Mathematics College
Answers
Answer 1
If 2 cups make 1 pint, and 2 pints makes 1 quart which would be 4 cups, then 1 pint + 1 quart would be equal to 3 pints. 2 x 3 = 6 ….. So, there are 6 cups of soda.
1 pint = 2 cups
1 quart = 4 cups
Sandy Sandy can divid 1 pint and 1 quart into 6 cups of Soda.
Related Questions
It takes a bus 1 hour and 30 minutes to travel 42 miles.
Calculate the average speed of the bus in mph.
If your answer is a decimal, give it to 1 d.p.
Answers
28 mph is the average speed of the bus in mph.
What is speed?
The speed of a change in an object's location in any direction. The distance traveled relative to the time it took to travel that distance is how fast something is moving.
Meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) are the most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed = distance x time is the speed formula. The meter per second, also known as the m/s or ms1, is the SI unit of velocity.
time = (1+ 1/2)hr = 3/2 hr = 1.5 hr
distance = 42 miles
average speed = total distance/total time
42/1.5 = 28 mph
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Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.
Answers
The number of arrangements when the order is considered is 12, Number of ways when the order is not considered is 6.
Permutaions and combinations:
By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things.
The act of placing every member of a set into a certain sequence or order is known as permutation.
The combination is a method of choosing things from a group in which (unlike permutations) the order of the choices is irrelevant.
The formula for Permutations is given by
ⁿP[tex]_{r}[/tex] = (n!)/(nr)!
The formula for Combinations is given by
[tex]_{n}[/tex]C[tex]_{r}[/tex] = (n!)/r!(n  r)!
Here we have
4 letters A, B, C, and D
We need to choose 2 letters from the given 4 letters
When the order of the choices is taking consideration we use the formula of Permutations
The number of ways of arrangements, ⁴P₂ = (4!)/(42)!
= [tex]\frac{4\times 3\times\ 2!}{2!}[/tex] = [tex]4 \times 3[/tex] = 12
When the order of the choices is not taking consideration we use the formula of Combinations
Number of ways of arrangements, ₄C₂ = (4!)/2!(4  2)!
= [tex]\frac{4\times 3 \times \ 2!}{2! \times 2!}[/tex] = [tex]\frac{4\times 3 }{2 \times 1 }[/tex] = [tex]2\times 3[/tex] = 6
Therefore,
The number of arrangements when the order is considered is 12, Number of ways when the order is not considered is 6.
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A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1.
If you make this wager vary many times, what will be the mean amount you win?
Answers
The mean amount won based on the expectation formula of probability will be  2/13.
What is probability?
The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Probability of winning = 4/52 = 1/13
Probability of lossing = 1  1/13 = 12/13
The mean amount or expectation is given as,
E(X) = 10 × (1/13) +  1(12/13)
E(X) = 10/13  12/13
E(X) =  2/13
Hence "The mean amount won based on the expectation formula of probability will be  2/13".
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a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
Answers
a. The inverse variation relationship between a and b can be expressed as a = k/b^2, where k is a constant. We are given that a is 1 when b is 3, so we can substitute these values into the equation to find k: 1 = k/(3^2). Solving for k, we get k = 9.
Substituting this value of k back into the equation a = k/b^2, we can find a when b is 5: a = 9/(5^2) = 9/25 = 0.36. Therefore, a is 0.36 when b is 5.
b. To find the distance it takes for a car traveling at 65 miles per hour to stop, we can use the equation for direct variation: d = kv^2, where d is the distance, v is the speed, and k is a constant. We are given that it takes 112 feet for a car traveling at 40 miles per hour to stop, so we can substitute these values into the equation to find k: 112 = k(40^2). Solving for k, we get k = 0.0056.
Substituting this value of k back into the equation d = kv^2, we can find the distance it takes for a car traveling at 65 miles per hour to stop: d = 0.0056(65^2) = 2256 feet. Therefore, it takes 2256 feet for a car traveling at 65 miles per hour to stop.
Find the missing number/s so that the equation has One solution.
Select all that apply.
__x + 3 = –4x + 17
a
2
b
5
c
7
d
4
Answers
Answer: Choice A, Choice B, Choice C
In other words, it's nearly everything but choice D.
====================================================
Explanation:
Let's say we select "2" as the thing to fill the blank.
2x+3 = 4x+17
2x+4x = 173
6x = 14
x = 14/6
x = 7/3
We get one solution in this case.
The same applies for the values 5 and 7. I'll let you do those steps.
In contrast, if we filled the blank with 4, then,
4x+3 = 4x+17
4x+4x = 173
0x = 14
0 = 14
We get a contradiction which leads to "no solutions".
Visually, the equations y = 4x+3 and y = 4x+17 are parallel lines that never intersect. We need them to intersect if we want a solution. Recall that parallel lines have equal slopes but different yintercepts. Both sides have a slope of 4 in this case.
Therefore, the quick rule of thumb is this: if the slopes are not equal, then the linear equation has exactly one solution.
Find the 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7.
Answers
The 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7 is [tex]\frac{7}{19683}[/tex].
What is geometric sequence?
A unique kind of sequence is a geometric sequence. Every term in the series (apart from the first term) is multiplied by a fixed amount to determine the following term. In other words, we multiply the current phrase in the geometric sequence by a constant term (called the common ratio), and then divide the current term in the geometric sequence by the same common ratio to discover the previous term in the geometric sequence.
nth term of geometric series
a(n) = a(1) * r^(n1)
You are given a(1) = 7, r = 1/3 and n = 10.
a(10) = 7 * 1/3^(101)
[tex]7\left(\frac{1}{3}\right)^{101}$$[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$$\begin{aligned}& \left(\frac{1}{3}\right)^{101}=\frac{1^{101}}{3^{101}} \\& =7 \times \frac{1^{101}}{3^{101}}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& 1^{101}=1 \\& =7 \times \frac{1}{3^{101}} \\& 3^{101}=19683 \\& =7 \times \frac{1}{19683}\end{aligned}$$[/tex]
Convert element to fraction: [tex]$\quad 7=\frac{7}{1}$[/tex]
[tex]=\frac{7}{1} \times \frac{1}{19683}$$[/tex]
Apply the fraction rule: [tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{7 \times 1}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$7 \times 1=7$[/tex]
[tex]=\frac{7}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$1 \times 19683=19683$[/tex]
[tex]=\frac{7}{19683}[/tex]
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at the Mayfair Stella, Mary, cris, Elli won 60 prizes altougheter. Mary won one third of them, Stella won one fifth of them, and illli got one fourth of the total. how many prizes did chris win
Answers
The number of prizes that Chris won out of 60 will be 13.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
At the Mayfair Stella, Mary, Cris, and Elli won 60 awards altogether. Mary won 1/3 of them, Stella won 1/5 of them, and Elli got 1/4 of the aggregate.
Then the number of prizes that Chris won is given as,
⇒ 60  60 / 3  60 / 5  60 / 4
⇒ 60  20  12  15
⇒ 60  47
⇒ 13
The number of prizes that Chris won out of 60 will be 13.
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Profit margin ratio 294\3800
Answers
Stepbystep explanation:
12.93 is the answer of this question.
Suppose f(x)=x^(2) and g(x)=(3x)^(2). Which statement best compares the graph of g(x) with the graph of f(x) ?
A. The graph of g(x) is horizontally compressed by a factor of 3 .
B. The graph of g(x) is shifted 3 units to the right.
C. The graph of g(x) is vertically stretched by a factor of 3 .
D. The graph of g(x) is horizontally stretched by a factor of 3 .
Answers
Explanation it’s c Answer is C
How much simple interest is made on an investment of $800 for 7 years at 6%
Answers
Answer:
$1,136
Stepbystep explanation:
The simple interest equation is A = P(1 + rt)
P is the original amount invested (in this case, it is $800)r is the interest rate (in this case, it is 0.06 or 6%)t is the years (in this case, it is 7 years)
From here, we can just plug in the values into the equation to get 800(1 + 0.06 x 7) = $1136
Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven.
The city of Raleigh, NC charges $ 1.95 fee and $ 2.70 per mile for each cab ride.
Answers
The equation of Total Charges will be $1.95 + ($2.7 * x)
What is Linear Equation in One Variable?
A linear equation is a onevariable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
The equation of Total Charges will be
Let, the total distance in miles be x
Then,
Total Charges = $1.95 + ($2.7 * x)
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Music Company A charges a $ 15 membership fee and $ 0.75 each to download a song. Music Company B charges $ 0.90 each to download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money? Justify your answer using mathematics.
Answers
(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.
(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
What is Linear Equation in One Variable?
A linear equation is a onevariable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
Let, Songs Downloaded be x
Total Charges of Company A = 15 + 0.75*x
Total Charges of Company B = 0.9*x
(i) Total Charges by Company A = Total Charges by Company B
15 + 0.75*x = 0.9*x
15 = 0.15*x
x = 100 songs
(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150
= 15 + 112.5 = $127.5
Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135
I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
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The monthly cost of water use is a linear function of the amount of water used (HCF). The cost for using 16 HCF of water is $39.04, and the cost for using 44 HCF is $79.64. What is the cost for using 22 HCF?
Answers
Answer:
The cost for using 22 HCF is $47.74

Equation of line:
y = mx + b, where m slope, b yintercept
Given values can be interpreted as pairs of coordinates of the two points:
(16, 39.04) and (44, 79.64)
Find the slope of the line:
m = (79.64  39.04)/(44  16) = 40.6/28 = 1.45
Find the yintercept, by substituting coordinates of one point:
39.04 = 1.45*16 + b39.04 = 23.2 + bb = 39.04  23.2b = 15.84
The equation becomes:
y = 1.45x + 15.84
Find the value of y when x = 22:
y = 1.45*22 + 15.84 = 31.9 + 15.84 = 47.74
A pilot flew a jet from City A to City B, a distance of 2400 mi. On the return trip, the average speed was 20% faster than the outbound speed. The roundtrip took 5 h 30 min. What was the speed from City A to City B?
Answers
The speed from City A to City B is 873.33 mi/h.
What is the speed, distance and time?
That is speed = distance ÷ time. Or to put it another way, distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.
Let's call the speed from City A to City B x. The speed on the return trip was 1.2x. The total distance traveled was 2400 + 2400 = 4800 mi. The total time taken was 330 minutes, which is 330/60 = 5.5 hours. The average speed is the total distance traveled divided by the total time taken, so:
4800 mi / 5.5 h = 873.33 mi/h
The total speed for both legs of the trip is 873.33 + 873.33 = 1746.66 mi/h
The speed for just one leg of the trip is half of the total speed, so the speed from City A to City B is 1746.66/2 = 873.33 mi/h.
Hence, the speed from City A to City B is 873.33 mi/h.
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Round to the nearest degree
Answers
The measure of angle A of the triangle is 50°.
How to find angles of the triangle?
Eight angles are created when a transversal intersects two parallel lines. The pair of nonadjacent interior angles that are on the same side of the transversal are known as the same side internal angles.Two angles that are inside (between) the two lines, more especially on the same side of the transversal, are referred to as same side inside angles.
Similar side interior angles therefore:
have unique vertices or no shared verticesstraddle two lineswas developed on the same transverse side of theCointerior angles are another name for "same side interior angles."
So, ∠C = ∠A
∠A = 50°
Hence, the measure of angle A of the triangle is 50°.
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PLEASE best explanation gets brainliest
Answers
Answer:
55
Stepbystep explanation:
Because you would minus 180125 to get angle 1 and they said that angle 2 is parallel so they would be the same anwser so the answer is 55.
a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles.
b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles.
Answers
a) minimum of nine hikers might have covered the distance between 6 and 17 miles because it falls within the standard interval of 10 ≤ x ≤ 15.
b) The maximum no. of hikers who might have covered the distance between 6 and 17 miles is 19.
What do minimum and maximum value mean?
Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the xcoordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.
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Two numbers when multiplied equals 63 if one number is x and the other number is greater than x by 2
a) represent the information given in equation form
b) express as a quadratic equation
c) solve the quadratic equation to find possible values of x
d) if told that the two numbers are positive numbers what are the values of the two original numbers?
Answers
The values of the two original numbers are 7 and 9.
Two numbers when multiplied equal 63 if one number is x and the other number is greater than x by 2.
As per the given phrase, the information given in equation form is as
x × (x + 2) = 63
It expresses as a quadratic equation:
x² + 2x  63 = 0
Solve the quadratic equation to find possible values of x
x² + 9x  7x  63 = 0
x(x + 9)  7(x + 9) = 0
(x + 9)(x  7) = 0
(x + 9) = 0 and (x  7) = 0
x = 9 and x = 7
Since we were told that the two numbers are positive numbers so take x = 7.
Thus, the values of the two original numbers are 7 and 9.
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The sum of a number and six is four less than six times the number
Answers
4  6x is linear equation .
What in mathematics is a linear equation?
A linear equation is a firstorder (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the yintercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
A linear equation's graph almost always takes the shape of a straight line.
Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
let the number be =x
4  6x
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Do You Know How?
3. Estimate 452 ÷ 21.
4. Complete.
21)4 52

R
Remember
to check that
your answer is
reasonable.
Answers
452 ÷ 21 is equal to [tex]$21 \frac{11}{21}$[/tex].
What is Quotient?
When we divide a number, the result we ultimately obtain is the quotient. Division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). For instance, three groups of 15 balls each need to be equally split. Therefore, the division formula is 15 3 = 5 when we divide the balls into three equal groups. Here, the quotient is 5, so. This implies that there will be 5 balls in each group.
[tex]$\frac{452}{21}=21$[/tex] Remainder 11
Convert to mixed number: Quotient= [tex]$\frac{\text { Remainder }}{\text { Divisor }}$[/tex]
[tex]$\frac{452}{21}=21 \frac{11}{21}$[/tex]
[tex]$=21 \frac{11}{21}$[/tex]
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By looking at the equation of the leastsquares regression line, you can see that the correlation between height and arm span is (a) greater than zero. (b) less than zero. (c) 0.93 . (d) 6.4 (e) Can't tell without seeing the data.
Answers
As per the given least square regression line, the correlation between the height and the arm span is (a) greater than zero.
Regression line:
In statistics, regression line refers the an estimate of the line that describes the true, but unknown, linear relationship between the two variables.
Given,
Here we need to find the correlation between the height and the arm span by using the given least square regression line.
Let us consider the following situation,
"Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm)."
While we looking into this one we have identified that the predicted function y = 6.4 + 0.93x, is defines the value of height.
So, here y is the dependent variable and the x is the independent value.
This means that the value x is smaller comparatively y value.
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let a 5 c 1 2 3 4 5 6 2 1 3 5 4 6 d and b c 1 2 3 4 5 6 6 1 2 4 3 5 d . compute each of the following. a. a21 b. ba c. ab
Answers
(A×B)∩(A×C)={(1,4),(2,4),(3,4)}
In mathematics, a set is a logically arranged group of items that can be represented in either setbuilder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set. Check the set symbols here as well.
The various kinds of sets, symbols, and operations are described by the set theory.
Given,
A={1,2,3},B={3,4} and C={4,5,6}
A×B={(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)}
A×C={(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)}
∴ (A×B)∩(A×C)={(1,4),(2,4),(3,4)}
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PLEASE HELP WILL MARK BRAINLIEST..Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
x= 2, x=7
P(x)=
Answers
A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²5x14
What is a polynomial function?
A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or nonnegative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
x= 2, x=7
Given,
P(x) = 0
This polynomial function has the roots,
x= 2, x=7
So,
(x+2)(x7)
We have to multiply both of them we get,
P(x)=(x+2)(x7)
0=x²5x14
x²5x14=0
Therefore, P(x)=x²5x14 is the polynomial function.
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14. A zip wire is shown as the dashed line AC in the diagram.
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
CD=2.6 BD=12
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5⁰.
Work out the least possible height of the post $A B$ Give your answer correct to 3 significant figures.
Answers
The least possible height of AB is 3.650 m.
What is a word problem?
A word problem is described as a few phrases outlining a "reallife" situation where a problem needs to be solved using mathematics.
For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: partpart whole, separate and join, and multiply and divide.
Given, CD=2.6 m, BD=12 m
From the figure,
or, tan x = [tex]\frac{AB  2.6}{12}[/tex]
or, tan 5 [tex]\leq \frac{AB  2.6}{12}[/tex]
When AB be least, then
[tex]\frac{AB  2.6}{12}[/tex] = tan 5
or, AB = (12*tan 5) + 2.6
or, AB = 3.650 m
Hence, the least possible height of the AB is 3.650 m.
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Part 1: Two custodians are painting the hallway in the school, starting
at opposite ends at 10:00 a.m. By noon, if Jon has painted 1/5 of the
hallway and Dan has painted 25% of the hallway, who has painted the
most?
25
Part 2: What percentage of the job needs to be completed after lunch
Answers
Answer: Part 1: Dan, Part 2: 55%
Stepbystep explanation:
1. By noon, Jon has painted 1/5 (or 20%) of the hallway and Dan has painted 25% of the hallway. Therefore, Dan has painted more of the hallway than Jon.
2. In total, the two have painted 45% (20% + 25% = 45%) of the hallway by lunchtime. Therefore, 55% (100%  45% = 55%) needs to be painted after lunch.
Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 1 + cos  SXST, with n = 3, 4, and 6. Illustrate each case with a sketch similar to the figure shown below.
Answers
The upper and lower sums for f(x) = 1 + cos  SXST, with n = 3, 4, and 6 is 10.1913798 and 10.19913798.
What is upper and lower sums?
Using rectangles that are both enscribed in and circ*mscribed by a curve, we may approximate the area under a curve. The total area of the rectangles that are inscribed is the lower sum, while the total area of the rectangles that are circ*mscribed is the higher sum.
[tex]$n=6: \quad \Delta x=\frac{2 \pi}{6}$[/tex]
[tex]\begin{aligned}& \text { Lower sum }=\frac{2 \pi}{6}\left[f(\overline{4})+f\left(\frac{2 \pi}{3}\right)+f\left(\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)\right] \\& c_6=\frac{2 \pi}{6}[1+1.5+1.8660256+2+1.8660254+1.5] \\& c_6=10.1913798\end{aligned}[/tex]
upper sum:
[tex]\begin{aligned}& =\frac{2 \pi}{6}\left[f\left(\frac{2 \pi}{3}\right)+f\left(\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)+f(\pi)\right] \\R_6 & =\frac{2 \pi}{6}[1.5+1.8660254+2+1.8660254+1.5+1] \\R_6 & =10.1913798]\end{aligned}[/tex]
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How to subtract fractions with different denominators? Please explain step by step
Answers
Answer: 20/48
(simplified) 5/12
Stepbystep explanation:
We will use 6/8  2/6 for our example
6/8  2/6
Multiply the denominator on the right side by the denominator on the left side: 6x8 = 48
Make 48 the denominators on both sides: /48, /48
Now multiply the denominator on the left side with the numerator on the left side: 6x6 = 36
Make the first fraction's numerator 36: 36/48
Now multiply the denominator on the left side by the numerator on the right side: 8x2 = 16
Now make 16 the numerator of the second fraction: 16/48
Now that the denominators are the same, we can subtract!
36/4816/48 = 20/48
Now to simplify:
divide 20/48 by 4 = 5/12
So the answer is 20/48 and when it is simplified it comes out to 5/12
This is how you subtract fractions with different denominators.
You can use the same method when adding, the only difference is that instead of adding in the last step, you add instead!
In the system below, use equation (1) with equation (2) to eliminate x. Then use equation (1) with equation (3) to eliminate x.
xy2z=4 (1)
x+3yz=8 (2)
2xy4z=1 (3)
What is the new 2 × 2 system?
a) 2y – 3z = 12 –3y – 8z = 7
b) 2y – 3z = 12 –3y + 8z = 7
c) 2y – 3z = 12 –2y – 6z = 3
Answers
The new 2 × 2 system of equation is
2y – 3z = 12
–3y – 8z = 7
What are linear equations ?
If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.
How do you solve linear equations with 3 variables?
Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method.
Given Equations:
xy2z=4 ............(1)
x+3yz=8 ..........(2)
2xy4z=1 ........(3)
Given Condition 1: use equation (1) with equation (2) to eliminate x
According to the condition,
xy2z=4 ........(1)
x+3yz=8 ......(2)
On adding (1) and (2), we get
(11)x +(1+3)y +(12)z = 4+8
2y  3z = 12
Given Condition 2: use equation (1) with equation (3) to eliminate x
xy2z=4 .......(1)
2xy4z=1 ..(3)
on multiplying (1) both the sides with 2 , we get
2x  2y 4z = 8
On adding with (3), we get
2x  2y 2z = 8
2xy4z=1
3y  8z = 7
Thus, The new 2 × 2 system of equation is
2y – 3z = 12
–3y – 8z = 7
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Consider the function c(x) = (x + 5)(x  2)².
1. What are the zeroes of c(x)?
2. What is the degree of c(x)?
Answers
Stepbystep explanation:
Set each binomial equal to 0, solve for x.
[tex](x + 5) = 0[/tex]
[tex]x =  5[/tex]
[tex](x  2) {}^{2} = 0[/tex]
[tex]x  2 = 0[/tex]
[tex]x = 2[/tex]
The zeroes are 5, and 2(with a multiplicity of 2)
We have a degree of 3.
[tex](x + 5)(x {}^{2}  4x + 4)[/tex]
the first term in each binomail when using FOIL, become x^3 since that is the highest degree, 3 is the degree of c.
Two Truths & One Lie: Which of the 3 statements below is a lie? Explain how you made your decision.
x=2 y=5 z=7
Answers
Answer:
The 3rd statement is a lie and other two are truth.
Stepbystep explanation:
when two same numbers with power are divided their respective powers are subtracted.
1.
[tex] {b}^{a } \div {b}^{c} = {b}^{a  c} [/tex]
Using this formula for
[tex] {b}^{9} \div {b}^{y} = {b}^{4} [/tex]
[tex] {b}^{9  5} = {b}^{4} [/tex]
Here RHS =LHS
so the equation is true
2.
[tex] {b}^{z} \div {b}^{x} = {b}^{5} [/tex]
[tex] {b}^{7  2} = {b}^{2} [/tex]
Here RHS=LHS,
so the equation is true
3.
[tex] {b}^{8} \div {b}^{x} = {b}^{8} [/tex]
[tex] {b}^{8  2} = {b}^{8}[/tex]
Here RHS is not equal to LHS
so the equation is false
For more explanation ,
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