Therefore, the perimeter of the polygon formed by connecting the points A(3,4), B(3,1), C(8,1), and D(8,4) is 12 units.
What is perimeter?Perimeter is the total distance around the boundary or the outside of a two-dimensional shape such as a polygon. It is the sum of the lengths of all the sides of the shape. The perimeter is typically measured in units of length, such as meters, centimeters, feet, or inches. The concept of perimeter is used in many areas of geometry and mathematics, as well as in other fields such as architecture, engineering, and construction.
Here,
To find the perimeter of the polygon formed by connecting the points A(3,4), B(3,1), C(8,1), and D(8,4), we need to calculate the distance between each pair of adjacent points and then add up these distances.
We can use the distance formula to find the distance between two points:
distance = √[(x2 - x1)² + (y2 - y1)²]
So, the distance between points A and B is:
AB = √[(1 - 4)² + (3 - 3)²]
= √[(-3)² + 0²]
= √9
= 3
The distance between points B and C is:
BC = √[(1 - 1)² + (8 - 3)²]
= √[0² + 5²]
= √25
= 5
The distance between points C and D is:
CD = √[(4 - 1)² + (8 - 8)²]
= √[3² + 0²]
= √9
= 3
The distance between points D and A is:
DA = √[(4 - 4)² + (3 - 3)²]
= √[0² + 1²]
= √1
= 1
Now we can add up these distances to find the perimeter:
perimeter = AB + BC + CD + DA
= 3 + 5 + 3 + 1
= 12
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graph each equation by using a table -3=5x-y
The graph of the equation is shown below
Graph of linear equations
From the question, we are to graph the given equation
The given equation is
-3 = 5x - y
To graph the equation,
First we will determine the x-intercept and y-intercept
x-intercept
Put y = 0 in the equation
-3 = 5x - 0
-3 = 5x
x = -3/5
y-intercept
Put x = 0 in the equation
-3 = 5(0) - y
-3 = 0 - y
-3 = -y
y = 3
Using the x-intercepts and y-intercepts, we can plot the graph of the equation.
The graph of the equation is shown below
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How many hours is enough for practicing the piano every day, and is setting hours the best way to practice?
Answer:
DOWN BELOW
Step-by-step explanation:
It is recommended that pianists spend between 30 minutes and 4 hours practicing each day. The practice sessions will differ for beginners and advanced pianists depending on their level of ability. Beginners will benefit the most from shorter sessions.
which of the following are solutions to the quadratic equation check all that apply x ^ 2 + 10x + 25 = 2
Answer:
to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore
x^2 + 10x + 25 - 2 =2 - 2
therefore
x^2 + 10x +23 = 0
now since the equation cannot be factored, we use the formula.
x= \(\frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)
where
a=1
b=10
c=23
note we use the coefficients only.
therefore x = \(\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}\)
=\(\frac{-10-+\sqrt{100-92} }{2}\)
=\(\frac{-10-+\sqrt{8} }{2}\)
then we form two equations according to negative and positive symbols
x=\(\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}\)
therefore x = \(-5+\sqrt{2}\) or x=\(-5-\sqrt{2}\)
The Boston Celtics have won 16 NBA championships over approximately 50 years. Thus is may seemreasonable to to assume that in a given year the Celtics win the title with probability p = 16=50 = 0:32,independent of any other year. Given such a model, what would be the probability of the Celtics winningeight straight championships
Answer:
0.0001 = 0.01% probability of the Celtics winning eight straight championships.
Step-by-step explanation:
For each year, there are only two possible outcomes. Either the Celtics are the champions, or they are not. Each year is independent of other years. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
What would be the probability of the Celtics winning eight straight championships?
Each year, we have that \(p = 0.32\)
Eight straight championships: \(P(X = 8)\) when n = 8. So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 8) = C_{8,8}.(0.32)^{8}.(0.68)^{0} = 0.0001\)
0.0001 = 0.01% probability of the Celtics winning eight straight championships.
If
m
�
�
⌢
=
5
4
∘
m
GT
⌢
=54
∘
and
m
�
�
⌢
=
16
0
∘
m
YC
⌢
=160
∘
, find
m
∠
�
m∠W.
Answer:
∠ W = 53°
Step-by-step explanation:
the measure of the secant- secant angle W is half the difference of the measures of the intercepted arcs , that is
∠ W = \(\frac{1}{2}\) (YC - GT) = \(\frac{1}{2}\) (160 - 54)° = \(\frac{1}{2}\) × 106° = 53°
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
Answer:
4 the answer is 4
Step by step explanatin:
b is the midpoint of segment ac. a has coordinates (-3, 4) and b has coordinates (-1 1/2, 1). find the coordinates of c
The coordinates point C of the given line segment AC is C(0, -2) whose midpoint is at B.
How to calculate a midpoint of a line segment?To calculate the midpoint of a line segment, find the average for the coordinates of the endpoints of the line segment. I.e.,
Consider a line segment AC, B is its midpoint.
So, the coordinates of B are (Where we have A(x1, y1) and C(x2, y2))
B(x, y) = \((\frac{x1+x2}{2}, \frac{y1+y2}{2})\)
Calculation:It is given that, B is the midpoint of a line segment AC.
Where A has coordinates as (-3, 4) and B has coordinates as (-1 1/2, 1).
So, the coordinates of the other end point C of the given line segment are calculated as
B(x, y) = \((\frac{x1+x2}{2}, \frac{y1+y2}{2})\)
⇒ (-1.5, 1) = \((\frac{-3+x2}{2}, \frac{4+y2}{2})\)
⇒ -1.5 = (-3 + x2)/2 and 1 = (4 + y2)/2
⇒ -3 = -3 + x2 and 2 = 4 + y2
⇒ x2 = 0 and y2 = 2 - 4 = -2
Therefore, point C has coordinates as (0, -2).
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Mindy spent $6.24 fir a new binder,$1.95 for a notebook,and $5.59 for a new pack of her favorite mechanical pencils. About how much did she spend?
Answer:
13.78
Step-by-step explanation:
6.24+1.95+5.59 = 13.78 dollars
Answer:
13.78
Step-by-step explanation:
P=x-2 ÷ x+1 for whar value of x is P equal to zero
Answer:
x = 2
Step-by-step explanation:
P = \(\frac{x-2}{x+1}\)
P will equal zero when the numerator is equal to zero , that is
x - 2 = 0 ( add 2 to both sides )
x = 2
P = 0 when x = 2
What is the slope of the line in the graph?
-4/3
-3/4
3/4
4/3
Answer:
i think the answer is -3/4
Shen the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were clients who did Plan A and who did Plan B. On Thursday there were clients who did Plan A and who did Plan B. Shen trained his Wednesday clients for a total of hours and his Thursday clients for a total of hours. How long does each of the workout plans last?
The length of time that it will take for each of the workout sessions would be: Plan A = 1.5 hours, and Plan B = 0.5 hours.
What would be the length of the sessions?The length of the sessions can be obtained by first obtaining drawing a system of equations for the two cases. On Wednesday, we can represent the sessions as follows:
2A + 12B = 9 hours
On Thursday, we would have
5A + 3B = 9 hours
2A + 12B = 9 Eqn 1
5A + 3B = 9 Eqn 2
Multiply equation 2 by -4
2A + 12B = 9
-20A - 12B = -36
2A - 20A = 9 -36
-18A = -27
Divide both sides by -18
A = 1.5 hours
For B, substitute A in the first equation
2(1.5) + 12B = 9
3 + 12B = 9
12B = 9 - 3
12B = 6
Divide both sides by 12
B = 0.5
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Complete Question:
Ann the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 2 clients who did Plan A and 12 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Ann trained her Wednesday clients for a total of 9 hours and her Thursday clients for a total of 9 hours. How long does each of the workout plans last?
Given an undirected graph G= (V, E) determined by the adjacency matrix as follows:
01001
10111
01010
01101
11010
The number of odd degree vertices of the graph is
Select one
A.2
B.4
C.3
D.1
if anyone knows the question please help me :(
The degree of a vertex is defined as the number of edges that touch the vertex. The (i, j)-th entry of the adjacency matrix tells you whether vertex i touches vertex j (1 if yes, 0 if no). Then the degree of vertex i is equal to the sum of the i-th row in the adjacency matrix.
• vertex 1 : degree = 0 + 1 + 0 + 0 + 1 = 2
• vertex 2 : degree = 1 + 0 + 1 + 1 + 1 = 4
• vertex 3 : degree = 0 + 1 + 0 + 1 + 0 = 2
• vertex 4 : degree = 0 + 1 + 1 + 0 + 1 = 3
• vertex 5 : degree = 1 + 1 + 0 + 1 + 0 = 3
So, the correct answer is A. 2.
Answer ASAP but only if you are SURE about it
Answer:
It's A, 6.86 × 10⁴
Step-by-step explanation:
In scientific notation, you have the base, and the 10. The 10 is represented next to an exponent, whereas the base is a whole number and a decimal. If the decimal is moved right, the exponent following the 10 becomes negative. Left, it becomes positive. In this instance, the decimal is being moved left, thus the exponent is positive.
Answer:
A
Step-by-step explanation:
All my work is provided in the attached Screenshot! :)
Jolene invests her savings in two bank accounts, one paying 3 percent and the other paying 9 percent simple
interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual
interest is 3120 dollars. How much did she invest at each rate?
Amount invested at 3 percent interest is $____
Amount invested at 9 percent interest is $___
Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.
To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.
For the 3 percent interest account:
Interest_3_percent = x × 0.03
For the 9 percent interest account:
Interest_9_percent = 2x × 0.09
We know that the total annual interest is $3120, so we can set up the equation:
Interest_3_percent + Interest_9_percent = 3120
Substituting the above equations, we have:
x × 0.03 + 2x × 0.09 = 3120
Simplifying the equation:
0.03x + 0.18x = 3120
0.21x = 3120
Dividing both sides of the equation by 0.21:
x = 3120 / 0.21
x = 14857.14
Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.
Answer:
Step-by-step explanation:
X is the amount invested at 6%
Y is the amount invested at 9%
0.06X + 0.09Y = 4998
X = 2Y
0.06(2Y) + 0.09Y = 4998
.12Y + 0.09Y = 4998
0.21Y = 4998
21Y = 499800
Y = 499800/21 = 23800
So X = 2*23800 = 47600
$47,600 is invested at 6% and $23800 is invested at 9%
1.3 Do Activity 1.4.1 from your Study Guide. Give a concise account (do not copy and paste) of the main points of the principle of "Caring about the development of students' mathematical proficiency". (6)
The principle of "Caring about the development of students' mathematical proficiency" is a vital component of the teaching process.
As a teacher, you must be concerned about your student's growth in mathematics to support their success in the subject. The main points of this principle are as follows:
1. Supporting Students: The teacher must strive to provide effective support for each student's learning, based on their needs.
2. Encouraging Students: The teacher should encourage students to improve their proficiency in mathematics and support their learning by providing suitable opportunities for them.
3. Problem-Solving Skills: Teachers must help students develop problem-solving skills to tackle challenging mathematical problems.
4. Feedback and Assessment: The teacher must provide timely feedback and assessment to support the student's growth in mathematics. This feedback should be constructive and should aid in the student's development of mathematical proficiency.
5. Encouraging Student Reflection: The teacher should encourage students to reflect on their learning experiences to recognize areas where they need more support. The development of a student's mathematical proficiency should be the focus of a teacher's teaching, learning, and assessment practices.
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The function f(c)=c/20 represents the number of ferry boat trips, f(c) needed to transport c cars in one day. If there are no more than 5,000 cars transported by the ferryboat daily, what is the maximum value for the function f?
Answer:
250
Step-by-step explanation:
Equation is f(c)= c/20
We know that there are NO MORE than 5,000 cars transported.
New equation would be
f(5000) =5000/20
5k divided by 20 is 250
less or equal to 250 in a euation would be
f(c) < or equal to 250
random khan question and I haven't done this in a year, I'm struggling.
Answer:
Add maybe
Step-by-step explanation:
add the 500+400+200 try that hope it helps have a great day
Estimate the sum of 379+409=
Answer:
Round both numbers to 1 significant figure.
400+400=800
800 is the answer.
write the following as comparison as a ratio reduced to lowest terms of 149 minutes to 9 hours
Gianni used 6 gb out of 8 gb includes in his cell phone plan. What percent of his data did he use
Answer:
75%
Step-by-step explanation:
If he used 6 out of 8 gb of his cell phone plan we can write that as a fraction as 6/8.
We can simplify 6/8 to 3/4. And 3/4 when divided is equal to 0.75 which when written as a fraction is 75%.
I hope this helps!
Question 15 of 60
Choose the symbol that correctly compares the fractions below.
8 8
-?-
10 10
OA. None of these are correct.
OB. <
C. >
OD. =
SUBMIT
Answer:
D
Step-by-step explanation:
Jalaysha is three years less than twice as old as Ben, and Maureen is two years older than Ben. Write an expression for Jalaysa and Maureen's ages in terms of Ben'sunknown age, b.
Write in simplest Standard Form
jalaysha age:
Maureen's age:
Answer:
3 - 2 x b
For jalaysha's age.
b + 2
Is maureen's age
Answer:
3-2*b=j
2+b=m
Step-by-step explanation:
6(-3) - | -5 | + | 3 | =
16
-10
-20
Answer:
its negative 20
Step-by-step explanation:
-20
18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answer:
\(y = 4x-3\)
Step-by-step explanation:
The coordinates are (-0.5,-5) and (2,5)
Finding the slope, m:
=> Slope = \(\frac{rise}{run}\)
=> Slope = \(\frac{5+5}{2+0.5}\)
=> Slope = \(\frac{10}{2.5}\)
=> Slope = 4
Now, y-intercept, b:
Taking any of the two coordinate and putting it in the slope intercept equation:
=> Point = (x,y) = (2,5)
So, x = 2, y = 5
=> \(y = mx+b\)
=> 5 = (4)(2) + b
=> 5 = 8 + b
=> b = 5-8
=> b = -3
Now, Putting in slope intercept equation:
=> \(y = mx+b\)
=> \(y = 4x-3\)
Gradient (m) = x2-x1
y2-y1
considering
y1 = -5 y2 = 5
x1 = -0.5. x2 = 2
m = 2-(-0.5)
5-(-5)
m = 5.5
10
m = 11. = 0.55
20
equation of a line is given by
y-y1 = m+(x-x1)
y-(-5) =0.55 + {x-(-0.5)}
y+5 = 0.55 + x+0.5
making y the subject
y = 0.55 +0.5 -5 + x
y = -3.95 + x
Evaluate the expression,
if x = 12, y = 8, and z = 3.
5y +
XIN
Rumus suatu fungsi di nyatakan dengan f (x) = 2x + 5. Jika f(a) = 7, nilai a adalah
Step-by-step explanation:
As my previous answer got deleted for being wrong (in which it was right), I will answer again.
The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.
This is proof that it is right, and that there are some corrupt admins on brainly.
How to get to this solution?
Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).
If we do so, we get 2a + 5 = 7.
Solving this equation, we get a = 1.
Simplify: 4.25(17.18 − 9.25) s
Step-by-step explanation:
Subtract 9.25 from 1718.
4.25 * 1708.75s
Multiply 4.25 by 1708.75.
7262.1875s
Solution - 7262. 1875s
Solution of the expression is,
⇒ 33.70 s
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ 4.25(17.18 − 9.25) s
Now, We can simplify as;
⇒ 4.25(17.18 - 9.25) s
⇒ 4.25 × 7.93 s
⇒ 33.70 s
Thus, Solution of the expression is,
⇒ 33.70 s
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Juan sold a bicycle at a discount of 15%. If the selling price was $340, find the usual price of the bicycle.
Answer: $400
Step-by-step explanation:
Discount = 15%
The original price/value of an item is always 100%
So selling price (%) = original price - discount = 100%-15% = 85%
We got selling price as 85%
This implies that 85% = 340
Let's find 1% first, then 100%
1% = 340÷85 = 4
100% = 4 × 100 = $400
The usual (normal/original) price is $400
Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let's represent the usual price of the bicycle by P.
Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).
We can express this relationship as an equation:
S = 0.85P
We also know that the selling price of the bicycle was $340.
Substituting S = $340 into the equation above, we get:
$340 = 0.85P
To find P, we can solve for it:
P = $340 / 0.85
P = $400
Therefore, the usual price of the bicycle was $400.
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Statistical data of breakdowns of computer XXX show that the duration for trouble-free operation of the machine can be described as a gamma distribution with a mean of 40 days and a standard deviation of 10 days. The computer is occasionally taken out for maintenance in order to insure operational condition at any time with a 95% probability.
1. How often should the computer be scheduled for maintenance? Should it be shorter or longer than the mean of 40 days?
2. Three XXX computers were acquired at the same time by an engineering consulting firm. The computers are operating under the same environment, workload, and regular maintenance schedule. The breakdown times between the computers, however, may be assumed to be statistically independent. What is the probability that at least one of the three machines will break down within the first scheduled maintenance time?
1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.
2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns
1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.
To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.
Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:
reliability = 0.95
time = maintenance interval
Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.
2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.
The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:
Probability of no breakdowns = (reliability of a single machine)^3
Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:
Probability of at least one breakdown = 1 - Probability of no breakdowns
By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.
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