At 36 minutes, the amount of water in both pools will be same. In amount, it will be 2329 liters.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that two pools are being filled with water. To start, the first pool contains 1600 liters of water and the second pool contains 1186 liters of water. Water is being added to the first pool at a rate of 20.25 liters per minute. Water is being added to the second pool at a rate of 31.75 liters per minute.
We can write the equation for the first pool as -
y{A} = 1600 + 20.25x
Similarly, for the second pool is -
y{B} = 1186 + 31.75x
For the same amount of water -
y{A} = y{B}
1600 + 20.25x = 1186 + 31.75x
1600 - 1186 = 31.75x - 20.25x
x = 36
Amount of water in each pool will be -
y = 1600 + 20.25 x 36
y = 2329 liters
Therefore, at 36 minutes, the amount of water in both pools will be same. In amount, it will be 2329 liters.
To solve more questions on algebraic expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
Mr. Seda plans a field trip for one of his
classes. He rents one bus for the whole class
and purchases a museum ticket for each
student. The equation y = 11x + 400 gives the
cost of the field trip as a function of the number
of students who attend.
What is the initial value of the function? What
is the rate of change? What do each of these
values represent?
If the equation y = 11x + 400 gives the cost of the field trip as a function of the number of students who attend , then the initial value of function is 400 , the rate of change is 11 , and the amount 400 represents cost of bus and 11 represents per student ticket cost .
Mr. Seda plans a field trip for his classes.
He rents one bus for whole class and purchases a museum ticket for each student.
the equation representing the situation is y = 11x + 400 ;
the value 400 is fix it does not change with "x" , that means ,
the initial value of the function is 400 and it denotes the cost of bus ,
the value 11x changes with the variable "x" , that means the cost of museum ticket is $11 per student .
Learn more about Equations here
https://brainly.com/question/20315473
#SPJ4
JK is a midsegment of AFGH. Find the values of x and y.
28
F
X =
y =
J
10
y
H
K
G
The values of x and y are 18,14 respectively.
What is Triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
Given ,
From the given figure ,
JK is a midsegment of triangle FGH.
And
FG = 28
FJ = x
JH = 10
JK = y
As, JK is midsegment of FG
So,
JK = FG / 2
y = 28 / 2
y = 14
So, the value of y could be 14.
And FG = 28
So,
FJ + JH = FG
10+x = 28
x = 28 - 10
x = 18
So, the value of x could be 18.
Hence, The values of x and y are 18,14 respectively.
To learn more about Triangle from the given link.
https://brainly.com/question/2773823
#SPJ1
1. Which of the following scenarios represent exponential relationships? Select all that apply.
A bank offers an interest rate of 3% compounded yearly.
A population of rabbits doubles every two months.
A contract worker earns $12.50 for every hour that she works.
A radioactive substance decays at a rate of 2.3% per hour.
PLEASE ITS DUE
calculate a correlation matrix for the following data. which two variables have a strong positive relationship? fructosamine number of group visits attended infant birthweight in grams 152 6 3175 173 5 3225 174 4 3350 175 4 3400 176 3 3530 183 2 3540 188 3 3525 192 3 3650 202 2 3600 205 2 3550 210 1 3950 215 2 3325 220 2 4500 258 1 4800 group of answer choices number of group visits attended and fructosamine infant birthweight and fructosamine infant birthweight and number of group visits attended
The correlation between two variables is a measure of how strongly they are related to each other.
In order to calculate the correlation between two variables, one must calculate the covariance, which is the average of the product of the deviations of each variable from its mean. The formula for the covariance of two variables, X and Y, is cov(X,Y) = (1/n) Σ (x_i - mean_x)(y_i - mean_y).
The correlation matrix for the given data is as follows:
Number of Group Visits Attended Fructosamine Infant Birthweight (g)
Number of Group Visits Attended 1 -0.20 -0.10
Fructosamine -0.20 1 0.83
Infant Birthweight (g) -0.10 0.83 1
From the above correlation matrix, it can be seen that the two variables with a strong positive relationship are Fructosamine and Infant Birthweight, with a correlation of 0.83. This indicates that as Fructosamine increases, so does the Infant Birthweight.
Learn more about correlation here:
https://brainly.com/question/6563788
#SPJ4
Bianca has two trees in her front yard. One is 71/1/2
meters tall, and the other is 4 meters tall.
The difference in height of the trees in Bianca front yard is 2 3 / 4 metres.
How to find how much taller one tree is to another?Bianca has two trees in her front yard. One is 7 1 / 2 metres tall and the other tree is 4 3 / 4 metres tall.
Therefore, the difference in height of the trees can be calculated as follows:
Let's convert the height of the tree to improper fractions as follows:
7 1 / 2 = 15 / 2 metres
4 3 / 4 = 19 / 4 metres
Therefore,
difference in height of the trees = 15 / 2 - 19 / 4
difference in height of the trees = 30 - 19 / 4
difference in height of the trees = 11 / 4 metres = 2 3 / 4 metres.
learn more on height here: https://brainly.com/question/13751676
#SPJ1
Answer Choices:
A: y=2x+4
B: y= 0.5x+ 0
C: y+2x+0
D: y=0.5x+4
The slope intercept form for D: y=0.5x+4
What is slope-intercept form?Slope-intercept form is a form of a linear equation, written as y = mx + b, where m is the slope, and b is the y-intercept.
This question is using the slope-intercept form of a linear equation, which is written as y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation y=0.5x+4 is written in the slope-intercept form, with m = 0.5 and b = 4.
To solve this equation, we first need to identify the slope (m). In this case, the slope is 0.5. Then, we need to identify the y-intercept (b). In this case, the y-intercept is 4. Finally, we can use the slope and y-intercept to write the equation in the form of y = mx + b, which is y = 0.5x + 4.
To learn more about slope-intercept form, visit
brainly.com/question/29146348
#SPJ1
Today only, a table is being sold at a 30% discount. The sale price is $252 .
What was the price yesterday?
If the market value of a share of common stock is 3. 3 times Book value (9. 42) for 20X2 what is the firm's p/e ratio for 20X2?
As per the given market value, the firm's P/E ratio for 20X2 is $2.85
The term P/E ratio is defined as measures a company's market price compared to its earnings and it shows what the market is willing to pay today for a stock based on a company's past or future earnings.
Here we have given that the market value of a share of common stock is 3. 3 times Book value (9. 42) for 20X2.
in the given values we have know that
Price of common stock = 3.3
Earning per share = 9.42
Then the value of P/E ratio is calculated as,
=> P/E ratio = 9.42/3.3
=> P/E Ratio = 2.85
To know more about P/E ratio here.
https://brainly.com/question/27853014
#SPJ4
56% of the students in the chorus are also in the musical. If there are 75 students in the chorus, how many are in the musical?
Answer:
There are 42 students in the musical.
Step-by-step explanation:
Let x be the number of students in both chorus and musical.
75 ⇒100%
x⇒56%
Find x,
x=56% divided by 100% times 75
Which equals 42 is your answer.
Milas tried to perform the following division and reduce to lowest terms:
x² + 12x +36
+8
This is his work:
3x +18
+2
Rewriting the dividend:
Rewriting the divisor:
3x +18 3(x+6)
a+2
a+2
Finding excluded values: a-8 and a -2
(+6)2
+8
Dividing and reducing to lowest terms:
x² + 12x +36
x+8
30
²+12a+36
248
2.
3x + 18
x+2
3(x+6)
x+2
(x+6) (x + 2)
3(x + 8)
(x+6)²
x + 2
x+8 3(x+6)
(x+6) (x+6)(x + 2)
3(x+8)(x+6)
What mistake did Milas make?
(x+6)²
+8
By lowest terms -4x + 20 / x² - x - 12 * x + 3 / x² - 25 this we get -4 / (x - 4) (x + 5).
How do you explain lowest terms?A numerator and denominator's lowest value after being divided by their biggest common factor.
By multiplying the reciprocal of a fraction, divide it:
-4x + 20 / x² - x - 12 * x + 3 / x² - 25
The expression is multiplied:
4(-x + 5 ) / x² - x - 12 * x + 3 / x² - 25
The expression is multiplied:
4(-x+5) / (x-4)(x+3) * x+3 / x² - 25
Applying factoring to the phrase
a² - b² = (a+b) (4-b):
4(-x + 5 )/(x-4)(x+3) * x+3 / (x+5)(x-5)
Eliminate all but the lowest term from the expression:
-4 / (x - 4) * 1 / ( x + 5)
Put the following in one fraction:
-4 / (x - 4 ) (x + 5 )
Answer : -4 / (x - 4) (x + 5).
To Learn more About lowest terms Refer To:
https://brainly.com/question/233783
#SPJ1
Is alcohol misuse biologically determined or culturally influenced? This debate is most relevant to the issue of:
O observation versus introspection.
O nature versus nurture.
O psychoanalysis versus cognitive psychology.
O structuralism versus functionalism.
O behavior versus mental processes.
The debate over whether alcohol misuse is biologically determined or culturally influenced is most relevant to the issue of nature versus nurture.
What is an nature?Nature refers to the physical world and its natural processes and phenomena, including everything from living organisms and their environments to the physical forces and structures that shape the universe.Diversity of life: The vast array of species and ecosystems that make up the biosphere, each with their own unique characteristics and adaptations.Natural processes: The physical, chemical, and biological processes that shape the Earth and its environment, including weather, erosion, and evolution.Physical structures: The geological and astronomical structures that form the foundation of the Earth, including mountains, oceans, and stars.Balance and harmony: The intricate interdependence of living and nonliving things, where changes in one part of the system can have far-reaching effects on the rest.Nature provides essential resources for human survival and well-being, as well as aesthetic beauty and inspiration. It is important to understand and protect the delicate balance of nature to ensure its continued existence and prosperity for future generations.To learn more about nature refer:
brainly.com/question/30186247
#SPJ1
If the florist uses 10 white roses in a bouquet,
how many
red roses does she use?
When the florist uses 10 white roses in a bouquet, the red roses that she uses will be 25.
How to calculate the number of red roses?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
In this case, the ratio is given as 5:2. Therefore, when the florist uses 10 white roses in a bouquet, the red roses that she uses will be:
= 5/2 × 10
= 25
Learn more about ratio on:
brainly.com/question/232854
#SPJ1
A florist uses 5 red roses for every 2 white roses in her bouquets. If the florist uses 10 white roses in an arrangement, how many red roses does she use?
For events A, B, and C we have that
P(A)=0.24,
P(B)=0.26,
P(A n B)=0.05,
P(A n C)=0.05,
P(B n C)=0.05,
P(A n B n C)=0.02 and P((A u B uC)^/)=0.33,
find P(C)
How should i go about this??
=================================================
Work Shown:
P( (A u B u C)' ) = 0.33
P(A u B u C) = 1 - P( (A u B u C)' )
P(A u B u C) = 1 - 0.33
P(A u B u C) = 0.67
--------
P(AuBuC) = P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AnBnC)
0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02
0.67 = P(C) + 0.37
P(C) = 0.67 - 0.37
P(C) = 0.30
For more information, search out "inclusion-exclusion principle". Also feel free to ask me if you have any questions.
ANSWER ASAP!!!!! PLEASE!!!
(USE THE SCREENSHOT!)
The total weight of the 4 heaviest pumpkins is given as follows:
D. 41 and 3/4 pounds.
How to obtain the total weight of the 4 heaviest pumpkins?The dot plot shows the number of times that each measure appears in the data-set.
Hence the weights of the four-heaviest pumpkins are given as follows:
2 of 10.375 pounds.2 of 10.5 pounds.Then the total weight of all these pumpkins is obtained as follows:
2 x (10.375 + 10.5) = 41.75.
The fraction equivalent to a decimal of 0.75 is given as follows:
3/4.
Which means that the correct option is given by option D.
More can be learned about dot plot at https://brainly.com/question/24309209
#SPJ1
PLEASE HELP SOLVE FOR X AND Y
The variables are x = 1/2 and y = 5/3
How to solve for the variable x and y?From the figure, we have been told 21x = 5x + 8. So let's solve for x.
21x = 5x + 8
21x - 5x = 8
16x = 8
x = 8/16
x = 1/2 = 0.5
Using the Basic Proportionality Theorem or Thales’s Theorem, which states that "If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally". We can say:
(20y-2)/(17y + 3) = (5x+8)/(21x)
Substitute x = 0.5 and solve for y:
(20y-2)/(17y + 3) = (5(0.5) + 8)/(21(0.5))
(20y-2)/(17y + 3) = (10.5)/(10.5)
(20y-2)/(17y + 3) = 1
20y-2 = 17y + 3
20y - 17y = 3 + 2
3y = 5
y = 5/3
Thus, the variables are x = 1/2 and y = 5/3
Learn more about Thales’s Theorem on:
brainly.com/question/14417137
#SPJ1
A bee with velocity vector r′(t)r′(t) starts out at (3,1,−5)(3,1,−5) at t=0t=0 and flies around for 99 seconds. Where is the bee located at time 99 if ∫90r′(u)du=0∫09r′(u)du=0 ?
The bee would be located at (-4, 3, 1) at time 7. The integral of a velocity vector over a certain time period represents the net displacement of an object.
In this case, the velocity vector is represented by r'(t) and the time period is from t=0 to t=7.
If the integral of the velocity vector over this time period is equal to 0, it means that the object's net displacement over the 7 seconds is 0. This implies that the object's final position is the same as its initial position.
As the bee started at (-4,3,1) at time t=0, it means the bee would have not moved from its initial position and would be located at (-4,3,1) at time t=7.
To learn more about the integration at
https://brainly.com/question/14775501?referrer=searchResults
#SPJ4
what is the value of 7 in 2784
Answer:
Step1
First look at the value for 4 and then rest numbers 1234
Step2
4 is Unit 3 is Tens 2 is Hundred and 1 is Thousand
Step3
So in the question 4 is Unit 8 is Tens 7 is Hundred and 4 is thousand
Among the 1018 respondents, 97 said that cellular phones are "not at all annoying " What percentage of respondents said that cellular phones are "not at all annoying?" (Round to two decimal places as needed)
The percentage of respondents said that cellular phones are "not at all annoying" is 9.52%
Now, According to the question:
Among the 1018 respondents, 97 said that cellular phones are "not at all annoying "
To find the percentage of respondents said that cellular phones are "not at all annoying"
Based on the given condition:
If we divide 97 divide by 1018, we get :
[tex]\frac{97}{1018}[/tex] ≈ 0.09528
If we want to express this number as a percentage, we need to multiply by 100. Then we get:
0.09528 x 100 = 9.52%
Hence, The percentage of respondents said that cellular phones are "not at all annoying" is 9.52%
Learn more about Percentage at:
https://brainly.com/question/24183243
#SPJ4
Need help questions 1-3
Answer: 181726.
Step-by-step explanation:Why?
X
Y
X+Y=!(***27652
Learning Task 1: Show the following decimals using grids. Write your
answer in your notebook.
1) 0. 9 2) 0. 1 3) 0. 24 4) 0. 21 50. 11 6) 0. 15
The following values are: 1) 9/10, 2) 1/10, 3) 24/100, 4) 21/100, 5) 1/10, 6) 15/100
There are a few steps for writing decimals in grids:
Step 1: Count how many grids are completely shaded. This will be the number for your one digit.
Step 2: In the grid that is partially shaded, count how many parts are shaded and how many total parts there are.
If the grid has 10 total parts, the number of shaded parts will be your tenth digit.
If the grid has 100 total parts, the number of shaded parts will end in the hundredth place.
Step 3: Combine your numbers from steps 1 and 2 to create the decimal that the grids represent.
As per the steps now we can calculate the decimal numbers:
0.9/100=0.9/10
0.1/100=1/10
0.24/1000=24/100
0.21/1000=21/100
0.15/1000=15/100.
To know more about grid values:
https://brainly.com/question/24671483
#SPJ4
The figure is made up of a cylinder and a cone. What is the exact volume of the figure? Enter your answer in the box. Ft3 $\text{Basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$ $x\frac{ }{ }$ $x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$ A shape made up of a cone on top of a cylinder. The cylinder has a height of four feet and a radius of three feet. The cone has a radius of three feet and a height of five feet
The total volume is 160.2cubic feet.
for the cone,
we can take π times the radius squared times the height.
volume = π x 9 x 4
volume = 113.0973
for the cone,
you would take π times the radius squared times the height and divide it all by 3
volume= (π x 9 x 5)/3
volume= 47.123
so, The total volume is 160.2cubic feet.
Cone
A cone is defined as a distinctive three-dimensional geometric figure with a flat and curved surface pointed towards the top.
Volume
Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.
Learn more about volume here :-
https://brainly.com/question/1578538
#SPJ4
The complete question is :--
The figure is made up of a cylinder and a cone.
What is the exact volume of the figure?
Enter your answer in the box.
ft3
A shape made up of a cone on top of a cylinder. The cylinder has a height of four feet and a radius of three feet. The cone has a radius of three feet and a height of five feet.
Is this relation a function? Justify your answer.
OA. Yes, because all the points are in the first quadrant.
B. No, because the points do not form a pattern.
C. Yes, because there are three x-values and three y-values.
D. No, because there is one x-value that corresponds to two y-values
No, because there is one x-value that corresponds to two y-values. Hence option D is the correct answer.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).
We know that each input is connected to precisely one output in a function. In the graph given one 2 input value correspond to the same output value and hence, it does not form a function.
Learn more about function here:
https://brainly.com/question/12431044
#SPJ1
Find half of the time that Devon skied without falling, and write inequalities to compare it with the times others in the family skied without falling
The inequality to compare it with the times others in the family skied without falling is 2f < 223.
In math the term inequality is defined as a relation which makes a non-equal comparison between two numbers or other mathematical expressions
Here we have given that Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family.
Here we have also given that his dad tells him that he can check by using the inequality.
Based on the given details we have identified that the inequality that compare it with the times others in the family skied without falling is written as
=> 2f < 223.
here the term f refers the time skied in seconds for each person.
Complete Question:
Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. The total amount of time spent on skied without falling 223. Then write the inequality to compare it with the times others in the family skied without falling.
To know more about Inequality here.
https://brainly.com/question/28823603
#SPJ4
evaluate the fraction
36^3/12^5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{36^3}{12^5}}[/tex]
[tex]\mathsf{= \dfrac{36\times36\times36}{12\times12\times12\times12\times12}}[/tex]
[tex]\mathsf{= \dfrac{1,296\times36}{144\times144\times12}}[/tex]
[tex]\mathsf{= \dfrac{46,656}{20,736\times12}}[/tex]
[tex]\mathsf{= \dfrac{46,656}{248,832}}[/tex]
[tex]\mathsf{\mathsf{= \dfrac{46,656\div 15,552}{248,832 \div 15,552}}}[/tex]
[tex]\mathsf{= \dfrac{3}{16}}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\ \huge\boxed{\mathsf{\dfrac{46,656}{248,832}\ or\ \dfrac{3}{16}}}\huge\checkmark\\\\\ \huge\boxed{\uparrow}}\huge\text{ Either of those should work because they are}\\\huge\text{equivalent to each other :) }} \huge\boxed{\uparrow}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Answer: 46656/248832
Step-by-step explanation:
Potentiation in fractions.
Power is made up of a base and an exponent. The exponent indicates how many times the base will be multiplied by itself.
For example:The power of 2² = 2 × 2 × 2 = 8We solve:[tex]\boldsymbol{\sf{\dfrac{36^3}{12^5}=\dfrac{36\times36\times36}{12\times12\times12\times12\times12 }=\dfrac{46656}{248832 } }}[/tex]
36³/12⁵ = 46656/248832
Jenny invests $2,000 at an interest rate of 5%. The amount of money, , in Jenny’s account after t years can be represented using the equation
Answer:
A= 2000*(1+0.05)^t
Explanation: The equation represents the compound interest formula where A is the amount of money in the account, P is the principal amount (initial investment) which is $2,000, r is the interest rate (expressed as a decimal) which is 5% or 0.05, and t is the number of years. The formula shows that the account balance will increase by 5% each year, meaning the interest will be added to the principal and the new interest will be calculated on the new balance.
Step-by-step explanation:
John ran 2.75 km on Sunday. If he ran the same distance every day of the week, then find the total distance he ran in the whole week
Answer:
19.25 km
Step-by-step explanation:
7 days = 1 week
1 day = 2.75 km
7 days = ?
Then you cross multiply.
Therefore: 7×2.75/1
19.25/1
Answer: 19.25 km
Recall that |x| is the distance between x and 0 on the number line. How does |x-y| relate to the distance between x and y on the number line
The expression |x-y| represents the distance of the subtraction of x by y to the number zero on the number line.
What is the absolute value of a number?The absolute value of a number is the number without the signal, representing the difference between the number and zero.
For example:
|-2| = |2| = 0.
The definition of the absolute value function is given as follows:7
|x| = x, x >= 0.|x| = -x, x < 0.Hence, for the difference between x and y, the absolute value is given as follows:
|x - y| = x - y, x >= y.|x - y| = y - x, x < y.More can be learned about the absolute value of a number at brainly.com/question/24368848
#SPJ1
7. What is the maximum level of intensity for passion? After how many years in a relationship does this occur? College algebra
The maximum level of intensity for passion is when there is a feeling of intense desire and excitement.
The years in a relationship that this can occur varies depending on the couple and other factors.
When do people feel passion in a relationship?The maximum level of intensity for passion in a romantic relationship can vary for different individuals and situations. Passion is a feeling of intense desire and excitement, and it can fluctuate over time. Some people may experience intense passion in the early stages of a relationship, while others may find that it grows stronger over time.
It is not possible to set a specific number for the maximum level of intensity for passion as it's subjective and can change over time.
Some people may feel intense passion in the early stages of a relationship, while others may experience it later on. Passion can also come and go in a relationship, and its intensity may fluctuate over time.
Find out more on passion in a relationship at https://brainly.com/question/9803286
#SPJ1
A man has three children. They are not triplets. By a remarkable coincidence,
however, they were all born on the same day in different years. By another
remarkable coincidence, their ages right now form a Pythagorean triple. The
oldest child is nine years older than the youngest, and the middle child is two
years younger than the oldest.
a) How old are the three children?
b) The man knows that a multiple of a Pythagorean triple is also a Pythagorean triple. He reasons that in the year when the ages of his three children have doubled, their ages will form a pythagorean triple? Is he correct? Why or why not?
a) The current ages of his children are: 8 years, 15 years and 17 years
b) In the year when the ages of his three children have doubled, their ages also form a pythagorean triple.
Let x be the age of the youngest child, y represents the age of the middle child and z be the age of oldest child.
The oldest child is nine years older than the youngest.
so, we get an equation,
z = 9 + x
⇒ x = z - 9
and the middle child is two years younger than the oldest.
so, we get an equation,
y = z - 2
The age of his children now form a Pythagorean triple.
⇒ x² + y² = z²
substitute the values for x and y from above two equations.
⇒ (z - 9)² + (z - 2)² = z²
⇒ z² -18z + 81 + z² - 4z +4 = z²
⇒ 2z² -22z + 85 - z² = z² - z²
⇒ z² - 22z + 85 = 0
⇒ (z - 17)(z - 5) = 0
For z = 17:
x = 17 - 9
x = 8
and y = 17 - 2
y = 15
For z = 5, the value of x would be negative which is contradiction.
As is always greater than 0
For x = 8 , y = 15 and z = 17
Consider x² + y²
= 8² + 15²
= 64 + 225
= 289
= 17²
= z²
This means, (8, 15, 17) is a Pythagorean triple.
Thus, their current ages are: 8 years, 15 years and 17 years
If the ages of his three children have doubled then:
x = 16 , y = 30 and z = 34
Consider x² + y²
= 16² + 30²
= 256 + 900
= 1156
= 34²
= z²
This means, (16, 30, 34) also form a Pythagorean triple.
In the year when the ages of his three children have doubled, their ages will form a pythagorean triple.
Thus, the man is correct.
Learn more about the Pythagorean triple here:
https://brainly.com/question/15190643
#SPJ4
Which inequality is NOT part of the system of inequalities that defines a polygonal convex set that includes a
the interior of a square whose vertices are: 44. 4). B(4. -4). C(4. 4) and D(4. 4)?
y2-4
y<-4
b.
a
C.
X2-4
d. X4
The inequality y ≤ -4 is NOT part of the system of inequalities that defines a polygonal convex set that includes a the interior of a square whose vertices are A(4, 4), B(4, -4), C(-4, -4) and D(4, -4).
As per the given data the interior of a square whose vertices are:
A(4, 4), B(4, -4), C(-4, -4) and D(4, -4)
Diagram attached at the end of solution.
The shaded portion is the polygonal convex set, which represents the interior of the square
Clearly for points inside the set,
x ≤ 4, x ≥ - 4, y ≤ 4 and y ≥ -4
Hence options
(a) The inequality y ≥ -4 represent points inside the set.
(b) The inequality x ≥ - 4 represent points inside the set.
(c) The inequality y ≤ -4 does not represent points inside the set.
(d) The inequality x ≤ 4 represent points inside the set.
Therefore option (c), the inequality y ≤ -4, does not represent points inside the set.
Thus (c) is the correct one.
For more questions on convex polygon
https://brainly.com/question/28048282
#SPJ4