The required length of one of the longest sides is 29 in the given pentagon.
The pentagon has 3 sides of length (2x - 1) and 2 sides of length (x + 5) and the perimeter of the pentagon is 127.
We know that the perimeter of the pentagon is the total length of all its sides, so we can set up the following equation:
3(2x - 1) + 2(x + 5) = 127
Apply the distributive property of multiplication,
6x - 3 + 2x + 10 = 127
Combine the likewise terms of the equation,
8x + 7 = 127
Finally, we can solve the equation by subtracting 7 from both sides and dividing both sides by 8:
8x = 120
x = 15
Therefore, the length of one of the longest sides is (2 × 15 - 1) = 29.
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What is the relationship between the points on the line and solutions to the linear equation?
The relationship between the points on the line and solutions to the linear equation is, the equation has a solution at each point along the line.
In the given question, we have to find the relationship between the points on the line and solutions to the linear equation.
The equation has a solution at each point along the line. This simply means that it is easy to tell whether an ordered pair is a solution to an equation. The ordered pair is a solution to the equation if it lies on the line drawn by the linear equation.
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Sofia is dividing 8 by 22. If she continues the process, what will keep repeating in the quotient?.
The integer numbers that will be repeating in the quotient is 36, the decimal representation of the fraction is 0.3636...
When 8 is divided by 22 we get the fraction 8/22 , when simplified this fraction gives 4/11 .
Now we will divide the numerator by the denominator we get:
4 ÷ 11 = 0.363636...
Thus, it is a repeating decimal .
Hence the numbers 36 will constantly repeat itself.
A quotient is the result of dividing two numbers. The quotient is a mathematical phrase that can also be used to refer to the integer component of a division, fraction, or ratio.
The term "quotient" has been used in many mathematical disciplines to depict structures generated by disassembling larger structures. Given a set with an equivalence relation specified on it, a "quotient set" having particular equivalence classes as items can be formed.
A quotient group is generated by dividing a group into numerous comparable co-sets, and a quotient space is formed by dividing a vector space into numerous comparable linear subspaces.
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an argument is sound if it is group of answer choices valid and has a true conclusion. invalid but has a true conclusion. valid and has true premises. invalid but has true premises
Yes a sound argument has true conclusion this statement is true.
1. A valid argument must have a true conclusion.
This statement(1) is false. A valid argument must have a true conclusion only if all of the premises are true. So it is possible for a valid argument to have a false conclusion as long as at least one premise is false.
2.A sound argument must have a true conclusion.
This Statement(2) is true.
If an argument is sound, then it is valid and has all true premises. Since it is valid, the argument is such that if all the premises are true, then the conclusion must be true. A sound argument really does have all true premises so it does actually follow that its conclusion must be true.
3. If a valid argument has a false conclusion, then at least one premise must be false.
this statement(3) is true
A valid argument cannot have all true premises and a false conclusion. So if a valid argument does have a false conclusion, it cannot have all true premises. Thus at least one premise must be false.
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PLEASE HELP
im stuck on itt
4. Definition of midpoint
5. Definition of an equilateral triangle
6. SSS
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 2.
The area of the surface = [tex]\pi \sqrt{14}[/tex] sq. units
As given in the question the part of,
plane ⇒ x + 2y = 3z = 1
cylinder = [tex]x^{2} + y^{2} = 3[/tex]
Let take P = projection on plane x + 2y + 3z = 1
The surface area of the equation is given by,
∫∫ₚ √{1+(∂z/∂x)² + (∂z/∂y)²} dA
Using the coordinate of the cylinder,
x = n cos [tex]\alpha[/tex] , y = n sin [tex]\alpha[/tex]
= [tex]x^{2} + y^{2} = (n cos \alpha )^{2} + n sin \alpha ^{2}[/tex]
= [tex]n^{2} (cos^{2}\alpha + sin^{2}\alpha )[/tex]
= [tex]n^{2}[/tex] x 1 = [tex]n^{2}[/tex]
= [tex]n^{2}[/tex] = 2 ⇒ n = [tex]\sqrt{2}[/tex]
Therefore, P = {(r,θ)/ 0 ≤ r ≤ [tex]\sqrt{2}[/tex], 0 ≤ θ ≤ 2π}
x +2y + 3z =1
⇒ z = 1/3(1 - x - 2y)
∂z/∂x = -1/3 ; ∂z/∂y = -2/3
According to the formula of surface area,
= ∫∫ₚ √{1+ (-⅓) ² + (-⅔) ²} dA
= 14 /3 [tex]\int\limits_0^{2\pi } \int\limits_0^{\sqrt{3} }[/tex] dA is an area of region P
= [tex]\sqrt{14}[/tex] / 3 [tex]\int\limits_0^{2\pi } \int\limits_0^{\sqrt{3} }[/tex]r. dr. d[tex]\alpha[/tex]
= [tex]\sqrt{14}[/tex] / 3 [tex]\int\limits_0^{2\pi }[/tex] [tex][r^{2} / 2 ]^{\sqrt{3} }_0[/tex] .d[tex]\alpha[/tex]
= [tex]\sqrt{14}[/tex] /3 [tex]\int\limits_0^{2\pi }[/tex]3/2. d[tex]\alpha[/tex]
= [tex]\sqrt{14}[/tex] /2 [tex][\alpha ]^{2\pi }_ 0[/tex]
= [tex]\sqrt{14}[/tex] /2[[tex]2\pi[/tex] - 0]
= [tex]\pi \sqrt{14}[/tex]
Therefore, the area of the surface = [tex]\pi \sqrt{14}[/tex] sq. units
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Name the corresponding angle to angle 4.
HELP THIS IS DUE IN 10 MINSSSS
A: angle 6
B: angle 8
C: angle 2
D: angle 5
The corresponding angle to angle 4 is angle 8.
What is corresponding angle?When two parallel lines intersect any other line, corresponding angles are formed in matching corners or corresponding corners with the transversal.Corresponding Angles are on the same side of the transversal as the transversal and in a similar matching location.If the transversal intersects two parallel lines perpendicularly, the corresponding angles can be supplementary (i.e. at 90 degrees). In this case, each corresponding angle will be 90 degrees, and their sum will be 180 degrees (i.e. supplementary).For example, in the figure that is given question,∠4 and ∠8 are corresponding angles and thus congruent. Other corresponding angle pairs are ∠3 and ∠7, ∠1 and ∠5, and ∠2 and ∠6.To learn more about corresponding angles refer to :
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solve the following counting problems: (a) a spider has one sock and one shoe on each of its eight legs, in how many different orders can the spider put on its socks and shoes? (assume that a shoe must be on top of a sock). (b) an elevator starts at the basement with 10 people and discharges them all by the time it reaches the top ??oor, number 6. in how many ways could have the people get o?? the elevator if it only ma??ers the number of people that le?? on each ??oor?
Therefore , a)different orders can the spider put on its socks and shoes is [tex]\frac{16!}{(2!)^{8} }[/tex] and b)the total no of ways for people to discharge from lift is 14112 ways.
What is combination?Selections are another name for combinations. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them. We write n C r to represent the number of distinct r-selections or combinations among a set of n objects. Compared to arrangements or permutations, combinations are different.
Here,
Each dressing sequence may be uniquely characterized by a series of two 1s, two 2s,..., and two 8s; the spider is said to put the sock on leg x in the first instance, and the shoe on leg x in the second instance.
The solution would be 16! if each number were unique.
However, because 8 words appear twice, the solution is
=> [tex]\frac{16!}{(2!)^{8} }[/tex]
Thus different orders can the spider put on its socks and shoes is [tex]\frac{16!}{(2!)^{8} }[/tex]
Thus,
Part A: When the elevator operator can't tell who is who.
Currently, there are 6 floors and 10 persons, and each floor loses one.
so 8+6-1=13
applying combination
=>[tex]C^{13} _{5}[/tex] = 1287 ways.
Part 2: When the elevator attendant separates males from ladies.
There are 3 females and 5 males.
The formula for choosing five men is (5 + 6)-1= (10).
Applying combination
=> .[tex]C^{10} _{5}[/tex]= 252 ways
techniques to choose ladies = 3+6-1=8
Applying combination
=> [tex]C^{8} _{5}[/tex] = 56 ways
Total no. of ways
=> 252*56 = 14112 ways.
Therefore , the total no of ways for people to discharge from lift is 14112 ways.
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a control chart for a bottled product requires that a sample consisting of a single bottle contain between 350 and 360 milliliters of product. sample data, taken when the bottling process was in control, indicate that bottles contain an average of 355 milliliters, and you know that the bottling process has a standard deviation of 4 milliliters when in control. given that the bottling process is in control, what portion of its output will fall outside the limits of the chart?
So, bottling process is in control thus .0124 portion is fall outside the limit.
What is standard deviation ?In statistics, the standard deviation measures how widely distributed or how much a set of values might vary. While a high standard deviation denotes that values are scattered throughout a wider range, a low standard deviation suggests that values are normally close to the set's mean.
Here,
A sample consisting of a single bottle contain between 350 and 360 milliliters of product is taken
Since ,
bottles contain an average of 355 milliliters, has Standard deviation = 4 milliliters
using fomula
Sd= 4 milimeters
upper bound 360
an lower bound = 350
So, bottling process is in control thus .0124 portion is fall outside the limit.
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Ray has nine cards numbered 1 to 9
1 2 3 4 5 6 7 8 9
Ray takes at random three of these cards.
He works out the sum of the numbers on the three cards and records the result.
Work out the probability that the result is an even number.
The probability of the result is 11/21.
What is a combination?A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.
Ray has 4 even numbered cards and 5 odd numbered card.
Ray takes at random three of these cards.
Let, all the three cards are even numbered card.
So, the sum of even numbers is even.
Suppose, two cards are odd numbered and one card is even numbered.
And the combination of 2 odd numbered card and one even numbered card is even.
Now, the possible outcomes;
= {C³₄ + C¹₄C²₅} / C³₄
In order to solve the combination:
Simplify,
{C³₄ + C¹₄C²₅} / C³₄
= [ 3! / {4! x (4-3)!} + 1!/{4! x (4-1)!} x 2!/{5! x (5-2)!} ] / [3! / 4!x (4-3)!]
= 11/21
Therefore, the probability is 11/21.
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question 171 pts a random sample from a normal population is obtained, and the data are given below. find a 90% confidence interval for . 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545 what is the lower bound of the confidence interval (round off to the nearest integer)?
The information is provided below using a random sampling from a healthy population. a 90% confidence interval for . 114 is the lower bound of the confidence interval.
To find the lower bound of the 90% confidence interval, we need to calculate the 5th percentile of the data. To do this, use the formula that goes like this:
5th percentile = 114 + (0.90 * (512 - 114))
= 114 + (0.90 * 398)
= 114 + 358.2
= 472.2
Therefore, the lower bound of the 90% confidence interval is 472 (rounded to the nearest integer).
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if line CE bisects line FG, DG= DE, CE= 42 feet and CD= 29 feet, find FG
The length of segment FG is 26 feet.
What is Straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.
Given that line CE bisects line FG.
DG= DE,
The length of segment CE is forty two feet.
CE=42 feet.
The length of segment CD is Twenty nine feet.
CD=29 feet.
We need to find the length of FG.
Firstly let us find the length of DE.
CE-CD=DE
42-29=13 feet.
As DG=DE then the length of DG is 13 feet.
DG=DF=13
FG=DG+DF
=13+13=26 feet.
Hence, if line CE bisects line FG, DG= DE, CE= 42 feet and CD= 29 feet then FG is 26 feet.
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The area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
Answer:
Step-by-step explanation:
yall weird ok
Two sisters have decided to watch all the episodes of a popular TV show on DVD. Ella has already watched 4 episodes and will continue to watch the show at a rate of 2 episodes per day. Sophia, who hasn't yet seen the show, will start watching 4 episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How long will that take? How many episodes will each sister have watched at that point?
Answer: 8 episodes it would have been 2 days
so 8 episodes will be watched for them to be caught up with each other
there were 425 guests at a hotel. 170 guests ordered food. what percentage of the guests ordered food?
Answer: 40%
Step-by-step explanation:
Take 170 divided by 425, then times 100% = 40%
So 40% of the guests ordered food!
A shipping container will be used to transport several 50-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 9500 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 50-kilogram crates that can be loaded into the shipping container.
Answer:
To write and solve an inequality that can be used to determine the number of 50-kilogram crates that can be loaded into the shipping container, we need to first find the total weight of the crates that can be loaded into the container. The maximum weight that can be loaded into the container is 27500 kilograms, and other shipments weighing 9500 kilograms have already been loaded, so the total weight of the crates that can be loaded is 27500 kilograms - 9500 kilograms = 18000 kilograms.
Next, we need to divide the total weight of the crates that can be loaded by the weight of each crate to find the number of crates that can be loaded. Since each crate weighs 50 kilograms, the number of crates that can be loaded is 18000 kilograms / 50 kilograms = 360 crates.
To express this as an inequality, we can use the following equation:
x <= 360
This inequality states that the number of crates that can be loaded into the shipping container (x) must be less than or equal to 360. Therefore, the number of 50-kilogram crates that can be loaded into the shipping container is x <= 360.
Step-by-step explanation:
Gabriella's four test scores are 80%, 92%, 80%, and 84%. What is her mean score?
76
84
80
88
Answer:
84%
Step-by-step explanation:
To find the mean, you use a formula.
You add up all the numbers, then divide that by how many numbers you have:
80 + 92 + 80 + 84
336 / 4 = 84
thus 84 is the answer
What is the slope of the line that passes through the points (-5, 6) and (-9, -6)
The slope of the line that passes through the points (-5, 6) and (-9, -6) is 3
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Let the given points as shown:
(x1,y1)= (-5, 6) and (x2,y2)= (-9, -6)
Slope = m = (y2-y1) /( x2-x1)
= (-6-6) /(-9-(-5))
= -12/-4
= 3
So, the slope of the line that passes through the points (-5, 6) and (-9, -6) is 3
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20 pionts if you help me!!!! and brainlest !!!!
in the GIF TYSM ⇅
a. The solution to the system of equations is: (4, 12).
b. The graph is shown below.
c. (4, 12) is the point of intersection. It confirms the solution from part a.
What is the Solution of a System of Equations?The solution of a system of equations can be described as the value of x and y of a point, that makes both equations true. It is the point where the two lines of the equations of the system intersect.
If we are given two tables, the ordered pair that appears in both table is considered the solution of the system.
a. The ordered pair, (4, 12) appears in both tables. Therefore, the solution is: (4, 12).
b. The graph of the ordered pairs from each table are sketched in the image shown below, where the green line is for the first table, and the blue line is for the second table.
c. The point of intersection of the graph is (4, 12), this confirms the solution from part a.
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A shirt is on sale for 25% off. If the original price was $120, what is the sale price?
Answer:
If a shirt is on sale for 25% off and the original price was $120, then the sale price is $90. This is because 25% of $120 is $30, and when we subtract this amount from the original price, we get $120 - $30 = $90.
In general, if an item is on sale for x% off and the original price was y dollars, then the sale price is y - (x/100) * y dollars. For example, if the discount is 25% and the original price is $120, then the sale price would be $120 - (25/100) * $120 = $90.
Step-by-step explanation:
Answer:
The sale price is $90
Step-by-step explanation:
Given;A shirt is on sale for 25% off. If the original price was $120.To Find;The sale price.Now,
(120 × 25) ÷ 100 = $30
Here, we get 25% of $120 is $30
So,
$120 - $30 = $90
Thus, The sale price is $90
the dolphins at the washington aquarium are fed 1/2 of a bucket of fish each day. the sea otters are fed 2 1/3 times as much fish as the dolphins. how many buckets of fish are the sea otters fed each day?
The number of buckets of fish that the sea otters fed each day is 7/6 buckets .
In the question ,
it is given that ,
the number of buckets of fish that the dolphin are fed at the Washington aquarium = 1/2 bucket
the sea otters are fed [tex]2\frac{1}{3}[/tex] times as many as fish .
So , the number of buckets that are fed to otters is = (7/3) × (number of buckets eaten by fish)
Substituting the values of number of buckets eaten by fish ,
we get
= (7/3) × (1/2)
Simplifying further ,
we get ,
= 7/6 buckets .
Therefore , the sea otters are fed 7/6 buckets of fish each day .
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Can someone help with a step by step answer to This?
And a an answer to what the end behaviors are, Thank you to whoever helps.
The end behaviours of the functions are f(x) = x⁴ - x³ - 16x³ + 4x + 48
As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝
How to determine the end behaviours of the functions?The equation of the function is given as
f(x) = x⁴ - x³ - 16x³ + 4x + 48
Calculate f(∝) and f(-∝).
So, we have
f(∝ ) = ∝ ⁴ - ∝ ³ - 16∝ ³ + 4∝ + 48
So, we have;
f(∝) = ∝
Also, we have
f(-∝ ) = -∝ ⁴ - (-∝) ³ - 16(-∝) ³ - 4∝ + 48
Evaluate;
f(∝) = -∝
This means that the end behaviours of the functions are;
As x ⇒ +∝, f(x) ⇒ +∝
as x ⇒ -∝, f(x) ⇒ -∝
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Mrs.Galicia dropped a ball from the top of a tower. At the same time, her son, Antonio, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-4t+22.
The height of Antonio's rocket after t seconds can be represented by the linear function: p(t)=-2t+12.
What are the two solutions to this system? Show your work algebraically.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.
The system's two potential fixes are
t = 3.099 tennis ball
launch of a rocket, t = 6
Antonio's rocket's height is the unreasonable solution, because the path was followed should not be a linear function.
At 2.32 seconds, the rocket and tennis ball both reach the same height.
How can the two systems be solved?The two equations of motion are
b(t) = -t² - 4t + 22.
p(t) = -2t + 12
The answer to the quadratic equation is
b(t) = -t^2 - 4t + 22.
t = 3.099 OR t = -7.099
use positive hence t = 3 seconds
The linear equation's answer is
t = 6
The linear equation is the answer that is unreasonable in this case. because projectile motion does not follow a linear path
duration to reach the same height
-2t + 12 = -t^2 - 4t + 22.
-t^2 - 2t + 10
When the equation is solved,
t = 2.3166 OR -4.3166
select the positive number.
t = 2.32 s
2.32 s is needed to reach the same height.
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5,2,4/5 find the 10th term
an organization wants to select a committee of 3 members from a group of 11 eligible members. how many different committees are possible?
the 165 different committees are possible in combination.
What is combination?
If the order of the selections is unimportant, a combination is a mathematical choice made from a collection of various elements (unlike permutations). An apple and a pear are just one of three conceivable combinations if three fruits, such as an orange, an apple, and a pear, are provided. A k-combination of a set S is, technically speaking, a subset of the k distinctive elements of S. Alternatively said, two combinations are identical if and only if they have the same members. (How each set's members are ordered is not crucial.) the number of k-combinations given a set of n elements
That would be equal to the Combinations of 11 items taken 3 at a time.
C(n , k) = n!/[k!(n - k)!]
= 11!/[3!*(11 - 3)!]
= 11!/(3!*8!)
= 11*10*9/3*2
= 15*11
=165
Hence the 165 different committees are possible in combination.
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Find the value of sin K rounded to the nearest hundredth, if necessary.
Answer: sin K =
24
L
18
M
Submit Answer sin k=
Answer:
Step-by-step explanation:
IS =K
Find ℎ(−5) when ℎ(x) = −3|x − 1| + 4
Answer:
ℎ(−5) is −14.
Step-by-step explanation:
To find the value of ℎ(−5), we plug −5 in for x in the expression for ℎ(x):
ℎ(−5) = −3|−5 − 1| + 4
To evaluate the absolute value, we need to find the distance between −5 and 1 on the number line. Since the absolute value function is always non-negative, the distance between −5 and 1 will be positive.
To find the distance between −5 and 1, we subtract the smaller number from the larger number:
|−5 − 1| = |−6| = 6
Now we can plug this value into the expression for ℎ(−5) to find its value:
ℎ(−5) = −3 * 6 + 4
ℎ(−5) = −18 + 4
ℎ(−5) = −14
Therefore, the value of ℎ(−5) is −14.
To join Planet Fitness, there is a registration fee of $30 and a monthly fee of $10. Write an equation relating the total cost, C, of the gym membership to the number of months, m, enrolled.
Total cost , C become 30 + 10m
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
It is given that the registration fees is $30 and monthly fees be $10
Let the number of months be represented by m
Total cost, C = 30 + 10m
Therefore, Total cost , C become 30 + 10m
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On a sunny fall day, Paul and his family go to an orchard to pick apples for their famous apple
pies. First, they pick enough Golden Delicious apples to fill a bag. Then, they pick enough
Honeycrisp apples to fill another bag. The bag of Honeycrisp apples weighs 18 pounds. In all,
Paul's family picks 22 pounds of apples.
Which equation can you use to find the weight w of the Golden Delicious apples?
w + 18 = 22
Type here to search
W
18
Submit
= 22
Solve this equation for w to find the weight of the Golden Delicious apples.
pounds
w 18 = 22
Bi
18w = 22
Work it out
Vide
The equation that can use to find the weight w of the Golden Delicious apples w + 18 = 22.
The weight of the Golden Delicious apples is 4 pounds.
What is a linear equation?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x + 3 = 8 only has one variable.
Given that, Paul's family picks 22 pounds of apples.
They pick a bag of Honeycrisp apples weighs 18 pounds.
Assume that they take Golden Delicious apples with weight w.
Then the total weight of the bag is 18 + w.
The equation is
18 + w = 22
Subtract 18 from both sides:
18 + w - 18 = 22 - 18
w = 4
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Given f (x) = -2x+1 and g(x) =3x determine the value of f (4) + g(-1)
Answer:
-11
Step-by-step explanation:
f(4)=-2(4)+1
f(4)= -8+1
f(4)= -7
g(x)= 3(-1)
g(x) = -4
f(4)+g(-1)= -7+(-4)
-7-4
-11
hopes this helps
Answer:
-11 just took the test and that was mine
Step-by-step explanation:
What is the mass of an object on the moon when its mass on the earth is 20kg?
The mass of an object on the moon will be same that is 20 Kg when it's mass on the Earth is 20 Kg .
In the question ,
it is given that ,
the mass of the object on the Earth is 20 Kg .
we have to find the mass of the same object on the moon ,
We know that Mass is defined as the numerical measure of its inertia ,
and weight is calculated as
weight = mass × gravity ,
and mass is a constant quantity ,
So , the mass remain unchanged that is 20Kg .
Therefore , the mass of the object on the moon will be same as of Earth that is 20 Kg .
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