A fence was installed around the edge of a rectangular garden. The length, 1, of the fence was
5 feet less than 3 times its width, w. The amount of fencing used was 90 feet.
Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Answers
The dimensions of the garden are a width of 44 feet and a length of 127 feet.
To model this situation, we can set up a system of equations based on the given information.
Let's denote the width of the rectangular garden as w and the length of the fence as 1. The length of the fence is 5 feet less than 3 times its width, so we can write the equation:
1 = 3w - 5
The amount of fencing used is 90 feet, so the perimeter of the rectangle (which is equal to the amount of fencing used) can be expressed as:
2w + 2(1) = 90
Simplifying the second equation, we have:
2w + 2 = 90
Now, we can solve this system of equations algebraically to determine the dimensions of the garden.
First, we'll solve the second equation for w:
2w + 2 = 90
2w = 90 - 2
2w = 88
w = 44
Now, we can substitute the value of w into the first equation to find the length:
1 = 3w - 5
1 = 3(44) - 5
1 = 132 - 5
1 = 127
The garden's width and length are therefore 127 feet and 44 feet, respectively.
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Related Questions
After increasing steadily for centuries, the total annual catch of all wild fish peaked in 1989; since that time, the total catch for most species has declined or plateaued, prompting conservation efforts designed to help prevent population crashes and possible extinctions.
(A) fish peaked in 1989; since that time, the total catch for most species has declined or plateaued, prompting
(B) fish peaked in 1989, but with the total catch since then declining or plateauing in the case of most species, prompting
(C) fish had peaked in 1989; since that time, the decline or plateau of the total catch for most species, which prompted
(D) fish, which peaked in 1989, and, in the case of most species, it has declined or plateaued since, prompted
(E) fish, which peaked in 1989 but has since declined or plateaued for most species, and this prompted
Answers
B) fish peaked in 1989, but with the total catch since then declining or plateauing in the case of most species, prompting conservation efforts designed to help prevent population crashes and possible extinctions.
(B) fish peaked in 1989, but with the total catch since then declining or plateauing in the case of most species, prompting
Plateauing refers to the phenomenon where an individual's progress or improvement in a particular area, such as learning a new skill or achieving a fitness goal, slows down or even stops altogether. This can be frustrating for the individual, who may feel like they have hit a "plateau" and are not making any further progress despite continued effort. Plateauing can occur for a variety of reasons, such as overtraining, lack of variation in training or practice, inadequate rest and recovery, or reaching a natural limit in performance.
Overcoming plateaus often requires making changes to training or practice routines, such as introducing new exercises or techniques, increasing intensity or frequency of training, or taking adequate rest and recovery time.
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how long is a meter
you can not use google
Answers
1 km=1000 m
1 m=100 cm
please mark as brainliest
The FM radio station KAMB broadcast from an antennae atop a 150 meter tall radio tower at a frequency of 90 MHz with a total radiated power of 40 kilowatts. Neighbors have complained about problems they attribute to excessive radiation from the tower, but the city engineer who measured the radiation level near the base of the tower found it to be well below the accepted standard. You have been hired by the HOA to assess the engineer's report. You know a few things about electromagnetic radiation and therefore conclude that we must find the optimum place on the ground to measure the maximum radiation emitted from the antennae. From your extensive knowledge in physics, you know that the intensity of radiation, I, is given by the formula:
I=12/32π*Psin2(θ)/r^2
where P is the power output, r is the distance from the top of the tower to the point on the ground, and θ is the angle measured from the tower to r.
Find the distance R from the base of the tower to the optimum location for taking the radiation reading. (m)
What is the maximum radiation reading from the ground in kw/m^2
If the city code requires that electromagnetic radiation be under 200 microwatts per square meter, is this antenna operating within city code? Yes or No
Answers
Answer: 150 m, 5.305*10^-5 kW/m^2, No
Step-by-step explanation:
See attachment, hope this helps
Using the radiation intensity formula we will have to:
a) \(150 m\)
b) \(5.305*10^{-5} kW/m^2\)
c)No
From the data informed, we have:
\(h=150m\\P=40KW\)
Using the given formula and performing some mathematical operations:
\(I=\frac{12Psin^2(\theta)}{32(\pi)r^2} \\I= \frac{12(40)(R/r)^2}{32(\pi)r^2} \\= \frac{15R^2}{r^2\pi } \\= \frac{15R^2}{(R^2+150^2)^2\pi} \\\)
deriving the given equation, we will have:
\(=\frac{(R^2+150^2)^22R-R^2(2(R^2+150^2))2R}{(R^2+150^2)^2}\)
So from this equation we have that the answer of the letter A corresponds:
\(R=150\)
For letter B we will have to develop this equation:
\(I= 5.30X10^{-5}\)
As for the letter C, when converting the value found, it should give 200 microwatts, which is false.
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identify the open intervals on which the function is increasing or decreasing. (select all that apply.) f(x) = sin x -1, 0 < x < 2 π
Increasing:
A. (π/2, 3π/2)
B. (0, π/2)
C. (3π/2, 2π)
D. (0, [infinity])
E. (-[infinity],0)
Answers
The intervals on which function f(x) = sin x -1 increasing or decreasing is (0, π/2) (B).
The given function is f(x) = sin x -1, 0 < x < 2 π.
A sinusoidal function is a function that can be written in the form f(x) = a sin(bx + c) + d or f(x) = a cos(bx + c) + d, where a, b, c, and d are constants.
The graph of the given function is a sine curve shifted downward by 1 unit.
The function is increasing on the interval (0, π/2) because the slope of the curve is positive on this interval.
The function is decreasing on the interval (π/2, 3π/2) because the slope of the curve is negative on this interval.
The function is increasing again on the interval (3π/2, 2π) because the slope of the curve is positive on this interval.
Therefore, the correct answer is option B. (0, π/2).
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(2.4 x 10') + (4.87 x 10)
Answers
Answer:
2.4*10+4.87*10
24+103
127
Step-by-step explanation:
What is the equation of the yellow line
Answers
Answer:
y = -\(\frac{5}{3}\) x -2
Step-by-step explanation:
The line is going down to the right so it has the negative slope, with a y- intercept of (0, -2) and a slope of m = rise/run = -5/3
Suppose that tuition at a state college was $3,500 per year in 1995 and has been increasing at a rate of $225 per year. Write an equation to model the cost of tuition as a function of time. Use that equation to predict the cost of tuition in the year 2007.
Answers
Answer:
$7384.94Step-by-step explanation:
step one:
let us calculate the percentage increase
(225/2)*100
=0.06428*100
=6.42%
We know that the expression for exponential formula is
\(y = ab^x.\)
where
a = the amount before measuring growth or decay
= $3500
r = decay rate = 6.42%= 0.0642
x = number of time intervals that have passed that is between 1995 and 2007= 12years
since this problem is on groth we are going to replace "b" with (1+r),
hence the formula to model the cost is
\(y = a(1+r)^x.\)
\(y=3500(1+0.0642)^1^2 \\\\y=3500(1.0642)^1^2 \\\\y=3500*2.109983 \\\\y=7384.94\)
The cost of tuition in the year 2007 (12 years later) would be
$7384.94
The top and bottom lines are parallel. what is the value of X?
Answers
Answer:
B, the answer is B or C believe me
Step-by-step explanation:
Explanation:
(alternate interior angle)
75+45+x=180
120+x=180
x=60
Angie's class took a field trip to the art museum. They left school at 10:25 A.M. It took them 1 hour and 15 minutes to drive to the museum. They stayed at the museum for 1 hour and 55 minutes. What time was it when Angie's class left the museum?
Answers
according to my answer this is wrond because you are wrong
Step-by-step explanation:
palhschal pagal
I don’t know how to write it down on a piece of paper
Answers
Jaime wrote 4.4-0.33=1.1 .Is his answer reasonable why or why not?
Answers
Answer: No it would be 4.07
=1.1
Step-by-step explanation: Subtract 0.33 from 4.4
Find the mean of the following set: 30, 16, 29, 14, 21
Answers
Answer:
the mean is 18.2, median is 16, and there is no mode
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
mean is the average of the number.you have to add up all the number then divide it by how many numbers there are.
your question is :30,16,29,14,21 (5 number)
(30+16+29+14+21) / 5 = 22
Which expression equals 24? Responses A (4 x 2) + 3(4 x 2) + 3 B (4 + 3) - 2(4 + 3) - 2 C (4 x 2)(3)(4 x 2)(3) D (2 + 4)(3)(2 + 4)(3) E (4 - 2) + 3
Answers
The expression that equals 24 is (4 x 2)(3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
(The options are given twice, consider once)
Consider option C.
(4 x 2)(3)
=8 (3)
=8 x 3
=24
So, the expression that equals 24 is (4 x 2)(3).
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The angle of a triangle is 44°, 44°, and x°. What is the value of x°?
Answers
56+(−56)=
−240+370=
−5.7+(−4.2)=
Answers
Answer:
Step-by-step explanation:
1st one is 0
2nd is 130
3rd is 9.9
How many five-digit numbers are there that contain the digit 1 (at least) three times in a row?
Answers
Answer:
So you say you want some 5 digit numbers eh? Let’s consider some boundaries. 5 digit numbers range from 10,000 - 99,999. So our number is guaranteed to be between 0 and 90000.
Sometimes it’s much easier to work with concrete things. Such as the number of numbers that don’t contain any 3s. It’s really more difficult to put our finger on “at least 1” anything so we try to steer clear of it.
Anyways we’ve got 90000 numbers that have at least 1 or 0 3’s. Find one and we know the other.
So no 3’s at all right? Well you have 8 choices for the first digit (can’t choose 0 and you can’t choose 3). And then for the remaining 4 digits you have 9 choices. So that’s
8∗94=52488
Back to our initial equation, we have
90000−8∗94=37512 5 digits numbers without any 3s.
A quick (or maybe not so quick) matlab script confirms such calculations.
credits to : Trevor Squires
it is not possible to use a relational operator and math operators in the same expression.
Answers
It is possible to use a relational operator and math operators in the same expression.
In programming, you can use relational operators (e.g., <, >, ==, !=) and math operators (e.g., +, -, *, /) together in the same expression. This is often used in conditional statements or loops to compare calculated values.
For example, consider the following expression:
`if (2 * 3) > (4 + 1)`
In this expression, we have math operators (*) and (+) and a relational operator (>). The math operations are evaluated first, resulting in:
`if (6) > (5)`
Then, the relational operator (>) is evaluated, and the expression becomes:
`if True`
The expression is true because 6 is greater than 5.
It is possible to use both relational operators and math operators in the same expression, which can be useful in various programming situations such as conditional statements or loops.
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When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial? mc030-1. Jpg.
Answers
The expression that can be added to both sides of the given quadratic equation to change it to a perfect square trinomial is \(\frac{b^2}{4a^2}\) .
The standard form of perfect square trinomial is given as:
\(ax^2 + bx + c\)
here,
a = coefficient of x² .
b = coefficient of x.
c = constant .
Given the quadratic equation:
\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)
The above equation is needed to be changed to a perfect square trinomial.
To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.
Therefore, the term to be that is needed to be added to the given quadratic equation is \(\frac{b^2}{4a^2}\) .
Now, the quadratic equation can be written as:
\(x^{2} + \frac{b}{a} x + \frac{ b^{2}}{4a^{2}} = \frac{-c}{a} + \frac{ b^{2}}{4a^{2}}\)
Therefore, \(\dfrac{b^2}{4a^2}\) should be added to both sides to convert it into the perfect polynomial.
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The given question is incomplete. Probably the complete question is:
When deriving the quadratic formula by completing the square what expression can be added to both sides of the given equation to create a perfect square trinomial?
\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)
How are fractions and ratios the same? How are they different?
Answers
Answer:
Step-by-step explanation:
Ratios depend on the numbers that are being compared. When you are describing a part of a whole, a fraction is appropriate. When you are comparing two numbers, a ratio is appropriate.
Basically you can write ratio as fraction
Ex-4:2, 4/2
See what I mean?
please help me with this question
Answers
Answer:
About -6
Step-by-step explanation:
What figure below has exactly 2 lines of symmetry?
Answers
Answer:
C.
Step-by-step explanation:
A has 8 lines of symmetry, because they're all the same.
B has 4 lines of symmtery because those are all the same
C has only 2 because the vertical lines are symmetrical to each other, but not to the horizontal lines
D has 10 symmetrical lines because they're all the same
Need help !!!!!!!!!!!!!
Answers
Answer:
tan0= UR/RX
tan6°=8/RX
⇒RX=8/tan6
⇒ RX=8/0.1051
⇒RX≈76.11
---------------------
Hope it helps...
tan0= UR/RX
tan6°=8/RX
RX=8/tan6RX=8/0.1051RX≈76.11Hope it is helpful to you ☺️
Review Find the slope and y-intercept of the line. - 6x + y = 14.
Answers
Answer:
Step-by-step explanation:
1. Combine Terms.
Add 6x to both sides. This should cancel out the -6x on the left. And add 6x to the right.
This should give you
\(y = 6x + 14\)
2. Your y-intercept would be the constant (the number that stands alone ) and your slope would be the coefficient (the number beside the x).
Final Answer :
slope = \(\frac{6}{1}\) or simply \(6\)
y-intercept = \(14\)
A 20-foot ladder leans up against the side of a building so that the foot of the ladder is 10 feet from the base of the building. How far up the
building does the ladder reach? Round your answer to the nearest tenth.
18.1
17.3
15.9
16.4
Answers
Answer:
17.3
Step-by-step explanation:
To solve this equation, you need to use the pythagorean theorem which is:
\(a^{2} +b^{2}= c^{2}\)
a= length
b= height
c= hypotenuse
First, substitute in your values for the equation:
\(10^2+b^{2} =20^{2}\)
Then, use the squares in the equation:
\(100+b^{2} =400\)
Then, subtract 100 from both sides to isolate b:
\(b^{2} =300\)
Finally, square root both sides to get your answer:
\(b=17.3205080757\)
Then round to the nearest tenth which gives you 17.3.
Answer: 17.3 ft
Step-by-step explanation:
(b) if we simulate more rolls of the die, do you expect to get the same sequence of outcomes? why or why not?
Answers
No, because the numbers are arbitrary values between 1 and 6 and thus every roll has six (equally) possible outcomes.
What is probability in rolling a die?
A sample space is simply the collection of all potential outcomes. Simply put, you have to consider every scenario that could possibly occur. When you roll the dice, every conceivable throw will be your sample space. The likelihood of getting any side of the dice is 1/6 because there are six possible results. Rolling a 1 has a 1/6 chance of happening, a 2 has a 1/6 chance, and so on.
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pls help Find the missing angle
Answers
Answer:
Step-by-step explanation:
Using trigonometry:
Sin(x)=8/11
x=sin^-1(8/11)
x= 46.6582417727776
x= 46.65 to decimal places
x= 46.7 to 1 decimal place
x= 47 to 2 s.f.
8x-12=-8x-12
What is the answer to this equation
Answers
Answer:
Any value for x will always be true
Step-by-step explanation:
Step 1: Add 8x to both sides
Step 2: Add 12 to both sides.
Step 3: Divide both sides by 16.
x=0 (Any value)
Add 8x to both sides:
16x-12=-12
Add 12 to both sides:
16x=0
Divide both sides 16:
x=0/16
x=0
The transformation from the function f (x)=3x to the function f(x)=3x+4 indicates
Answers
Answer:
Moving 4 to the right on the x axis
Step-by-step explanation:
There are 40 boys in 6th grade. The number of girls in 6th grade is 30. Carly says that means the ratio of the number of boys in 6th grade to the number of girls in 6th grade is 4:7. Is this statement true or false?
Answers
Answer:
False
Hope this helps and mark 5 stars and brainlliest please.
Step-by-step explanation:
Answer: false
Step-by-step explanation:
It’s 4:3 and not 4:7 because the 7 was never mentioned in the problem
Linda throws a dart that hits the square shown below: What is the probability that the dart hits a point in the circle?
18%
21.5%
78.5%
81%
Answers
Answer:
78.5
Step-by-step explanation: