A linear problem is always convex, because anything linear is convex.
What is linear programming?
A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.
A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
Every linear function has a concave shape. However, only convex polygons (possible sets of linear programs) exist.
A linear problem is always convex, because anything linear is convex.
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Let n be the number of trials and p be the probability of success in the binomial distribution. Under which conditions do the Binomial and Poisson distributions give approximate results? n → [infinity], p → 0 n → [infinity], p → 1 n → 0, p → 0 n → 0, p → 1
Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
Unlike, in the case of a Binomial distribution, for a Poisson distribution, the knowledge of number of trials to get the observed number of successes is not required. The Poisson distribution has only one parameter namely “m” the mean number of successes per given unit of time.
The Poisson distribution is often taken as a limiting case of Binomial distribution, under the following conditions.
The number of trails is indefinitely large i.e., n → ∞
The probability of success, “p” is very small i.e., p → 0
np is finite i.e., np = m where p = m/n and q = 1 – m/n and m > 0.
However, it is not defined if “n” is large means how large and “p” is closed to zero means how small? It is left to the readers to assume how large n should be and how small p should be? As mentioned earlier, the Poisson distribution is often described as a limiting case of Binomial distribution.
Based on the results of the study , published by me clearly proves that even when 10 ≤ n ≤50 and p ≤ 0.2, the Poisson distribution can be a good approximation to Binomial distribution.
Hence the answer is Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
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alex has $600 in her checking account. she wants to spend a part of this money on a computer. she wants to have at least $250 left in her checking account after buying the computer. write an inequality that can be used to find t, the amount of money in dollars that alex can spend on the computer, and solve for t.
An inequality that can be used to find t the amount of money in dollars is
c)t ≤ 350, t is less than or equal to 350. So, correct option is c.
In science, a disparity or an inequality is a connection which makes a non-equivalent examination between two numbers or other numerical expressions. It is utilized generally normal to look at two numbers on the number line by their size. There are a few unique documentations used to address various types of disparities:
The documentation a < b implies that an is not as much as b.
The documentation a > b implies that an is more noteworthy than b.
Regardless, an isn't equivalent to b. These relations are known as severe inequalities, implying that an is completely not exactly or rigorously more prominent than b. Identicalness is barred.
We have Alex total amount =$600 and amount which he want on his account after spending is $250.
So,t+250 ≤600
=>t≤ 600-250
=>t≤ 350.
Hence, option c is correct.
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(Complete question) is:
Alexandra has $600 in her checking account. She wants to spend part of this money on a computer. She wants to have at least $250 left in her checking account after buying the computer. The inequality shown can be used to find t, the amount of money in dollars that Alexandra can spend on the computer.
Which inequality represents all possible values of t?
a)t ≥ 350,
t is greater than or equal to 350
b)t ≤ 850,
t is less than or equal to 850
c)t ≤ 350,
t is less than or equal to 350
d)t ≥850,
t is greater than or equal to 850
Select all the equivalent solution sets to the compound inequality 27>−1/2(4x+6)≥100?
A. −15
B. −10.5
C. −10.5
D. −15
E. −10.5
F. −15
G. −15
a credit card company surveys its customers to determine the number of times they use the card each month. there are 5,500 customers and 2,756 indicate that they use the card at least twice each month. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The standard deviation of the sampling w would be 0.06.
What is a standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
Population proportion
[tex]p=\frac{2756}{5500} \\\\\\p=0.501091\\\\p=0.501[/tex]
The mean of the sampling distribution for samples of size n=70 customers = 0.501
The standard deviation of the sampling distribution for samples of size n=70 customers is
[tex]=\sqrt{\frac{p* (1-P)}{n}} \\\\=\sqrt{\frac{ 501091(1-0.501091) }{2}}\\\\ = 0.059761 \\\\=0.06[/tex]
Hence, the standard deviation of the sampling w would be 0.06.
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a grandfather, two fathers and two sons bought passage for a voyage together and everyone paid for one berth each. how many berths did they buy in total?
The total number of tickets they bought was 3.
What is a math riddle?
To solve a math riddle, children must translate a few sentences from a real-life scenario into the correct combination of mathematical equations. Children can decipher any code, including math riddles, using logic, creative problem-solving, and common sense.
Total 3 tickets-
Grandfather-Also Father of His son
Father-Also son of his father.
Son.
So Two fathers and two sons.
Hence, a total of 3 tickets were bought.
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Mya saved
$
640
for food for her family’s upcoming vacation. Breakfast is included with the hotel, but lunch and dinner are not. When Mya cooks lunch or dinner it costs, on average,
$
16
. When the family goes to a restaurant for lunch or dinner it costs, on average,
$
63
. Let
c
represent meals that Mya cooks and let
r
represent meals the family eats at a restaurant. Write an inequality to represent the situation.
The inequality to represent the situation is 16c + 63r ≤ 640.
What is simple inequality?
Mathematical expressions with simple inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given, total saving = $640
Mya cooks lunch or dinner = $16
restaurant for lunch or dinner = $63
For c meals that Mya cooks = 16c
For r meals, the family eats at a restaurant = 63r
Total cost = 16c + 63r
Based on conditions, 16c + 63r ≤ 640
Hence, the inequality representing the situation is 16c + 63r ≤ 640.
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Question
The points in the table lie on a line. Find the slope of the line.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{4 }{7 +3} \implies \cfrac{ 4 }{ 10 } \implies \cfrac{2 }{ 5 }[/tex]
in a study to compare the perceived effects of two pain relievers, 200 randomly selected adults were given the first pain reliever, and 93% indicated appreciable pain relief. of the 450 individuals given the other pain reliever, 96% indicated experiencing appreciable relief. a) give an estimate for the difference in the proportions of all adults who would indicate perceived pain relief after taking the two pain relievers. provide a 95%-confidence interval for the estimate.
7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
Given that,
In a study comparing the perceived effects of two painkillers, 200 randomly chosen persons were given the first one, and 93% reported noticeably lessening of their pain. 96% of the 450 people who received the other painkiller reported feeling noticeably relieved.
We have to estimate the percentage of adults overall who would say they felt their pain was relieved after taking each painkiller. give the estimate's 95% confidence interval.
We know that,
p=(186+432)/(200+450)
p=0.95
We get
L.B= 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)
L.B= 0.07
Therefore, 7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.
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you need to buy some chicken for dinner tonight. you found an ad showing that the store across town has it on sale for $3.19 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.59 a pound. is it worth the extra drive? first, determine what information you need to answer this question, then click here to display that info (along with other info). how much chicken will you be buying? 3 pounds how much far are the two stores? my neighborhood store is 2.1 miles away, and takes about 7 minutes. the store across town is 8.5 miles away, and takes about 23 minutes. how kind of mileage does your car get? it averages about 19 miles per gallon in the city. how many gallons does your car hold? about 17 gallons how much is gas? about $3.83/gallon right now. going to the close store is cheaper going to the further store is cheaper the cheaper option saves you $
Yes, it is worth the extra drive, going to the further store is cheaper.
The cheaper option saves you $0.09.
Given:
Price or sale = $3.19 a pound
1.) Neighborhood store
Distance = 2.1 miles away
As, the car averages about 19 miles per gallon,
=2.1 miles / (19 miles/gallon)
= 0.1105 gallons of gas < 17 gallons
The gas is about $3.83/gallon, then the cost be
=0.1105 gallons x ($3.83/gallon)
= $0.42
The chicken is sold for $3.59 a pound, and you need 3 pounds, then you would pay:
= 3 pounds x ($3.59/pound)
= $10.77
So, the total is
= $0.42 (gas) + $10.77 (chiken)
= $11.19
2.) Store across town
Distance = 8.5 miles away
The car averages about 19 miles per gallon, then you would need:
=8.5 miles / (19 miles/gallon)
= 0.447 gallons of gas < 17 gallons
The gas is about $3.83/gallon, then the gas would cost:
=0.447 gallons x ($3.83/gallon)
= $1.71
The chicken is sold for $3.19 a pound, and you need 3 pounds, then you would pay:
= 3 pounds x ($3.19/pound)
= $9.57
The total cost
= $1.71 (gas) + $9.57
= $11.28
Thus, $11.19 < $11.28, then it is worth the extra drive.
Hence, cheaper option saves you= $11.28 - $11.19 = $0.09
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a manufacturer must test that his bolts are 4.00cm long when they come off the assembly line. he must recalibrate his machines if the bolts are too long or too short. after sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14cm. he knows that the population standard deviation is 0.83cm. assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?
p < 0.05, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.
Given,
The test statistics formula for finding the z-score is,
z = (X - μ)/(σ/√n)
Where,
X = sample mean
μ = population mean
σ = population standard deviation
n = sample size
This z-score is used to determine the p-value. The null hypothesis is not rejected if p > α, and it is rejected if p < α.
Here,
The population mean μ = 4.00
The sample size n = 196
The sample mean X = 4.14
The standard deviation σ = 0.83
The significance level α = 0.05
So, the hypothesis is:
The null hypothesis: H0: μ = 4
The alternative hypothesis: Ha: μ ≠ 4
Thus, the test statistic value is,
z = (X - μ)/(σ/√n)
= (4.14 - 4)/(0.83/√196)
= 2.36
So, for z = 2.36, the p-value is 0.009137
Therefore,
The provided significance level of 0.05 is not met by the p-value of (0.009137). Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.
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what is $0.4\overline 8 0.\overline{37}$? express your answer as a common fraction in lowest terms.
The answer of the given expression as a common fraction in lowest terms is 437/495 .
In the question ,
it is given that ,
the expression is 0.4overline 8 + overline 0.37 ,
that can be written as [tex]0.4\overline{8}[/tex] + [tex]0.\overline{37}[/tex]
On further simplifying the above expression further ,
we get ,
= (48 - 4)/90 + 37/99
= 44/90 + 37/99
taking the LCM of 90 and 99 as 990 and solving further ,
we get ,
= 484/990 + 390/990
= ( 484 + 390 )/990
= 874/990
in lowest form it is = 437/495 .
Therefore , the answer to the expression is 437/495 .
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Explain how you know that the sum of 2,3,and -2 is positive without computing
Technically, it would be impossible to truly know without "computing" at all, but once you add 2 and 3, you would be able to know that the sum of all three numbers of positive without accounting for the -2, because 6 is a greater absolute value than -1.
Some examples:
12 + - 4
7 + - 3
18 + -10
All will be positive because those positive numbers (12, 7, 18) are greater than the others (4, 3, 10).
Express five eighths as a decimal.
A. 0.375
B. 0.40
C. 0.625
D. 0.875
Answer:
C. 0.625
Step-by-step explanation:
5 divided by 8 is .625
A.
.625
8 5.000
- 48
20
- 16
40
- 40
0
B.
or you can multiply by 8 the answers to see if you get 5
A. 0.375 * 8 = 3
B. 0.40 * 8 = 3.2
C. 0.625 * 8 = 5
D. 0.875 * 8 = 8
C.
if you dont have to you could estimate using the first number after the decimal to see if you get 5
A. 0.375
first number after the decimal is 3
3 * 8 = 24 ≈ 2.4 ≈ 3
B. 0.40
first number after the decimal is 4
4 * 8 = 32 ≈ 3.2 ≈ 3
C. 0.625
first number after the decimal is 6
6 * 8 = 48 ≈ 4.8 ≈ 5
D. 0.875 * 8 = 8
Which of the following lines have the greatest slope? EXAM DUE IN 20 MINUTES!!
In a class of 25 students, 5 have a cat and 9 have a dog. There are 3 students who have a cat and a dog. What is the probability that a student has a cat given that they do not have a dog?.
The probability that:
A student has a cat and they do not have a dog = 1/8 or 0.125.
Use the concept of probability defined as:
Probability is the ratio of:
The number of favorable outcomes to the total number of outcomes for an event's taking place.
Given that,
The number of students in the class = 25
[tex]5[/tex] students have a cat.
[tex]9[/tex] students have a dog.
[tex]3[/tex] students have both a cat and a dog.
The objective is to find the probability that given that they don't have a dog, a student has a cat.
To find the probability that one of the pupils has a cat because there isn't a dog in the class:
First, determine the total number of pupils without a dog..
Since there are 25 students in total and 9 have a dog,
Now, 25 - 9 = 16
So the number of students who do not have a dog = 16
Now, determine the number of students who have both a cat and a dog.
According to the question:
There are 3 students who have both,
Subtract this from the percentage of students who own cats.
Therefore,
5 - 3 = 2
So, there are 2 students who have a cat but not a dog.
[tex]Probability = \frac{\text{(Number of students with only a cat)}}{\text{ (Number of students who do not have a dog)}}[/tex]
Probability = 2 / 16
Probability = 1 / 8
Hence,
The required probability that a student has a cat given that they do not have a dog = 1/8 or 0.125.
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A factory process requires 3 steps to finish a product. The steps each have a mean completion time of u = 10 seconds and a standard deviation of o = 5 seconds. The time it takes to complete each step is independent from the other steps. Let I be the total completion time of the 3 steps on a randomly chosen product.
Answer:
square root 75
Step-by-step explanation:
In this lesson, you sketched polynomial functions using factors and rewrote them in general form.
1 Use the factors to sketch each cubic function and label the zeros. Then rewrite the function
in general form.
F(x) = (x+3)(-x + 5)2 - 2x)
To view the sketched cubic function and label the zeros using the factors check the attached image and the rewrite the function in general form is
2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] -26x + 30.
What do you mean by factors and give example?A number or algebraic expression that divides another number or expression evenly that is with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.
Given that :
f(x) = (x + 3)(-x + 5)(2 - 2x)
To find : zeroes of f(x) , sub f(x) = 0
(x + 3)(-x + 5)(2 - 2x) = 0
x + 3 = 0
x = -3
- x + 5 = 0
x = 5
2 - 2x = 0
x = 1
The zeroes are -3 , 1 , 5
Rewrite the function in general form
f(x) = (x + 3)(-x + 5)(2 - 2x)
= (- [tex]x^{2}[/tex] + 2x + 15 )(2 - 2x)
f(x) = 2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] - 26x + 30
Therefore, f(x) = 2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] - 26x + 30 is a general form.
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One karaoke location, Singing Star, is charging $20 for 10 songs. Construct a graph to model the relationship between cost and number of songs.
A graph to model the proportional relationship between cost and number of songs is shown in the image attached below.
How to construct the required graph?Mathematically, a proportional relationship and the constant of proportionality can be represented or modeled with the following equation or mathematical expression:
y = kx
Where:
x represents the cost in dollars.y represents the number of songs.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for a song as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 10/20
Constant of proportionality (k) = 0.2
Therefore, an equation for any number of song for this karaoke is given by:
y = 0.2x.
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Mr. Jones has driven 180 miles to Dallas. He has 60% of the trip left to go. How many more miles does Mr. Jones have to drive to get to his destination? Round your answer to the nearest whole mile.
Mr Jones have to drive 270 miles to get to his home
How to find the number of miles Mr Jones have to driveThe question is a percentage problem, percentage deals with a fraction hundred and used to solve the problem
From the equation 180 miles represents 40% of the journey
let the total journey be x, hence we say
0.4x = 180
x = 180 / 0.4
x = 450 miles
Then the 60% left is calculated
60% of 450
= 0.6 * 450
= 270 miles
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what is the answer i need answers now
describe how nonresponse might lead to bias in this survey. does the stated margin of error account for this possible bias?
The margin of error does not take into account the bias caused by nonresponse.
What is nonresponse bias?
The phenomenon known as participation bias, also known as non-response bias, occurs when a disproportionate number of participants have certain characteristics that have an impact on the results of surveys, polls, and other types of research.
Nonresponse bias happens when a portion of the sample's respondents fail to respond. The main distinction in this instance is that the error arises from a lack of respondents rather than the collection of false data.
Usually, the number of responses is used to calculate the margin of error. You can treat a sample from a finite population as infinite if the sampling fraction is small, but if the sampling fraction is high (say, more than 10% of the population size), you must make a finite population correction.
So, the non-response bias is not taken into account by the margin of error.
Longer commuters might take less time to complete a survey.
This would result in our estimate from the sample being lower than the actual mean travel time to work.
Hence, the margin of error does not take into account the bias caused by nonresponse.
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in how many ways may a student mark a 20 questions test, if 7 questions mark correctly and 13 incorrectly?
The 20 questions test answers may a student mark 8192 ways.
What is the combinations?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Since there are 20 questions, and each question can be answered in if 7 questions mark correctly and 13 incorrectly then:
7 questions can be answered correctly.
13 questions can be answered incorrectly.
The 2 questions can be answered in
2 × 2 ways.
The 3 questions can be answered in 2×2×2 ways and so on.
So we have:
1 × 1 × 1 × 1 × 1 × 1 × 1 × 2¹³
= 8192
Hence, the 20 questions test answers may a student mark 8192 ways.
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Let x and y be some integers. Consider the following statement: If xis odd and y is odd, then xy is odd. Proof. Assume that x is odd and y is odd. Then there exists some k integers such that x=2k+1 and m=2k+1. Then xy=(2k+1)(2k+1)=4k2+4k+1=2(2k2+2k)+1. Since 2k2+2k is an integer because k is an integer then xy is odd. The proof is correct but the statement is incorrect The statement is correct, but the proof is incorrect. The statement and proof are incorrect. The statement and the proof are correct.
hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.
Odd number integers = 2k + 1, where k is integer
Even number integer = 2k
Odd integer + even integer
= 2k + 1 + 2k
= 4k + 1
= 2(2k) + 1
Let 2k = t, where t is integer
= 2t + 1
= Odd integer by definition
If number is 2t + 1 where t belongs to integer, then it is odd integer.
Hence proved.
The question is incomplete. The complete question is :
Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd
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a consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. what is the probability that a car chosen at random will need a) norepairs? b) nomorethanonerepair? c) some repairs?
The probability that a car chosen to random will need:
A) no repairs: 72%
B) No more than one repairs: 89%
C) some repairs: 11%
The total amount of cars that will need some type of repair is 28%; 17% will need to be repaired once + 7% will need to be repaired twice + 4% will need to be repaired more than two times.
The amount of cars that wouldn´t need any type of repairs is the total amount of cars minus the percentage that need some type of repair:
100% - 28% = 72%.
The amount of cars that will need no repairs or only one repair is the total amount of cars minus the percentage that need more than one of repair:
100% - (7% + 4%) = 89%.
The amount of cars that need some repairs is the sum of those cars that need two repairs plus those that need three or more repairs:
7% + 4% = 11%
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if the flow rate in an artery has been reduced to 12% of its normal value by a blood clot and the average pressure difference has increased by 22%, what percent of the original is the radius of the reduced artery?
The percentage by which the radius of the artery reduces is 1.44% of original radius.
According to Poiseuille’s law, we got that there is relation between radius, length, average pressure for blood which is flowing in our body and that relation is is given by
Q = ((P₂-P₁)πr⁴) /(8ηl)
where Q is flow rate
P is the pressure
r is the radius of the artery
η is the viscosity
Now,we have given that Flow rate is reduced by 12%,new flow rate is 88% of normal value.
Also, we have also given that pressure is increased by 22%,so new pressure is 122% of initial value,
therefore Q = ((P₂-P₁) × π × r⁴) /(8ηl)
=>(Q-12Q/100)=[((122 / 100) × P₁-P₁) × π × r₂⁴] / (8ηl)
=>(88 / 100)Q=(22 / 100)×(P₁ × π × r₂⁴)/(8ηl)
=>(88/22)Q=(P₁ × π × r₂⁴)/(8ηl)
=>[[4 × (8ηl)] × Q]/ (P₁ × π)=r₂⁴
=>4r₁ =r₂⁴
=>r₂=√2r₁
or r₂=1.44% of original radius.
Hence, by 1.44% radius of artery would reduce.
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I went to dinner and the dessert was 17% of the $85 meal. How much did we spend on dessert?
Answer:
$14.45
Step-by-step explanation:
To make the equation easier you would have to make the percent decimal and to do that move it twice to the left. So it would be 0.17 x 85 which is 14.45 and add that dollar sign there. :)
what is the smallest possible perimeter for a rectangle whose area is 16 in2?
Answer: 4in
Step-by-step explanation:
A square and rectangle the same perimeter. Each side of the square measures 4x+4 units. The rectangle measures x and 2x+13 units on opposite sides. Find the value of x and the perimeter of the figure?
Answer:
x = 1, p = 32
Step-by-step explanation:
4(4x+4) = 2(x+2x+13)
16x+16 = 6x+26
10x+16=26
10x=10
x=1
4(4(1)+4) = 4(4+4) = 4(8) = 32
4.) 2x + 3y = 12
x + y = 5
Answer:
x = 3
and
y = 2
Step-by-step explanation:
Find the value of u² - v² when u = 5 and v = 3
Answer: 16
Step-by-step explanation:
u=5
v=3
u² - v²
5² - 3²
——————————
5² = 5 • 5 = 25
3² = 3 • 3 = 9
——————————
25 - 9 = 16