In linear equation, 3464.1016 feet is the shortest length of fence that the Ranch owner can use.
What is linear equation definition and example?
An equation in which there is only one variable is known as a linear equation in one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.Let L represent the length of the field.
Let W represent the width of the field.
Let F represent the length of fence needed.
L*W=500000
2L+3W=F Both length sides+both width sides+ fence across the width.
Let's look at the first equation again:
L*W=500000
W=(500000/L)
Now we can substitute (500000/L) for W in the second equation.
2L+3(500000/L)=F
2L+1500000/L=F
Now we have a function. We can input any length, and we'll know length needed. But how can we find the length needed so that F is as small as it can be? If you know derivatives, there's an exact way. The next easiest way to do it is to graph.
Manner 1: Derivative
Set the derivative to zero...when the length stops going down and starts coming back up, it'll be at it's lowest point.
2L+1500000^-1=F
F'=2-1500000^-2
0=2-1500000^-2
1500000/(L^2)=2
1500000=2L^2
1500000=L^2
L=866.025
Now, we know that L=500000/W
so 866.025=500000/W
W=500000/866.025
W=577.35027 feet.
Now,
2L+3W=2(866.025)+3(577.35027)
Minimum fencing needed: 3464.1016 feet.
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What’s the slope of this line?
X
6
9
15
21
у
-5
-7
-11
-15
Slope is [tex]\frac{-2}{3}[/tex] of coordinates (6,5) and (9,-7).
What is slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; however, there is no obvious reason for this. The slope of a curve at a point in differential calculus is defined as the slope of the tangent line at that point as a generalization of this practical definition. The slope can be determined between any two locations when the curve is represented by a series of points in a diagram or list of point coordinates. Maybe when the curve is represented as a continuous function.
Given Data
coordinates - (6,-5) and (9,-7)
slope of the line denoted as m
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{-7-(-5)}{9-6}[/tex]
m = [tex]\frac{-2}{3}[/tex]
Slope is [tex]\frac{-2}{3}[/tex]
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Annalise buys a pair of sunglasses for 30% off and saves $15. What is the original price of the pair of sunglasses?
*
Answer:
$50
Step-by-step explanation:
We will call x the original price of the sunglasses.
We can create the equation below using the information given.
[tex]x*\frac{30}{100} =15[/tex]
Now solve for x.
[tex]x = 15*\frac{100}{30}[/tex]
[tex]x = \frac{100}{2}[/tex]
[tex]x=50[/tex]
Omar buys eggs and lemons at the store.
He pays a total of $26.10.
He pays a total of $6.30 for the eggs.
• He buys 6 bags of lemons that each cost the same amount.
How much does each bag of lemons cost?
Answer:
Each bag of lemons cost $3.30
Step-by-step explanation:
The equation will be
6x = 26.10 - 6.306x=26.10−6.30
Solve for x to get,
6x = 19.86x=19.8
x = 3.3x=3.3
Answer:
$3.30 for each bag of lemons
Step-by-step explanation:
We know that Omar only bought both lemons and eggs. We also know that the total amount of money he spent on groceries is $26.30 and that the eggs are worth $6.30 out of the total.
So, if we can subtract the cost of the eggs from his total cost of groceries to find how much the lemons cost. After that we can divide the cost of all the lemons, which is $19.80, by the number of bags, which is 6, to find how much each bag costs.
(26.10 - 6.30) / 6 = ?
19.8/6 = 3.30
Can you solve this please.
The simplified expression of (x¹² ÷ x⁴). x³ is x¹¹
How to solve expression?The expression can be solved as follows:
(x¹² ÷ x⁴). x³
The law of indices can be used to solve the expression.
Therefore,
[tex]\frac{x^{a} }{x^{b} } = x^{a - b}[/tex] and [tex](x^{a} )^{b} = x^{ab}[/tex] and [tex]x^{a} .x^{b} = x^{a+b}[/tex]
Hence,
(x¹² ÷ x⁴) = x¹² / x⁴ = x¹²⁻⁴ = x⁸
Therefore,
(x⁸). x³ = x⁸⁺³
Finally,
x⁸⁺³ = x¹¹
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How would I answer and what would be the answer?
Given the exression:
[tex]\frac{x-1}{x+4}-\frac{4x-11}{x+4}[/tex]Let's solve the expression and identify the error.
Since both expressions have the same denominator, let's combine the numerators:
[tex]\frac{(x-1)-(4x-11)}{x+4}[/tex]Apply distributive property:
[tex]\begin{gathered} \frac{x-1-4x-(-11)}{x+4} \\ \\ \frac{x-1-4x+11}{x+4} \end{gathered}[/tex]Combine like terms in the numerator:
[tex]\begin{gathered} \frac{x-4x-1+11}{x+4} \\ \\ \frac{-3x+10}{x+4} \end{gathered}[/tex]The error in the problem was that distributive property was not applied when the numerators were combined.
ANSWER:
[tex]\frac{-3x+10}{x+4}[/tex]Pedro has scores of 81, 80, 82, 88 after four tests. What score must he make on his fifth test to have an average of 76 or greater?
Answer:
he must make sure he gets up to 49 and higher to obtain an average of 76 or greater
Step-by-step explanation:
logically from 49 - 100 :)
Simplify the expression:
a^-2
1/[tex]a^{2}[/tex] is the answer.
How to simplify the expression?Given,
a^-2
Solution:
a^-2
Expand it
a^-2 = 1/a^2
= 1/[tex]a^{2}[/tex]
Therefore,
a^-2 = 1/[tex]a^{2}[/tex]
1/[tex]a^{2}[/tex] is the answer.
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the expression 2x squared minus -x squared is equivalent to
2x² - x²
Factor:
x²(2 - 1)
x²(1)
x²
--------------------------------------------
(3x² + x + 8) + (x² - 9)
Add like terms:
(3x² + x²) + x +(8 - 9)
4x² + x - 1
-----------------------------------------------
-3x² - 7x + 9 - 5x² + 6x - 4
Add like terms:
(-3x² - 5x²) + (-7x + 6x) + (9 - 4)
-8x² - x + 5
Mark operates a small sign-making business. He finds that if he charges x dollars for each sign, he sells 37−x signs per week. What is the smallest number of signs that he can sell to have an income of $300 in one week?
The smallest number of signs that he can sell to have an income of $300 in one week is 12.
The price of one sign is x
Number of signs he sells per week = 37-x
The total earning from selling these is x(37-x) which is given as $300
(37- x) x = 300
37x - x² = 300
x² - 37x + 300 = 0
As per formula to find base in a quadratic equation
[tex]x =\frac{37 - \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 - \sqrt{1369-1200 } }{2} \\x =\frac{37 - \sqrt{169 } }{2} \\x = \frac{37-13}{2}\\ x = \frac{24}{2}\\ x = 12[/tex]
The other base can be
[tex]x =\frac{37 + \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 + \sqrt{1369-1200 } }{2} \\x =\frac{37 + \sqrt{169 } }{2} \\x = \frac{37+13}{2}\\ x = \frac{50}{2}\\ x = 25[/tex]
Therefore the smallest number of signs that he can sell to have an income of $300 in one week is 12.
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Which of the following is LEAST associated with human capital?
a)medical treatment that reduces time off of work due to illness or injury.
b)maintenance of fully automated production facilities
c)a college course in accounting
d)an on-the-job training course in the latest production methods.
Answer:
Hope it helps you
Step-by-step explanation:
(a) medical treatment that reduces time off of work due to illness or injury.
Round to the place value of the underlined digit 698, 07 to the underline number is six
The place value of the underlined digit (6) is tens of thousands and should be rounded to 70,000.
What is a place value?A place value simply refers to a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousandsIn this scenario, the place value of the underlined digit (6) is tens of thousands and 9 is the next digit to six (6). Therefore, we would add one (1) to the underlined digit (6) and then change all of the other digits to zero (0) as follows:
69,807 = 70,000
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a final exam in math 160 has a mean of 73 with standard deviation 7.2. if 22 students are randomly selected, find the probability that the sample mean of their test scores is less than 75
The probability is that the mean of their test scores is less than 70.
What is probability?
A probability is a number that reflects tha chance of particular event will occur.
Sol-
As per the question given-
Mean = 73
Standard daviation=7.2
Number of students randomly selected =22
Let's take n number for experiment of outcomes.
The number of favorable outcomes can be denoted by x.
The formula to calculate the probability is -
probability = favorable
Outcomes/total outcomes =x/n
The number of standard daviation form the mean is called z.
Z = (x-¥)/€
Z=(75-73)(7.2/√22)
Z= -37.0582965
P(z<-37.05)
= 37.05
There for the probability is 37.05.
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The width of a rectangle is 15 cm less than the length. The perimeter is
8 cm. Find the rectangle's dimensions.
If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm
The width of a rectangle is 15 cm less than the length
Consider the length of the rectangle as x
The the width of the rectangle = x-15
The perimeter of the rectangle = 150 cm
The perimeter of the rectangle = 2(l+w)
Where l is the length and w is the width
Substitute the values in the equation
2(x+(x-15))=150
2(2x-15)=150
4x-30 = 150
4x = 180
x = 45 cm
The width of the rectangle = x-15
= 45-15
= 30 cm
Hence, If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm
The complete question is
The width of a rectangle is 15 cm less than the length. The perimeter is
150 cm. Find the rectangle's dimensions.
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Daniel and his three friends are sharing the cost of a pizza. The pizza costs $13.00. If Daniel has
$5.00, how much will he have left after he pays his share?
Answer: 1.75
Step-by-step explanation:
13/4 = 3.25
5.00-3.25
1.75
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was 6.5% and the tax in the second city was 6% The total hotel tax paid for the two cities was $748.75. How much was the hotel charge in each city before tax?
Based on the taxes in the first city and the tax in the second city as well as the total hotel tax paid in the two cities, the hotel charge for each city before taxes was:
First city - $5,750Second city - $6,250How to find the hotel charge?The hotel charge before taxes was $500 higher in the second city than in the first. Assuming the charge in the first city was x, the charge in the second city was:
= x + 500
The total charge in the first city would be:
0.065x + 0.06(x + 500) = 748.75
0.065x + 0.06x + 30 = 748.75
0.125x + 30 = 748.75
0.125x = 748.75 - 30
0.125x = 718.75
x = 718.75/0.125
x = $5,750
The total charge in the second city would be:
= 5,750 + 500
= $6,250
In conclusion, the charges in the first and second cities are $5,750 in the first city and $6,250 in the second city.
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Y=x when x increases by 5 what does y increase by
If 343 is the third proportional of A and B, where a:b= 1:7 then the value of a+b will be
HELP I GIVE BRAINLIEST!!!!!
Drop Down 1
(2 in)(10 ft/1 in) = 20 ft
Drop Down 2
This means the scale factor is 1:2, and thus the new length will be 3 inches.
Can somebody help me with question number 4?
nswer:
[tex]\begin{gathered} x\text{ = -4} \\ y\text{ = 3} \end{gathered}[/tex]Explanation:
ere, we want to solve the syastem of linear equations simultaneously by elimination
We have this as:
[tex]\begin{gathered} -4x+\text{ 3y = 25} \\ 6x-5y\text{ = -39} \end{gathered}[/tex]We start by multiplying the first equation by 6 and the second by 4. We have this as:
[tex]\begin{gathered} -24x\text{ + 18y = 150} \\ 24x-20y\text{ = -156} \end{gathered}[/tex]Add both equations as follows:
[tex]\begin{gathered} -2y\text{ = -6} \\ y\text{ = }\frac{-6}{-2}\text{ = 3} \end{gathered}[/tex]To get x, we multiply the first equation by 5 and the second by 3
We have this as:
[tex]\begin{gathered} -20x\text{ + 15y = 125} \\ 18x-15y=-117 \end{gathered}[/tex]We proceed to add both equations:
[tex]\begin{gathered} -2x\text{ =8} \\ x\text{ = }\frac{8}{-2} \\ x\text{ = -4} \end{gathered}[/tex]if a population has a mean of 30, if 3 points are added to each score how do you calculate the mean for the new distribution
When the population has a mean of 30, if 3 points are added to each score, the mean for the new distribution is 33.
How to illustrate the information?It should be noted that mean simply means the average of a given set of numbers that are given. The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.
In this case, the population has a mean of 30 a and 3 points are added to each score.
In this case, the new mean will be the addition of the numbers. This will be illustrated as:
= 30 + 3
= 33
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Hello, help me please)
olution:
iven;
[tex]\log_52x=3[/tex][tex]\log_52x=3[/tex]Applyin the power property of logarithm given as;
[tex]\log_ba=c\Leftrightarrow a=b^c[/tex]Thus;
[tex]\operatorname{\log}_52x=3\Leftrightarrow2x=5^3[/tex]Simplify further, we have;
[tex]\begin{gathered} 2x=5\times5\operatorname{\times}5 \\ \\ 2x=125 \end{gathered}[/tex]ivide both sides by 2;
[tex]\begin{gathered} \frac{2x}{2}=\frac{125}{2} \\ \\ x=\frac{125}{2} \end{gathered}[/tex]NSWER:
[tex]x=\frac{125}{2}[/tex]pleaseee helpp meeee
Given:
The given expression is,
[tex]25^x[/tex]Required:
To select the equivalent expression.
Explanation:
Mr. Salcedo was driving at a constant speed. He drove 120 3/4 miles in 3 hours. At that speed, how
many miles will he drive in 7 1/2 hour? How many miles will he drive in one hour?
He will cover 301.875 miles in 7.5 hours at a unit speed of 40.25 miles per hour.
What is unit rate?A ratio that compares two amounts of different types of units is called a rate. When a unit rate is expressed as a fraction, the denominator is 1 unit.
Rate = Distance/Time
If Mr.Salcedo was driving at 120 3/4 miles in 3 hours, his unit rate will be calculated as:
Unit rate =[120 3/4]/3
Unit rate = 483/12
Unit rate = 40 1/4 miles/hr
This shows that he drove 40 1/4 miles/hr.
The miles he drove in 7 1/2 hour is expressed as;
Miles driven = 161/4 * 15/2
Miles driven = 301.875 miles
Hence the miles that he will drive in 7.5 hours is 301.875miles and the unit rate is 40.25 miles/hr
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3/4+6 and 2/4÷1 and 3/5
The answer is a) 27/6 b) 1/2 c) 0.6 = 6/10 = 3/5 and their sum is 5.6
What are the various mathematic operations?The four basic arithmetic operations in Maths, for all real numbers, are:
→ Addition (Finding the Sum; ‘+’)
→ Subtraction (Finding the difference; ‘-’)
→ Multiplication (Finding the product; ‘×’ )
→ Division (Finding the quotient; ‘÷’)
In this given question ;
a) [tex]\frac{3}{4}[/tex] + 6
first take LCM so we will get : [tex]\frac{3+24}{6}[/tex] = [tex]\frac{27}{6}[/tex]
b) [tex]\frac{2}{4}[/tex]÷ 1
this implies [tex]\frac{1}{2}[/tex] ÷ 1 = [tex]\frac{1}{2}[/tex]× 1 = [tex]\frac{1}{2}[/tex]
c) [tex]\frac{3}{5}[/tex] = 0.6
If we were to solve a + b + c we get : 27/6 = 4.5
b= 1/2 = 0.5
so 4.5+ 0.5 + 0.6 = 5.6
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(x + a)(x + 2)(3x + 1) = bx³ + cx² + dx - 10
Find the values of a, b, c and d.
HELPPPPP
How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?
Answer:
Polynomials with a negative constant term are not perfect squares, hence polynomial 4, with constant term of -121, is not a perfect square.
What are perfect square expressions?
Perfect square expressions are formed in two ways, either with the square of the sum or the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².
Square of the subtraction: (a - b)² = a² - 2ab + b².
The constant term is the final term. Since this term is squared, it will always be positive for perfect squares, hence if the constant term is negative, it will guarantee that the polynomial is not a perfect square.
For the expressions in this problem, we have that:
The expression with a constant term of 36 can be a perfect square, as 36 is a positive number.
The expression with a constant term of -121 cannot be a perfect square, as -121 is a negative number.
Hope this helps :)
Step-by-step explanation:
Which number is equivalent to 3^(4)÷3^(2)
the answer is definitely 9
Jessica makes $24,000 a year, butreceives weekly paychecks. If 12% ofher check is withheld for federaltaxes, what is her required weeklydeduction, including FICA?
The weekly deduction, including FICA is a $60
Define percentage.
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Given,
Jessica makes in a year = $24000
She receives weekly pay checks is = 12%
We know, in 1 month there are 4 weeks and for 12 months there are 48 weeks.
so, Jessica makes per week = $24000 / 48
= $500
And, we know Jessica receives 12% paychecks then,
find, 12% of weekly payment
⇒12% of 500
⇒ (12 * 500) / 100
⇒$60
Hence, The weekly deduction, including FICA is a $60
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To find the solution to |3x + 2|= 4, which two equations must you solve?
Answer:
YOU MUST SOLVE ---> |3x + 2|
Step-by-step explanation:
|3x + 2| = 4
-2 -2
3x = 4
x = 0.75
HOPE this HELPED
for each of the points identify the axis or constant where the point is located 8.7 and 2.3 
The given points are located in the 1st quadrant.
How to determine which quadrant?Refer to the attachment.
Since the two points x or abscissa = 8.7 and ordinate or y axis = 2.3 and both the numbers are positive thus they belong to the First quadrant.
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