Answers
Using distributive property, each expressions are write in an appropriate form. The expression are shown below.
What is distributive property?This characteristic states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend separately by the number and then combining the results collectively.
According to the property, the outcomes are the same whether the numbers in parenthesis are added before or after multiplication. In situations when the polynomial cannot be combined together before being multiplied, the distributive property is very helpful. Using this property the following expression are solved.
4(6 + 7) = 4.6 + 4.7
14.1 - (14 - 9) = 14 (1 - 9)
5 (z - 10) = 5.z - 5.10
8.6 + 8.2 = 8 (6 + 2)
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Related Questions
22. last year for sales of units, hurst ltd had sales of £ , variable expenses of £ , and fixed costs of £ . what would be the break-even point in units?
Answers
The break-even point in units can be calculated if the sales price per unit (P) is known. In conclusion, the break-even point in units is an essential calculation that helps companies understand their financial performance and determine the minimum level of sales they need to achieve to cover their costs and start generating a profit.
Break-even point in units = Fixed costs / (P - Variable expenses per unit)
= Fixed costs / (P - Variable expenses / Sales)
The break-even point is a crucial calculation in the field of business and finance, as it represents the level of sales at which a company's expenses and revenue are equal, and there is no profit or loss. In this scenario, Hurst Ltd's break-even point in units can be calculated based on its sales, variable expenses, and fixed costs.
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PLS HELP NEED THIS NOW!
Answers
a. 8cm ( AD=BD)
b. 8cm ( BD=BC) , Triangle BCD is equilateral
c. 8 cm ( DC = BD)
d Perimeter of ABCD is AD+DC+BC+AB= 8+8+8+11=35
Definition of TriangleA triangle is a two-dimensional plane shape formed by three sides in the form of straight lines and has three angles. Besides having 3 sides or ribs and angles, the properties of a triangle have an angle of 180°.
The Nature of the equilateral TriangleThe following are the properties of an equilateral triangle, including:
Has three sides that are the same length. It has the same angles, which are 60° each. It has three axes of symmetry that intersect at exactly one point. Can be placed on the frame in exactly six ways.Learn more about triangle at https://brainly.com/question/25813512
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#13
Points (1,-1), (3, 2), and (7, -3) are three vertices of a
parallelogram. How many parallelograms can be created using
these three vertices?
O One
O Two
O Three
O Four
Identify the coordinates of each point that could be the fourth
vertex. Select all that apply.
(9,-2)
(-3,2)
(5,4)
(9,0)
(-3, 4)
(5, -6)
(5,-4)
(3,2)
Answers
Answer:
Two parallelograms can be created using these three vertices. The fourth vertex of the first parallelogram would have the coordinates (9,-2), and the fourth vertex of the second parallelogram would have the coordinates (-3,4). The other coordinates given are not valid for the fourth vertex of a parallelogram.
Answer:
three
(5,-6)
(9,0)
(-3,4)
A triangle having area of √135 square meter and perimeter 18 meter has a side 4 meter. Find the measurement of the remaining two sides.
Answers
The measurement of the remaining two sides of the triangle be 4cm and 6cm.
How to find the measurement of the remaining two sides of the triangle?Given :- Perimeter of triangle = 18m.
Area of triangle = √135m².
One side of triangle = 8m.
Triangle is a plane figure with three straight sides and three angles.
Let the equation be Area of ∆ = 1/2bh
= 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B
= √( s(s-a)(s-b)(s-c) ) [ where s = (a + b + c)/2 ]
By using Heron's formula to get the Area of triangle,
s = (Perimeter /2) = (18/2) = 9m.
Putting values now we get :-
√(s(s-a)(s-b)(s-c) ) = √135
substitute the values in the above equation, we get
√[9(9-8)(9-b)(9-c)] = √135
Squaring Both sides we get,
9 × 1 × (9-b)(9-c) = (√135)² = 135
Dividing both sides by 9, we get,
(9-b)(9-c) = 15
81 - 9c - 9b + bc = 15
simplifying the above equation, we get
81 - 9(b + c) + bc = 15
9(b + c) - bc = 81 - 15
9(b + c) - bc = 66 -------- (1).
Also, if Rest two sides are b and c, we get,
→ 8 + b + c = 18
→ (b + c) = 18 - 8 = 10 cm. ------ (2).
Putting value of (2) in (1) , we get,
→ 9 × 10 - bc = 66
simplifying the above equation, we get
→ bc = 90 - 66
→ bc = 24 ------------ (3).
We do Factors of (3), we just have to check now, which satisfy Equation (2) also . (sum of Factors will be 10).
24 = ( 1, 24) , (24, 1), ( 2,12), (12,2) , (3,8) ,(8,3) , (4,6),(6,4)
We can see (4,6) or (6,4) Satisfy the (2).
Therefore, the measurement of the remaining two sides of the triangle be 4cm and 6cm.
The complete question is:
the perimeter of a triangular garden is 18 m. if its area is under root 135 m^2 and one of the tree sides is 8 m, find the remaining two sides
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This is an example of an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.
Find the measurement of the remaining two sides?In this particular triangle, the side with a measurement of 4 meters is one of the two equal sides, meaning the remaining two sides must also have a measurement of 4 meters. To calculate the area and perimeter of the triangle, we can use the following formulas: Area = 1/2 x base x height Perimeter = a + b + c Given that the area of the triangle is √135 square meter and the perimeter is 18 meter, we can plug these values into the formulas to solve for the remaining measurements of the triangle.For the area, we can solve for the height by rearranging the formula: Height = 2 x area / base Height = 2 x √135 / 4 Height = 3√3 For the perimeter, we can solve for the remaining two sides by rearranging the formula: a + b + c = 18 a + b = 18 - 4 a + b = 14 Therefore, the two remaining sides of the triangle have a measurement of 4 meters, and the remaining height of the triangle has a measurement of 3√3 meters.To learn more about isosceles triangle refer to:
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The table below shows how far a person driving in their car was able to go over different intervals of time. Perform a regression to model the data, using the form y = kx + h. What is your value for k? (Round your answer to the nearest tenth.)
Answers
Answer:
kxh is the answer to this question
[HELP FAST WILL GIVE BRAINLIEST] Identify the explicit formula for the sequence given by the following recursive formula:
Answers
Answer:
f(n) = 4n - 6
Step-by-step explanation:
the explicit formula for an arithmetic sequence is
f(n) = f(1) + (n - 1)d
where f(1) is the first term and d the common difference
given the recursive formula
f(n) = f(n - 1) + 4
this allows a term in the sequence to be found by adding the common difference d to the previous term.
here f(1) = - 2 and d = 4 , then explicit formula is
f(n) = - 2 + 4(n - 1) = - 2 + 4n - 4 = 4n - 6
Work out the equation of the line shown below.
Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
Answers
An equation of the line shown above in slope-intercept form is y = x/8 + 5/2.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided in the graph above, we have the following data points on its line:
Points on the x-axis = (60, 140).Points on the y-axis = (10, 20).At data point (60, 10), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 10 = (20 - 10)/(140 - 60)(x - 60)
y - 10 = 1/8(x - 60)
y = x/8 - 7.5 + 10
y = x/8 + 5/2
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Three students, Deion, Bashir, and Arianys, line up one behind the other. How many
different ways can they stand in line?
Answers
The correct answer is 6 , that is 3! (3 factorial).
If the direction is not take into consideration then 3 students can stand in 3*2*1 =6 ways.
Like In the first place there can be any of the three, in the second place there can be either of the two left and then the last place .
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Can anyone factor these equations?
Answers
7) The factors of the expression (x² + 17x + 60) is, (x + 5) (x + 12)
8) The factors of the expression (x² - 6x - 27) is, (x + 3) (x - 9)
9) The factors of the expression (2x² - 18x + 28) is, 2 (x - 2) (x - 7)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We can factor as;
7) The factors of the expression (x² + 17x + 60) is,
⇒ x² + 17x + 60
By using quadratic formula as;
⇒ x = - 17 ± √(17² - 4×1×60 / 2
⇒ x = - 17 ± √289 - 240 / 2
⇒ x = - 17 ± √49 / 2
⇒ x = - 17 ± 7 / 2
⇒ x = - 17 + 7 / 2
⇒ x = - 10/2
⇒ x = - 5
And, x = - 17 - 7 / 2
⇒ x = - 24/2
⇒ x = - 12
Thus, The factors of the expression (x² + 17x + 60) is,
⇒ (x + 5) (x + 12)
8) The factors of the expression (x² - 6x - 27) is,
⇒ x² - 6x - 27
⇒ x² - 9x + 3x - 27
⇒ x (x - 9) + 3 (x - 9)
⇒ (x + 3) (x - 9)
Thus, The factors of the expression (x² - 6x - 27) is,
⇒ (x + 3) (x - 9)
9) The factors of the expression (2x² - 18x + 28) is,
⇒ 2x² - 18x + 28
⇒ 2 (x² - 9x + 14)
⇒ 2 (x² - 7x - 2x + 14)
⇒ 2 (x (x - 7) - 2 (x - 7))
⇒ 2 (x - 2) (x - 7)
Thus, The factors of the expression (2x² - 18x + 28) is,
⇒ 2 (x - 2) (x - 7)
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Evaluate the expression and write your answer in the form a+bi.
√−25
Answers
The express in the form of a + bi would be 0 + 5i.
What is meant by Complex numbers?Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to (√-1). A pair of real and imaginary numbers combined in the form a + bi.
When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.
Let the given expression be [tex]$\sqrt{-25}$$[/tex].
We have to evaluate the expression.
[tex]$$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$[/tex]
The express in the form of a + bi = 0 + 5i.
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Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers. Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5} Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6} Which statement is true for the data sets? Group of answer choices The mean study time of students in Class A is less than students in Class B. The range of study time of students in Class A is less than students in Class B. The mean and median study time of students in Class A and Class B is equal. The median study time of students in Class B is greater than students in Class A. The mean study time of students in Class B is less than students in Class A.
Answers
The mean study time of students in Class B is less than students in
Class A.
Option E is the correct answer.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Class A:
{2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}
Mean:
(2 + 5 + 7 + 6 + 4 + 3 + 8 + 7 + 4 + 5 + 7 + 6 + 3 + 5 + 4 + 2 + 4 + 6 + 3 + 5) / 20
= 96/20
= 4.8
Arrange the numbers in order.
= 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8
Median = 5
Range = Highest - Lowest = 8 - 2 = 6
Class B:
{3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}
Mean:
= (2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7 + 7 = 84/20
= 4.2
Arrange the numbers in order.
= 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7
Median = 4
Range = Highest - Lowest = 7 - 2 = 5
Thus,
Mean of class A > Mean of class B
Median of class A > Median of class B
Range of class A > Range of class B
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a soup can has a diameter of 278 inches and a height of 414 inches. how many square inches of metal are required to make the soup can?
Answers
Are required 482,972.60 in^2 of metal to make the soup can
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2
The formula and procedure to solve this geometry exercise is:
A= (2* π *r * h) + (2 * π * r²)
Where:
A = areah = height r = radiusProblem information:
d = 278 inh = 414 inA = ?Using the formula of the cylinder area we get:
A= (2* π *r * h) + (2 * π * r²)
A= [2* π *(278/2) * 414] + [2 * π * (278/2)²]
A= [2* π *(139) * 414] + [2 * π * (139)²]
A= [2* π *(139) * 414] + [2 * π * (139)²]
A = 361575.18 in^2 + 121397.42 in^2
A = 482,972.60 in^2
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Blaine is two years older than three times a jillion’s age Jillian is also 16 years younger than Blaine. How old is Blaine
Answers
Answer:
SLAY
Step-by-step explanation:
UWU
what is the unsigned base 9 equivalent of the following unsigned decimal integer value? 6239124 blank 1. fill in the blank, read surrounding text. 12658420
Answers
The unsigned base 9 equivalent of the following unsigned decimal integer value is [tex](6239124)_{8} = (12658420)_{9}[/tex].
We can determine Base 9 equivalent is as follows:
Iteratively divide the integer by 9 until the quotient equals 0.
The integer value is 6239124.
Now we divide integer value 6239124 by 9 until quotient is equal to 0.
6239124 ÷ 9 = 693,236, Remainder = 0
693,236 ÷ 9 = 77,026, Remainder = 2
77,026 ÷ 9 = 8,558, Remainder = 4
8,558 ÷ 9 = 950, Remainder = 8
950 ÷ 9 = 105, Remainder = 5
105 ÷ 9 = 11, Remainder = 6
11 ÷ 9 = 1, Remainder = 2
1 ÷ 9 = 0, Remainder = 1
[tex](6239124)_{8} = (12658420)_{9}[/tex]
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The complete question is:
What is the unsigned base 9 equivalent of the following unsigned decimal integer value?
[tex](6239124)_{?} = (12658420)_{?}[/tex]
special right triangle
Answers
B= 6 √ 3
Reasoning> same angle
the radius of earth is 6371 km. how many times longer is the diameter of earth than the piece of wood's length? use scientific notation.
Answers
The [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.
The radius of earth is 6371 km.
Let's say the length of the piece of wood is L.
The diameter of the Earth is 2 times its radius
The radius of our planet, The Earth, is the distance from the center of the Earth to a point on or near its surface, and it ranges from nearly 6,378 km to nearly 6,357 km.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. The area and circumference of a circle are also measured in terms of radius.The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle. It is usually denoted by ‘d’ or ‘D’.
Diameter = 2 x RadiusThe diameter of the Earth is 2 times its radius, or 2 x 6371 km = 12742 km.
The diameter of the Earth is 12742 km / L times longer than the length of the piece of wood.
In scientific notation, we can express this as:
12742 km / L = [tex]1.2742*10^4 km / L[/tex]
The [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.
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evaluate the expression 4(3-2)^3+2(-8) and justify each step
Answers
Answer:-12
Step-by-step explanation: First you will have to deal with the things in parenthesis and the exponent. So after cubing the 3 and 2 the equation you will then multiply and then add them rest of the numbers to get -12
Use the points (-3, 5) and (8, -17) to write an equation in standard form (show all work)
Answers
Answer:
2x+y=-1
Step-by-step explanation:
I can't really explain,But the equation is AX+BY=C
Your are to receive $2007 in 5 years, or you can opt to receive an equivalent amount today. At 6% nominal interest, what amount should you receive today? a. $1300 b. $1400 c. $1500 d. $1600
Answers
At 6% nominal interest, the amount should you receive today is (d) $1600.
The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or complete sum.
The present value of $2007 received in 5 years can be calculated using the formula:
PV = FV / (1 + r)^t
Where:
PV is the present value
FV is the future value ($2007)
r is the nominal interest rate (6%)
t is the time period (5 years)
So, PV = $2007 / (1 + 0.06)^5 = $1600
Therefore, you should receive $1600 today if you want an equivalent amount.
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What is the area of rhombus KLMN? Rhombus 467.4 in 387.6 in 289 in 287.3 in
Answers
The area of rhombus KLMN is 287.3 in²
What are rhombuses?A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
Given:
Since, the diagonals of a rhombus bisects each other at a right angle,
Let they bisect at O,
so, KM = 2MO = 2KO = 2×11.4 = 22.8 in
Thus, Δ KON is a right triangle,
Using Pythagoras theorem,
KN² = KO² + ON²
ON = √17²-11.4²
ON = 12.611 in
LN = 2×12.611
LN = 25.22 in
Then, Area of a rhombus = 1/2 × diagonal 1 × diagonal 2
Area = 1/2 × 25.22 × 22.8
= 287.3 in²
Hence, the area of rhombus KLMN is 287.3 in²
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proms friend gives him a row of pascal’s triangle and asks which row it comes from. prom adds the numbers and obtains a sum of 65 536. which row do the numbers come from? 34 18 17 16
Answers
The correct answer is row number 16 since the sum is 65536 in
pascal's triangle which equals to the 2 power of 16 , that is 4th option.
Pascal's triangle, in algebra, a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)n. This triangle is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle. In any row of Pascal's triangle, the sum of the first, third, fifth, … numbers is equal to the sum of the second, fourth, sixth numbers.
(1+x)n=(n0)+(n1)x+(n2)x2+⋯+(nr)xr+⋯+(nn−1)xn−1+(nn)xn.
We know that , 2^16 = 65536
Therefore, the numbers come from the row number.16
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d is inversely proportional to r.
d = 7 when r = = 8
a) Use the information above to write an
equation for d in terms of r.
b) What is the value of d when r =
Give any decimal answers to 1 d.p.
= 5?
Answers
Answer: 11.2
Step-by-step explanation:
a) d= k/r
=> 7= k/8
=> k= 7x8
therefore, k=56
b) d=k/r
=> d=56/ 5
so, d= 11.2
The value of d is 7 when r = 5.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
d is inversely proportional to r.
This can be written as,
d ∝ 1/r
d = k/r
Now,
d = 7 when r = = 8
This means.
7 = k/8
k = 56
Now,
Substituting r = 8.
d = 56/8
d = 7
Thus,
d = 7.
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consider a game of nim with four piles, of sizes 9, 10, 11, 12. (a) is this position a win for the next player or the previous player (assuming optimal play)? describe the winning first move. (b) consider the same initial position, but suppose that each player is allowed to remove at most 9 chips in a single move (other rules of nim remain in force). is this an n- or p-position?
Answers
This is a position a win for the next player; the first player's winning move is to remove 2 chips from the pile with size 11, and if each player is allowed to remove at most 9 chips in a single move, then this is a P-position, and the previous player has won.
(a) The outcome of a game of Nim depends on the XOR (exclusive or) of the sizes of the piles. The XOR of 9, 10, 11, and 12 is 2, which means that this is a P-position (i.e., the previous player has won).
To determine the winning first move, we must find a combination of pile sizes that results in a new XOR of 0. One way to do this is to remove 2 chips from the pile with size 11, resulting in 9, 10, 9, and 12. The XOR of these new pile sizes is 0, which means that this is an N-position (i.e., the next player will win).
The first player's winning move is to remove 2 chips from the pile with size 11.
(b) The maximum number of chips that can be removed in a single move is 9, so the players are restricted in the amount they can remove. However, the outcome of the game still depends on the XOR of the pile sizes. In this case, the XOR of 9, 10, 11, and 12 is 2, which means that this is still a P-position and the previous player has won.
The winning first move, as described above, would still be to remove 2 chips from the pile with size 11.
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There are counters of four different colours in a bag. A counter is taken out at random.
This table shows the probabilities of different colours.
Colour gold silver bronze white
Probability 0.05 0.15 0.55
Find the probability that the counter is
a. gold or silver
b. not gold
c. silver or bronze
Answers
a)
P (gold or silver) is 0.20
b)
P (not gold) is 0.95
c)
P (silver or bronze) is 0.70
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Color gold silver bronze white
Probability 0.05 0.15 0.55 0.25
Now,
The probability that the counter is
a)
P (gold or silver)
= 0.05 + 0.15
= 0.20
b)
P (not gold)
= 1 - 0.05
= 0.95
c)
P (silver or bronze)
= 0.15 + 0.55
= 0.70
Thus,
The probabilities are given above.
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A home was bought 4 years ago. The purchase price was $92,000 and the buyer made a down payment of $11,000. The current loan balance is $79,000. The house was recently appraised for $116,000. What is the equity?
a)13,000
b)24,000
c)35,000
d)37,000
Answers
If the current loan balance is $79,000 and the house was recently appraised for $116,000, the equity in the house would be worth d) $37,000.
The home was bought at a price of $92,000 and a down payment of $11,000 was made. It is also given that the current loan balance is $79,000.
Also, the house was recently appraised for $116,000. We are asked to calculate the equity.
Now, equity is defined as the sum of money the owner of an item would receive if they sold it and all associated debts were settled is known as equity. For example, if one person owns a house which has a value of $100,000 and he has a mortgage of $40,000. Then, the equity in the home would be worth $60,000.
Here, in this question, the current debt is $79,000 and the current value of the house is $116,000.
So, the equity in the home would be:
Equity = 116,000 - 79000 = $37,000
Hence, the equity in the house would be worth $37,000.
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which expressions are equivalent to 5(x+7)+7(x+5)
Answers
Equivalent to 5(x+7)+7(x+5) is expression 12x + 70 .
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given expression
5(x+7)+7(x+5)
Using distributive property
= 5x + 35 + 7x + 35
Adding like terms
= 12x + 70
Hence, expression 12x + 70 is equivalent to 5(x+7)+7(x+5).
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Yesterday the temperature at noon was 28.6°F. By midnight, it had dropped by 30.7°F. What was the temperature at midnight?
Answers
The correct answer is -2.1°F. You do this by simply subtracting 28.8 by 30.9. When doing this, you get
-2.1. So the temperature at midnight was -2.1°F.
Step-by-step explanation:
state where in the ty plane the hypothesis of theorem are satisfied
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The ty plane the hypothesis of theorem are satisfied
The hypothesis of a theorem is a statement or assumption that is made in order to prove a mathematical result.
The hypothesis of the Tychonoff theorem is satisfied in a variety of different spaces, including compact spaces and metrizable spaces.
This theorem is important because it provides a useful tool for understanding the properties of topological spaces, which are spaces that have certain structures that allow for the study of continuous functions and mappings.
In summary, the hypothesis of the Tychonoff theorem is a necessary condition for the theorem to be proven and is satisfied in a variety of different spaces.
Understanding the hypothesis and the spaces in which it is satisfied is crucial for understanding the theorem and its applications in mathematics.
Complete Question:
State where in the ty-plane the hypotheses of Theorem
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Given that the econd term of a equence i 8 and the fourth term i 2, Franci wrote the explicit rule an = 4 · ( 1 4 )n − 1 for the equence. Complete the explanation of hi error
Answers
Francis made an error in writing the explicit formula. The correct formula should be an = 4 * (1/4)⁽ⁿ⁻¹⁾, not an = 4 * (1/4)ⁿ⁻¹. The exponent should be (n-1), not just n, to correctly represent the sequence where the second term is 8 and the fourth term is 2.
Explicit Formula Error CorrectionTo determine the error in Francis' formula, we need to apply it to the known terms of the sequence and see if it produces the correct values. For example, for the second term, n = 2, so using Francis' formula:
an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)¹ = 4 * 1/4 = 1
But the second term of the sequence is 8, not 1. So the formula is incorrect.
Similarly, for the fourth term, n = 4, so using Francis' formula:
an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)³ = 4 * 1/64 = 1/16
But the fourth term of the sequence is 2, not 1/16. So the formula is still incorrect.
Therefore, we can conclude that the formula written by Francis is not correct and needs to be corrected to accurately describe the sequence.
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five whole positive numbers add up to 47 one of the numbers is a multiple of nine the other four numbers are equal
Answers
The positive whole numbers are 27 and 5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the 5 positive whole numbers be a, b, c, d and e.
One of the numbers is a multiple of nine the other four numbers are equal.
Now, 9a+b+b+b+b=47
9a+4b=47
If b=1
9a=43
Here, we don't get whole number.
If b=2
9a=39
Here, we don't get whole number.
If b=3
9a=35
Here, we don't get whole number.
If b=4
9a=31
Here, we don't get whole number.
If b=5
9a=27
a=3
Substitute a=3 in equation 9a+4b=47
b=5
Therefore, the positive whole numbers are 27 and 5.
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