The vector equation of the tangent line is <9t+9, t+2, t^2>.
To find the tangent line to the curve at t=1, we need to find the derivative of r(t) and evaluate it at t=1.
r(t) = 9t <1> + 1 <2> + t^2 <3>
Taking the derivative of r(t) with respect to t, we get:
r'(t) = 9 <1> + 1 <0> + 2t <3>
Evaluating r'(1), we get:
r'(1) = 9 <1> + 1 <0> + 2(1) <3> = 9 <1> + 2 <3>
So the vector equation of the tangent line at t=1 is:
r(1) + tr'(1) = <9,1,1> + t<9,2,0>
Simplifying, we get:
<9t+9, t+2, t^2>
So the vector equation of the tangent line is <9t+9, t+2, t^2>.
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How do you work this problem?
Answer:
Attached. Hope this helps
Earline needs to save $367.50 for her summer vacation. She plans on saving $52.50 per week. In 6 weeks, will she have enough money? Explain.
Hint: write a multiplication equation
ben bought six and three fifths bags of rocks to use in his garden. He used four and one fifth bags. How many bags does Ben have left?
Answer:
To find the answer, we need to subtract the amount of bags Ben used from the amount he bought:
6 and 3/5 - 4 and 1/5
To subtract fractions, we need to have a common denominator. The smallest common denominator for 5 and 20 is 20, so we'll convert both fractions:
6 and 3/5 = 6 * 5/5 + 3/5 = 30/5 + 3/5 = 33/5
4 and 1/5 = 4 * 20/20 + 1/5 = 80/20 + 1/5 = 81/20
Now we can subtract:
33/5 - 81/20
We need to convert the mixed number to an improper fraction and find a common denominator:
33/5 - 81/20 = 132/20 - 81/20
Now we can subtract:
132/20 - 81/20 = 51/20
So Ben has 51/20 bags of rocks left. This can be simplified to 2 and 11/20 bags.
Answer:
2 2/5
Step-by-step explanation:
6 3/5 - 4 1/5 = 2 2/5
find the number of outcomes in the complement of the given event. out of 216 books in a bookcase, 155 are nonfictional.
The number of outcomes in the complement of the given event is 61.
The complement of the event "choosing a nonfictional book from the bookcase" is "choosing a fictional book from the bookcase. "Number of outcomes in complement = Total number of books - Number of nonfictional books
The number of outcomes in the complement is equal to the total number of books in the bookcase minus the number of nonfictional books in the bookcase:
Number of results in complement = Number of nonfiction books - Overall number of books = 216 - 155 = 61
Therefore, there are 61 outcomes in the complement of the given event.
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consider the following proof attempt for conjecture : 1. - premise 2. - existential instantiation for (1) 3. - simplification rule for (2) 4. - universal generalization for (3) mark all statements that describe errors in this proof.
Conjectures are unsubstantiated claims. A theorem is created when someone proves a conjecture. In logic types that deal with conjunctions, the rule of simplification is a valid argument. The rule of inference that states that ∀xP(x) is true given the premise that P(c) is true for all elements c in the domain is known as universal generalization.
The Conjecture Rule
Conjectures are unsubstantiated claims. A theorem is created when someone proves a conjecture.
We seek to understand a conjecture on three levels: we want to know what it means, we want to know why we think the claim is true, and we want to know how it fits into a larger set of ideas.
Rule for Simplification
In logic types that deal with conjunctions, the rule of simplification is a valid argument.
This includes propositional and predicate logic, as well as natural deduction.
(1) Proof Rule: If we can reach a conclusion ϕ∧ψ, we can infer ϕ.
(2): If we can reach a conclusion ϕ∧ψ, we can infer ψ.
Rule of Universal Generalization
The rule of inference that states that ∀xP(x) is true given the premise that P(c) is true for all elements c in the domain is known as universal generalization. When we show that ∀xP(x) is true by taking an arbitrary element c from the domain and showing that P(c) is true, we are using universal generalization. The element c that we choose must be arbitrary and not a specific domain element.
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The complete question is:
Write about the conjecture rule, simplification rule, universal generalization rule.
Cecily purchases a box of 100 paper clips. She puts 37 /100 of the paper clips in a jar on her desk and puts another 6 /10 in her drawer at home. Shade a grid that shows how many of the paper clips are in Cecily's jar and drawer, then write the fraction tbe grid represents.
If Cecily purchases a box of 100 paper clips. She puts 37 /100 of the paper clips in a jar on her desk and puts another 6 /10 in her drawer at home. The number of the paper clips that are in Cecily's jar is: 43.
How to find the number of the paper clips?Here is a grid to show the number of paper clips that Cecily has in her jar and drawer:
JAR | DRAWER
|
37 | 60
|
100 | 100
The fraction that the grid represents is :
37/100 + 6/100 = 43/100.
Therefore, Cecily has 43 out of 100 paper clips in her jar and drawer.
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prove or disprove the following proposition. for all nonnegative integer x, x can be expressed by the sum of at most two squares and a cube of nonnegative integers.
The proposition is false, and there exist nonnegative integers x that cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.
This proposition is false. A counterexample is x = 7.
Assume for the sake of contradiction that there exist nonnegative integers a, b, and c such that x = a² + b² + c³. Since a² and b² are always nonnegative, we must have c³ ≤ 7. The only possible values for c are 0, 1, and 2, since 3³ = 27 > 7.
For c = 0, we have x = a² + b², which is the sum of two squares, and is a well-known result.
For c = 1, we have x = a² + b² + 1. However, it is a known result that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 7 is of the form 4(8×0 + 7), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.
For c = 2, we have x = a² + b + 8. Similarly, it can be shown that a sum of two squares cannot be equal to a number of the form [tex]4^{k}[/tex](8m + 7) for some nonnegative integers k and m. Since 8 is of the form 4(8×1 + 0), it cannot be expressed as a sum of two squares, and therefore, x cannot be expressed as the sum of at most two squares and a cube of nonnegative integers.
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Jesse wishes to draw a square of equal area to a given circle with diameter 1 inch.
What is the side length of the square that will give the closest approximation to the area of the circle described?
a. s = π/2 inches
b. s = 3/4 inches
c. s = 8/9 inches
d. s = 1/2 inches
e. s = π/4 inches
The side length of the square that will give the closest approximation to the area of the circle described is e. s = π/4 inches
What is the Area of a Circle?The region encircled by a circle with a radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.
The area of a circle with a diameter of 1 inch is given by the formula πr^2, where r is the radius of the circle. The radius of the given circle is 1/2 inch, so its area is approximately π * (1/2)^2 = π/4 square inches.
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7x-5y=
12z+2y to the 2nd power=
2xy+8z=
The values of the expressions are 7x - 5y = -1, 12z + 2y² = 6 and 2xy + 8z = 4
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
x = 2, y = 3 and z = -1
Substitute the known values in the given equations, so, we have the following representation
7x - 5y = 7 * 2 - 5 * 3
7x - 5y = -1
12z + 2y² = 12 * -1 + 2 * 3²
12z + 2y² = 6
2xy + 8z = 2 * 2 * 3 + 8 * -1
2xy + 8z = 4
Hence, the expressions have their values to be -1, 6 and 4
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Complete question
Consider the following expressions:
7x-5y=
12z+2y²=
2xy+8z=
Determine the values when x = 2, y = 3 and z = -1
What is the average rate of change of f(x) over the x-interval [8,64] for the function
f(x) = 10\sqrt[3]{x}-5 (if equation doesn't make sense, copy/paste it into a math solver. I have the answer, i just need an in-depth answer to how to get the answer pleaseee)
The average rate of change of the function, [tex]f(x) = 10\sqrt[3]{x}-5[/tex] over the interval of x=8 to x=64 is calculated as: 0.357.
How to Find the Average Rate of Change of a Function?The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
The average rate of change = f(b) - f(a) / b - a.
Given the following:
The function is: [tex]f(x) = 10\sqrt[3]{x}-5[/tex]
Interval is: x = 8 to x = 64
Therefore:
a = 8
b = 64
f(a) = f(8) =
[tex]f(x) = 10\sqrt[3]{8}-5\\\\f(x)=10*(2)-5\\\\f(x)=20-5\\\\f(x)=15[/tex]
f(a) = f(8) = 15
f(b) = f(10)
[tex]f(x) = 10\sqrt[3]{64}-5\\\\f(x)=10*(4)-5\\\\f(x)=40-5\\\\f(x)=35[/tex]
f(b) = f(64) = 35
Therefore:
Average rate of change =
[tex]=\frac{f(b)-f(a)}{b-a}\\\\=\frac{35-15}{64-8} \\\\=\frac{20}{56} \\\\=0.357[/tex]
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Can someone help me please another graph
Step-by-step explanation:
the function
Kendal(x) = y = 90
is just a flat line (that's why people call it a flat rate). it does not matter how many hours it takes, it costs the same.
the function
Mona(x) = 10x + 70
as we know, $10 per hour, plus $70 for the material, which is the same cost no matter how many hours it takes.
the solution, when both cost the same, means again both functions are equal at that point :
90 = 10x + 70
20 = 10x
x = 20/10 = 2 hours
after 2 hours both cost the same : $90.
the graphic should look like the attached picture.
the flat line is at y = 90. that means it is a horizontal line that goes through the y gridline marker 90.
just draw the line along the y 90 gridline from left to right.
Mona's graph goes through the solution point (2, 90) and the point for x = 0 : (0, 70) because y = 10×0 + 70 = 70.
for (0, 70) you go from 0 the y-axis straight up to the gridline marker 70 and mark the point there.
for (2, 90) you go on the x-axis from 0 to the right to the gridline marker 2. from there you go straight up to the y gridline 90. and you mark the point there.
and both lines intersect at (2, 90), which is the solution.
can you see and understand it now how that works ?
The cost is $90
What is graphing?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The function for Kendal(x) is:- y = 90
The function for Mona(x) :- 10x + 70
$10 per hour, plus $70 for the material
The solution, when both cost the same, means again both functions are equal at that point :
90 = 10x + 70
20 = 10x
x = 20/10 = 2 hours
after 2 hours both cost the same : $90.
Graph the lines both lines intersect at (2, 90), which is the solution.
Hence, the cost is $90
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Poor fitness in adolescents and adults increases the risk of cardiovascular disease. In a study of 3110 adolescents and 2205 adults, researches found 33.9% of adolescents and 14% of adults were unfit; the percentage was similar in adolescent males 32.5%) and females 35%), but was higher in adult females 16.2%) than in adult then in adult males 11.2%) Chart of Percentage Unfit vs Age Group, Gender 35 30 25 20 15 10 Gender Age Group A B C A B C Adult (a) Match the bars on the chart with the appropriate category from the table Bar B Overall Bar C Male v Bar A Femalev (b) Comment on the interesting features of your graphical display
(a) Bar A: A, Bar B: O, Bar C: F
(b) One interesting feature of the graphical display is the clear difference in the percentage of individuals who are considered unfit between adolescents and adults.
(a) Bar A: Adolescents
Bar B: Overall (both adolescents and adults)
Bar C: Adult Males vs. Adult Females
(b) The percentage of unfit individuals is much higher in adolescents (33.9%) than in adults (14%). Additionally, within the adult group, the percentage of unfit individuals is higher in females (16.2%) than in males (11.2%). Another interesting feature is that there is no significant difference in the percentage of unfit individuals between male and female adolescents.
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Applications of Quadratics. Only 2 questions please help.
Answer: look at the images for the answer ( the first image is for #1 and the second image is for #2 )
Step-by-step explanation:
A plane leaves an airport and flies due north. Two minutes later, a
second plane leaves the same airport flying due east. The flight
plan shows the coordinates of the two planes 10 minutes later. The
distances in the graph are measured in miles. Use the Pythagorean
Theorem to find the distance shown between the two planes.
(Example 2)
The distance between the two planes after 10 minutes is 10 miles.
Step by step explanationWe can use the Pythagorean Theorem to find the distance between the two planes. According to the theorem, the distance between two points in a plane is given by the equation:
d = √( (x2 - x1)^2 + (y2 - y1)^2 )
where (x1, y1) and (x2, y2) are the coordinates of the two points.
The first plane is flying due north, so its position after 10 minutes will be (0, 10). The second plane is flying due east, so its position after 10 minutes will be (10, 0).
We can plug these coordinates into the equation to find the distance between the two planes:
d = √( (10 - 0)^2 + (10 - 0)^2 )
d = √( 100 )
d = 10
So the distance between the two planes after 10 minutes is 10 miles
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Find the product.
112⋅213
Write the answer as a mixed number.
Answer:3 1/2
[tex]\frac{3}{2} times\frac{7}{3} =\frac{21}{6} =3\frac{3}{6} = 3\frac{1}{2}\\[/tex]
Step-by-step explanation:
Translate the sentence into an inequality.
Seven increased by the product of a number and 10 is at least 22.
Use the variable b for the unknown number.
The correct inequality is,
⇒ 7 + 10b ≥ 22
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.
Given that;
Translate the sentence into an inequality,
''Seven increased by the product of a number and 10 is at least 22.''
Now,
Let an unknown variable = b
Hence, We can formulate;
⇒ 7 + b × 10 ≥ 22
⇒ 7 + 10b ≥ 22
Therefore, The correct inequality is,
⇒ 7 + 10b ≥ 22
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10. Order the following from least to greatest and then place them in the correct locat
{-3 1/3, 9/2,√15, 16/5 , √6
Answer:
Step-by-step explanation:
-3 1/3 goes to between -3 and -4
9/2=4 1/2 between 4 and 5
[tex]\sqrt{15}[/tex] between 3 and 4
16/5=3 1/5 between 3 and 4
\sqrt{15} between 2 and 3
Let p= "x>7,"q="x=7," and r="12>x." Select the symbolic form for each of the following statements. (a) x≥7p∨rp∼qp∨qp∧qq∼r (b) 12>x>7r∧pr∼pr∨pp∧qp∼q(c) 12>x≥7p∧(q∨r)r∧(p∨q)r∧(p∼q)r∨(p∧q)r∼(p∨q)
(a) p ∨ r: "x≥7 or 12>x.", (b) r ∧ p: "12>x and x>7." and (c) r ∧ (q ∨ p) : "12>x and (x=7 or x>7),
" which simplifies to "12>x." The second part, (p ∨ q) ∧ r ∨ (p ∼ q) ∧ r ∨ (p ∧ q) ∧ r ∼ (p ∨ q), is always true when r is true, so it is equivalent to r. Thus, the entire statement is equivalent to "12>x and (x=7 or x>7)."
(a) p ∨ r: This statement is a logical disjunction, also known as an "or" statement. It is true if either the left side (p) is true or the right side (r) is true, or both. The statement "x>7" is equivalent to "x≥7 or x=7", so the statement p ∨ r can be read as "x≥7 or 12>x."
(b) r ∧ p: This statement is a logical conjunction, also known as an "and" statement. It is true only if both the left side (r) and the right side (p) are true. The statement "12>x" is equivalent to "x<12", so the statement r can be read as "x<12." Combining this with the statement p (x>7) gives "12>x>7."
(c) r ∧ (q ∨ p): This statement is a conjunction of r and a logical disjunction (q ∨ p). As we saw in part (a), p is equivalent to "x≥7 or x=7", so the statement (q ∨ p) can be read as "x=7 or x≥7". Combining this with the statement r (12>x) gives "12>x and (x=7 or x>7)", which can be simplified to "12>x."
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Someone help me with these math problems
Answer: this doesnt seem complete, like what are we supposed to explain with that
Step-by-step explanation:
solve the following system of equations graphics on the set of axes below
Answer:
(1, -6)
Step-by-step explanation:
3x + y = -3
y = -3x - 3
Use the Venn diagram to determine the roster form of set (A-C)'
Using the Venn diagram to determine the roster form of set (A-C)' = { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }.
What are the elements for (A - C )?The difference of the sets A and C in this order is the set of elements which belong to A but not to C.
A - C = elements in set A but not in set C
A - C = { 3, 4 , 8 }
The A minus C complements include the following;
(A - C)' = { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }
Thus, using the Venn diagram to determine the roster form of set (A-C)' depends on the number of elements in the universal set.
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To conserve water, many communities have developed water restrictions. The water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $54 and $82 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)
Answer:
I can lead you with this equation: 1.41x + 29 = Cost
I think it will be easy from here on for you.
Step-by-step explanation:
The height of a 20-inch tall plant that grows 5 inches each month for x months.
I would assume its 4
Suppose a researcher Is Interested in the effects of a new treatment on extraversion. She randomly selects four participants (n=4), Implements the new treatment, and asks them to complete a personality test. The participants achieve the mean score of M- 115 on the test. The personality test has the population mean of μ- 100 and a-30. Is the sample mean an especially unlikely result based on the population parameters for the personality test? That is, can the researcher conclude that the new treatment has an effect on extraversion? Show your work.
A one-sample t-test can be used to determine whether the sample mean of M=115 is a particularly improbable outcome given the population parameters.
The test's null hypothesis is that the new treatment has no impact on extraversion, in which case the population mean remains at or above 100. The alternative theory is that the new treatment has an impact on extraversion, causing the population mean to deviate from the reference value of 100.
Using the following method, we can determine the test's t-statistic:
(M - ) / (s / sqrt(n)) t
Where M denotes the sample mean, denotes the population mean, s denotes the population standard deviation, and n denotes the sample number.
By entering the numbers we have:
t = (115 - 100) / (30 / sqrt(4)) = 3.33
The measure has n-1 = 3 degrees of freedom. We can use a calculator to determine the critical t-value, which is roughly 3.182, using a two-tailed t-test with alpha = 0.05 and 3 degrees of freedom.
The sample mean is a particularly improbable result based on the population parameters for the personality test because the calculated t-value of 3.33 is higher than the critical t-value of 3.182, and we can therefore reject the null hypothesis.
The evidence from the sample allows the researcher to draw the conclusion that the novel treatment has an impact on extraversion.
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The program below is intended to count the number of prime numbers in a list called numbers and display the result. The program uses the procedure isPrime (n), which returns true if n is a prime number
and false otherwise.
The program does not work as intended.
Which two lines of code should be removed so that the program will work as intended? Select two answers.
The first line that should be removed is the print statement. The code should not display the result right away, as this will prevent it from counting the number of prime numbers in the list.
The second line of code that should be removed is the second statement, which checks to see if the index is equal to 0. This line of code is unnecessary, as the prime numbers are already tested in the if statement before it.
In order for the program to work as intended, the code should only include the if statement that checks to see if the number is a prime number, the for loop that iterates through the list and increments the counter for each prime number found, and the print statement that displays the result at the end. This will ensure that the program counts the number of prime numbers in the list and displays the result correctly.
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Compare the total number of students that attended 6 or more baseball games to the number of students that attended 1 or less
The ratio will be equal to 13:15 for the students who attended the games.
What is a ratio?The ratio actually compares the data of two numbers. It identifies that the one data is how many times the other data.
Melanie randomly selected 15 seventh-grade students and asked them how many soccer games they had attended this school year. Each student's number of games attended is listed below 3. 2 , 6, 4, 7, 0, 4, 5, 0, 1, 2, 3, 2, 1, 4
Here, the number of students who did not attendgames=2 [since there are 2 0s]
The total number of students = 15
Number of students attending games= 15-2=13
The ratio will be equal to 13: 15
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The complete question is given below.
Melanie asked 15 random seventh-grade students how many soccer games they attended this school year. The number of games attended by each student is listed below. 2, 3, 6, 4, 7, 0, 4, 5, 0, 1, 2, 3, 2, 1, 4 What is the ratio of the total number of surveyed students who attended soccer games to the total number of students surveyed?
12x + 51y = 156
- 8x - 34y = - 104
14. Look for Relationships Does this system have one solution, no solutions, or infinitely many solutions? Write another system of equations with the same number of solutions that uses the first equation only.
12x+51y=156
-8x-34y= -104
Anοther system οf linear equatiοns with the same number οf sοlutiοns is 12x + 51y = 156
24x + 102y = 312
What is linear equatiοn?A linear equatiοn is a mathematical equatiοn that describes a straight line in a twο-dimensiοnal space. It is an equatiοn that has οnly οne independent variable and οne οr mοre cοefficients that represent the slοpe and intercept οf the line.
The general fοrm οf a linear equatiοn is: y = mx + b
Where: y is the dependent variable x is the independent variable
m is the slοpe οf the is the y-intercept
Accοrding tο the questiοn:
Tο determine whether this system οf equatiοns has οne sοlutiοn, nο sοlutiοns, οr infinitely many sοlutiοns, we can use variοus methοds such as substitutiοn οr eliminatiοn. Here, we'll use the eliminatiοn methοd:12x + 51y = 156-8x - 34y = -104
Tο eliminate οne οf the variables, we need tο find a cοmmοn multiple οf the cοefficients οf x οr y in bοth equatiοns. In this case, the cοmmοn multiple is 17, because 51 and -34 have 17 as a cοmmοn factοr:12x + 51y = 156 (multiply by 2)-16x - 68y = -208 (multiply by 2)
Nοw, we can add the twο equatiοns tο eliminate
y:12x + 51y = 156-16x - 68y = -208---------------4x - 17y = -52
We can sοlve fοr y in terms οf x:-4x - 17y = -5217y = -4x + 52y = (-4/17)x + 52/17This is the equatiοn οf a line in slοpe-intercept fοrm, with slοpe -4/17 and y-intercept 52/17.
We can alsο write anοther system οf equatiοns with the same number οf sοlutiοns that uses the first equatiοn οnly by multiplying bοth sides οf the equatiοn by a cοnstant
12x + 51y = 156
24x + 102y = 312
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suppose a third row of tiles identical to the ones above is added to the model. How does that change the two expressions? Please helpp!
Two equivalent expressions for the model include the following:
4 + 6x.
2(2 + 3x).
Assuming a third row of tiles identical to the ones above is added to the model, the two expressions becomes;
6 + 9x.
3(2 + 3x).
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided about the algebra tile model, we can logically deduce the following:
Positive signs (+) = 4
Negative signs (-) = 6
Expression = 4 + 6x
By factoring, we have:
4 + 6x = 2(2 + 3x).
By adding a third row of tiles identical to the ones above, we have the following expression:
Positive signs (+) = 6
Negative signs (-) = 9
Expression = 4 + 6x + 2 + 3x = 6 + 9x
By factoring, we have:
6 + 9x = 3(2 + 3x).
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If the possibility of winning is 1/5 what is the possibility of losing
Answer:
4/5
Step-by-step explanation:
Because 1/5 is winning chance.
and the rest percentage will be losing
Estimate 3 1/2 -1 1/3
The estimated difference of 3 1/2 and 1 1/3 is 2 1/6.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Are two fractions 3 1/2 and 1 1/3.
Now, The difference between 3 1/2 and 1 1/3 would be,
1/2 - 1/3 is 1/6 and 3 - 1 is 2,
So, The estimated 3 1/2 -1 1/3 is 2 1/6.
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