Question 2(Multiple Choice Worth 1 points) (02.01 LC) Simplify negative 3 over 5 ÷ 7 over 6. negative 7 over 10 negative 18 over 35 18 over 35 7 over 10
Answers
Answer:
-18/35
Step-by-step explanation:
Related Questions
Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he
has to go. If Yan made 8 stops with no extra steps, which expression best shows another way to write the product of
the number of ladder rungs that Yan climbed?
A. 4+4+4+4
B. 8+8+8+8
C. (-1)(4+4+4+4)
D. (-8)+(-8)+(-8)+(-8)
Answers
Answer:
A. 4+4+4+4 ...............
Answer - B.
Question -Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he
has to go. If Yan made 8 stops with no extra steps, which expression best shows another way to write the product of
the number of ladder rungs that Yan climbed?
A. 4+4+4+4
B. 8+8+8+8
C. (-1)(4+4+4+4)
D. (-8)+(-8)+(-8)+(-8)
Why - The answer is B because if you read the question, it says basically, 4x8 and to solve that the hard way it is 8+8+8+8 meaning 8, 4 times. So the answer is B. YES A IS WRONG!
Translate the triangle.
Then enter the new coordinates.
Answers
Answer:
A'(0, 13)B'(1, 11)C'(-2, 11)Step-by-step explanation:
You want the coordinates of the image of the triangle defined by A(3, 4), B(4, 2), and C(1, 2) after it has been translated by (-3, 9).
TranslationThe translation amounts are added to the corresponding coordinates:
(x, y) ⇒ (x -3, y +9)
A(3, 4) ⇒ A'(3 -3, 4 +9) = A'(0, 13)
B(4, 2) ⇒ B'(4 -3, 2 +9) = B'(1, 11)
C(1, 2) ⇒ C'(1 -3, 2 +9) = C'(-2, 11)
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solve the given boundary-value problem. y'' 7y = 7x, y(0) = 0, y(1) y'(1) = 0
Answers
The solution to the given boundary-value problem is y(x) = 2sin(pi*x) + x, where y(0) = 0 and y(1) = y'(1) = 0.
To solve the given boundary-value problem, we first write the differential equation in standard form
y'' + 7y = 7x
Next, we find the general solution of the homogeneous equation y'' + 7y = 0
The characteristic equation is r^2 + 7 = 0, which has roots r = ±√(7)i. Thus, the general solution of the homogeneous equation is
y_h(x) = c₁*cos(√(7)x) + c₂sin(√(7)*x)
where c₁ and c₂ are constants to be determined by the initial conditions.
Now, we find a particular solution of the non-homogeneous equation y'' + 7y = 7x
A particular solution of the non-homogeneous equation is y_p(x) = Ax + B, where A and B are constants. Substituting this into the differential equation, we get
0 + 7(Ax + B) = 7x
Solving for A and B, we get A = 1 and B = 0. Thus, a particular solution of the non-homogeneous equation is y_p(x) = x.
Therefore, the general solution of the given differential equation is
y(x) = c1*cos(√(7)x) + c2sin(√(7)*x) + x
Using the first initial condition y(0) = 0, we get
c1 = 0
Using the second initial condition y(1) = 0, y'(1) = 0, we get
c₂sin(√(7)) + 1 = 0
c₂sqrt(7)*cos(√(7)) = 0
Since c₂ cannot be zero, the second equation gives us cos(sqrt(7)) = 0, which implies sqrt(7) = (2n+1)*pi/2 for some integer n. Thus, the possible values of √(7) are
√(7) = pi/2, 3pi/2, 5pi/2, ...
Therefore, the general solution of the differential equation that satisfies the boundary conditions is
y(x) = (2/n)sin(npi*x) + x, where n is an odd integer.
In particular, the solution satisfying the given initial conditions is
y(x) = (2/1)sin(pix) + x = 2sin(pi*x) + x
Hence, the solution of the problem is y(x) = 2sin(pi*x) + x, where y(0) = 0 and y(1) = y'(1) = 0.
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The nth term of sequence S is 2n+5
The nth term of sequence T is 3n - 6
(a) Show that 91 is a term in sequence S.
b) Show that 91 is not a term in sequence T
Answers
The term 91 is present in sequence S at n = 43, and the term is not a part of the sequence T.
What is sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted, and order is important. Similar to a set, it has members.
Given that:
a = 91
Substitute the value of a in the given sequence.
Sequence S:
a = 2n+5
91 = 2n + 5
91 - 5 = 2n
n = 43
Sequence T:
a = 3n - 6
91 + 6 = 3n
n = 97/3
As the terms present in a sequence cannot be a fraction we figure that 91 is not present in sequence T.
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Choose the expression that represents "three less
than seven times a number."
3x - 7
7X-3
3x + 7
17X+3
7x + 3x
Answers
Answer:
none of your options are right
Step-by-step explanation:
Three less than seven times a number:three : 3, less than : (-), seven : 7, times : (multiplication symbol), a number : (x)
the answer is : 3 - 7 (x)
: 3-7x
What simple interest rate would allow $6000 to grow to an amount of $14550 in 10 years?
Answers
Answer:
\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \: 14.25 \: \% \: }}}}}\)
Step-by-step explanation:
Given,
Principal ( P ) = $ 6000
Amount ( A ) = $ 14550
Time ( T ) = 10 years
Rate ( R ) = ?
Finding the Interest
The sum of principal and interest is called an amount.
From the definition,
\( \boxed{ \sf{Amount = \: Principal + Interest}}\)
plug the values
⇒\( \sf{14550 = 6000 + Interest}\)
Swap the sides of the equation
⇒\( \sf{6000 + Interest = 14550}\)
Move 6000 to right hand side and change its sign
⇒\( \sf{Interest = 14550 - 6000}\)
Subtract 6000 from 14550
⇒\( \sf{Interest = \: 8550 \: }\)
Interest = $ 8550
Finding the rate
\( { \boxed{ \sf{Rate = \frac{Interest \times 100}{Principal \times Time}}}} \)
plug the values
⇒\( \sf{ Rate = \frac{8550 \times 100}{6000 \times 10} }\)
Calculate
⇒\( \sf{Rate = \frac{855000}{60000} }\)
⇒\( \sf{Rate = 14.25 \: \% \: }\)
Hope I helped!
Best regards!!
A viral video had 100,000 views on the first day. Each day, the number of views is 60% of the previous day. How many views will the video receive
on the fourth day?
O 21,600
O 36,000
12,960
O 60,000
Answers
Answer:
21600
Step-by-step explanation:
On the second day, the number of views will be:
100,000 x 0.6 = 60,000
On the third day, the number of views will be:
60,000 x 0.6 = 36,000
On the fourth day, the number of views will be:
36,000 x 0.6 = 21,600
On the fifth day, the number of views will be:
21,600 x 0.6 = 12,960
On the sixth day, the number of views will be:
12,960 x 0.6 = 7,776
On the seventh day, the number of views will be:
7,776 x 0.6 = 4,665.6
So, the video will receive approximately 4,666 views on the seventh day.
Answer:
21 600 views
Step-by-step explanation:
1. Day - 100 000 views
2. Day - 100 000 × 0,6 = 60 000 views
3. Day - 60 000 × 0,6 = 36 000 views
4. Day - 36 000 × 0,6 = 21 600 views
PLEASE HELP ME TO SOLVE THIS QUESTION
3.Xavier's salary increases by 2% each year.
In 2010 , his salary was £40,100
i) Calculate his salary in 2015 and give your answer to the nearest pound.
ii) In which year did Xavier's salary first greater than £47,500
Answers
i) Based on exponential growth, Xavier's salary in 2015 is £44,274.
ii) The year that Xavier's salary first became greater than £47,500 would be 2019.
What is exponential function?Exponential functions show the relationship between two variables and a variable exponent with a periodic constant rate of growth or decay in the value of something
Annual increase in Xavier's salary = 2% or 0.02
Xavier's salary in 2010 = £40,100
The number of years between 2015 and 2010 = 5 years
Exponential Function:i) y = £40,100(1.02)^5
= £44,273.64
= £44,274
ii) £47,500 = £40,100(1.02)^t
t = 9 years
= 2019 (2010 + 9)
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Mariah is planting a rectangular rose garden. In the center of the garden, she puts a smaller rectangular patch of grass. The grass is 2 feet by 3 feet. What is the area of the rose garden?
Answers
The area of the rose garden is 129 sq. ft.
Consider the following diagram.
The dimensions of the rectangular garden:
length = 15 ft and width = 9 ft
Using the formula for the area of rectangle,
The area of the rectanguler garden would be,
A₁ = 15 × 9
A₁ = 135 ft²
In the center of the garden, she puts a smaller rectangular patch of grass. And the dimensions of the grass is 2 feet by 3 feet.
The area of rectangular patch is:
A₂ = 2 × 3
A₂ = 6 ft²
So, the area of the rose garden would be,
A = A₁ - A₂
A = 135 - 6
A = 129 ft²
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Find the complete question below.
Find F'(x): F(x) = Sx² 1 (t³ - 4t² + 2)dt
Answers
The derivative of F(x) is F'(x) = 2x³ - 8x² + 4x.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.
Let's compute F'(x):
F(x) = ∫[1 to x²] (t³ - 4t² + 2) dt
To differentiate the integral with respect to x, we'll use the Leibniz integral rule:
F'(x) = d/dx ∫[1 to x²] (t³ - 4t² + 2) dt
According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.
F'(x) = (x²³ - 4x²² + 2) d(x²)/dx - (1³ - 4(1)² + 2) d(1)/dx [applying the chain rule to the upper limit]
F'(x) = (x²³ - 4x²² + 2) (2x) - (1 - 4 + 2) (0) [using the power rule for differentiation]
F'(x) = 2x(x²³ - 4x²² + 2)
F'(x) = 2x³ - 8x² + 4x
Therefore, the derivative of F(x) is F'(x) = 2x³ - 8x² + 4x.
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An analyst for FoodMax estimates that the demand for its "Brand X" potato chips is given by: In Qyd = 10.34 – 3.2 In Px+4Py+ 1.5 In Ax = where Qx and Px are the respective quantity and price of a four-ounce bag of Brand X potato chips, Pyis the price of a six-ounce bag sold by its only competitor, and Axis FoodMax's level of advertising on brand X potato chips. Last year, FoodMax sold 5 million bags of Brand X chips and spent $0.25 million on advertising. Its plant lease is $2.5 million (this annual contract includes utilities) and its depreciation charge for capital equipment was $2.5 million; payments to employees (all of whom earn annual salaries) were $0.5 million. The only other costs associated with manufacturing and distributing Brand X chips are the costs of raw potatoes, peanut oil, and bags; last year FoodMax spent $2.5 million on these items, which were purchased in competitive input markets. Based on this information, what is the profit-maximizing price for a bag of Brand X potato chips? Instructions: Enter your response rounded to the nearest penny (two decimal places). $
Answers
The profit-maximizing price for a bag of Brand X potato chips is approximately $3.35.
To determine the profit-maximizing price, we need to find the price that maximizes the profit function. The profit function can be expressed as follows:
Profit = Total Revenue - Total Cost
Total Revenue (TR) is calculated by multiplying the quantity sold (Qx) by the price (Px):
TR = Qx * Px
Total Cost (TC) includes the costs of advertising, plant lease, depreciation, employee payments, and the costs of raw materials:
TC = Advertising Cost + Plant Lease + Depreciation + Employee Payments + Raw Material Costs
Given the information provided, last year FoodMax sold 5 million bags of Brand X chips, spent $0.25 million on advertising, and incurred costs of $2.5 million for raw materials.
To find the profit-maximizing price, we differentiate the profit function with respect to Px and set it equal to zero:
d(Profit)/d(Px) = d(TR)/d(Px) - d(TC)/d(Px) = 0
The derivative of the total revenue with respect to the price is simply the quantity sold:
d(TR)/d(Px) = Qx
The derivative of the total cost with respect to the price is found by substituting the given demand equation into the cost equation and differentiating:
d(TC)/d(Px) = -3.2 * Qx
Setting these two derivatives equal to each other:
Qx = -3.2 * Qx
Simplifying the equation:
4.2 * Qx = 0
Since the quantity sold cannot be zero, we solve for Qx:
Qx = 0
This implies that the quantity sold, Qx, is zero when the price is zero. However, a price of zero would not maximize profit.
To find the profit-maximizing price, we substitute the given values into the demand equation:
5 million = 10.34 - 3.2 * Px + 4 * Py + 1.5 * 0.25
Simplifying the equation:
5 million = 10.34 - 3.2 * Px + 4 * Py + 0.375
Rearranging terms:
3.2 * Px = 14.34 - 4 * Py
Substituting the given value of Py as 0 (since no information is provided about the competitor's price):
3.2 * Px = 14.34 - 4 * 0
Simplifying:
3.2 * Px = 14.34
Dividing both sides by 3.2:
Px = 4.48
Thus, the profit-maximizing price for a bag of Brand X potato chips is approximately $4.48. However, since the price is limited to the nearest penny, the profit-maximizing price would be approximately $4.48 rounded to $4.47.
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um help again. i’m terrible with math so an answer would really help thxs :)
Answers
Answer:
20
Step-by-step explanation:
skip count by 2
To determine chilling hours for an area count the cumulative number of hours between November 1st and February 15th that the air temperatures is between 32 and 45 degrees F. Group of answer choices True False
Answers
The statement "To determine chilling hours for an area, count the cumulative number of hours between November 1st and February 15th that the air temperature is between 32 and 45 degrees F" is true.
In horticulture, chilling hours are the number of hours in which the air temperature is between 32 and 45 degrees Fahrenheit and are commonly used in fruit crop production to determine the required winter rest period. It is calculated between November 1st and February 15th since these months are considered the winter season and are known for their cool temperatures.
Chilling hours are an essential factor in determining the growth, development, and yield of fruit trees, which require a particular amount of chilling hours to flower and bear fruit.
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Please look at the image
Answers
Step-by-step explanation:
the exterior angle at every interior angle will be found by 180 minus the interior because angles on a straight line add to 180 degrees
The sum of the exterior angles in a shape always add up to 350 degrees
Which expression below can Cynthia use to find the cost for a backage that weighs w pounds?
0. A. W + 3.50
O B. 3.50
w
O c. 3.50 - w
OD 3.50W
Answers
Answer:
A
Step-by-step explanation:
Many businesses and organizations insist that official communications use professional-looking fonts, such as times new roman. fonts characterized as less professional, such as comic sans, should be avoided. a student would like to determine if font choice makes a difference in the average grade on a typed response in english classes. there are currently four english classes available from which the student can collect data, and each class has a similar writing assignment. at the start of the assignment, students are randomly assigned a font, either times new roman or comic sans, and then complete the assignment. the teachers grade the assignments, and the mean grade for each font is found.Method A: At the start of the assignment, students choose a font, either Times New Roman or Comic Sans, and then complete the assignment.Method B: At the start of the assignment, students are randomly assigned one of two fonts, either Times New Roman or Comic Sans, and then complete the assignment.In both methods, the teachers grade the papers received, and the mean grade for each font is determined.Which method describes an experiment?a. Method A is an experiment because the students choose their own font.b. Method B is an experiment because the students are randomly assigned a font.c. Both methods describe experiments because both fonts are used on the assignment.d. Neither method describes an experiment because a third font should be included for comparison.
Answers
Hope this helps.
Huey can wash 6 cars or mow 3 lawns in one hour. Dewey can wash 3 cars or mow 3 lawns in one hour. Louie can wash 3 cars or mow 6 lawns in one hour. They each work 8 hours per day. If two of them wash cars and one mows lawns then at most they can wash cars and mow lawns. Enter whole numbers.
Answers
At most, they can wash 96 cars and mow 96 lawns.
To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.
Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.
Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.
Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.
Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.
The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.
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whar are the formulae of - sin , tan , cosec, cos
Answers
Answer:
Now, the formulas for other trigonometry ratios are: Cot θ = 1/tan θ = Adjacent side/ Side opposite = AB/BC. Sec θ = 1/Cos θ = Hypotenuse / Adjacent side = AC / AB. Cosec θ = 1/Sin θ = Hypotenuse / Side opposite = AC /BC
Tan=Opposite/Adjacent
Cosec=Hypotenuse/Opposite
Cos=Adjacent/Hypotenuse
Instructions: List the domain and range of the following relation.
Answers
Step 1
A relation is a relationship between sets of values. In math, the relation is between the x-values and y-values of ordered pairs. The set of all x-values is called the domain, and the set of all y-values is called the range.
Step 2
Find the domain
\(\lbrace0,4,6,7\rbrace\)Step 3
Find the range
\(\lbrace1,3,5\rbrace\)If bc+ad=b solve for a (please show work)
Answers
Answer:
a = \(\frac{b-bc}{d}\)
Step-by-step explanation:
Given
bc + ad = b ( subtract bc from both sides )
ad = b - bc ( isolate a by dividing both sides by d )
a = \(\frac{b-bc}{d}\)
COMPLETELY simplify the following. (Show Work) (Worth a lot of points)
Answers
Answer:
\(\frac{27y^6}{8x^{12}}\)
Step-by-step explanation:
1) Use Product Rule: \(x^ax^b=x^{a+b}\).
\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)
2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).
\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)
3) Use Rule of Zero: \(x^0=1\).
\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)
4) use Product Rule: \(x^ax^b=x^{a+b}\).
\((\frac{3y^3}{2x^{3+1}y} )^3\)
5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).
\((\frac{3y^{3-1}x^{-4}}{2} )^3\)
6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).
\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)
7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).
\(\frac{(3y^2)^3}{2x^4}\)
8) Use Multiplication Distributive Property: \((xy)^a=x^ay^a\).
\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)
9) Use Power Rule: \((x^a)^b=x^{ab}\).
\(\frac{27y^6}{(2x^4)^3}\)
10) Use Multiplication Distributive Property: \((xy)^a=x^ay^a\).
\(\frac{26y^6}{(2^3)(x^4)^3}\)
11) Use Power Rule: \((x^a)^b=x^{ab}\).
\(\frac{27y^6}{8x^12}\)
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Answer:
\(\displaystyle \frac{27y^{6}}{8x^{12}}\)
Step-by-step explanation:
\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)
Notes:
1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied
2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))
3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator
Hope this helped!
Find the volume of a cone that has a radius of and a height of 1.
Answers
the volume of the cone would be 2.36 I hope this helps ❤️
Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two eights
Answers
The probability of drawing two eights is 16/2,704, which simplifies to 1/169, or approximately 0.59%.
There are a total of 52 cards in each deck, so there are 52 x 52 = 2,704 possible combinations of cards that could be drawn.
To calculate the probability of drawing two eights, we need to determine the number of ways we can draw two eights and then divide that by the total number of possible combinations.
There are four eights in each deck, so there are 4 x 4 = 16 ways to draw two eights (one from each deck).
Therefore, the probability of drawing two eights is 16/2,704, which simplifies to 1/169, or approximately 0.59%.
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Determine the slope of a line that passes through the following points.
(3,4), (5,7)
Answers
Answer:
6/4 and can be simplified as 3/2
Step-by-step explanation:
Please help with this question
Answers
Answer:
I'm not sure but it could be y = 2x² - 6x - 8
PLS HELP WITH THIS ASSIGNMENT OMG ITS SO HARD FOR ME
Answers
The new coordinates of each of the triangle coordinates are;
1) A'(-12, 6), B'(3, 9), C'(-9, 18)
2) A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)
3) X'(-8, 2), Y'(2, 14), Z'(8, 8)
4) X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)
5) A'(-8, 4), B'(2, 6), C'(-6, 12)
6) X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)
7) X'(-20, 5), Y'(5, 35), Z'(20, 20)
8) A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)
How to carry out dilation in transformation?Dilation is a transformation whereby an image size could increase or even decrease but will retain the same shape as the original one. Therefore, we will simply multiply each coordinate by the scale factor;
The coordinates of both triangles are given as;
Triangle ABC = A(-4, 2), B(1, 3), C(-3, 6)
Triangle XYZ = X(-4, 1), Y(1, 7), Z(4, 4)
1) The dilation transformation of triangle ABC by a scale factor of 3 means we multiply each ABC coordinate by 3 to get;
A'(-12, 6), B'(3, 9), C'(-9, 18)
2) The dilation transformation of triangle ABC by a scale factor of 1/2 means we multiply each ABC coordinate by 1/2 to get;
A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)
3) The dilation transformation of triangle XYZ by a scale factor of 2 means we multiply each XYZ coordinate by 2 to get;
X'(-8, 2), Y'(2, 14), Z'(8, 8)
4) The dilation transformation of triangle XYZ by a scale factor of 1/4 means we multiply each XYZ coordinate by 1/4 to get;
X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)
5) The dilation transformation of triangle ABC by a scale factor of 2 means we multiply each ABC coordinate by 2 to get;
A'(-8, 4), B'(2, 6), C'(-6, 12)
6) The dilation transformation of triangle XYZ by a scale factor of 1/3 means we multiply each XYZ coordinate by 1/3 to get;
X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)
7) The dilation transformation of triangle XYZ by a scale factor of 5 means we multiply each XYZ coordinate by 5 to get;
X'(-20, 5), Y'(5, 35), Z'(20, 20)
8) The dilation transformation of triangle ABC by a scale factor of 1/4 means we multiply each ABC coordinate by 1/4 to get;
A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)
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Convert 3.1415 x 10^-2 to standard notation.
Answers
In a short sentences please, Prove that the sum of two rational numbers is rational. THANK YOU!!!
Answers
The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.
How does this work?A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.
When we add two rational numbers together, we can use the following formula:
a/b + c/d = (ad + bc) / bd
where a, b, c, and d are integers and b and d are not equal to zero.
This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.
For example, if we want to add 1/2 and 2/3 together, we can use the formula above:
1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6
Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.
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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).
If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.
Is x^(-2) 5 a polynomial expression? Why or why not?.
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The diameter of a circular pizza is 24 in. How much pizza is eaten (in square inches) if half of it is consumed? (Pie and л... hmmmm...interesting...)
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Using the formula of area of a circle, about 226.08in² has been eaten
How much pizza is eaten?The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:
Area = π * r²
where π is approximately 3.14 and r is the radius of the circle.
Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.
Let's calculate the area of the entire pizza first:
Area = 3.14 * 12²
Area = 3.14 * 144
Area ≈ 452.16 square inches
Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:
Area of half of the pizza = 452.16 / 2
Area of half of the pizza ≈ 226.08 square inches
Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.
Learn more on area of a circle here;
https://brainly.com/question/15673093
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