Mei worked 8 hours and Kara worked 7 hours when Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour.
Let's use the following variables to represent the unknowns in the problem:
Let M be the number of computers Mei built
Let K be the number of computers Kara built
We can set up a system of equations based on the given information:
M + K = 17 (the total number of computers built is 17)
0.8M + K = 15 (the total time worked is 15 hours)
We can solve for one of the variables in terms of the other by using the first equation:
M = 17 - K
Now we can substitute this expression for M into the second equation:
0.8(17 - K) + K = 15
13.6 - 0.8K + K = 15
0.2K = 1.4
K = 7
So Kara built 7 computers. We can use the first equation to find how many computers Mei built:
M + 7 = 17
M = 10
Therefore, Mei built 10 computers.
Now we can find how long each girl worked by multiplying the number of computers by their respective build times:
Mei: 10 computers x 0.8 hours per computer = 8 hours
Kara: 7 computers x 1 hour per computer = 7 hours
Therefore, Mei worked 8 hours and Kara worked 7 hours.
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The complete question is :
Mei and Kara build computers from parts and sell them to make a profit. Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour. together they worked 15 hours and built 17 hours and built 17 computers. how many hours did each girl work ?
x + 4y = 1 3x + 5y = 10
Step-by-step explanation:
x + 4y = 10 ---(1)
13x + 5y = 10 ---(2)
(1) x 13 : 13x + 52y = 130 ---(3)
(3)-(2) : 47y = 120
y = 120/47 ---(4)
sub (4) into (1)
x + 4y = 10
x + 4(120/47) = 10
x = -10/47
Trina has 232 books to put onto shelves. Each shelf can hold 38 books. She plans to fill each shelf before starting the next. She finds that 232÷38 is 6 r4. How many books will be on each shelf?
The last shelf will have 4 books on it. So Trina will put 38 books on each of the first 6 shelves, and 4 books on the last shelf.
Trina has 232 books to put onto shelves, and each shelf can hold 38 books. Since she plans to fill each shelf before starting the next, we can divide the total number of books by the number of shelves to find how many books will be on each shelf.
Dividing 232 by 38, we get:
232 ÷ 38 = 6 with a remainder of 4
This means that Trina can fill 6 shelves completely with 38 books each, and will have 4 books left over that won't fill a full shelf. To find how many books will be on each shelf, we simply divide the total number of books by the number of full shelves:
38 books per shelf x 6 shelves = 228 books
So there will be 228 books on the first 6 shelves. To find how many books will be on the last shelf, we subtract the number of books on the full shelves from the total number of books:
232 total books - 228 books on full shelves = 4 books
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I need to know the rate of change of the area of a rectangle based off the information in the provided image.
The answer of the given question based on the rate of change of the area of a rectangle the answer is is decreasing at a rate of 8 units²/second.
What is a Rectangle?A rectangle is geometric shape that has four straight sides and four right angles. It is two-dimensional figure that can be described as parallelogram with four right angles. A rectangle has two pairs of parallel sides and opposite sides of equal length..
we are given that the length of the rectangle is increasing at a rate of 4 units/second and the width of the rectangle is decreasing at a rate of 3 units/second.
To find the rate of change of the area of the rectangle, we can use the chain rule of differentiation:
dA/dt = (dA/dl) * (dl/dt) + (dA/dw) * (dw/dt)
We can find dA/dl and dA/dw by taking the partial derivatives of the area formula with respect to l and w, respectively:
dA/dl = w
dA/dw = l
Substituting these values and the given rates of change into the chain rule formula, we get:
dA/dt = (w) * (4) + (l) * (-3)
Substituting l = 10 and w = 8 (from the given image), we get:
dA/dt = (8) * (4) + (10) * (-3) = 8 units²/second
Therefore, the rate of change of the area of the rectangle is decreasing at a rate of 8 units²/second.
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Ben owns an ice cream shop. Last quarter's income was $9,000; his cost of goods was $575, and his total expenses were $5,000.
What is Ben's Net Income for the last quarter?
Type a comma to separate the digits and type the $ symbol when you enter your answer as shown below:
Example: $15,300
Answer:
$3,425
Step-by-step explanation:
Net income is the income made after all expenses and cost of goods are deducted.
Last quarter income $9000
All expenses are goods ($575) + total expenses ($5000) = $5575
Net income = $9000 - $5575
Net income = $3,425
Put these locations in order from most minutes of sunlight during summer months to least minutes of sunlight during summer months
From most minutes of sunlight to least minutes of sunlight during summer, the order would be Winnepeg, Philadelphia, Houston and Porto Alegre.
How does the number of sunlight hours change depending on your location?The number of sunlight hours increases as you move to the north, indeed in places like Alaska there can be 24 hours of sunlight near the summer solstice. Based on this principle, the correct order for the places given would be:
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 10. There are two dots above 6, 7, and 9. There are three dots above 8.
Which of the following is the best measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 8.
The median is the best measure of center, and it equals 7.3.
The mean is the best measure of center, and it equals 7.3.
The median is the best measure of center, and it equals 8.
HELP FAST
A stem and leaf plot showing the movie length in minutes shown. The stems from top to bottom are 8, 9, 10, 11, 12, 13. The first column of leaves is 1, 0, 4, 1, 5, 2. The second column of leaves is 3, 3, 4, 3, 9, 6. The third column of leaves is blank, 7, 7, 5, 9, blank. The fourth column of leaves is blank, blank, 9, blank, blank, blank.Type in the five-number summary for the data shown on the right.
The minimum of the data is
.
The first quartile is
.
The median of the data is
.
The third quartile is
.
The maximum of the data is
.
The minimum οf the data is 81, the first quartile is 94, the median οf the data is 105, the third quartile is 129, and the maximum οf the data is 133.
What is stem and leaf plοt?A stem and leaf plοt is a graphical representatiοn οf a dataset that is used tο display and οrganize individual values. The plοt is made up οf twο parts: the "stem" and the "leaf." The stem is the left-hand side οf the plοt and represents the first οne οr twο digits οf the values, while the leaf is the right-hand side οf the plοt and represents the remaining digits.
This plοt shοws the distributiοn οf the data and allοws yοu tο quickly see the range οf values, the shape οf the distributiοn, and any οutliers οr gaps in the data.
The stem and leaf plot represents the following data:
Stem/Leaf Value
8 1 3 813
9 0 3 4 7 903, 934, 974
10 4 7 104, 107
11 5 15
12 9 129
13 13
The five-number summary for the data is as follows:
The minimum of the data is 81.
The first quartile is 94.
The median of the data is 105.
The third quartile is 129.
The maximum of the data is 133.
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Answer:
minimum-81
first Q-95
median-109
third Q-127
maximum-136
Step-by-step explanation:
yurrrrr
The following system of equations are given:
3x+z+y=8
5y-x=-7
3z+2x-2y=15
4x+5y-2z=-3
a. Is it possible to solve for any of the variables using only Equation #1 and Equation #2? Explain your answer. If possible, solve for the variables using only equations #1 and #2.
b. Is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3? Explain your answer. If possible, solve for the variables using only equations #1, #2, and #3.
c. If you found solutions in part b, do these solutions also hold for Equation #4?
The solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.
What is Linear Equation ?
Linear equation can be defined as equation in which highest degree is one.
We can solve for one variable using Equations #1 and #2, but not for all three variables. From Equation #2, we can solve for x in terms of y as x=5y+7. Substituting this expression for x into Equation #1 gives:
3(5y+7)+z+y=8
Simplifying this equation, we get:
16y+z=-13
We still have two unknowns, y and z, so we cannot solve for any variable using only Equations #1 and #2.
b. It is possible to solve for all three variables using Equations #1, #2, and #3. We can use the following steps to solve for the variables:
Use Equation #2 to solve for x in terms of y as x=5y-7.
Substitute this expression for x into Equation #3 to get:
3z+2(5y-7)-2y=15
Simplifying this equation, we get:
13y+3z=29
Substitute the expression for x from Step 1 into Equation #1 to get:
3(5y-7)+z+y=8
Simplifying this equation, we get:
16y+z=29
Solve for z in terms of y by subtracting the equation from Step 3 from the equation from Step 2:
(13y+3z)-(16y+z)=29-(-13)
Simplifying this equation, we get:
-3y+2z=42
Solve for z in terms of y by adding twice the equation from Step 1 to the equation from Step 4:
2(5y-7)+(-3y+2z)=42
Simplifying this equation, we get:
7y+2z=56
Solve for y by adding the equation from Step 4 to twice the equation from Step 5:
(7y+2z)+2(-3y+2z)=56+84
Simplifying this equation, we get:
5z=196
So, z=39.2. Substituting this value for z into the equation from Step 4 gives:
-3y+2(39.2)=42
Solving for y, we get y=-9.6. Finally, substituting the values for y and z into the equation from Step 1 gives:
x=5(-9.6)-7=-55.
Therefore, the solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.
c. To check if the solution found in part b holds for Equation #4, we substitute the values of x, y, and z into Equation #4 and see if the equation is satisfied:
4(-55)+5(-9.6)-2(39.2)=-3
Simplifying this equation, we get:
-220-48-78.4=-3
This equation is not satisfied, so the solution found in part b does not hold for Equation #4. Therefore, the system of equations does not have a unique solution.
Therefore, the solution for the system of equations using Equations #1, #2, and #3 is x=-55, y=-9.6, z=39.2.
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On the cartesian plane to the right, a) Sketch the restricted sine function on the interval from [−2π,2π] and label at least 3 points b) Sketch the inverse sine function and label at least 3 points c) Sketch the line y=x to demonstrate the inverse functions are reflections of each other across this line
a) For sin Functions :points (−2π, 0), (0, 0), and (2π, 0). Graph look in wave form
b) For inverse sine function:points (−2π, 0), (0, 0), and (2π, 0). Graph look in wave form
c) sine function and the inverse sine function are reflections of each other across the line y=x
a) To sketch the restricted sine function on the interval from [−2π,2π], we need to plot a few points from the sine function. Using the point (−2π, 0), (0, 0), and (2π, 0), we can then connect the dots to form the graph of the sine function. The graph should look like a wave with a period of 2π, and the points we used should be marked along the graph.
b) To sketch the inverse sine function, we need to plot points from the inverse sine function. Using the point (−2π, 0), (0, 0), and (2π, 0) as we did before, we can connect the dots to form the graph of the inverse sine function. This graph should look like a wave with a period of 2π, and the points we used should be marked along the graph.
c) To demonstrate the inverse functions are reflections of each other across the line y=x, draw a line y=x on the same graph. We can then observe that the sine function and the inverse sine function are reflections of each other across the line y=x.
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find the lateral surface area of a square 14 mm 13mm 6 mm
The lateral surface area of the square is 784mm².
What is square?Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.
If the square has a side length of 14 mm, then all sides are equal in length.
The lateral surface area of a square is simply the perimeter multiplied by the height of the shape. Since a square has equal length and width, the perimeter of the square is simply 4 times its side length. Therefore, we have:
Perimeter = 4 × 14 mm = 56 mm
The height of the shape is the same as the length of any of its sides, which is also 14 mm. Therefore, we have:
Lateral Surface Area = Perimeter × Height = 56 mm × 14 mm = 784 mm^2
Therefore, the lateral surface area of the square is 784mm².
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find the lateral surface area of a square box with dimensions 14 mm, 13mm and 6 mm.
Please help!! 50 points I just need the answers no explanation
In a box of 7 different banknotes 1, 2, 5, 10, 20, 50, 100 dollars. You pick at random 2 notes from this box. Let X is the larger number in these two notes, and Y be the smaller one.
(a) Find the distributions of X, Y and their joint distribution.
(b) Find the distribution of Z=X-Y.
(c) Compute E(X), Var(X), E(Z) and Var(Z).
The distribution of X is P(X = x) = 1/7 for x = 1, 2, 5, 10, 20, 50, 100 and Distribution of Y is P(Y = y) = 1/6 for y = 1, 2, 5, 10, 20, 50, 100, y ≠ X and their joint distribution is P(X = x, Y = x) = 0.
Find the joint distribution?(a) The possible values of X and Y are as follows:
(i) X can be any of the 7 banknotes.
(ii) Y can also be any of the 7 banknotes, except the one that was already picked for X.
Since each of the 7 banknotes is equally likely to be picked, the probability distributions of X and Y are both uniform distributions over the set {1, 2, 5, 10, 20, 50, 100}:
P(X = x) = 1/7 for x = 1, 2, 5, 10, 20, 50, 100
P(Y = y) = 1/6 for y = 1, 2, 5, 10, 20, 50, 100, y ≠ X
The joint distribution of X and Y can be computed as follows:
P(X = x, Y = y) = P(X = x) × P(Y = y|X = x)
Since the second banknote must be smaller than the first, we have:
P(Y = y|X = x) = 1/(6 - 1) = 1/5, for y ≠ x
And for y = x:
P(Y = x|X = x) = 0
Therefore:
P(X = x, Y = y) = 1/7 × 1/5 = 1/35, for x ≠ y
P(X = x, Y = x) = 1/7 × 0 = 0
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Addison and Bert are in the same reading group at school. The book they're reading right now is 256 pages long. Addison has read 102 pages so far and decides to read 16 pages every day until she finishes the book. Bert has read 142 pages, and he plans to read 11 pages every day.
How many days will it be until Addison and Bert have each read the same number of pages in total? How many pages will they each have read?
In
days, Addison and Bert will each have read
pages.
Answer:
3,194
Step-by-step explanation:
Multiply 102 by 16.
Then multiply 142 by 11.
Now add the answer you got from both questions.
There's your answer.
Which line is a graph of the equation: –2x + 5y = 10? Number graph ranging from negative five to five on the x axis and negative six to two on the y axis. Four lines are drawn in blue on the graph. Lines a and c have a positive slope and are parallel to each other. Lines b and d have a negative slope and are parallel to each other. Lines a and b intersect at (zero, two), and lines c and d intersect at (zero, negative two). Responses line a line a line b line b line c line c line d
Answer: The equation is of line "b"
Step-by-step explanation:
I need help this question is so confusing!
The bearing of B from C is calculated to be 115 degrees
The bearing of D from B is calculated to be 213.65 degrees
How to find the bearingsThe bearing from B to C is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The direction of movements describes a right triangle of
opposite = 30 km
adjacent = 30 km
The bearing is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 30 / 30
tan x = 1
x = arc tan 1
x = 45 degrees
The bearing is 90 + 45 = 115 degrees
The bearing of D from B
x = arc tan (45/30)
x = 56.31
90 - 56.31 = 33.65
180 + 33.65 = 213.65 degrees
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Can anyone help me with this?
Answer: y-bdjd-=jgj
Step-by-step explanation:
because in chemestry 534 page their ids all the rullers
Select the correct answer.
Answer:
C
Step-by-step explanation:
IF YU SQUARE 6 YU GET 36 AND 36×3=108
AND THAT BRINGS C TO BE THE CORRECT ANSWER
Find the area of the shaded region
Answer:
15x² - 64x + 64
Step-by-step explanation:
To find the area of shaded region, we will first find the area of the whole shape then subtract the area of the white region.
The area of a square is calculated by multiplying the one side with itself:(4x-8)×(4x-8) = 16x² - 64x - 64 is the area of the whole shape
x*x = x²
Now subtract x² from the whole area16x² - 64x - 64 - x² = 15x² - 64x - 64
Which algebraic expression is equivalent to -2(4x - 5y - 5x)?
Answer: -2x-10y
Step-by-step explanation:i'm in the 8th grade so i know im right
Claudia organizes a team carpool with 5 vans. Each van carries 2 adults and an equal number
of children. There are 30 people in the carpool
altogether. Determine how many children are
in each van
Number of children in the each van is 4.
Let's start by using algebra to solve the problem. Let's call the number of children in each van "x".
Since each van carries 2 adults and "x" children, the total number of people in each van is:
2 + x
And since there are 5 vans in total, the total number of people in the carpool is:
5(2 + x) = 10 + 5x
We know from the problem that there are 30 people in the carpool altogether, so we can set up the equation
10 + 5x = 30
Solving for "x", we get:
5x = 20
x = 4
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i need help on this please
The volume of the larger cylinder is 4 times greater than the volume of the smaller cylinder.
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height.
V = πr²h.
The radius of the cylinder is squared, meaning that when the radius is squared, the volume is multiplied by 2² = 4, hence the correct sentence is given as follows:
The volume of the larger cylinder is 4 times greater than the volume of the smaller cylinder.
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Write a decimal and a fraction for the shaded part of the diagram.
A decimal and fraction and shaded part of the first diagram second diagram is 100/100 or 1 and 0.63 or 63/100 respectively.
What is fraction?
A fraction is a way of expressing a part of a whole, or a part of a group, by using two numbers separated by a line. The number above the line is called the numerator, and the number below the line is called the denominator.
The first 10 by 10 matrix is fully colored, which means all 100 cells are colored. Therefore, the fraction of colored cells is:
100/100 = 1
The decimal representation of this fraction is simply 1.
For the second 10 by 10 matrix, the first 6 columns are fully colored, which means there are 6 x 10 = 60 colored cells. The 7th column has only the first 3 rows colored, which means there are 3 colored cells in this column. Therefore, the total number of colored cells is:
60 + 3 = 63
The fraction of colored cells is:
63/100
To convert this fraction to a decimal, we can divide the numerator by the denominator:
63 ÷ 100 = 0.63
Therefore, the shaded part of the second matrix is 0.63 or 63/100.
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please help if you can I will give brainliest- Black tape is used to create the lines and circles for a basketball court. How much tape is used in all? Use π=3.14.
Answer:
see below.
Step-by-step explanation:
So first, find the perimeter.
94*2= 188
50*2=100
100+188=288ft <----This is our perimeter
Next, find the length of the center line.
It is 50 feet.
Next, we are going to figure out the circumference of the big half circle.
C=[tex]\pi[/tex]d
C=(3.14)(44)=138.16 <------circumference of a WHOLE circle.
Divide 138.16 by 2 to get the half circle
138.16/2=69.08
There are 2 half circles, so multiply 69.08 by 2 to get 138.16
Next, we need to find the circumference of the center circle.
C=(3.14)(12)=37.68
Finally, add all the totals together
288+50+138.16+37.68=513.84 FEET <---dont forget units.
simplify 4divide root 5 plus 5 minus 3 divide root 5 minus root 2
Answer:[tex]\frac{25+\sqrt{5} -5\sqrt{2} }{5}[/tex]
Step-by-step explanation:
Math: When is an equation true?
Answer:
When an equation contains an equal sign "=", then it is an equation. The statement may be true, for example, "apple = apple," or it may be false, for example, "apple = sloth."
share 80 in the ratio 1:4:5
Answer:
8,32,40
Step-by-step explanation:
we can show 1:4:5 as 1k:4k:5k,
1k+4k+5k=10k
10k=80
k=8
so, 1k=8
4k=32
5k=40
Answer: The answer is 8, 32, 40
Step-by-step explanation:
1= 1 over the total of ratio times the number that we are sharing
1+4+5= 10
1= 1/10 times 80= 8
4= 4/10 times 80= 32
5= 5/10 times 80= 40
4. The fabrication team will be starting with 20-ft lengths of the
tubing. How many 20-ft lengths are needed for each workbench?
(Hint: To convert inches to feet, divide by 12.)
The number of lengths required by the fabrication team for each workbench is 2.5 units.
What is length of an object?The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric form or object. For instance, the length and width of a rectangle define its dimensions. In the International System of Quantities, length is also a quantity having the dimension distance.
The total length of the workbench is given as 589.95.
Given that, 20 ft lengths are used for fabrication.
Thus, the number of lengths required are:
N = 589.95/ 20 (12) = 2.457 = 2.5
Hence, the number of lengths required by the fabrication team for each workbench is 2.5 units.
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The complete question is:
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
1) The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill.
2) The solution x=60 represents the total food bill.
These both answers are correct.
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Since there are 8 group of friends, and the total amount spent by them is $76 including the tip i.e $16.
If x is the food bill our equation can be:
(x+16)/8 = 76/8
Solving the equation
(x+16)/8 = 9.5
x+16= 9.5*8
x= 76 -16
x= 60
The food bill is x=60.
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Segment FR is 14 units long. The coordinates for F and R are -2x +6 and 4x-7. Find the possible coordinates for F and R
The possible coordinates for F and R are (-3, y) and (7, y), where y is any real number, or (8, y) and (-11, y), where y is any real number.
We are given that segment FR is 14 units long and its endpoints have coordinates (-2x + 6, y) and (4x - 7, y), where y is the y-coordinate of both endpoints. To find the possible coordinates for F and R, we need to find values of x and y that satisfy the length condition and the endpoint conditions.
Using the distance formula, we can set up an equation for the length of segment FR:
sqrt((4x - 7 - (-2x + 6))^2 + (y - y)^2) = 14
Simplifying this equation, we get:
sqrt((6x - 13)^2) = 14
6x - 13 = ±14
Solving for x, we get:
x = 27/6 or x = -1
Case 1 x = 27/6
Substituting x = 27/6 into the endpoint coordinates, we get:
F = (-2(27/6) + 6, y) = (-3, y)
R = (4(27/6) - 7, y) = (7, y)
So, one possible set of coordinates for F and R is (-3, y) and (7, y), where y can be any real number.
Case 2: x = -1
Substituting x = -1 into the endpoint coordinates, we get:
F = (-2(-1) + 6, y) = (8, y)
R = (4(-1) - 7, y) = (-11, y)
So, another possible set of coordinates for F and R is (8, y) and (-11, y), where y can be any real number.
Therefore, the possible coordinates for F and R are:
(-3, y) and (7, y), or (8, y) and (-11, y), where y is any real number.
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Please help super confused
The value of the function notations are;
a) d(20) = 10
b) d(0) = 0
c) d(20) < d(30)
d) d(0) = 0
e) d(30) = d(40)
f) d(t) = 5, when t = 5
How to Interpret Function Notation?
The notation f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value, or independent variable. The letter y is replaced by f(x) and represents the output value, or dependent variable.
a) d(20)
The value of distance (d) when the time is 20 is; 10
b) d(0)
The value of distance (d) when the time is 0 is; 0
c) d(20) = 10
d(30) = 20
Thus;
d(20) < d(30)
d) The value of the time at d = 0 is 0. Thus;
d(0) = 0
e) d(30) = 20
d(40) = 20
Thus; d(30) = d(40)
f) d(t) = 5
The value of t at d = 5 is;
t = 5
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