The lengths of the four sides of a
quadrilateral (in inches) are consecutive integers. If
the perimeter is 110 inches, find the value of the longest of the four side lengths.
Answers
The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
According to the given question.
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).
Also, it is given that the perimeter of the quadrilateral is 110 inches.
⇒ x + x+1 + x + 2 + x + 3 = 110
⇒ 4x + 6= 110
⇒ 4x = 110 -6
⇒ 4x = 104
⇒ x = 104/4
⇒ x = 26 inches
Thereofore, the length of the sides of the quadrilaterals is given by
x = 26 inches
x + 1 = 26 + 1 = 27 inches
x + 2 = 26 + 2 = 28 inches
x + 3 = 26 + 3 = 29 inches
Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
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Related Questions
I WILL PICK BRAINLEIST!!!!!!!!! + 15 points
Rate of change tells how something....
A. constantly changes
B. can be made
C. looks and feels
Answers
Answer:
I’m going to said A
Step-by-step explanation:
IMA In a certain Algebra 2 class of 23 students, 7 of them play basketball and 12 of them play baseball. There are 9 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball
Answers
Answer:
19/28 or about 68%
Step-by-step explanation:
7 + 12 + 9 = 28
7 + 12/28
19/28
Octagonal houses were popular in the 19th century one reason was that an octagon with the same perimeter as a square encloses a greater area than the square. To the nearest square ft, find the areas of an octagon and a square with perimeters of 80 ft.
Answers
Answer:
octagon: 483 ft²square: 400 ft²Step-by-step explanation:
You want the areas of an octagon and a square, each with a perimeter of 80 ft.
SquareThe side length of a square is 1/4 of its perimeter, so the square of interest has a side length of ...
(80 ft)/4 = 20 ft
The area is the square of the side length, so the area of the square is ...
A = s²
A = (20 ft)² = 400 ft²
OctagonA regular octagon has 8 sides of equal length, so the side length is ...
(80 ft)/8 = 10 ft
The area is found by the formula ...
A = 2(1 +√2)s²
A = 2(1 +√2)(10 ft)² ≈ 483 ft²
The area of the octagon is about 483 square feet; about 400 square feet for the square.
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Jakob buys lunch at school on Mondays, Wednesdays, and Thursdays. He spends $3.50 for each lunch. Which equation can be used to find the number of weeks, w, it will take Jakob to spend $84 on lunch?
Answers
Answer:
(3 times 3.50) w = 84
Answer:
84
Step-by-step explanation:
(3 times 3.50) w = 84
The little twelve football conference has two divisions, with nine teams in each division. each team plays each of the other teams in its own division once. how many conference games are scheduled
Answers
Nine times nine, or 81 games, were played by each team in the opposite division. In the conference phase of the tournament, there are 144+81, or 225 games.
What is a conference in football?Each of the nine teams in a division plays the other teams twice. Thus, the total number of games played in a division is 9*8*2*2, or 72 games (team 1 vs team 2 and team 2 vs team 1 game is one game).
Similar to the other division, teams in divisions play a total of 144 games, or 72 games divided by two.
since each division's teams compete in games
The total number of games played by each team in the other division is 9 X 9, or 81 games. There are 144+81, or 225 games, in the conference portion of the tournament.
Therefore, the answer is 225 games.
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A manufacturer of screened sweatshirts includes a shipping charge of $5.99 on all online orders. Customers also pay 2.5% tax on their purchases. There is a linear relationship between c, the cost of the items purchased, and t, the total cost including shipping and tax. Select each statement that correctly represents the relationship between c and t. Mark all that apply. *
Answers
Answer:
t = 1.025c + 5.99
Step-by-step explanation:
Recall : general for of a linear equation is given by :
y = mx + c
Given the following :
Item cost = c
Shipping charge = $5.99
Tax on purchases = 2.5%
Total cost, t
t = c + tax + shipping cost
Tax on purchase : 2.5% * item cost ; 0.025c
Shipping = $5.99
Hence,
Total cost, t = c + 0.025c + 5.99
t = 1.025c + 5.99
Factor the following binomial using the difference of squares?
(49x^2 – 9)
Answers
You have 8 donuts to share evenly between you and your four brothers.
Which fraction describes how many donuts each of you will receive?
Answers
If a sample mean is 96, which of the following is most likely the range of possible values that best describes an estimate for the population mean?
Answers
Answer:
80,112
Step-by-step explanation:
Answer: (80, 112)
Step-by-step explanation: a p e x
x 8 x 7 x 5 x 6 a planned building was going to be 100 feet long, 75 feet deep, and 30 feet high. the owner decides to increase the volume of the building by 10% without changing the dimensions of the depth and the height. what will be the new length of this building?
Answers
The new length of the building will be 110 feet.
Volume of Cuboid:
Volume of cuboid is
V = length x breadth x height cubic unit
Given,
The building was going to be 100 feet long, 75 feet deep, and 30 feet high.
Therefore, the volume will be:
= 75 × 100 × 30 ft³
= 225000 ft³
Now owner decided increase the volume of the building by 10% without changing the dimensions of the depth and the height.
There was an increase by 10%,
New volume will be,
V' = 225000 + (10% × 225000)
= 247500 ft³
Therefore, the new length will be:
as,
Volume = length x breadth x height
length = Volume/ (breadth x height)
New length will be
= 247500/(30 × 75)
= 110 feet
Thus the new length of the building will be 110 feet.
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Whats a quadrilateral
Answers
a rural lot runs 500 feet east/west along its northern boundary, and 600 feet east/west along its southern boundary. its eastern boundary runs 200 feet due north/south, while its western boundary runs 224 feet in a diagonal northeast/southwest direction. the cost of the land is $6 per square foot. what is the cost of this lot?
Answers
The cost of this lot is $307,200.
To find the cost of this rural lot, we first need to calculate its area, and then multiply the area by the cost per square foot. Let's follow these steps:
1. Since the lot has an irregular shape, divide it into two triangles. The first triangle has a base of 500 feet (east/west along its northern boundary) and a height of 200 feet (eastern boundary). The second triangle has a base of 100 feet (600 - 500 feet along the southern boundary) and a height of 24 feet (224 - 200 feet along the western boundary).
2. Calculate the area of each triangle:
Triangle 1: A1 = (base x height) / 2 = (500 x 200) / 2 = 50,000 sq. ft.
Triangle 2: A2 = (base x height) / 2 = (100 x 24) / 2 = 1,200 sq. ft.
3. Add the areas of the two triangles to find the total area of the lot:
A_total = A1 + A2 = 50,000 + 1,200 = 51,200 sq. ft.
4. Finally, multiply the total area by the cost per square foot to find the cost of the lot:
Cost = A_total x $6 = 51,200 x $6 = $307,200.
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(4x+2)(x-3)
Expand and simplify
Answers
\(\\ \sf\longmapsto (4x+2)(x-3)\)
\(\\ \sf\longmapsto 4x(x-3)+2(x-3)\)
\(\\ \sf\longmapsto 4x^2-12x+2x-6\)
\(\\ \sf\longmapsto 4x^2-10x-6\)
Answer:
Step-by-step explanation:
(4x + 2)(x - 3) =4x *(x -3) + 2*(x -3)
= 4x*x - 3*4x + x*2 - 3*2
= 4x² - 12x + 2x - 6 {Combine like terms}
= 4x² - 10x - 6
Please help Ill give brainy pleas help please -
Answers
1 Pedro has a stand where he sells tea and lemonade. He sells lemonade for $3 per
cup and tea for $5 per cup. This weekend, Pedro sold 2 times as much lemonade
as he did tea. Let T represent the number of cups of tea he sold, and L represent
the number of cups of lemonade he sold He earned a total of $130. What do the
expressions 5T and 3L, represent in the system of equations?
5T+3L-130
L=2T
Answers
5T represents 5 cups of Tea while 3L represents 3 cups of Lemonade.
What is a Linear Equation?A Linear Equation is an equation of a line. Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
In the system of equation;
5T+3L-130 ---1
L=2T ---2
From equation 1;
5T represents 5 cups of Tea while 3L represents 3 cups of Lemonade.
From equation 2;
2 cups of tea equal a cup of lemonade
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What happens to the volume of a rectangular prism when its length is tripled? A. it is doubledB. it remains the sameC. it is tripledD. it is multiplied by 27
Answers
The volume of a rectangular prism is given by the next formula:
\(\begin{gathered} V=l\cdot w\cdot h \\ \\ l=\text{length} \\ w=\text{width} \\ h=\text{height} \end{gathered}\)If you triple the length you get:
\(\begin{gathered} V=3l\cdot w\cdot h \\ \\ V=3(l\cdot w\cdot h) \end{gathered}\)Then, if just the length of a rectangular prism is tripled the volume is also tripled
Plzz help mehjDutch hchch h
Answers
Answer:
See belowStep-by-step explanation:
Given the data set of 15 where:
Mean = 7Median = 6Mode = 5The minimum is 1 and the maximum is 10As per given we conclude
The set will have 7 numbers before 6 and 7 numbers afterSum of 15 numbers is 15*7 = 105The most used number is 5a) Possible set is:
1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10b) Add number 20, the set will be:
1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10, 20The mean is different as we have now more numbers with different sum:
(105 + 20)/(15 + 1) = 125/16 = 7.8125The median is different now and moves to the right as 20 added to the far right:
(6 + 9)/2 = 7.5The mode stays same as still most used number is 5:
5
Draw a pair of intersecting lines that forms a pair of complementary angles. Explain your reasoning.
Answers
A pair of intersecting lines that forms a pair of complementary angles is as drawn below.
What are the pair of complementary angles?
Remember that complementary angles are defined as angles which sum is equal to 90°.
Besides, each of the pairs of opposite angles made by two intersecting lines are called vertical angles. Now, from congruent proofs, we know that that vertical angles are congruent. In another words, they have the same measure.
Thus, we have to draw two vertical angles that measure:
90° ÷2 = 45°
This image is as drawn below in the attached file.
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What is the meaning of descriptive statistics?
Answers
Descriptive statistics describe, show, and summarize the basic features of a dataset found in a given study, presented in a summary that describes the data sample and its measurements.
For a good example of a descriptive statistic, look no further than a student's grade point average (GPA). GPA collects data points generated from various grades, grades and tests and then aggregates them to provide an overall picture of a student's average academic performance. Please note that GPA does not predict or infer future performance. Instead, it provides a simple summary of students' academic performance based on values extracted from the data.
Here is an even simpler example. Suppose that the data set 2, 3,
, 5 and 6 is the sum of 20. The mean of the data set is
, which is obtained by dividing the sum by the number of values (20 divided by 5 is
).
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Enter the correct answer in the box.
Molly has $45 in her wallet, which is 3 times as much money as her brother has.
Write an equation to represent this situation, where a represents the amount of money Molly’s brother has.
45 =
Answers
Answer: 45 divided by 3 equals 15
he has 15 dollars
Step-by-step explanation: 45= 3 times 15
Answer: 45=3a a=15
Step-by-step explanation:
We know that Molly has $45 or 3 times the amount of money her brother has, and a represents the amount of money her brother has. So we would multiply a by 3. In order to find a we just divide 45 by 3.
what is the image point of (6,4) after a translation left 2 units up 4 units?
Answers
Answer:
(4,8)
Step-by-step explanation:
6 minus 2 and 4 plus 4
Left=minus
Right=Plus
Down=minus
Up=Plus
Answer:
(4, 8)
Step-by-step explanation:
HELP ME SOLVE THIS QUESTION PLEASE GUYS
Answers
Answer:
A ≈ 55.6 cm²
Step-by-step explanation:
The area (A) of the shaded region is calculated as
A = area of circle × fraction of circle
central angle of shaded region = 360° - 230° = 130° , then
A = πr² × \(\frac{130}{360}\)
= π × 7² × \(\frac{13}{36}\)
= 3.14 × 49 × \(\frac{13}{36}\)
≈ 55.6 cm° ( to the nearest tenth )
Given EE = 20^−5y(cos(5x) ax + cos(5x)ay,
Find: |EE| at P(/ 6 , 0.1, 2);
A unit vector in the direction of E at P;
The equation of the direction line passing through P.
Answers
The value of |EE| at P(/ 6 , 0.1, 2) is |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|.
To find the magnitude |EE| at point P, we substitute the coordinates of P (x, y, z) into the expression for EE and calculate the magnitude using the Pythagorean theorem.
Given EE = 20^(-5y)(cos(5x) ax + cos(5x)ay), we evaluate it at P(/6, 0.1, 2):
|EE| = |20^(-5y)(cos(5x) ax + cos(5x)ay)|
Substituting the coordinates of P, we have:
|EE| = |20^(-5(0.1))(cos(5(/6)) ax + cos(5(/6))ay)|
Simplifying further:
|EE| = |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|
To find a unit vector in the direction of E at point P, we divide the vector EE by its magnitude |EE|.
Unit vector in the direction of E at P = EE / |EE|
Substituting the values, we have:
Unit vector in the direction of E at P = (20^(-5y)(cos(5x) ax + cos(5x)ay)) / |EE|
Finally, to find the equation of the direction line passing through point P, we use the parametric form of the line equation, which is:
(x - x₀) / a = (y - y₀) / b = (z - z₀) / c
where (x₀, y₀, z₀) is the given point on the line and (a, b, c) is the direction vector. In this case, the direction vector is the unit vector in the direction of E at point P. Substitute the values of P and the direction vector into the equation, and simplify if necessary to obtain the equation of the line passing through P.
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The value of |EE| at P(/ 6 , 0.1, 2) is |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|.
To find the magnitude |EE| at point P, we substitute the coordinates of P (x, y, z) into the expression for EE and calculate the magnitude using the Pythagorean theorem.
Given EE = 20^(-5y)(cos(5x) ax + cos(5x)ay), we evaluate it at P(/6, 0.1, 2):
|EE| = |20^(-5y)(cos(5x) ax + cos(5x)ay)|
Substituting the coordinates of P, we have:
|EE| = |20^(-5(0.1))(cos(5(/6)) ax + cos(5(/6))ay)|
Simplifying further:
|EE| = |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|
To find a unit vector in the direction of E at point P, we divide the vector EE by its magnitude |EE|.
Unit vector in the direction of E at P = EE / |EE|
Substituting the values, we have:
Unit vector in the direction of E at P = (20^(-5y)(cos(5x) ax + cos(5x)ay)) / |EE|
Finally, to find the equation of the direction line passing through point P, we use the parametric form of the line equation, which is:
(x - x₀) / a = (y - y₀) / b = (z - z₀) / c
where (x₀, y₀, z₀) is the given point on the line and (a, b, c) is the direction vector. In this case, the direction vector is the unit vector in the direction of E at point P. Substitute the values of P and the direction vector into the equation, and simplify if necessary to obtain the equation of the line passing through P.
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-35÷6=
-350÷6-350-6=
350 - 60 =
Answers
Answer:
The first one is 5.83 or -5 5/6
The second one is -414 1/3
The last one is 290
How many integers between 1 and 1000 meet the criteria below. Simplify your answer to an integer. • the digits are distinct the digits are odd • the digits are in ascending order
Answers
Answer:
Step-by-step explanation:
I am assuming that the number 1 is not included.
This is an arithmetic sequence of integers with first term 1 and last term 999.
Number required = (999-1) / 2
= 499.
There are 20 integers between 1 and 1000 that meet the given criteria.
To find this answer, we can start by noticing that there are only five odd digits: 1, 3, 5, 7, and 9. Therefore, any integer that meets the criteria must be made up of some combination of these digits.
Next, we can focus on the requirement that the digits be distinct. This means that we cannot repeat any of the odd digits within the same integer. We can use combinations to count the number of ways to choose three distinct odd digits from the set {1, 3, 5, 7, 9}:
5C3 = (5!)/(3!2!) = 10
Finally, we need to consider the requirement that the digits be in ascending order. Once we have chosen our three distinct odd digits, there is only one way to arrange them in ascending order. So each combination of three odd digits corresponds to exactly one integer that meets all the criteria.
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Use the figures to complete the statements proving the converse of the Pythagorean theorem.
Drag and drop a phrase, value, or equation into the box to correctly complete the proof.
To prove the converse of the Pythagorean theorem, we must show that if △ABC has sides of a, b, and c such that a² + b² = c² , then △ABC is a right triangle.
Define △DEF so that it is a right triangle with sides a, b, and hypotenuse x. By the Pythagorean theorem, a² + b² = x² .
Since a² + b² = c² and a² + b² = x², it must be true that c² = x². Since sides of triangles are positive, then we can conclude that Response area. Thus, the two triangles have congruent sides and are congruent.
Finally, if △ABC is congruent to a right triangle, then it must also be a right triangle.
Two right triangles with points labeled in capital letters and sides labeled in lower case letters.
Answers
Answer:
def
Step-by-step explanation:
trust meh
took quiz
Answer:
it is DEF
Step-by-step explanation:
i did the k12 quiz
in a class, there are 18 girls and 14 boys. if the teacher selects two students at random to attend a party with the principla, what is the probabilt
Answers
The probability that the two students are of the Opposite gender is 0.508
It is given that there are a total number of 32 students of which 18 are girls and 14 are boys. Let us assume that the Probability of getting a girl is indicated by P(G) and the probability of getting a boy is indicated by P(B).
Probability of getting a Girl and a boy = P(GB)
Probability of getting a boy and a girl = P(BG)
Sampling will be done without replacement
Now, the probability of getting two students of the opposite gender can be determined by:
=> P(GB) + P(BG)
First, we will find P(GB)
=> P(GB) = P(G) + P(B)
=> P(GB) = (18/32) + (14/31)
=> P(GB) = 0.2540
Similarly, for P(BG)
=> P(BG) = P(B) + P(G)
=> P(BG) = (18/32) + (14/31)
=> P(BG) = 0.2540
we will find out the probability of selecting two students by
=> P(GB) + P(BG)
=> 0.2540 + 0.2540
=> 0.508
Hence, the probability of selecting two students at random of the opposite gender will be 0.508
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Complete Question:
In a class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal, what is the probability that the two students are the opposite gender?
measuring the entire population is usually preferred over measuring a sample from the population.
T/F
Answers
The given statement "Measuring the entire population is usually preferred over measuring a sample from the population" is False because measuring the entire population is often impractical or impossible.
When dealing with large populations, it is typically more feasible to gather data from a representative sample rather than measuring the entire population. This approach saves time, resources, and effort. Sampling allows statisticians to make reliable inferences about the population based on the characteristics observed in the sample.
Carefully chosen samples can accurately reflect the population's attributes and provide valuable insights.
However, it is crucial to ensure that the sample is representative and unbiased to avoid potential sampling errors and ensure the validity of the conclusions drawn from the data.
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Find the area of the square pyramid represented by this net.
Answers
Answer:
64 sq cm
Step-by-step explanation:
square area formula is length times width, so we multiply 4 x 4
4x4 = 16 square cm
triangle area formula is base x height x 1/2 (divide by two)
4 x 6 = 24 x 1/2 = 12
multiply 12 by four to account for all triangles
12 x 4 = 48
add both areas
16 + 48 = 64
The surface area of this net is 64 sq cm.
Calculate the mass of naf that will be required to make your standard 1 solution: 250 ml, 0.1m f- solution.
Answers
The mass of NaF that is required to make a standard 1 solution of 250 ml 0.1 M F- solution is 5.45 g of NaF. The number of moles in a solution is the concentration in moles per litre multiplied by the volume in litres.
To calculate the mass of a solute required, we need to first calculate the number of moles required. We can then use the molar mass of the solute to calculate its mass.To calculate the number of moles required in this question, we can use the formula:n = c × V where n is the number of moles, c is the concentration in moles per litre and V is the volume in litres. We have:c = 0.1 M
and V = 0.25 L
Substituting these values into the formula gives:n = 0.1 mol/L × 0.25 L
= 0.025 mol
Now we can use the molar mass of NaF to calculate its mass. The molar mass of NaF is 41.99 g/mol (22.99 g/mol for Na and 19.00 g/mol for F).
We have:n = 0.025 mol
solving for mass:m = n × M
where M is the molar mass of NaF.
Substituting gives:m = 0.025 mol × 41.99 g/mol ≈ 1.05 g
However, this is the mass required to make 0.25 L of solution. To make 1 L of solution, we would need to multiply the mass by 4. Therefore, the mass of NaF required to make a standard 1 solution of 250 ml 0.1 M F- solution is:1.05 g × 4 = 4.20 g Rounding this to two significant figures gives:4.2 g NaF.
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