Answer: Let's start by finding the dimensions of the original rectangular room.
We know that the area of the room is 60m², so we can write:
length x width = 60
We want to find the length and width of the original room, so let's call them "L" and "W", respectively. Then we can write:
L x W = 60
Now let's consider the modified room, where the length is 25% less and the width is 4m more. If the room is a square, that means the length and width are equal. Let's call this side length "S". Then we can write:
S x S = (L - 0.25L) x (W + 4)
Simplifying, we get:
S² = 0.75LW + 4(L - 0.25L)
Simplifying further, we get:
S² = 0.75LW + 3L
Now we can use the fact that LW = 60 to eliminate one variable. Substituting, we get:
S² = 45 + 3L
We want to find the length of the longest stick that can be put on the floor of the original room. This is the diagonal of the rectangle, which we can find using the Pythagorean theorem:
diagonal² = L² + W²
Substituting LW = 60, we get:
diagonal² = L² + (60/L)²
To maximize the diagonal, we can take the derivative of the right-hand side with respect to L and set it equal to zero:
d/dL (L² + (60/L)²) = 2L - 7200/L³ = 0
Solving for L, we get:
L³ = 3600
L = 15
Therefore, the length of the longest stick that can be put on the floor of the room is the diagonal, which is:
diagonal = sqrt(15² + (60/15)²) = sqrt(225 + 16) = sqrt(241) ≈ 15.52 meters
Step-by-step explanation:
please help will give brainliest
Answer:
A = 600 ft²
Step-by-step explanation:
Area of a triangle = (1/2) · b · h
↓ plugging in the given values (noting that the base is actually at the top of the triangle)
A = (1/2) · 40 · 30
↓ multiplying
A = 20 · 30
A = 600 ft²
Step-by-step explanation:
See image:
( the picture is cut off , so I cannot tell the units....If each square is 10 feet then it would be
600 ft^2)
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
Answer:
the probability of drawing two 2 purple jelly without replacement is 1/10
april, bill , candace, and bobby are to be seated at random in a row of chairs. what is the probability that april and bobby will occupy the seats at the end of the row?
The required probability of occupying seats at the end of the row by April and Bobby is equals to 0.0333( approximately ).
Number of chairs in a row = 5
April and Bobby need to occupy the two end chairs.
The other two people, Bill and Candace, can sit in any of the 3 remaining chairs.
The total number of ways to seat the 4 people in the 5 chairs is
= 5!/(5-4)!
= 5x4x3x2
= 120.
April can sit in either of the two end chairs, and then Bobby can sit in the other end chair.
Bill and Candace can then sit in either of the two remaining chairs, in either order.
The number of ways to seat April and Bobby at the ends of the row is,
= 2x1x2x1
= 4.
Probability that April and Bobby will occupy the seats at the end of the row is,
4/120
= 1/30
= 0.0333( approximately ).
Therefore, the probability of April and Bobby occupy seats at the end of the row is 1/30 or approximately 0.0333.
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The above question is incomplete , the complete question is:
April, bill , candace, and bobby are to be seated at random in a row of 5 chairs. What is the probability that April and bobby will occupy the seats at the end of the row?
Question 5 (20 points)
The midpoint M and one endpoint of AB are given. Find the coordinates of the other endpoint.
A(-8,4) and M(5,-9).
a
(10,-22)
b
(18,-8)
c
(18,-22)
d
(6,-22)
Answer:
(18,-22)Step-by-step explanation:
We can use the midpoint formula to find the coordinates of the other endpoint of AB. The midpoint formula is:
M = ((x1 + x2)/2, (y1 + y2)/2)where M is the midpoint of AB, (x1, y1) are the coordinates of one endpoint of AB (in this case, A), and (x2, y2) are the coordinates of the other endpoint of AB (which we are trying to find).
Substituting the given values:
M = (5, -9)A = (-8, 4)M = ((x1 + x2)/2, (y1 + y2)/2)(5, -9) = ((-8 + x2)/2, (4 + y2)/2)Solving this system of equations for x2 and y2, we get:
-8 + x2 = 2(5) = 10 (multiplying both sides by 2)4 + y2 = 2(-9) = -18 (multiplying both sides by 2)
Adding 8 to both sides of the first equation, and subtracting 4 from both sides of the second equation, we get:
x2 = 10 + 8 = 18y2 = -18 - 4 = -22Therefore, the coordinates of the other endpoint of AB are (18, -22).The list shows the amount of flour in pounds used by a bakery each day for 15 16, 17, 18, 19, 20, 23, 24, 29, 30, 31, 32, 32, 32, 32, 35 Which box plot best displays a summary of these data?
Option C's box-plot best depicts a data representing the list that shows the bakery using the amount of flour in pounds each day for data 15, 16, 17, 18, 19, 20, 23, 24, 29, 30, 31, 32, 32, 32, 32, and 35.
What exactly is a box plot?
The data in the five-number summary is represented by a box-whisker plot, also known as a box plot. This graph primarily displays the minimum observation, first-quartile, median, third-quartile, and maximum observation. A box is used to depict the first to third quartiles in a box plot. At the median, a vertical line segment goes through the box. The dots or line end points represent the minimum and maximum values or observations. The whisker represents the median of the data.
The following information is provided: 15,16,17,18,19,20,23,24,29,30,31,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32
1)Observation minimum=15
2)The maximum number of observations is 35.
3)The data's median:
Because the number of observations is even, the median will be the average.N=total number of observations
The median is the average or mean of the eighth and ninth observations.
= average of 24 and 29
=
=26.5
Median=26.5
4)First Quartile (Q1): the mean of the observations prior to the median.
=average of the first to seventh observations
= average of 15, 16, 17, 18, 19, 20, and 23
=
=18.28
5)Third quartile (Q3): Observational mean after median
=mean of the tenth to sixteenth observations
=average of 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32
=
=32
Q3-Q1 interquartile range (IQR)
=32-18.28
=13.72
Option-C contains a box plot that matches all of the values.
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Walter bought 2,000 cubic millimeters of clay for his sculpture. Now that he has molded the cone and the sphere, he wants to use the rest for decorations. How much clay does he have left for decorations?
Answer:
Step-by-step explanation:
Let's first find the total volume of clay used for the cone and the sphere:
For the cone, we need the formula for the volume of a cone: Vcone = (1/3)πr^2h, where r is the radius of the base and h is the height.
Let's assume the cone has a radius of 5 millimeters and a height of 10 millimeters. Then, the volume of the cone is:
Vcone = (1/3)π(5^2)(10) = (1/3)π(250) = 83.33 cubic millimeters (rounded to two decimal places)
For the sphere, we need the formula for the volume of a sphere: Vsphere = (4/3)πr^3, where r is the radius.
Let's assume the sphere has a radius of 4 millimeters. Then, the volume of the sphere is:
Vsphere = (4/3)π(4^3) = (4/3)π(64) = 268.08 cubic millimeters (rounded to two decimal places)
The total volume of clay used for the cone and the sphere is:
Vcone + Vsphere = 83.33 + 268.08 = 351.41 cubic millimeters (rounded to two decimal places)
To find the amount of clay left for decorations, we can subtract this volume from the original amount of clay:
2000 - 351.41 = 1648.59 cubic millimeters (rounded to two decimal places)
Therefore, Walter has 1648.59 cubic millimeters of clay left for decorations.
failing to reject h0 when h0 is true is select answer from the options below type i error. type ii error. no error. impossible.
If we reject H₀ when Hₐ is true, it is a type II error. The significance of the α level for a continuous measurement is the probability of Type I error. The strength of the test for alternatives is 1 minus elsewhere II. type error probability.
Type II error is a term used in the context of hypothesis testing to describe the error that occurs when people reject a false hypothesis that is actually true. A type II error creates a false positive, also known as an omission error. For example, a test for bacteria may give negative results when a patient is infected. This is a type II error because we accept a negative test even though it is false.
Type II error can be compared to Type I error, which rejects a false hypothesis as true, while Type II error describes the error that occurs when people refuse to reject the fact that it is a false fact. Even if the error does not arise from time, it rejects the other hypothesis.
Suppose a biotech company wants to compare the results of two drugs it uses to treat diabetes. The null hypothesis states that the two drugs are equally effective. The null hypothesis H₀ is the statement that the company wants to reject using a one-tailed test. Another theory, Hₐ, says that no two drugs have the same effect. Another theory Ha is the motivational state by rejecting the negative hypothesis.
The biotech company conducted a large clinical trial of 3,000 diabetics to compare treatments. The company divided 3,000 patients into two equal groups, one receiving treatment and the other receiving treatment. chose a significance level of 0.05; this indicates a willingness to accept that there is a 5% chance of rejecting the null hypothesis when true, or a 5% chance of making a Type I error.
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Complete Question:
Failing to reject H0 when H0 is true is
(1) Type I error.
(2) Type II error.
(3) no error.
(4) impossible.
rewrite each exponent as a single number to make this equation easier to work with. What are the values of 16 2 and 12 2 ?
Exponents are a mathematical notation used to represent repeated multiplication and are a fundamental tool in various fields. The values of [tex]16^2[/tex] and [tex]12^2[/tex] are [tex]16^2[/tex] = 16 x 16 = 256, [tex]12^2[/tex] = 12 x 12 = 144
To rewrite each exponent as a single number, we can evaluate them using multiplication. For example, [tex]16^2[/tex] can be rewritten as 16 x 16, which equals 256. Similarly, [tex]12^2[/tex] can be rewritten as 12 x 12, which equals 144.
The exponent is a small number written above the base, which indicates the number of times the base should be multiplied by itself.
For example, the exponent 3 written above the base 2 means that we should multiply 2 by itself three times: 2 x 2 x 2 = 8. So, [tex]2^3[/tex] is equal to 8.
So, the values of [tex]16^2[/tex] and [tex]12^2[/tex] are:
[tex]16^2[/tex] = 16 x 16 = 256
[tex]12^2[/tex] = 12 x 12 = 144
By evaluating the exponents as single numbers, we can simplify the expressions they appear in and make them easier to work with.
They are used to represent large and small numbers in a compact form, and they simplify calculations by allowing us to perform repeated multiplication more efficiently.
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David's minimum payment is 2.5% of his new balance. His new balance is 820.00. What is the minimum payment?
Answer:
20.50
Step-by-step explanation:
2.5/100 * 820.00
= 20.50
Gary has a sheet of wrapping paper that is 96 cm long and 50 cm wide. He plans to use it to wrap a box with a surface area of 4,900 cm square. Does he have enough paper? If not, how much more paper does he need?
Answer: No it would not be enough , he will need 100 cm more of paper.
Step-by-step explanation:
First ,
The area of paper is
= 96 × 50
= 4800
How much more paper he needs = 4900 - 4800
= 100 cm
I hope this helps
translate the word problem below into an equation, then solve. The medieval spice merchant wants to blend some garlic powder, which costs 38 cents per pound, with 7 pounds of ground pepper, which costs 44 cents per pound, to create a big batch of medieval smelling salt worth exactly 40 cents per pound. How many pounds of the garlic powder should he use?
Answer:
Step-by-step explanation:
x = pounds of gralic powder
x + 7 = pounds of medieval smelling salt
(.38)(x) + (7)(.44) = (x + 7)(.40)
.38x + 3.08 = .40x + 2.80
.38x - .38x + 3.08 = .40x - .38x + 2.80
3.08 = .02x + 2.80
3.08 - 2.80 = .02x + 2.80 -2.80
.28 = .02x
.28/.02 = .02x/.02
14 = x
use 14 pounds of garlis powder
6x−11>67 Solve the inequality by entering the correct answer in the box.
The solution to the inequality 6x - 11 > 67 is x > 13.
What is an inequality?An inequality in mathematics is a comparison between two numbers or expressions that shows one to be bigger than, less than, or not equal to the other. In algebra, inequalities are frequently used to illustrate the connections between variables. Symbols like (less than), > (greater than), (less than or equal to), (greater than or equal to), and can be used to denote an inequality (not equal to). For representing restrictions or limitations on a system, such as the maximum or minimum quantity of a resource that may be used, in real-world applications, inequalities are frequently employed.
The given inequality is:
6x−11>67
Adding 11 to both sides, we get:
6x > 78
Dividing both sides by 6, we get:
x > 13
Hence, the solution to the inequality 6x - 11 > 67 is x > 13.
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which of the following equations is of a parabola with the vertex at (1,-2) ?
Answer: y=(x-1)^2 - 2
Step-by-step explanation:
The equation for a parabola in this situation is y = a(x - h)^2 + k, h being the x point and k being the y point. Plug in the values, and you get y=(x-1)^2 - 2.
a fair coin is flipped four times. What is the probability it lands exactly once. show a full solution
Answer:
1/4
Step-by-step explanation:
10 POINTS! PLEASE HELP! URGENT! ONLY CORRECT ANSWERS!
Answer:1.98
Step-by-step explanation: I know
Answer:
1 ft squared
Step-by-step explanation:
area = base x height / 2
2/3 x 3 = 2/2=1
demarcus wants to know if the day of the week or the time of the day impacts exam scores more. he sets up a between-subjects (independent groups) factorial design and he has 6 conditions (3 x 2 design). he needs to have 50 people in each condition. how many total people would he need to recruit for his study?
Demarcus would need to recruit a total of 300 people for his study.
To determine this, you can follow these steps:
1. Identify the number of conditions in the factorial design. In this case, it is a 3 x 2 design, which means there are 6
conditions (3 levels of one factor multiplied by 2 levels of the other factor).
2. Determine the number of participants needed for each condition. Demarcus needs 50 people in each condition.
3. Multiply the number of conditions by the number of participants per condition. In this case, 6 conditions x 50
participants per condition = 300 total participants.
So, Demarcus needs to recruit 300 people for his between-subjects factorial design study.
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g two roommates take the bus to campus. there are two types of busses: local and express. the number of busses that arrive in an hour is poisson distributed with mean of 20. twenty-five percent of busses are express and seventy-five percent are local. the type of bus is independent. express busses take 16 minutes and local busses take 28 minutes. the first roommate always takes the first bus to arrive. the second roommate takes the first express bus to arrive. what is the difference between the expected total time for the trip (waiting and travel) for the first roommate and the second roommate.
The difference between the expected total time for the trip (waiting and travel) for the first roommate and the second roommate is 0 hours.
To calculate the expected total time for the trip (waiting and travel) for both roommates, we need to find the waiting time and travel time for each roommate.
Step 1: Calculate the arrival rates of local and express buses.
There are 20 buses arriving per hour, with 75% local and 25% express. Thus,
Local bus arrival rate: 20 * 0.75 = 15 buses per hour
Express bus arrival rate: 20 * 0.25 = 5 buses per hour
Step 2: Calculate the waiting time for each roommate.
The waiting time for buses is the inverse of the arrival rate.
First roommate waiting time (first bus): 1 / 20 = 0.05 hours
Second roommate waiting time (first express bus): 1 / 5 = 0.2 hours
Step 3: Calculate the expected travel time for each roommate.
First roommate travel time: 0.75 * 28 + 0.25 * 16 = 21 + 4 = 25 minutes (0.4167 hours)
Second roommate travel time: 16 minutes (0.2667 hours)
Step 4: Calculate the expected total time for the trip for each roommate.
First roommate total time: Waiting time + Travel time = 0.05 + 0.4167 = 0.4667 hours
Second roommate total time: Waiting time + Travel time = 0.2 + 0.2667 = 0.4667 hours
Step 5: Find the difference between the expected total time for both roommates.
Difference = First roommate total time - Second roommate total time = 0.4667 - 0.4667 = 0 hours.
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Help me answer this plss
The area of wrapping paper required by Gabriella to wrap a gift box in the shape of rectangular prism is 718 ft².
What is area?
The region covered or bounded by any two dimensional shape is called its area. The area of rectangular prism,three dimensional shape, will be the sum of the areas of all the faces of that prism.
Here the area of gift wrapping paper can be found by evaluating the surface area of rectangular prism.
Area of wrapping paper= Area of all six faces of rectangular prism
=Area of Surface₁ +Surface₂+Surface₃+ Surface₄ + Surface₅ + Surface₆
Dimensions of Surface₁: Length=13 ft , Width= 11 ft
Area of Surface₁= Length x Width
= 13 x 11
= 143 sq. ft
Dimensions of Surface₂: Length=13 ft , Width= 9 ft
Area of Surface₂= Length x Width
= 13 x 9
= 117 sq. ft
Dimensions of Surface₃: Length=13 ft , Width= 11 ft
Area of Surface₃= Length x Width
= 13 x 11
= 143 sq. ft
Dimensions of Surface₄: Length=13 ft , Width= 9 ft
Area of Surface₄= Length x Width
= 13 x 9
= 117 sq. ft
Dimensions of Surface₅: Length=11 ft , Width= 9 ft
Area of Surface₅= Length x Width
= 11 x 9
= 99 sq. ft
Dimensions of Surface₆: Length=11 ft , Width= 9 ft
Area of Surface₆= Area of Surface₅= 99 sq. ft
Total Area of paper=Sum of all areas of six faces
=143+117+143+117+99+99
=718 sq. ft
718 ft² wrapping paper is required to wrap the gift.
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Refer to the attachment below indicating the numbered faces.
an airplane door is 19 feet off the ground and the ramp has a 31 angle of elevation. What is the length of the ramp (y)?
The length of the ramp (y) is C. 36.9 feet
We can use trigonometry to find out the answer. Here we have given the opposite side length and the angle of elevation. Hence we can use the trigonometric ratio of tangent.
Let's see the steps for solving the problem.
Let AB be the height of the airplane door from the ground, and BC be the ramp's length. Also, let angle BAC be the angle of elevation of the ramp from the ground.
So,angle BAC = 31°andAB = 19 feet.
To find the length of the ramp (BC), we can use the tangent ratio of the angle of elevation.
tan θ = perpendicular/base
Here, the perpendicular is AB and the base is BC.tan 31° = AB/BC
Now, substitute the given values in the equation.
tan 31° = 19/BC
1/√3 = 19/BC
√3 = 19/BC
BC = 19/√3 feet [dividing both sides by √3]
We need to simplify the above answer.
We can multiply and divide the numerator by √3.BC = 19/√3 * √3/√3BC = 19√3/3
Therefore, the length of the ramp is BC = 19√3/3 feet.
Hence, the correct option is (C) 36.9 feet.
The question was incomplete, Find the full content below:
An airplane door is 19 feet off the ground and the ramp has a 31 angle of elevation. What is the length of the ramp (y)?
A. 31.6 feet
B. 22.2 feet
C. 36.9 feet
D. 9.8 feet
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The buying rate and selling rate of Australian dollar in a bank are Rs.132 and Rs 132.85 respectively.how much Australian dollar should be bought and sold by the bank to get Rs 7000 profit.find it.
Answer:
Let x be the amount of Australian dollars the bank buys and sells.
The bank earns a profit by selling the Australian dollars at a higher rate than it bought them.
Profit = Selling rate - Buying rate
Profit per unit = Selling rate - Buying rate = Rs.132.85 - Rs.132 = Rs.0.85
To earn a profit of Rs. 7000, the bank must sell x Australian dollars at a profit of Rs.0.85 per unit, so:
Profit = x * 0.85
x = Profit / 0.85
x = 7000 / 0.85
x = 8235.29
Therefore, the bank should buy and sell 8235.29 Australian dollars to earn a profit of Rs.7000.
How do I find the area of the shape
Answer:
To find the area of a shape, you need to know the formula for the specific shape you are dealing with. Here are some common shapes and their corresponding area formulas:
Rectangle: A = l x w (where A is the area, l is the length, and w is the width)Square: A = s^2 (where A is the area and s is the length of one side)Triangle: A = (1/2)bh (where A is the area, b is the base of the triangle, and h is the height)Circle: A = πr^2 (where A is the area and r is the radius)Once you have identified the shape and the formula for its area, plug in the appropriate values and calculate the area. Make sure to label your answer with the correct units (e.g. square inches, square feet, etc.).
consider three data sets (also, in data set symmetry). 242 probability and statistics for computer scientists (1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1, 13, 21, 21, 20, 19 (2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24, 18, 16, 20, 21, 20, 23, 33 (3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15, 39, 53, 23, 41, 78, 15, 35 (a) for each data set, draw a histogram and determine whether the distribution is rightskewed, left-skewed, or symmetric. (b) compute sample means and sample medians. do they support your findings about skewness and symmetry? how?
a) Histogram for first , second and third data set is present in first, second and third above figure and it shows data is
left-skewed, symmetric and right-skewed.
b) Sample means for first, second and third data set are 14.96667, 20.83, 41.3 respectively. Sample medians for first, second and third data set are 15.5, 21, 39.5 respectively. Yes, they support our findings about skewness and symmetry.
We have three data sets of probability and statistics for computer scientists are present below, (1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1, 13, 21, 21, 20, 19
(2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24,
18, 16, 20, 21, 20, 23, 33
(3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15, 39, 53, 23, 41, 78, 15, 35
a) Histogram is defined as a bar graph like representation of data that buckets a range of classes into columns along the horizontal x-axis.
Histogram representation of data set 1 say X₁ with frequency is present as above in first figure.From the above histogram, the data looks left-skewed.
Histogram representation of data set 2 say X₂ with frequency is present as above in second figure.From the above histogram, data looks like almost symmetric.
Histogram representation of data set 3 say X₃ with frequency is present as above in third figure.From the above histogram, the data looks right-skewed.
b) Sample mean and median :
The mean is the Arithmetic average of a data set. The Sample median value at the middle value of the ordered set of sample values. In case of an even number of values, use the arithmetic mean of the two straddling the center point.As we see here data values are larges in count. So, for making the process easy we can use Excel command.
Enter all first data set in a column then apply the command input= mean(x₁ column) , output 14.96667
= median(x₁column) = 15.5
Now, Mean < Median => Data is left - skewed. Similarly, mean(x₂ column ) = 20.83333 and median(x₂ column) = 21
Mean = 20.83
Median = 21
Mean ≈ Median => Data is symmetric. input : = mean(x₃) ; output : 41.3
input : = median(x₃) ; output: 39.5
Mean = 41.3
Median = 39.5
Mean > Median => Data is right - skewed.
Based on the above calculations, we conclude that scenario 1 ( that is histogram method) has lesser cost and is preferable.
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please help 15 points
The numbers in this chart represent the number of minutes a group of five high school students spent talking on their cell phones one day.
Which of the following statements is true about this data?
A. The data set has two modes.
B. The data set has no mean.
C. The median is 41.
D. The mode and median are equal.
Answer:
It's probably C.
Step-by-step explanation:
41 is in the middle.
So technically speaking... It's the median?
It's definitely not A, that's for sure.
Edit: I was extremely wrong.
HELPP MY IXL IS DUE TMR : Find the distance between the points (-6.3, -5.6) and (-6.3, -9.9).
Using the distance formula we know that the distance between the given 2 points is 4.3 units.
What is the distance?The length of the line segment bridging two points on a plane is known as the distance between the points.
d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
So, use the distance formula:
d=√((x2 – x1)² + (y2 – y1)²)
Now, insert values:
d=√((x2 – x1)² + (y2 – y1)²)
d=√((-6.3 – (-6.3))² + (-9.9 – (-5.6))²)
d=√((-6.3 + 6.3))² + (-9.9 + 5.6))²)
d=√(0)² + (-4.3)²)
d=√18.49
d=4.3
Therefore, using the distance formula we know that the distance between the given 2 points is 4.3 units.
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Write the quadratic equation whose roots are 2 and 4, and whose leading coefficient is 4.
(Use the letter to represent the variable.)
My shortest side stands alone
One of my sides is two less than five times it
The other side is two more than two times it.
Decode my numbers?
what is The square with A = 225 in^2 equal to
The answer is s=√225 in. The area of a square is A = s², meaning that the area of the square is equal to the length of one side of the square squared.
What is square?A four-sided polygon with all sides equal in length. The interior angles of a square are right angles, and the opposite sides are parallel. The four sides of a square meet at its four vertices.
In this case, s is the side length.
To find the side length, we must take the square root of 225 in², which is equal to 15 in.
Therefore, the side length of the square is s=√225 in.
This is because taking the square root of a number is the same as finding the number whose square is equal to the given number.
In this case, the number whose square is equal to 225 in² is 15 in.
Hence, the side length of the square is s=√225 in.
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∠3 is in a triangle with ∠4 and ∠5. Write and solve an equation to find the m∠3
we must have made an incorrect assumption along the way. One possible mistake is to assume that the exterior angle of ∠3 is formed by extending the side opposite to ∠3.
What is Triangle ?
In geometry, a triangle is a 2-dimensional polygon that is formed by connecting three non-collinear points with straight lines.
To find the measure of ∠3, we can use the fact that the sum of angles in a triangle is 180 degrees. Therefore, we can write:
∠3 + ∠4 + ∠5 = 180
However, we don't know the measures of ∠4 and ∠5, so we need to use additional information from the problem to find them.
Since ∠3 is in the same triangle as ∠4 and ∠5, we can use the fact that the exterior angle of a triangle is equal to the sum of its remote interior angles. In other words:
∠4 + ∠5 = exterior angle of ∠3
We don't know the measure of the exterior angle of ∠3 either, but we can use the fact that it is supplementary to ∠3. Therefore:
exterior angle of ∠3 + ∠3 = 180
Combining these equations, we can solve for ∠3:
exterior angle of ∠3 + ∠3 = 180
∠4 + ∠5 = exterior angle of ∠3
∠3 + ∠4 + ∠5 = 180
Substituting ∠4 + ∠5 for the exterior angle of ∠3 in the first equation, we get:
∠3 + (∠4 + ∠5) = 180
∠3 + (exterior angle of ∠3) = 180
Simplifying, we get:
∠3 + (∠4 + ∠5) = 180
2∠3 + (∠4 + ∠5) = 180
2∠3 + exterior angle of ∠3 = 180
Now, we need to know the value of the exterior angle of ∠3. It is formed by extending one of the sides of the triangle containing ∠3, ∠4, and ∠5, and it is equal to the sum of the other two angles in the triangle. We don't have enough information to determine which side is extended, so we will assume that it is the one opposite to ∠3. In this case, we have:
exterior angle of ∠3 = ∠4 + ∠5
Substituting in the equation above, we get:
2∠3 + ∠4 + ∠5 = 180
Now, we can solve for ∠3:
2∠3 + ∠4 + ∠5 = 180
2∠3 = 180 - (∠4 + ∠5)
2∠3 = 180 - (exterior angle of ∠3)
2∠3 = 180 - (∠4 + ∠5)
2∠3 = 180 - (∠3 + ∠4 + ∠5)
2∠3 = 180 - 180
2∠3 = 0
∠3 = 0
However, this result doesn't make sense, because an angle can't have a measure of 0 degrees in a triangle.
Therefore, we must have made an incorrect assumption along the way. One possible mistake is to assume that the exterior angle of ∠3 is formed by extending the side opposite to ∠3.
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Pregunta 4
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Considere la función:
y = x² + 2X +3
¿Cuáles son las coordenadas del vértice de la función dada?
The vertex form of the given function reveals that a = 1, h = -1, and k = 2 are true. Hence, the vertex's coordinates are (-1, 2).
what is function ?A function is a mathematical rule that gives each input value a distinct output value. A function, then, is a relationship between two sets of numbers in which each element of the first set (referred to as the domain) corresponds to exactly one element of the second set (called the range). An equation or formula that describes how input values are changed into output values defines a function, which is typically represented by a letter, such as f. For instance, the rule represented by the function f(x) = x2 produces the value x squared from any input value x.
given
We must finish the square and rewrite the function in vertex form in order to determine the vertex's coordinates for the provided function, y = x2 + 2x + 3.
y = x² + 2x + 3
y = (x + 1)² - 1 + 3 (completing the square)
y = (x + 1)² + 2 (simplifying) (simplifying)
A quadratic function's vertex form is denoted by y = a(x - h)2 + k, where (h,k) denotes the vertex's coordinates.
The vertex form of the given function reveals that a = 1, h = -1, and k = 2 are true. Hence, the vertex's coordinates are (-1, 2).
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Consider the function:
y = x² + 2X +3
What are the coordinates of the vertex of the given function?
Evaluate 4(x - 3) + 5x - x² for x = 3.
O A. -6
OB. -2
O C. 6
OD. 2