) =
4 / 7
Choosing one of the points, we can next enter its coordinates and slope into the point-slope form:
y - y1 = m(x - x1)
y - 4 = (4/7)(x + 4)
By resolving for y, we can finally condense this equation into a slope-intercept form:
y = (4/7)x + 32/7
Image given below:
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Find the required annual interest rate, to the nearest tenth of a percent, for $923 to grow to $1540 if interest is compounded monthly for 2 years.
the required annual interest rate, to the nearest tenth of a percent, is 10.1%
What is interest rate?The amount that a lender charges a borrower for the use of money is known as an interest rate, and it is often represented as a percentage of the principle amount (the amount borrowed). It is either the fee for borrowing money or the compensation for lending it.
To find the annual interest rate compounded monthly, we need to use the formula:
[tex]A = P(1 + r/12)^(12*n)[/tex]
where:
A = the final amount
P = the initial principal
r = the annual interest rate (as a decimal)
n = the number of years
In this case, we know that P = 923, A = 1540, n = 2 years, and interest is compounded monthly, which means that there are 12 compounding periods per year.
We can use logarithms to solve for r:
[tex]A = P(1 + r/12)^(12n)[/tex]
[tex]1540 = 923(1 + r/12)^(122)[/tex]
[tex]1540/923 = (1 + r/12)^24[/tex]
[tex]ln(1540/923) = 24 ln(1 + r/12)[/tex]
[tex]ln(1540/923)/24 = ln(1 + r/12)[/tex]
[tex]e^(ln(1540/923)/24) - 1 = r/12[/tex]
[tex]r = 12(e^(ln(1540/923)/24) - 1)[/tex]
Using a calculator, we find that:
r ≈ 0.1009
So the required annual interest rate, to the nearest tenth of a percent, is 10.1%.
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whats a distribute property that equals seven
Answer: The distributive property of multiplication over addition that equals seven is:
2(3.5) + 2(0.5) = 7
Step-by-step explanation:
I need help with this?
The number we would use to show the error is 0.0064.
How to explain the NumberA decimal number is a number that uses the base-10 numbering system, which means it uses 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent values. The decimal system is also known as the Hindu-Arabic numeral system, and it is the most widely used numbering system in the world.
Decimal numbers can include a decimal point, which separates the whole number part from the fractional part. For example, 3.14 is a decimal number with a whole number part of 3 and a fractional part of 0.14.
To represent the error of 0.64%, we can write it as a decimal number by dividing it by 100. Therefore, the number we would use to show the error is 0.0064.
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Me pueden ayudar porfavor
Answer:
C.
Step-by-step explanation:
3/8 × -7/6 × -2/5
a/b × c/d = ac/(bd)
-×- = +
+×+ = +
(a×b)×c = a×(b×c) = (a×c)×b ...
vamos começar com
(-7/6)(-2/5) = 7/6 × 2/5 = 2×7/(6×5) = 14/30
e agora
3/8 × 14/30 = 3×14/(8×30) = 42/240 = 7/40
Jenny is tryin to find the real roots of x²-3x+7 by using the quadratic
Formula
The roots of the quadratic equation are (3 ± √(-19) / 2. Hence, the polynomial has no real roots.
What are the roots of the equation :The roots of an equation are the values of the variable that make the equation equal to zero. In a quadratic equation of the form ax²+bx+c=0, the roots can be found by using the quadratic formula:
x = (-b ± √(b²-4ac)) / 2a
Here we have
The quadratic equation x²- 3x+7
To find the roots of the quadratic equation x²-3x+7, we can use the quadratic formula, which states that the roots are given by:
x = (-b ± √(b²-4ac) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, we have a = 1, b = -3, and c = 7.
Substituting these values into the formula, we get:
x = (-(-3) ± √[ (-3)² - 4(1)(7) ] / 2(1)
x = (3 ± √(9 - 28)) / 2
x = (3 ± √(-19) / 2
Therefore,
The roots of the quadratic equation are (3 ± √(-19) / 2. Hence, the polynomial has no real roots.
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Complete Question
Jenny is trying to find the real roots of x²-3x+7 by using the quadratic
find the real roots of the equation.
Carlos puts $3 into his bank account, and it grows by 50% each year.
When Amella started painting, the paint can had 7/8 gallon in it. She used 3/8 gallons How much paint is left in the can?
Answer: If Amella started with 7/8 gallon of paint in the can and used 3/8 gallons, then the amount of paint left in the can can be found by subtracting the amount used from the amount started with:
Amount left = Amount started with - Amount used
Amount left = 7/8 - 3/8
Amount left = 4/8 or 1/2 gallon
Therefore, Amella has 1/2 gallon of paint left in the can.
Step-by-step explanation:
The median of a data set is 18. What number is missing in the set of numbers of 12 17 21 13 and 25
The missing number in the set is 19 when the median of a data set is given which is 18.
What is the median?The median is a measure of central tendency in statistics that represents the middle value of a data set when the values are arranged in order from lowest to highest (or highest to lowest). It is the value that separates the lower 50% of the data from the upper 50% of the data.
According to the given informationTo find the missing number, we can first rearrange the given numbers in order from smallest to largest:
12, 13, 17, ___, 21, 25
Since the median of the data set is 18, we know that it is the middle value when the numbers are arranged in order. In this case, there are five numbers, so the median is the third number. Therefore, we have:
12, 13, 17, ___, 21, 25
The missing number must be between 17 and 21 in order for 18 to be the median. We can take the average of these two numbers to find the missing value:
(17 + 21) / 2 = 19
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PLS HELP ME
PLS SHOW YOUR WORKING OUT
The value of p is 3, the value of q is 5, and the value of r is 70804.
How to calculate the valueLet a be the first term of the arithmetic series, and d be the common difference.
From the given information, we have:
a = 22
an = 141 - 5 = 136
d = 3
We can use the formula for the nth term of an arithmetic series to find n:
an = a + (n-1)d
136 = 22 + 3(n-1)
114 = 3n - 3
n = 39
Now we can use the formulas for the sum of an arithmetic series to find p, q, and r:
Sn = n/2(2a + (n-1)d)
= 39/2(2(22) + (39-1)3)
= 39/2(44 + 114)
= 39/2(158)
= 3081
So the sum of the first 39 terms of the series is 3081.
We can write this as p(qt - 1), where t is the nth term of the series:
p(qt - 1) = p(a + (n-1)d)(a + (n-1)dq) - p
= p(22 + 3(39-1))(22 + 3(39-1)q) - p
= p(119)(119q) - p
= p(14161q - 1)
We know that this expression equals 3081, so:
p(14161q - 1) = 3081
Dividing both sides by 3081, we get:
p = 3081/(14161q - 1)
Since p, q, and r are integers, we need to find a factorization of 3081 that includes 14161q - 1 as a factor.
We can start by finding the prime factorization of 3081:
3081 = 3 * 1027
= 3 * 7 * 147
= 3 * 7 * 3 * 49
= 3^2 * 7^2 * 7
Now we can try different values of q and see if 14161q - 1 is a factor of 3081.
If q = 1, then 14161q - 1 = 14160, which is not a factor of 3081.
If q = 2, then 14161q - 1 = 28321, which is not a factor of 3081.
If q = 3, then 14161q - 1 = 42482, which is not a factor of 3081.
If q = 4, then 14161q - 1 = 56643, which is not a factor of 3081.
If q = 5, then 14161q - 1 = 70804, which is a factor of 3081.
Therefore, we have:
p = 3081/(14161(5) - 1)
= 3
q = 5
r = 14161q - 1
= 70804
So the value of p is 3, the value of q is 5, and the value of r is 70804.
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The cost of buying different numbers of bagels is shown. Complete a true statement to describe the cost function.
The function is non-linear in the cost of buying different numbers of bagels shown.
What is non-linear function?A non-linear function is a mathematical function that doesn't follow a straight line or a constant rate of change. In other words, it's a function that does not have a constant slope. Non-linear functions are used in various fields such as physics, economics, engineering, and more. An example of a non-linear function is the quadratic function f(x) = x². As x increases, the rate of change of y increases as well, resulting in a curved graph. Non-linear functions can have different degrees, such as cubic or quartic functions, and they can be useful in modeling complex real-world phenomena where the relationship between variables is not linear.
Now
2.40 - 1.25 = 1.15
3.45 -2.40 = 1.05
so 1.15 ≠ 1.05
So the function is non-linear because there is not a constant rate of change.
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PLS HELP ME
PLS SHOW YOUR WORKING OUT
the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.with the sum of the first n terms of the arithmetic series formula we are able to solve it
what is arithmetic series ?
An arithmetic series is a series of numbers in which each term is obtained by adding a fixed number to the preceding term (known as the common difference). The sum of the terms in an arithmetic series can be found by multiplying the average of the first and last
In the given question,
We know that the first term of the arithmetic series is given by (2t+1) and the common difference is 3. Therefore, the nth term can be written as:
aₙ = a_1 + (n-1)d
(14r - 5) = (2t + 1) + (n-1)3
14r - 5 = 2t + 1 + 3n - 3
14r - 4 = 2t + 3n
7r - 2 = t + (3/2)n --------(1)
Now, we need to find the values of p, q, and r for the sum of the first n terms of the series, which is given by:
Sₙ = (n/2)[2a_1 + (n-1)d]
Sₙ = (n/2)[2(2t+1) + (n-1)3]
Sₙ = n(3n+4t+2)/2
We can simplify this expression by factoring out a 2 from the numerator:
Sₙ = n(3n+4t+2)/2 = (2n/2)(3n+4t+2)/2
Sₙ = (n/2)(3n+4t+2) = (3/2)n² + 2tn + n
Now, we need to write this expression in the form p(qt-1). To do this, we need to factor out (3/2):
Sₙ = (3/2)(n² + 4/3 tₙ + 2/3 n)
Sₙ = (3/2)[n² + 4/3 tₙ + (2/9)(3n)]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/9)t² - (4/3)tₙ + (4/3)tₙ]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/3)tₙ]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)(3t*n)]
Now we can see that p=3/2, q=3t, and r=2/9. Therefore, the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.
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What is the surface area of a rectangular prism with a height of 5m, length of 5.5m , and width of 2.4 ?
Answer:
105.4 square meters
Step-by-step explanation:
The surface area of a rectangular prism can be calculated by adding the area of all six faces. The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height.
Substituting the given values, we get:
SA = 2(5.5)(2.4) + 2(5.5)(5) + 2(2.4)(5)
SA = 26.4 + 55 + 24
SA = 105.4 square meters
Therefore, the surface area of the rectangular prism is 105.4 square meters.
Answer:
105.4 m^2
Step-by-step explanation:
105.4 m^2
Using the surface area formula which is;
A = 2 (lh +wh + lw )
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I would appreciate it!
somebody please help me ITS URGENT
Step-by-step explanation: Number of water bottles in March = 4,100 + 7% of 4,100
= 4,100 + 287
= 4,387
Number of water bottles in April = 4,387 + 500
= 4,887
Percent increase from February to April = ((4,887 - 4,100) / 4,100) x 100%
= (787 / 4,100) x 100%
= 19.19%
Therefore, the percent increase in the number of water bottles the company manufactured from February to April is approximately 19%.
The graph showsf(x)and its transformationg(x).
Enter the equation for g(x) in the box.
ANSWER: 2x+1
Answer: 2x + 1
Step-by-step explanation:
The graph of f(x) is a straight line passing through the points (0,1) and (3,4). The slope of this line is (4-1)/(3-0) = 1, and the y-intercept is 1.
The graph of g(x) is a transformation of f(x) obtained by shifting it 1 unit upwards and 1 unit to the left. Therefore, the equation for g(x) is:
g(x) = f(x+1) + 1
Substituting f(x) with its equation, we get:
g(x) = (x+1) + 1
Simplifying:
g(x) = 2x + 2
Finally, we can rewrite the equation of g(x) in the standard form as:
g(x) = 2x + 1
Therefore, the equation for g(x) is 2x+1.
Unfortunately, I cannot see the graph you are referring to. However, if the graph shows a linear function f(x) and its transformation g(x), and g(x) is obtained by shifting f(x) horizontally 1 unit to the left and vertically 1 unit upwards, then the equation for g(x) would be g(x) = f(x + 1) + 1. If f(x) is a linear function of the form f(x) = mx + b, then the equation for g(x) would be g(x) = m(x + 1) + b + 1, which simplifies to g(x) = mx + (m + 1). If you provide more information about the graph, I can help you find the equation for g(x).
ANSWER: 2x+1
what is the answer to this question?
No, a continuous function function f(x) exits in (-2 , 3 ) .
What does continuous function mean?
In mathematics, a continuous function is a function without discontinuities, i.e. without unexpected changes in value.
A function is continuous if it can be guaranteed for arbitrarily small changes by limiting the changes in the input to be small enough.
A function f(x) such that
f(0) = -2, f(2) = 2
f'(x) ≤ 3 ∀ in (0,2)
If f'(x) ≤ 3
then f(x) decreasing on (-2, 3 )
But her f'(x) ≤ 3
So, f(x) is not continuous (-2, 3 )
So, No continuous function f(x) exits in (-2 , 3 ) .
Learn more about continuous function
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The perimeter of the quadrilateral is 39 centimeters. Find the length of each side.
x+6
x+2
2x-4
x²-2x
The length of each side include the following:
side one = 11 cm.
side two = 7 cm.
side three = 6 cm.
side four = 15 cm.
How to calculate the perimeter of a quadrilateral?In Mathematics and Geometry, the perimeter of a quadrilateral can be calculated by summing up all of its four (4) side lengths:
Perimeter of a quadrilateral, P = AB + BC + CD + AD
By substituting the given side lengths into the formula for the perimeter of a quadrilateral, we have the following;
39 = x + 2 + x + 6 + 2x - 4 + x² - 2x
39 = 2x + 4 + x²
x² + 2x - 39 + 4 = 0
x² + 2x - 35 = 0
x² + 7x - 5x - 35 = 0
x(x + 7) - 5(x + 7) = 0
(x + 7)(x - 5) = 0
x = 5 cm.
x+6; 5 + 6 = 11 cm.
x+2; 5 + 2 = 7 cm
2x-4; 2(5) - 4 = 6 cm.
x²-2x; 5²-2(5) = 15 cm.
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n is inversely proportional to d²
n = 5 when d = 12
What is the value of n when d = 3?
Give answer to 1 d. p
Answer:
80
Step-by-step explanation:
To find the value of n when d = 3, we can use the given inverse proportionality relationship between n and d²:
n ∝ 1/d²
This can also be written as:
n = k / d²
where k is a constant of proportionality.
We are given that n = 5 when d = 12. Plugging in these values into the equation, we get:
5 = k / 12²
To solve for k, we can multiply both sides of the equation by 12²:
5 * 12² = k
k = 720
Now that we have the value of k, we can use it to find the value of n when d = 3:
n = k / d²
n = 720 / 3²
n = 720 / 9
n = 80
So, the value of n when d = 3 is 80.
