Take the vertices as A(2,1), B(0,2), C(-1,1) and D (x2,y2) The fourth coordinate is (1, 1)
How to find the fourth coordinate?Let the vertices ABCD represent the parallelogram.
The diagonals AC and BD bisect each other [property of parallelogram]
Mid point of AC = Mid point of BD ……….. 1
Mid point of AC = (x1+x2)/ 2 and (y1+y2) /2)
=(2-1)/2, (1+1)/2
=(1/2 , 1)
Mid point of BD= (x1+x2)/2, (y1+y2)/2
=(0+x2)/2, (2+y2)/2)
From equation 1
(1/2 , 1)=(0+x2)/2, (2+y2)/2)
{(1/2 , 1/1)} = {(0+x₂)/2 , (1+y₂)/2}
This implies that
1/2 = x₂/2 and 1/1 = (2+y₂)/2
Cross and multiplying we have
2x₂=2 and 2=2+y₂
Making x and y the subject of the relations
x₂=1 and y₂= 1
Therefore the fourth vertex D is (1,1)
Learn more about the vertices of a parallelogram on https://brainly.com/question/6778341
#SPJ1
Solve and explain the method you chose to use (distributive property, FOIL, multiplying special cases): (c+3)^2
After resolving [tex](c+3)^{2}[/tex] , c = -3, and the approach is an example of the distributive property of equations.
What is equations?Its simplest form has been thought to be the figure is probably smallest equivalent fraction. How or when to determine the basic form. Look for shared factors throughout the denominator and numerator. A fractional number can sometimes be checked to discover if it is a power of 2. A statement having two equal sides and an equal sign in the middle is referred to as a mathematical equation. Every variable's degree courses are listed in descending order as in general form of any equation. The formula for a linear equation is x + b = 0. The general form of a three separate linear equation is an x + b y + c = 0. (or something similar). Either conditioned equations or identities are categories for mathematics. An identity holds true for whatever value of the variables.
Given,
[tex](c+3)^{2}[/tex]
= by using formulas of [tex](a+b)^{2}[/tex]
by distributive property
[tex]c^{2}[/tex] + [tex]3^{2}[/tex] + 6c
= [tex]c^{2}[/tex] + 9 + 6c
= [tex]c^{2}[/tex] + 6c + 9 = 0
[tex]c^{2}[/tex] + 3c + 3c + 9 = 0
= c ( c + 3 ) + 3 ( c + 3)
= (c + 3 )(c+ 3)
c = - 3
After resolving [tex](c+3)^{2}[/tex], c = -3, and the approach is an example of the distributive property of equations.
To know more about equation, visit
brainly.com/question/649785
#SPJ1
4. How many distinct 6-digit numbers can be made using the digits 1, 1, 1, 2, 2, 3?
a. 108
b. 60
c. 220
d. 216
e.729
Answer:
B. 60
Step-by-step explanation:
Since the digits 1, 1, 1, 2, 2, 3 are repeated, we use the concept of permutations with repetition. In this case, we can choose the first digit to be any one of the three, the second digit to be any one of the three, and so on. Therefore, the total number of distinct 6-digit numbers that can be made is 3 × 3 × 3 × 3 × 3 × 3 = 729.
However, we need to exclude the numbers that start with a 0 (i.e., numbers like 011112 or 001122). Therefore, the final answer is 729 - 3 = 726, which is the number of 6-digit numbers that do not start with a 0. The number of 6-digit numbers that start with a 0 is 3 (111120, 111202, 112102), so the total number of distinct 6-digit numbers is 726 - 3 = 60.
Use the Empirical Rule to estimate
The number of farms whose land and building values are between $1,200 and $1,400 is given as follows:
50 farms.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.Considering the mean of $1,300 and the standard deviation of $100, measures between $1,200 and $1,400 are within one standard deviation of the mean, hence the percentage is of 68%.
The total amount is of 74 farms, hence the amount relative to 68% of 74 is of:
0.68 x 74 = 50 farms. (rounded).
More can be learned about the Empirical Rule at https://brainly.com/question/10093236
#SPJ1
Maryann runs on a 3/4-mile track at the neighborhood trail. She runs 8 1/2 laps on Saturday.How many more laps does Maryann need to run on Sunday in order to run 10 1/2 total miles over two-day weekend?
A. 9.25 laps
B. 5 1/2 laps
C. 2 laps
D. 1.50 laps
Maryann needs to run 2 more laps to run on Sunday .
What does one lap mean?Lap can be referred as One complete trip around a race track οr from one end of a swimming pool to the other: Fοr example, Each lap of the track is 400 meters.
Given:
Maryann runs : 3/4-mile track
She runs on Saturday: 8 1/2 laps = 17/2
Total miles to cover = 10 1/2 = 21/2
more laps does Maryann need to run on Sunday
= Total miles to cover - She runs on Saturday
= 21/2 - 17/2
= 4/2
= 2
Hence , Maryann needs to run 2 more laps to run on Sunday .
Learn more about Total distance at:
brainly.com/question/24094847
#SPJ1
If ST = p + 31, RU = 6p + 14, and VW = 4p + 53, what is the value of p?
Answer:
If we subtract 14 from both sides of the equation for RU, we get 6p = RU - 14, or 6p = RU - 14. We can then substitute this expression for 6p into the equation for ST to get:
ST = p + 31
ST = (RU - 14) + 31
Expanding RU, we get:
ST = RU - 14 + 31
ST = RU + 17
Since RU = 6p + 14, we can substitute this expression into the above equation to solve for p:
ST = 6p + 14 + 17
ST = 6p + 31
Finally, we can subtract 31 from both sides of the equation to find p:
ST - 31 = 6p + 31 - 31
ST - 31 = 6p
ST - 31 = 6p
p = (ST - 31) / 6
So, to find the value of p, we need to know the value of ST.
4x - y = 3
3x + y = 4
Answer: (x, y) = (5/4, 2).
The given system of equations is:
4x - y = 3
3x + y = 4
We can solve for x and y using either substitution or elimination method.
By substitution, we can solve for y in one of the equations and substitute that value into the other equation to solve for x.
Starting with 4x - y = 3, we can add y to both sides to isolate x:
4x = 3 + y
Then, we can substitute this expression for y into the second equation:
3x + (3 + y) = 4
Expanding the right side, we get:
3x + 3 + y = 4
3x + 3 = 4 - y
3x = 1 - y
x = (1 - y)/3
Now, we can substitute the expression for x into the first equation:
4((1 - y)/3) - y = 3
4(1 - y)/3 = 3 + y
4 - 4y/3 = 3 + y
1 - 4y/3 = y + 3
-3y/3 = -2
y = 2
Finally, we can substitute the value of y into one of the original equations to find x:
4x - 2 = 3
4x = 5
x = 5/4
So, the solution to the system of equations is (x, y) = (5/4, 2).
resoudre [tex]30*\sqrt{5}² + 13*\sqrt{5}-6[/tex]
The simplified expression for this problem is given as follows:
[tex]43\sqrt{5} - 6[/tex]
How to simplify the expression?The expression for this problem is defined as follows:
[tex]30\sqrt{5} + 13\sqrt{5} - 6[/tex]
To simplify the expression, we combine the like terms, which are the terms that have the same rational, thus:
[tex]30\sqrt{5} + 13\sqrt{5} = 43\sqrt{5}[/tex]
Combining along with the subtraction by 6, the complete simplified expression is given as follows:
[tex]43\sqrt{5} - 6[/tex]
More can be learned about the simplification of expressions at https://brainly.com/question/723406
#SPJ1
Factor 1 - 2.25x8.
(1 - 1.5x 4) 2
(1.5 + x 4)(1.5 - x 4)
(1 + 1.5x 4)(1 - 1.5x 4)
The factor of 1 - 2.25x⁸ is (1 + 1.5x⁴) (1 - 1.5x⁴).
The correct option is C.
What is factorization?Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.
Given:
An expression,
1 - 2.25x⁸.
Simplifying to the factored form.
1² - (1.5x⁴)²
= (1 + 1.5x⁴) (1 - 1.5x⁴)
Therefore, (1 + 1.5x⁴) (1 - 1.5x⁴) is the factored form.
To learn more about the factorization;
https://brainly.com/question/28187946
#SPJ1
When planning a more strenuous hike, Erin figures that she will need at least 0.8 liters of water for each hour on the trail. She also plans to always have at least 1.50 liters of water as a general reserve. If x represents the duration of the hike (in hours) and y represents the amount of water needed (in liters) for a hike, the following inequality describes this relation: y greater or equal than 0.8 x plus 1.5
Answer:
the inequality y ≥ 0.8x + 1.5 accurately describes the relation between the duration of the hike (x) and the amount of water needed (y). This inequality means that for any duration of the hike (x), the amount of water needed (y) must be greater than or equal to 0.8x + 1.5.
Answer:
Step-by-step explanation:
3 liters of water for 4 hours of hiking.
9x-7y=-5
-3x+7y=11
how do we solve this?
The system of equations is solved by graphing as shown in the image, where the solution is (1, 2).
How to Solve a System of Equations by Graphing?A system of equations can be solved by graphing each line that represents each equation, then find the point where they both intercept.
Thus, the coordinates of the point where the two linear equations intercept will be the solution of the system of equations.
Given the system, 9x - 7y = -5 is the red line while -3x + 7y = 11 represents the blue line. Both intercept at (1, 2), which is the solution of the equations.
Learn more about the system of equations on:
https://brainly.com/question/25976025
#SPJ1
if Δabc≅Δpqr, then ac≅
ac is congruent to pr because those sides correspond
the SULT club has 4,000 members all age 25 with independent future lifetimes. The mortality for each member follows the Standard Ultimate LIfe Table. Calculate the largest N, using the normal approximation, such that the probability that there are at least N survivors at age 95 is at least 90%.
The largest N such that the probability that there are at least N survivors at age 95 is at least 90% is approximately 136.43.
The normal approximation can be used to estimate the number of survivors at a given age when the mortality follows the Standard Ultimate Life Table. The normal approximation assumes that the number of survivors follows a normal distribution.
Let X be the number of survivors at age 95. Then, the mean (μ) and standard deviation (σ) of X can be calculated using the following formula:
μ = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾
σ = √(4,000 * (1 - e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾) * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾)
Next, we can find the value of N such that P(X >= N) >= 0.9 using the standard normal distribution.
z = (N - μ) / σ
P(X >= N) = 1 - P(X < N) = 1 - Φ(z)
where Φ(z) is the cumulative distribution function of the standard normal distribution.
We want to find the largest N such that P(X >= N) >= 0.9, so we need to find the smallest z such that Φ(z) <= 0.1. The value of z can be found using a standard normal table or a calculator with normal distribution functions.
With a calculator, we get that z = 1.28. So, N = μ + z * σ.
Plugging in the values we calculated earlier, we get:
N = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾ + 1.28 * √(4,000 * (1 - e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾) * e⁽⁻⁰.⁰⁷³⁶⁽⁹⁵⁻²⁵⁾⁾)
N = 4,000 * e⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾⁾ + 1.28 * √(4,000 * (1 - e^⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾) * e^⁽⁻⁰.⁰⁷³⁶⁽⁷⁰⁾⁾
N = 4,000 * 0.0337 + 1.28 * √(4,000 * (1 - 0.0337) * 0.0337)
N = 132.8 + 1.28 * √(4,000 * 0.966 * 0.0337)
N = 132.8 + 1.28 * √(13.97376)
N = 132.8 + 3.63323
N ≈ 136.43
So, the largest N such that the probability that there are at least N survivors at age 95 is at least 90% is approximately 136.43.
Learn more about standard deviation here: brainly.com/question/23907081
#SPJ4
The figure below is a parallelogram. Based on what we know about consecutive angles of a parallelogram, write and equation and solve for x.
The value of x in the given paralellogram is 12.
What is parallelogram?
"It is a quadrilateral with parallel opposite sides."
"The opposite angles of parallelogram are equal. "
For given question,
Two of the angles in a parallelogram measure 8x° and 7x°
The measure of an angle opposite to 8x° is also 8x°
In a similar manner, an angle opposite to 7x° is measured as 7x°.
So, we have the four angles of parallelogram as 8x°, 7x°, 8x°, 7x°
We are know that the total angle of a quadrilateral is 360°.
⇒ 8x° + 7x° + 8x° + 7x° = 360°
⇒ (5 + 7 + 5 + 7) x = 360
⇒ 30x = 360
⇒ x = 12
Therefore, the value of x is 15.
Learn more about parallelogram here:
brainly.com/question/1563728
#SPJ1
The ratio of hydrogen atoms to nitrogen atoms in a container is 2:3 what is the value of 2:3
The value of 2:3 can be written as a fraction: 2/3.
What is the ratio?
In mathematics, a ratio is a comparison of two quantities, often expressed as a fraction or using the colon (:) symbol. Ratios are used to indicate the relative size or amount of two or more things.
For example, the ratio of the length of a rectangle to its width can be expressed as a fraction, where the numerator represents the length and the denominator represents the width.
The ratio of hydrogen atoms to nitrogen atoms is 2:3.
This means that for every 2 hydrogen atoms, there are 3 nitrogen atoms in the container. The value of the ratio 2:3 is a way of expressing the relative quantity of hydrogen atoms to nitrogen atoms in a simplified form. It can also be written as a fraction: 2/3.
Hence, the value of 2:3 can be written as a fraction: 2/3.
To learn more about the ratio, visit:
https://brainly.com/question/2328454
#SPJ1
At a local elementary school, 35 percent of all students have brown eyes, 45 percent have brown hair, and 60 percent have brown hair or brown eyes. A student will be selected at random from the school. Let E represent the event that the selected person has brown eyes, and let H represent the event that the selected person has brown hair.Are E and H mutually exclusive events?A- Yes, because P(E∩H)=0P(E∩H)=0.
B- Yes, because P(E∩H)=0.2P(E∩H)=0.2.
C- Yes, because P(E∩H)=0.6P(E∩H)=0.6.
D- No, because P(E∩H)=0.2P(E∩H)=0.2.
E- No, because P(E∩H)=0.6
The required events E and H are not mutually exclusive, because they can both occur at the same time.So D - No, because P(E∩H) = 0.20 is correct.
What are mutually exclusive events?The events E and H are not mutually exclusive, because they can both occur at the same time. In other words, a student can have both brown eyes and brown hair.
According to question:The probability that a student has both brown eyes and brown hair, P(E∩H), can be found using the formula:
P(E∩H) = P(E) + P(H) - P(E or H)
where P(E) is the probability of having brown eyes, P(H) is the probability of having brown hair, and P(E or H) is the probability of having either brown eyes or brown hair.
Given that:
P(E) = 0.35
P(H) = 0.45
P(E or H) = 0.60
So,
P(E∩H) = 0.35 + 0.45 - 0.60 = 0.20
So, the answer is D - No, because P(E∩H) = 0.20.
To know more about Probability visit:
brainly.com/question/15124899
#SPJ4
PLEASE HELP!
Solve the formula for the specified variable
V= APT for A
A=
It says a=v/pt is wrong
Making A the subject of the equation V = APT gives A = V/(PT)
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Given the equation:
V = APT
We need to make A the subject of the formula.
Firstly, divide both sides of the equation by P:
V/P = APT/P
AT = V/P
Secondly divide both sides of the equation by T:
(AT)/T = (V/P)/T
A = V/(PT)
The value is A = V/(PT)
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Graphing and substitution, please help!
Find the area of the right triangle.
Be sure to include the correct unit in your answer.
24 cm
25 cm
Answer:
300 cm^2
Step-by-step explanation:
An area of a triangle is b*h/2.
Therefore, plug in the base and height into the equation.
24cm * 25cm / 2 = area
600cm^2 / 2 = area
300cm^2 = area
What is the value of the expression above?
A 98
B 150
C 51
D 198
Answer:
C (51)
Explanation
What is an angle that is supplementary to ∠CGD
Answer:
Step-by-step explanation:
angle DGF
Please help me with the answer to this question
Answer:
1/36
Step-by-step explanation:
above is the answer
Troy set a goal for the total distance he wants to jog this week. He divided his goal evenly among the 5 jogs he planned for the week. Troy determined that each jog should be at least 2.8 miles to meet his goal.
Let x represent how many miles Troy wants to jog in all. Which inequality describes the problem?
The inequality describing the given problem is x/5 ≥ 2.8 and Troy should at least jog for 14 miles in total.
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, Troy set a goal for the total distance he wants to jog this week. He divided his goal evenly among the 5 jogs he planned for the week. Troy determined that each jog should be at least 2.8 miles to meet his goal.
x represent how many miles Troy wants to jog in all. We need to find an inequality describes the problem.
Since, he has divided his goal into 5 jogs and in total he did x jogs, therefore, jog for 1 day = x/5
Now, he set that each jog should be at least 2.8 miles to meet his goal.
That mean, he can jog 2.8 miles or more than it but not less than it,
Therefore, inequality will be,
x/5 ≥ 2.8
Now, finding x,
Multiply both sides by 5,
x ≥ 14
Hence, the inequality describing the given problem is x/5 ≥ 2.8 and Troy should at least jog for 14 miles in total.
Learn more about inequality, click;
https://brainly.com/question/28823603
#SPJ1
Joanna is currently watching 6.4 hours of T.V per day. She made a goal to reduce the amount to 1.6 hours per day . what is the amount now?
Answer: 4.8
Step-by-step explanation:
6.4 - 1.6 = 4.8
A Triangular Prism with equilateral triangle faces has Volume of 84cm³ and a Length of 12cm. Find the base area of this prism.
Got this on my test, don't know how to do it lol.
Answer:
7cm²
Step-by-step explanation:
volume of a triangular prism=1/2×b×h×l
1/2×b×h=cross sectional area
84cm³=C.A×12
C.A=84/12
base area=7cm²
1) How many more acres are there at Navajo Monument than at George Washington Carver Monument?
Number of acres more there at Navajo Monument than at George Washington Carver Monument is 120.
How to find the area of some object?Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.
Given;
The area of navajo monument= 360acres
The area of George Washington Carver Monument = 240 acres
Now
More area navajo monument has =area of navajo monument - area of George Washington Carver Monument
=360-240
=120
Therefore, the extra area navajo monument has is 120 acres.
Learn more about area here:
https://brainly.com/question/15096475
#SPJ1
Change from base 10 to base 4. It will be helpful to create a place value chart for base 4 before doing this problem. Show your thinking.
9^10
15^10
29^10
72^10
Challenge: 259^10
9¹⁰ can be expressed as base 4 with 22 and 15¹⁰ can be expressed as 33.
What is Expression?An expression is combination of variables, numbers and operators.
To change from base 10 to base 4, we need to express each number in terms of powers of 4. Here's how you can do this for each number:
9¹⁰ in base 4:
9 in base 10 can be expressed as 22
Base 4
So, (22)¹⁰ = 4¹⁰ x 2¹⁰ = 1048576 x 1024
= 1073741824 in base 10.
15¹⁰ in base 4
15 in base 10 can be expressed as 33 in base 4
Hence, 9¹⁰ can be expressed as base 4 with 22 and 15¹⁰ can be expressed as 33.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ1
Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0 . A random sample of 59 people is taken. Step 2 of 2 : What is the probability that the mean IQ score of people in the sample is less than 99 ? Round your answer to 4 decimal places, if necessary.
The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.
what is probability ?The probability that an event will happen or a claim will be correct is measured by statistical mechanics, a branch of mathematics. The possibility of an occurrence is a positive integer and 1, where about 0 represents how likely the event is to occur and value of 1 indicates certainty. A probability is a numerical illustration of the possibility that a specific activity will take place. Probabilities can also be expressed using percentages extending from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a comprehensive set of equally likely choices that lead to a specific occurrence.
given
This is Z's pvalue for X = 98. So
Z = 98 -100 / 15
Z = -0.133
Z = -0.133 pvalue of 0.4470
The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
Given f(x) = 8x ^ 2 + 16x + 6 and (g - f)(x) g(x) = x ^ 3 - 3x ^ 2 - 9 find (g-f)(x).
A) - x ^ 3 + 11x ^ 2 + 16x + 15
B) x ^ 3 + 5x ^ 2 + 16x - 3
C) x ^ 3 - 11x ^ 2 - 16x - 15
D) - x ^ 3 + 5x ^ 2 - 16x - 3
The combination of the difference of the functions (g - f)(x), where; f(x) = 8·x² + 16·x + 6 and g(x) = x³ - 3·x² - 9 is; x³ - 11·x² - 16·x - 15
The correct option is option C
C) x³ - 11·x² - 16·x - 15
What are some of the formula for the combination of functions?The combinations of functions can be found as follows;
Addition; (f + g)(x) = f(x) + g(x)
Subtraction; (f - g) = f(x) - g(x)
Multiplication; (f·g) = f(x) × g(x)
Division; (f/g)(x) = f(x)/g(x)
What is a function?
A function is a rule or law that maps an input variable into an output variable such that each element in the set of input variable is mapped to exactly one element in the set of the output variables.
The f(x) = 8·x² + 16·x + 6
g(x) = x³ - 3·x² - 9
Therefore;
(g - f)(x) = g(x) - f(x)
(g - f)(x) = x³ - 3·x² - 9 - (8·x² + 16·x + 6) = x³ - 11·x² - 16·x - 15
The correct option is therefore option C
C) x³ - 11·x² - 16·x - 15
Learn more on combining functions here: https://brainly.com/question/12000899
#SPJ1
Taye pays $0.06 sales tax on each dollar he spends. If he buys a new bike for $237.00, how much sales tax will Taye pay?
Answer: $14.22
Step-by-step explanation: 237*0.06
An account that compounds interest monthly has an annual percentage yield of 5.9%.
What is the annual interest rate for the account?
Answer: The annual percentage yield (APY) is the total amount of interest earned on an investment over a year, expressed as a percentage of the initial investment. The annual interest rate is simply the interest rate per year, expressed as a percentage.
To convert the APY to the annual interest rate, we can divide the APY by the number of times the interest is compounded in a year. If the interest is compounded monthly, then the number of times the interest is compounded in a year is 12.
So, the annual interest rate for the account is given by:
Annual interest rate = APY / number of times compounded in a year
= 5.9% / 12
= 0.49%
Therefore, the annual interest rate for the account is 0.49%.
Step-by-step explanation: