A company installs triangular pools at hotels. All of the pools are congruent and triangle JKL is congruent to triangle MNP in the figure. What is the perimeter of each pool?
Answers
The perimeter of each pool is 92 ft.
What is perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter.
Given, the triangles are congruent so,
20x-15 = 15x+15
=> 20x-15x = 15+15
=> 5x = 30
=> x = 30/5 = 6
Therefore, perimeter = (4x-4) + (5x+1) + 41
= (4x6 - 4) + (5x6 + 1) + 41
= 20 + 31 + 41
= 92
Hence, the perimeter of each pool is 92 ft.
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Related Questions
Using the formula r=d/t, where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 227.5 miles in 3.5 hours?
A. 65 mph
B. 75 mph
C. 85 mph
D. 95 mph
Answers
The rate/speed at which one must travel to cover 227.5 miles in 3.5 hours is 65 miles per hours.
What rate must one travel to cover 227.5 miles in 3.5 hours?Speed or rate is simply referred to as distance traveled per unit time.
It is expressed as;
r = d / t
Where r is the speed/rate, d is the distance and t is time elapsed.
Given the data in the question;
Distance d = 227.5 milesElapsed time t = 3.5 hoursSpeed/rate = ?To determine the rate at which one must travel to cover 227.5 miles in 3.5 hours, plug the given values into the equation above and solve for r.
r = d / t
r = 227.5 miles / 3.5 hours
r = 65m/h
r = 65mph
Therefore, the speed/rate one must travel is 65mph.
Option A)65mph is the correct answer.
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Hypotenuse is 13.5 the angle is 41 degrees what’s the opposite
Answers
If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units
The length of the hypotenuse = 13.5 units
The angle = 41 degrees
Here we have to use the trigonometric function
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
In this question hypotenuse and angles are given and we have to find the opposite side.
sin θ= opposite side / Hypotenuse
Substitute the values in the equation
sin 41 = Opposite side / 13.5
Opposite side = sin 41×13.5
= 8.86 units
Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.
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keiko says that when n is any positive integer, 1n always equals 1 and (-1)n always equals -1. I keiko correct justify your answer
Answers
The most appropriate choice for exponent will be given by-
Keiko is not correct because the exponent [tex](-1)^n[/tex] does not always give -1
What is exponent?
Exponent denotes how many times a number is multiplied by itself.
For example in [tex]2^4[/tex] = [tex]2 \times 2 \times 2 \times 2[/tex], here 2 is multiplied 4 times.
Suppose [tex]a^m = a \times a \times a \times a[/tex][tex].....[/tex] (m times), here a is the base and m is the power.
Here,
The given exponents are[tex](1)^n[/tex] and [tex](-1)^n[/tex]
[tex](1)^n = 1 \times 1 \times 1\times.....\times 1[/tex] (n times)
= 1
For [tex](-1)^n[/tex]
If n is even, [tex](-1)^n[/tex] = 1
If n is odd , [tex](-1)^n[/tex] = -1
But Keiko told that [tex](-1)^n[/tex] always results in -1
So, Keiko is not correct.
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the volume of a cylinder closed at one end is 2136cm³.. if its height is 14cm, find its diameter
Answers
Diameter = 13.93771776 cm
y= x^2 -2x -3 find the values of x when y=1
Answers
Answer:
x = 1 +sqrt(5)
x = 1 -sqrt(5)
Step-by-step explanation:
y= x^2 -2x -3
Let y = 1
1= x^2 -2x -3
Subtract 1 from each side
1-1= x^2 -2x -3-1
0 = x^2 -2x -4
Using the quadratic formula
x = - (-2) ±sqrt( (-2) ^2 -4(1)(-4))
----------------------------------------
2(1)
x = 2 ±sqrt( 4 +16)
------------------------
2
x = 2 ±sqrt( 20)
------------------------
2
x = 2 ±sqrt( 4*5)
------------------------
2
x = 2 ±sqrt(5)
------------------------
2
x = 1 ±sqrt(5)
ignore the one i chose! But can someone tell me what it is? And explain how you got it? Please and thank u!!
49 points will b givin
Answers
Answer:
1/4^3
Step-by-step explanation:
Initially, there were only 4 weeds at a park. The weeds grew at a rate of 15% each week. The following function represents the weekly weed growth: f(x) = 4(1.15)x. Rewrite the function to show how quickly the weeds grow each day and calculate this rate as a percentage.
f(x) = 4(1.15)7x; spreads at a rate of approximately 1.5% daily
f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily
f(x) = 4(1.157)x; spreads at a rate of approximately 2.66% daily
f(x) = 4(1.02)x; spreads at a rate of approximately 0.2% daily
Answers
The function to show how quickly the weeds grow each day is "f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily. Option B
How can we figure out the rate of increase in percentage terms each day?f(x) = 4(1.15)x = 4(1+ 0.15)x ................... (1)
Given that there are seven days in a week, the daily growth rate of the weeds may be estimated using equation (1) by dividing 0.15 (which stands for the 15% weekly growth rate) in the following manner:
f(x) = 4(1.15)x = 4(1+ 0.15/7)x
f(x) = 4(1 + 0.02)x
f(x) = 4(1.02)x
Since 0.02 is the same as 2%, this implies that the rate at which the weeds grow each day is 2%.
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A tourist exchanged BD$2000 into US dollars at the rate of
BD$1 = US$0.50. The bank charged commission of 1.5%.
How many US$ did the tourist receive?
Answers
US$ the tourist received finally is US$985.
How to find the amount he received?BD$2000 is there.
BD$1 = US$0.50
Bank charged a commission of 1.5%.
Solution:
For one BD i.e., BD$1 he gets US$0.50.
It is half the value of BD$.
By cross multiplication technique, you can find this.
Then for,
BD$2000 he will get US$ 1000.
Bank charges = 1.5%.
That is,
1.5/100*1000 = $15
US$ the tourist received finally = 1000-15
= $985
US$ the tourist received finally is US$985.
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Solve this inequality for x. 81-1'1/5x<55
Answers
The solution for the inequality is x < 11/130.
The problem we dealing with is related to inequality which is referred to as An inequality in mathematics could be a relationship that produces a non-equal comparison between two integers or other numerical expressions.
Since we are provided with inequality which is 81 - 11/5x < 55
Now multiplying both by 5x we get
81 × 5x - (11/5x) × 5x < 55 × 5x
=> 405x - 11 < 275x
=> 405x - 275x < 11
=> 130x < 11
=> x < 11/130
so it is the solution for the inequality 81 - 11/5x < 55
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choose the inequality shown by this diagram
Answers
Answer: C
Step-by-step explanation:
Starting off we need to understand what the circles are in inequalities.
A closed circle means that the number on the inequality is included in the solution. An open circle means that the number in the inequality is not included in the solution. A closed circle would use [tex]\leq or \geq[/tex]. An open circle would use < or >.
So, using these processes, -2<x[tex]\leq[/tex]7 would be the answer.
please help with any of these questions
Answers
Applying the slope formula, we have:
16. Slope = -9/4; Parallel slope = -9/4; Perpendicular slope = 4/9.
17. Slope = -4; Parallel slope = -4; Perpendicular slope = 1/4.
See explanation below for the rest answers.
How to Find the Slope of a Line?Slope of a line = change in y / change in x.
The slope of parallel lines are the same, while the slopes of two lines that are perpendicular to each other are negative reciprocals of each other, i.e. 1/a and -a can be the slopes of two lines that are perpendicular to each other.
In an equation given in slope-intercept form, y = mx + b, the slope is represented as "m".
16. Given, (3, 7) and (7, -2):
Slope (m) = (-2 - 7)/(7 - 3)
Slope = -9/4
Parallel slope = -9/4
Perpendicular slope = 4/9.
17. Given, y = -4x + 2,
Slope = -4
Parallel slope = -4
Perpendicular slope = 1/4.
18. Rewrite 5x - 2y = 8 in slope-intercept form:
-2y = -5x + 8
y = 5/2x - 4
Slope = 5/2
Parallel slope = 5/2
Perpendicular slope = -2/5.
19. Rewrite 4x + 3y = 2 in slope-intercept form:
3y = -4x + 2
y = -4/3x + 2/3
Slope (m) = -4/3
Substitute (a, b) = (2, -5), and m = -4/3 into y - b = m(x - a):
y - (-5)) = -4/3(x - 2)
y + 5 = -4/3(x - 2) [point-slope form]
20. Given, y = -5x + 2
Slope (m) = -5
Substitute (a, b) = (-4, -6), and m = -5 into y - b = m(x - a):
y - (-6) = -5(x - (-4))
y + 6 = -5(x + 4) [point-slope form]
21. Rewrite 9x - 3y = 6 in slope-intercept form:
-3y = -9x + 6
y = 3x - 2
The slope of y = 3x - 2 (9x - 3y = 6) is 3.
The slope of -3x - 5 is -3.
Therefore, the lines are neither parallel nor perpendicular.
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like terms
-3(u+6)-4(u+5)
Answers
The simplified form of like terms in -3(u+6) -4(u+5) is 7u = -38.
What are like terms?Similar variables and powers are defined as like terms. It is not necessary for the coefficients to agree. When two or more terms do not share the same variables or powers, they are said to be unlike terms. Unless there is a power, the variables' order is irrelevant.
What is an equation?Two expressions joined by an equal sign form a mathematical statement known as an equation.
Given that,
Expression is -3(u+6) -4(u+5)
Simplifying the equation,
-3u-18-4u–20 = 0
-7u -38 = 0
-7u = 38
7u = -38
Therefore 7u = -38 is the simplifief form of like term in -3(u+6) -4(u+5).
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Find the equation of the line use exact numbers y=
Answers
I WILL TAKE THE POINTS (0,7) AND (2,1) FROM THW GRAPH AND USE THEM TO GET THE GRADIENT.
[tex]m \frac{y2 - y1}{x2 - x1} \\ = \frac{1 - 7}{2 - 0} \\ m = \frac{ - 6}{2} \\ m = - 3[/tex]
I WILL USE THE POINT (0,7) TO FIND THE VALUE OF C IN THE GENERAL EQUATION.
[tex]7 = - 3(0) + c \\ c = 7[/tex]
THE EQUATION IS
[tex]y = - 3x + 7[/tex]
ATTACHED IS THE SOLUTION
Jalen needs a total of $85 to buy a new play station controller. he already has $25. if he saves $13 a week, what is the least number of weeks he must work to have enough money to buy a controller? a. 3 c. 5 d. 6 2
Answers
Answer:
5
Step-by-step explanation:
he needs $85 and he has $25,
so it will be 85-25=60
that means he would need $60 more. if he saves $13 every week, it will 60÷13= 4.6 weeks or approximately 5.
If the supplement of an angle is 12 degrees less than twice the measure of the angle, what is the measure of the angle?
Answers
The angle whose supplement is 12 degrees less than twice its measure is 64 degrees.
What is the measures of the supplementary angle?supplementary angles are angles that add up 180 degrees.
Given the data in the question;
Let x represent the first angle.
Measure of first angle = xMeasure of second angle = 2x - 12Numerical measures of the angles = ?Since the angle are supplementary, sum of angles = 180°
First angle + second angle = 180
x + ( 2x - 12 ) = 180
Solve for x
x + 2x - 12 = 180
3x - 12 = 180
3x = 180 + 12
3x = 192
x = 192/3
x = 64
Therefore, the measure of the angle 64 degrees.
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Hello,May I please request help for number 13 in the uploaded picture? We are to do the following: Write the first four terms of each seequence.
Answers
To solve this question, find the 4 first terms of the sequence.
The first term is a₁
a₁ is given and a₁ = 7
The second term is a₂
Given:
[tex]a_n=a_{n-1}+5[/tex]Then, let's find a₂ using the value of a₁
[tex]\begin{gathered} a_2=a_1+5 \\ a_2=7+5 \\ a_2=12 \end{gathered}[/tex]The third term is a₃
let's find a₃ using the value of a₂
[tex]\begin{gathered} a_3=a_2+5 \\ a_3=12+5 \\ a_3=17 \end{gathered}[/tex]The fourth term is a₄
let's find a₄ using the value of a₃
[tex]\begin{gathered} a_4=a_3+5 \\ a_4=17+5 \\ a_4=22 \end{gathered}[/tex]Answer:
The four first terms are:
a₁ = 7
a₃ = 12
a₃ = 17
a₄ = 22
Which statement is true about figures ABCD and A′B′C′D′? (1 point) A polygon ABCD has A at ordered pair negative 4, negative 3, B at negative 3, negative 1, C at negative 2 and negative 3, D at negative 3 and negative 4. A polygon A prime B prime C prime D prime has A prime at ordered pair 3, 4, B prime at ordered pair 1, 3, C prime at ordered pair 3, 2, and D prime at ordered pair 4, 3. a A′B′C′D′ is obtained by translating ABCD 4 units up and then reflecting it about the y-axis. b A′B′C′D′ is obtained by translating ABCD 4 units right and then reflecting it about the x-axis. c A′B′C′D′ is obtained by rotating ABCD counterclockwise by 180 degrees about the origin and then reflecting it about the y-axis. d A′B′C′D′ is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then reflecting it about the x-axis.
Answers
d A′B′C′D′ is obtained by rotating ABCD counterclockwise by 90 degrees about the origin and then reflecting it about the x-axis.
please help! Due In 2 minutes!Which lines are parallel and why?
Answers
Because the angles on the first quadrant of the bottom horizontal line are equal, we conclude that the two parallel lines are FM and GB,
Which lines are parallel?
We know that two lines are parallel if when intersected by the same line, the two give the same angles.
In the image, we can see only one pair of equal angles, which are the two ones represented by a red quarter circle.
Both of these angles are on line MB, this means that the two parallel lines are the ones that intersect MB (in this case are the two vertical lines).
Then we can conclude that the two parallel lines are FM and GB.
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Please help me with my math
Answers
Answer:
I see a right angle, so the transversal is perpendicular to the parallel lines. Therefore, x and y are supplementary and congruent, and so we have x = 90 and
y = 90.
Mia needs to bring at least 25 pieces of fruit to the school picnic. she is bringing both apples and oranges, and was told to be sure to bring more than 10 apples select all inequalities that model this situation
Answers
Answer:
2.5
Step-by-step explanation:
if it is divison then the answer would be 2.5
if its additin is 35
if subtraction it is 15
if multipcation 250
does anyone know how to solve this
Answers
I WILL USE THE LAWS OF EXPONENTS WHEN WE MULTIPLY POWERS OF THW SAME BASES WE KEEP ONE POWER AND ADD THE EXPONENTS.
[tex] = 7^{ - 5} \times 7^{2} \\ = {7}^{ - 5 + 2} \\ = {7}^{ - 3} \\ = \frac{1}{ {7}^{3} } \\ = \frac{1}{343} [/tex]
ATTACHED IS THE SOLUTION
A 10-question multiple choice test has 4 possible answers for each question. A student selects at least 6 correct answers
PLEASE HELP ME FAST
Answers
0.020 is a probability for student selects at least 6 .
What is a probability simple definition?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.Three main categories of probability exist: Probability in theory. Scientific Probability. Probability axiomatically.There are two ways to do it. You can either interpret this as
One minus the probability that the student will guess 5 or fewer
correct answers with a probability of a correct answer being = 1/4 ⇒
0.0197277069
The probability that the student will guess 4 or fewer wrong answers
with a probability of a wrong answer being = 3/4
binomcdf (10,3/4,4)
= 0.0197277069
Either way it rounds to 0.020
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Solve the quadratic equation.
6^{2} = 5x + 6
I would appreciate help with this, thanks in advance!
≧◠‿●‿◠≦
Answers
[tex]6 {x}^{2} - 5x - 6 = 0 \\ 6 {x}^{2} - 9x + 4x - 6 = 0 \\ (6 {x}^{2} - 9x) + (4x - 6) = 0 \\ 3x(2x - 3) + 2(2x - 3) = 0 \\ (3x + 2)(2x - 3) = 0 \\ 3x + 2 = 0 \\ \\ \\ or \\ 2x - 3 = 0 \\ x = \frac{ - 2}{3} \\ \\ or \\ \\ x = \frac{3}{2} [/tex]
I FACTORISED THE EQUATION FIRST WITH A SIMPLE METHOD OF MULTIPLYING THE COEFFICIENT OF
[tex] {x}^{2} [/tex]
and the constant number then find the factors that will give me the coefficient of x.
ATTACHED IS THE SOLUTION
Step-by-step explanation:
are you sure this is the whole information ?
because
6² = 5x + 6
is not called a quadratic equation.
it is a quadratic equation, when there is one term in x² involved.
I assume therefore, that your problem is
6x² = 5x + 6
that is then as basic quadratic equation
6x² - 5x - 6 = 0
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 6
b = -5
c = -6
x = (5 ± sqrt((-5)² - 4×6×-6))/(2×6) =
= (5 ± sqrt(25 + 144))/12 = (5 ± sqrt(169))/12 =
= (5 ± 13)/12
x1 = (5 + 13)/12 = 18/12 = 3/2
x2 = (5 - 13)/12 = -8/12 = -2/3
so, the 2 solutions for the quadratic equation are
x = 3/2 and x = -2/3
divided -6.5*10^-7 by 9.88*10^-8. Express your answer in scientific notation. Round the coefficient to two decimal places.
Answers
Scientific notation of the given expression divided -6.5 × 10^-7 by
9.88 ×10^-8 with two decimal places is equal to 6.58 × 10^0.
As given in the question,
Divided -6.5 × 10^-7 by 9.88 ×10^-8 we have,
= ( -6.5 × 10^-7 ) /( 9.88 ×10^-8 )
= ( -6.5 / 9.88) × 10^(-7 +8)
= 0.65789 × 10^1
Express above quotient in scientific notation form with two decimal is equal to
= 6. 58 × 10^0
Therefore, scientific notation of the given expression divided -6.5 × 10^-7 by 9.88 ×10^-8 with two decimal places is equal to 6.58 × 10^0.
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- Solve the system of equations by graphing.
y = x² - 3
x + y = -1
Answers
Answer: y=x2+3x−1
Hope this helps! :)
please help me very easy !
Answers
The domain and the range pf the curve was solved and the correct answer to the question is the last option which is
Domain x ≤ 2Range y ≤ 6How to find the domain and the rangeThe domain are the input values and are represented in the x axis while the range are the output values and represented in the y axis
From the graph
The extents of the graph on the x direction shows that the maximum value the curve or the graph reached is 2. Hence x is takes value from 2 to a minimum of -6The extents of the graph on the y direction shows that the maximum value the curve reached is 6. Hence x is takes value from 6 and to a minimum of -8We can conclude that the last option is the correct answer
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is x=1 and y=-8 parallel, perpendicular, or neither
Answers
Answer:
perpendicular
Step-by-step explanation:
The equations represent a vertical and horizontal line, respectively, which are perpendicular to each other.
John earns 20 dollars per hour and earns 1/2 times pay for overtime. If he works 50 hours this week how much money does he make?
Answers
John would make 1100$
Bailey, kacie, and kaiden drive a total of 50 miles to work each day. kacie drives twice as far as bailey and kaiden drive 10 miles farther than kacie. how far does each person drive?
Answers
Let Bailey drive x miles.
So, Kacie drove 2x miles.
Kaiden drove 2x + 10 miles.
According to the question,
x + 2x + 2x + 10 = 50
x = 8
Therefore, Bailey drove 8 miles and Kacie drove 16 miles, while Kaiden 36 miles.
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Johnson buys a newspaper each day.the cost of the newspaper is $1 per day except sunday.on sunday it cost $3. how much johnson spend on newspapers in 52 weeks.
Answers
By using the Unitary method, $468 was spent on newspapers in 52 weeks.
Unitary method is a method used for finding the unit cost in which we divide the total cost by the total number of articles and to find the cost of more than one article, we multiply the unit cost by the number of articles required.
Cost of newspapers in a week from monday to saturday = $(1 x 6) = $6
Cost of newspaper only on sunday of a week = $3
Cost of newspapers in a week = $(6 + 3) = $9
Therefore, the cost of newspapers in 52 weeks = $(52 x 9) = $468.
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