In AON networks, "node" is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.
What is Activity-on-Node (AON) diagram?Scheduling logic diagrams of the most fundamental kind. Any activity on the schedule that has no float; Total Float = 0; is considered a critical activity.
Between the project's start and finish, there are vital activity(s) that must be completed continuously. This is known as the critical path.
The importance of AON diagram are-
Because it helps identify the essential path, the arrow diagram is crucial for the project timeline. The critical route is used to determine the most effective schedule while still achieving the objectives required for a project to be successful. The critical path indicates the longest time of every dependent task.It is possible to organize tasks and determine not only when they must be finished but also which ones must be performed and which ones can be skipped while still reaching the project's goals and objectives by creating a schedule. An arrow diagram is essential because of this. It results in the project's ideal schedule.To know more about the AOA and AON networks, here
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Direct to Coordinates
plot the point A (2, 3) then, plot point b that is 4 right and 5 up from point A.
Plot the point C (9, 7). Then, plot another point D that is 8 left and 2 down from point C.
Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C which is at D(1, 5).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C which is at D(1, 5).
The location of point A, B, C and D is located on the graph.
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what is the measure of the largest side of an isosceles acute, if one side is 36
The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.
What is an isosceles triangle?A triangle with two sides and angles of equal length and degrees is an isosceles triangle.
Acute Triangle:-
A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.
Therefore, all the three angles are less than 90 degrees and two angles are equal.
If one angle is 36 degrees, the other two angles will be 72 degrees each.
If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..
Therefore, the angles will be 36°, 36° and 72°.
Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.
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Melissa is planning a rectangular vegetable garden with a square patch for tomatoes
The expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.
A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.
In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.
The side of the square is given to be x feet.
We are asked to write expressions for the length and width of the rectangular garden.
For the length of the rectangle:-
We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.
Thus, the length of the garden can be shown as the expression 3x + 2 feet.
For the width of the rectangle:-
We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.
Thus, the width of the garden can be shown as the expression x + 5 feet.
Thus, the expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.
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The provided question is incomplete. The complete question is:
"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.
Let x represent the length, in feet, of the square tomato patch.
Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.
Enter the correct answer in the box."
please im in a rush i need help
Answer:
28.5 ft²
Step-by-step explanation:
shaded area = area of triangle minus area of rectangle
shaded area = (1/2)bh - LW
base of triangle = 5 ft + 4 ft = 9 ft
height of triangle = 3 ft + 6 ft = 9 ft
shaded area = (1/2)(9 ft)(9 ft) - (4 ft)(3 ft)
shaded area = 40.5 ft² - 12 ft²
shaded area = 28.5 ft²
In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they can be used to create an algebraic expression.
VARIABLE is a symbol which is used for representation in a math.
According to the statement
we have to explain about the what is a variable.
So, VARIABLE is a symbol which is used for representation in a math.
It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.
A variable may also be called a data item.
It is used to represent a data like country name, name, age, date of birth etc.
we know that the every thing is changeable. So, like ther things variables are also changeable.
The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.
So, VARIABLE is a symbol which is used for representation in a math.
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A hotel packed a breakfast for each of three guests. Each breakfast should have consisted of three types of rolls, one each of nut, cheese, and fruit rolls. The preparer wrapped each of the nine rolls, and, once they were wrapped, the rolls were indistinguishable from one another. She then randomly put three rolls in a bag for each of the guests. Given that the probability that each guest got one roll of each type is m/n, where m and n are relatively prime integers, find m+n.
The probability that each guest of each type m+n will receive a roll is 79.
Given that the breakfast should have consisted of three types of rolls, one each of the nut, cheese and fruit rolls, and the cook should have wrapped each of the nine rolls.
The denominator of m/n equals the total number of possible role configurations assigned to the three people. It [tex]${9 \choose 3}{6 \choose3}$[/tex] is the same as the number of ways to choose three roles out of 9 to give to the first person [tex]${9 \choose 3}$[/tex], and three rolls of 6 [tex]${6 \choose3}$[/tex]. After that, the remaining three roles have no more configurations.
The numerator is the number of ways to assign a roll of each type to each of the three people, which can be done by defining the three types of roles such as flavored x, flavored y and flavored z.
xxx, yyy, zzz
So we have to choose one x, one y and one z to give to the first person. There are 3x, 3y and 3z to choose from, resulting in 3³ combinations. Multiply that by the combinations of xs, ys and zs for the second person, which is clearly 2³ since there are two of each letter left. simplify to our fraction m / n, which is 9/70. If you add them together, you get 9 + 70 = 79.
Thus, the probability that each guest has obtained a roll of each type is m / n, where m and n are relatively prime, so m + n is 79.
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On a balance scale, $3$ green balls balance $6$ blue balls, $2$ yellow balls balance $5$ blue balls, and $6$ blue balls balance $4$ white balls. How many blue balls are needed to balance $4$ green, $2$ yellow and $2$ white balls
The number of blue balls that are needed to balance four green, two yellow and two white balls is 16 blue balls.
Numbers of blue balls neededGreen(g)
Blue (b)
Yellow (y)
White (w)
First step is to formula an equation
3g=6b
g=2b
2y=5b
y=5/2b
4w=6b
w=3/2b
Second step is to substitute
4g+2y+2w
=4(2b)+2(5/2b)+2(3/2b)
=8b+5b+3b
=16b
Therefore 16 blue balls are needed.
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the diagonal of the rectangle is 15 cm and one of its sides is 9 cm. find the area of the rectangle.
The area of the rectangle is 108 square centimeters.
Given Information
The following information has been given in the question,
Length of the diagonal of the rectangle, l = 15 cm
Length of one of the sides of the rectangle, a = 9 cm
Let the other side of the rectangle be b.
Finding the Other Side of the Rectangle
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,
l² = a² + b² [∵ The diagonal makes the hypotenuse]
(15)² = (9)² + b²
b² = (15)² - (9)²
b² = 225 - 81
b² = 144
b = √144
b = 12 cm
Calculating the Area of the Rectangle
Area of the rectangle, A = a × b
A = 9 × 12
A = 108 cm²
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22. If 1 m,m/19 - 118°, and m/16 - 48°, calculate m/12.
0 0
103"
98
109⁰
110"
18
17
19 20
14
16
13
15
11
10
12
9
63
5
m
Answer: Option 4
Step-by-step explanation:
[tex]m\angle 20=62^{\circ}[/tex] (linear pair)
[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)
[tex]m\angle 12=110^{\circ}[/tex] (linear pair)
A popular roller coaster ride lasts 10 minutes. There are 20 people on average on the roller coaster during peak time. How many people are stepping onto the roller coaster per minute at peak time
There are 2 people are stepping onto the roller coaster per minute at peak time
According to statement
Given Flow time = 10 minutes.
Given Inventory = 20.
We use the formula then
I = R × T,
Therefore R = I / T.
Substitute the values in formula then
Flow rate = 20 / 10 = 2 people per minute.
So, There are 2 people are stepping onto the roller coaster per minute at peak time
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Lowest common multiple of 12,18,56
Step-by-step explanation:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
56 = 2 ×2 × 2 × 7
Now
Common factor = 2
Remaining factor = 2 × 3 × 2 × 3 × 7
LCM = RF × CF
= 504
hence the lCM of 12 , 18 and 56 is 504...
[tex]...[/tex]
equivalent to -8.2 - 5−8.2
The equivalent value of the given expression is -21.4
Difference of decimalsDecimals are values that include decimal points. Given the expression below
-8.2 - 5−8.2
Collect like terms
-8.2 −8.2 - 5
Convert to fractions
-82/10- 82/10 - 5
-164/10 - 5
-16.4 - 5
Take the sum
-21.4
Hence the equivalent value of the given expression is -21.4
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5 circles are shown. Circle D has a secant with length 12. Circle E has a radius with length 6. Circle H has a secant with length 6. Circle F has a diameter with length 12. Circle G has a diameter with length 12.
Circle A has a radius of 6. Which circles are congruent to circle A? Check all that apply.
circle D
circle E
circle F
circle G
circle H
The circle E, circle F and circle G are the circles which are congruent (similar) to the circle A has a radius of 6.
Let us discuss about the structure of each circles.
Circle DThe circle D has the secant with the length 12. The secant means the straight line joining two points on the circle. So, we can't conclude that the secant will always be the diameter. Hence, it has different shape compared to circle A.
Circle EThe circle E has the radius with length 6. The radius is same as the radius of the circle A. So, it is similar to the circle A.
Circle HThe circle D has the secant with the length 6. Similar to the condition of circle D, it is not congruent to circle A.
Circle FThe circle F has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.
Circle GThe circle G has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.
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Answer:
Circles E and F are congruent to circle A
Evaluate if m= 14.
m
2 + m =
Answer:
16
Step-by-step explanation:
You replace m with 14. 2 + 14 = 16.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Assuming equation:}[/tex]
[tex]\mathsf{\dfrac{m}{2} + m}[/tex]
[tex]\huge\textsf{If so, let's solve for your equation:}[/tex]
[tex]\mathsf{\dfrac{m}{2} + m}[/tex]
[tex]\mathsf{= \dfrac{14}{2} + 14}[/tex]
[tex]\mathsf{= 7 + 14}[/tex]
[tex]\mathsf{= 21}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{21}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square meters, of ΔABC.
a=7m, b=5m, c=6m
Answer: S=6√6 m².
Step-by-step explanation:
Heron's formula
[tex]\displaystyle\\\boxed {S=\sqrt{p*(p-a)(p-b)(p-c)} }[/tex],
a, b, c - sides of a triangle,
[tex]\displaystyle\\p=\frac{a+b+c}{2}[/tex]
S - triangle area.
a=7 m, b=5 m, c=6 m.
[tex]p=\frac{7+5+6}{2} \\p=\frac{18}{2} \\p=9 (m).[/tex]
Hence,
[tex]S=\sqrt{9*(9-7)*(9-5)*(9-6)}\\S=3*\sqrt{2*4*3}\\S=3*2*\sqrt{2*3} \\S=6\sqrt{6} \ (m^2).[/tex]
12.5% of a number is 25, find the number
Answer:
200
Step-by-step explanation:
Let's call the number x :
12.5% of x = 25
Changing 12.5% into decimal would be 0.125
Now we have the equation :
0.125x = 25
Divide both sides by 0.125 to make x the subject :
x = 25 ÷ 0.125
x = 200
To check we can substitute this value into the question :
12.5% of 200 = 25
Hope this helped and have a good day
What is the tax due for a single taxpayer reporting a taxable income of $65,725?
The tax due for the single taxpayer whose income is as described is; $14,459.5.
What is the tax due for the single taxpayer?It follows from the task content that the tax due for a single taxpayer whose taxable income is; $65,725 is to be determined.
Since, the taxable income falls between the range; $40,526 to $86,375, 22% of the income is the tax due and hence, the tax due can be evaluated as follows;
= (22/100) × $65,725
= 14,459.5
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PLEASE HELP ME I NEED HELP I'LL GIVE YOU BRAINLEST PLEASE I BEG YOU NICELY.
Can some one help me with this. This isn't school work this is math that I am doing at home on prodigy the app. I will mark you brainlest if you get this correct. Also look at both of the pictures one of them has a hint for you.
The perimeter of a rectangle is the sum of its side lengths.
A rectangle is special in that sides opposite one another have equal length. So if [tex]x[/tex] is the length of the horizontal sides, the total perimeter of the rectangle is
[tex]4\,\mathrm{cm} + 4\,\mathrm{cm} + x\,\mathrm{cm} + x\,\mathrm{cm} = (8+2x)\,\mathrm{cm}[/tex]
We're given the perimeter is actually 18 cm, so
[tex]8+2x = 18[/tex]
Solve for [tex]x[/tex].
[tex](8 + 2x) - 8 = 18 - 8[/tex]
[tex]2x = 10[/tex]
[tex]\dfrac12 \cdot 2x = \dfrac12 \cdot 10[/tex]
[tex]\boxed{x = 5}[/tex]
Write a paragraph summarizing the data set , 12,13,14,15,16,17,18,19,20,21,22,23,24,25. Included unit measure,the number of data , the shape of the distribution, value of appropriate measure of center , value of appropriate measure of spread
The number of observation given in the following data set 14. This is also called the size of the population.
What is the description for the above data?It is important to note that the above data possess the minimum value of 12 and the maximum value of 25. As indicated in the attached image, the data set is normally distributed.
The measures of central tendency are given as follows;
Median = 18.5; Mean = 18.5Standard Deviation = 4.03112887Variance = 16.25Mid Range = 18.5The quartiles are given as follow:Q1 --> 15
Q2 --> 18.5
Q3 --> 22
IQR = 7
Mean Absolute Deviation (MAD) = 3.5
Min = 12
Max = 25.
It is to be noted that the above indictors are called Descriptive Statistics.
What is the purpose of descriptive statistics?
The features of a sample or data set, such as a variable's mean, standard deviation, or frequency, are described or referred to as descriptive statistics.
We can better grasp a data sample's constituent parts by using inferential statistics.
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Find the area of the polygon formed whe these points are connected a(3,7)b(3,3)c(7,3)d(7,7)
Here, given
sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)
Let, 3 = x1 & 7= y1 , 3= x2 & 7= y2 , 7= x3 & 3= y3 , 7= x4 & 7= y4
[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}
[tex]\frac{1}{2}[/tex] (32)
16cm^2
Hence, the area of the polygon is 16cm2.
The formula for calculating the area of a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].
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Need help in this pls
Answer:
6
Step-by-step explanation:
The arc length is (2)(pi)(27)(40/360)=6pi.
So, k=6.
How many 4-digit positive integers are there for which there are no repeated digits, or for which there may be repeated digits, but all digits are odd?
The number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.
In this question,
Positive integers are 0,1,2,3,4,5,6,7,8,9
Total number of integers = 10
This can be solved by permutation concepts.
Case 1: 4-digit positive integers with no repeated digits,
First digit, cannot be zero. So remaining 9 digits.
Second digit, can be any digit other than the first digit. So 9 digits.
Third digit, can be any digits other than first and second. So 8 digits.
Fourth digit, can be any digits other than first, second, third digit. So 7 digits.
Thus, Number of ways of 4-digit positive integers with no repeated digits ⇒ (9)(9)(8)(7)
⇒ 4536 ways.
Case 2: 4-digit positive integers, there may be repeated digits, but all digits are odd
Odd integers are 1,3,5,7,9
Number of digits = 5
In this case, we can repeat the digits. So all places can have 5 possibilities.
Thus number of ways of 4-digit positive integers with repeated digits, but all digits are odd = (5)(5)(5)(5)
⇒ 625 ways.
Hence we can conclude that the number of ways of arranging 4-digit positive integers with no repeated digits is 4536 ways and number of ways of 4-digit positive integers with repeated digits, but all digits are odd is 625 ways.
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The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is
7/10. Find the number.
Write an equation with the following characteristics:
1. It uses x to represent the number.
2. It uses the information as it is given above.
3. It can be solved to answer the question.
Equation:
The number is:
Answer:
[tex]\sf Equation: \quad \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]
The number is 2.
Step-by-step explanation:
The reciprocal of a number is simply 1 divided by the number.
The reciprocal of a fraction is where the numerator and denominator are swapped (so the fraction is turned upside down).
Let x be the positive number.
The reciprocal of the positive number x:
[tex]\sf \implies \dfrac{1}{x}[/tex]
The reciprocal of 3 more than the number x:
[tex]\sf \implies \dfrac{1}{x+3}[/tex]
The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is 7/10:
[tex]\implies \sf \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]
To solve, make the denominators of the two fractions on the left side the same by multiplying them.
Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.
Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.
[tex]\implies \sf \dfrac{1(x+3)}{x(x+3)}+\dfrac{1(x)}{(x+3)(x)}=\dfrac{7}{10}[/tex]
[tex]\implies \sf \dfrac{x+3}{x(x+3)}+\dfrac{x}{x(x+3)}=\dfrac{7}{10}[/tex]
Add the numerators and keep the denominator so that there is now one fraction:
[tex]\implies \sf \dfrac{2x+3}{x(x+3)}=\dfrac{7}{10}[/tex]
Cross multiply:
[tex]\implies \sf 10(2x+3)=7x(x+3)[/tex]
Expand:
[tex]\implies \sf 20x+30=7x^2+21x[/tex]
Rearrange so the equation is equal to zero:
[tex]\implies \sf 7x^2+x-30=0[/tex]
Split the middle term:
[tex]\implies \sf 7x^2+15x-14x-30=0[/tex]
Factor the first two terms and last two terms separately:
[tex]\implies \sf x(7x+15)-2(7x+15)=0[/tex]
Factor out the common term (7x + 15):
[tex]\implies \sf (x-2)(7x+15)=0[/tex]
Apply the zero product property:
[tex]\sf (x-2)=0 \implies x=2[/tex]
[tex]\sf (7x+15)=0 \implies x=-\dfrac{15}{7}[/tex]
As x is a positive number, x = 2.
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Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.
The true statement about the plane include:
Points A, B, and D are on both planes. Point H is not on plane R.The line containing points F and G is on plane R.The line containing points F and H is on plane R.What is a vertical plane?It should be noted that a vertical plane simply passes through a vertical line.
In this case, Point H is not on plane R and the e line containing points F and G is on plane R.
The correct options are 1,2,4, and 5.
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Answer:
a,b,d,e
Step-by-step explanation:
What is the simplified base for the function f(x) = 2rootindex 3 startroot 27 endroot superscript 2 x?
Applying exponential properties, the simplified base for the function is given as follows:
[tex]f(x) = 2(3)^{2x}[/tex]
What is the function?The function is represented by the following definition:
[tex]f(x) = 2\sqrt[3]{27^{2x}}[/tex]
As an exponent, the function is given by:
[tex]f(x) = 2(27)^{\frac{2x}{3}}[/tex]
27 can be simplified as follows:
27 = 3 x 3 x 3 = 3³
Hence:
[tex]f(x) = 2(3^3)^{\frac{2x}{3}}[/tex]
Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:
[tex]f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}[/tex]
Hence the simplified base for the function is given as follows:
[tex]f(x) = 2(3)^{2x}[/tex]
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Choose the equation that satisfies the data in the table.
Answer:
Option A.
Step-by-step explanation:
Demonstration
[tex]y=\frac{7}{4} x+7[/tex]
for x = -4
[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]
for x= 0
[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]
for x= 4
[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]
Hope this helps
Suppose that events E and F are independent, P(E)=0.6, and P(F)=0.7.
What is the P(E and F)?
The probability P(E and F) is
(Type an integer or a decimal.)
Answer:
Step-by-step explanation:
hello :
P(E and F)=0.7×0.6 =0.42
Fill in the coefficients for the polynomial with degree 3, roots: x = 2, X =
-1, and x = 3, and with a leading coefficient of 1
The coefficients for the polynomial with degree 3, roots: x = 2, x =
-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.
It is given that the polynomial is of degree 3 and its roots are,
x = 2
x = -1
x = 3
Thus, the factors of the polynomial would be,
(x - 2), (x + 1), and (x - 3)
The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,
(x - 2)(x + 1)(x - 3)
= (x² -2x + x -2)(x - 3)
= (x² -x -2)(x - 3)
= x³ - 3x² - x² + 3x - 2x + 6
= x³ - 4x² + x + 6
= x³ + (-4)x² + x + 6
Hence, the required coefficients of the polynomial are, (-4) and 6.
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A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
Question 6) Neither (Not an inverse variation)
Question 7) Inverse variation
Question 8) Inverse variation
Step-by-step explanation:
These are the two formulas we need to know prior to solving the question.
Direct variation: c times x
Inverse variation: c times 1/x --> c/x
- Here, c is the constant
6. y = x + 7
This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.
7. 14 = xy
This equation is an inverse variation.
xy = 14
y = 14/x
14 is the constant, and the format is the same as for an inverse variation.
8. x = -8/y
This equation is an inverse variation.
yx = -8
y = -8/x
-8 is the constant, and the format is the same as for an inverse variation.
So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.
General forms
Direct
y=KxInverse
y=k/xso
#6
y=x+7Not inverse and direct also as 7 is present
#7
14=XYy=14/xYes
#8
x=-8/yy=-8/xYes
Tara has 4 and 4 over 5 feet of rope.
part a: how many 2 over 5 foot pieces can tara cut from the 4 and 4 over 5 feet of rope? show your work. (5 points)
part b: using the information in part a, interpret the meaning of the quotient in terms of the two fractions given. (5 points)
the answer box is a writing thing so might have to explain it differently
Part A - Tara cuts [tex]12[/tex] pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] feet of rope.
Part B - The quotient means the amount of foot pieces so it is [tex]12[/tex] foot pieces.
How can we find the foot pieces of [tex]2/5[/tex] from [tex]4\frac{4}{5}[/tex] rope. ?
from part A
we solve the fraction
[tex]4\frac{4}{5} =24/5[/tex] rope
And Tara needs to pieces of [tex]2/5[/tex] foot
So we need to divide
[tex]\frac{24/5}{2/5} \\=\frac{24}{5} *\frac{5}{2} \\=\frac{24}{2} \\=12[/tex]
For part B
When we using the information from part A we decide that the quotient means the amount of foot pieces Tara can cut from the [tex]4\frac{4}{5}[/tex] feet of rope.
Learn more about the pieces of rope is here:
https://brainly.com/question/28048536
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