Select all the correct answers. A farmer wants to build two fenced-off sections within his field, one in the shape of a rectangle and the other in the shape of a square. The side of the square must be equal to the width of the rectangle, x feet. The length of the rectangle must be 50 feet longer than its width. The field the farmer wants to build the two fenced sections in has an area of y square feet. The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet. In addition, the sum of the fenced areas must be less than the area of the field. This is the system of inequalities that represents this situation. Which points represent viable solutions?
Answers
(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that the side of the square must be equal to the width of the rectangle, x feet.
The length of the rectangle must be 50 feet longer than its width
The field the farmer wants to build the two fenced sections in has an area of y square feet.
The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet
the sum of the fenced areas must be less than the area of the field.
y≥x²+1000
y>2x²+50x
(20, 2,200) and (5, 3,000) are the viable solutions
Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
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Related Questions
d^2a/db^2 +a = 4b+10sin(b)
Answers
The given equation is a second order differential equation
What is a differential equation?In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
Isaac Newton listed three kinds of differential equations given -
[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]
Given is a differential equation as follows -
d²a/db² + a = 4b + 10sin(b)
The given equation is -
d²a/db² + a = 4b + 10sin(b)
Let y = a and x = b, then we can write -
d²y/dx² + y = 4x + 10sin(x)
A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -
d²y/dx² + P(x) dy/dx + Q(x) y = f(x)
For the equation given -
d²y/dx² + y = 4x + 10sin(x)
On comparing, we get -
P(x) = 0
Q(x) = 1
f(x) = {4x + 10sin(x)}
Therefore, the given equation is a second order differential equation.
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The quotient of x and 4 is at least 26
Answers
The given statement in the form of inequality is given as -
(x ÷ 4) ≥ 26.
What is inequality? Differentiate between equation and expression?inequality : An inequality is used to make unequal comparisons between two expressions or numbers.
expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.
equation : A mathematical equation is used to equate two expressions.
Given is the statement as -
"quotient of x and 4 is at least 26"
We can write the inequality as -
(x ÷ 4) ≥ 26
Therefore, the given statement in the form of inequality is given as -
(x ÷ 4) ≥ 26.
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what is the closest estimate of x where f(x) = g(x)?
Answers
x≈1.6
Anthony wants to buy a CD for $400 that earns 2.5% APR and is compounded
quarterly. The CD matures in 3 years. He will be paid the interest he earns
each quarter. How much interest will Anthony have earned on this CD after
the first quarter?
A. $10.00
B. $3.25
c. $1.25
D. $2.50
Answers
Answer:i think A
Step-by-step explanation:
-|-5| what is the absolute value
Answers
Answer:
-5
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
negative times negative equals positive
find the area of right angle triangle whose base 9, Height 8?
Answers
Answer:38cm2
Step-by-step explanation:
The area of right angle triangle is 36 sq.cm. Whose base 9, Height 8 .
Base is 9 cm.
8 centimeters tall.
Triangle area equals 1/2 x base x height
Triangle's area is 1/2 x 9 x 8 = 36 square centimeters.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
The surface inside a flat figure is measured by its area. Squares are used to measure area. To obtain the square units, multiply the length by the width.
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How do I even do thissss?
Answers
Please provide your question with a math problem in the form of an image or text.
You give tours on the Great Lakes and talk about points of interest. A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions. In that way, it can be a shorter time between the first and second flashes than between the second flash and the third flash
(when the first beacon comes around for the second time). One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. If the beacons are set 120 degrees apart along the rotation, ash shown below, what is this ratio?
Answers
The required ratio is 1:2.
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given that, A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions, it can be a shorter time between the first and second flashes than between the second flash and the third flash, One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. The beacons are set 120 degrees apart along the rotation
If the second beacon is 120° after the first, then the first is 360° -120° = 240° after the second.
Therefore, the ratio of the times between beacons is =
120° : 240° = 1 : 2
Hence, the ratio is 1 : 2
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Manuel will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60 and costs an additional $0.60 per mile driven
The second plan has no initial fee but costs $0.80 per mile driven.
For what amount of driving do the two plans cost the
same?
miles
What is the cost when the two plans cost the same?
3
Answers
From the given values and conditions, We need to form a equations and equate both sides to solve for the miles, The answer is 300 miles.
What is a equation?An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.
What is unitary method?The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.
x= miles
60+0.6x=0.8x
0.8x-0.6x=60
0.2x=60
x=60/0.2
=300 miles
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I'm not sure what I did wrong here, I only have one try at this question, please help!
Answers
Corresponding
Congruent
47
180
75
Alternate interior angle
Congruent
75
180
180
Most of it is correct, but your addition of angles 58 and 47 = 105. 180 - 105 = 75.
You need to correct that in two places.
It is 75, NOT 85.
See my attachment for corrections.
Find y.
7.54
6.76
18.55
29.83
Answers
The length of y in the triangle is 18.55 units.
How to find the side of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The side y of the triangle can be found using sine law.
Therefore,
a / sin A = b / sin B = c / sin C
Applying the sine law,
y / sin 106 = 15 / sin 51
cross multiply
y sin 51° = 15 sin 106°
divide both sides by sin 51°
y sin 51° / sin 51° = 15 sin 106° / sin 51°
y = 15 sin 106° / sin 51°
Therefore,
y = 15 × 0.96126169593 / 0.77714596145
y = 14.4189254391 / 0.77714596145
y = 18.5536589719
Hence,
y = 18.55 units
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Between 2020 and 2021, the population of a city increased by 20% In 2021, the population of the city was 420 000. What was the population of the city in 2020?
Answers
Answer:
350,000.00
Step-by-step explanation:
420,000.00 - 20% = 350,000.00
Increase percentage: 70,000.00
SOMEONE PLEASE HELPPP
Answers
The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;
[tex]\bar {x}[/tex] ≈ 13.05
Median = 13.60
What is the mean and median of a dataset?The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.
The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.
The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;
The number of data points = 28
The sum of the data is; (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5
The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05
The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;
2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2
The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;
Median = (12.6 + 14.6)/2 = 13.60
The median is 13.60
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Simplify the following expression: 3(5 – 12) + 4 ÷ 2
A. -19
B. 19
C. -23
D. -8.5
I think it's either A or B
Answers
3(5 - 12) + 4 ÷ 2 = - 19
A must be the answer
Which graph represents the solution to the following inequality? 3x - 2y ≥ 6
Answers
Answer:
First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.
For:
x
=
0
(
3
⋅
0
)
+
2
y
=
6
0
+
2
y
=
6
2
y
=
6
2
y
2
=
6
2
y
=
3
or
(
0
,
3
)
For:
y
=
0
3
x
+
(
2
⋅
0
)
=
6
3
x
+
0
=
6
3
x
=
6
3
x
3
=
6
e
d
)
(
3
)
x
=
2
or
(
2
,
0
)
We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.
graph{(x^2+(y-3)^2-0.125)((x-2)^2+ y^2-0.125)(3x+2y-6)=0 [-20, 20, -10, 10]}
Now, we can shade the left side of the line. And we need to make the boundary line a dashed line because the inequality operator does not contain an "or equal to" clause.
graph{(3x+2y-6) < 0 [-20, 20, -10, 10]}
Step-by-step explanation:
Ashley and Saskia each think of a number.
1 less than Ashley's number is equal to 3 lots of Saskia's number.
4 lots of Ashley's number added to Saskia's number is 95.
Using the information above, write and solve two simultaneous equations to work out Ashley's and Saskia's numbers.
Answers
Based on the the information provided above, Ashley's and Saskia's numbers are equal to 22 and 7 respectively.
How to work out Ashley's and Saskia's numbers?In order to write a system of equations to describe this situation, we would assign variables to Ashley's number and Saskia's number respectively, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent Ashley's number.Let the variable y represent Saskia's number.Translating the word problem into an algebraic equation, we have the following:
x - 1 = 3y .....equation 1.
4x + y = 95 .......equation 2.
Making x the subject of formula in equation 1, we have:
x = 3y + 1 .......equation 3.
Substituting equation 3 into equation 2, we have:
4(3y + 1) + y = 95
12y + 4 + y = 95
13y = 95 - 4
13y = 91
y = 91/13
y = 7.
For the value of x, we have:
x = 3y + 1
x = 3(7) + 1
x = 21 + 1
x =22.
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To make a batch of salad dressing, combine 11 tablespoons of
oil with 22 tablespoons of vinegar. How many tablespoons of
vinegar are needed for every tablespoon of oil?
Answers
You need 2 tablespoons of vinegar for every 1 tablespoon of oil.
What are a ratio and proportions?
A ratio is a way of comparing two or more values by division. A ratio expresses a relationship between two or more quantities. It is a comparison of one quantity to another. For example, the ratio of 3:2, 3 is being compared to 2.
A proportion is an equation that states that two ratios are equal. It can be written as:
a/b = c/d or a:b = c:d, where a,b,c,d are numerical values.
The ratio of tablespoons of vinegar to tablespoons of oil in the salad dressing is given by the ratio of the number of tablespoons of vinegar to the number of tablespoons of oil.
In this case, the ratio is 22 tablespoons of vinegar to 11 tablespoons of oil, or 22/11.
You can simplify this ratio by dividing both numerator and denominator by their greatest common divisor, that is 11
So the ratio of tablespoons of vinegar to tablespoons of oil is 2:1
Another way to express this is that for every 1 tablespoon of oil, 2 tablespoons of vinegar are needed.
So, If you want to know how many tablespoons of vinegar are needed for every tablespoon of oil you can use the proportion:
vinegar/oil = 22/11 = 2/1
Hence, you need 2 tablespoons of vinegar for every 1 tablespoon of oil.
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8z = 4x - 32
Please explain step by step
Answers
The solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
What is equation?An equation is a mathematical statement that states that two expressions are equal. It consists of an equals sign and two expressions, one on each side of the equals sign. Equations are used to solve for the value of the unknown expressions, and can be used to solve problems in various fields such as physics, chemistry, engineering, and mathematics.
1. Start by isolating the z variable by subtracting 4x from both sides of the equation. This will give us: 8z = -32.
2. Divide both sides of the equation by 8. This will give us: z = -4.
3. Finally, substitute z = -4 into the original equation and solve for x. This will give us: 4x = 32, so x = 8.
Therefore, the solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
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Complete questions as follows-
8z = 4x - 32
Please explain step by step how to solve 8z = 4x - 32.
XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip
Answers
Total Liabilities + Equity = $220,000.
Total Assets = $220,000.
What is Ratio Analysis and Balance Sheet?
The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.
One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.
Here we are given in the Question,
Assets
Cash = $45,000
Inventory = $41,000
Property = $134,000
Liabilities
Notes = $55,000
Wages = $56,000
and
Equity
Stock = $50,000
Investment = $59,000
Total Liabilities + Equity = ( Notes + wages ) + (stock + Investment)
Total Liabilities + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)
Total Liabilities + Equity = $220,000.
Total Assets = Cash + Inventory + Property
Total Assets = $45,000 + $41,000 + $134,000
Total Assets = $220,000
Therefore,
Total Liabilities + Equity = Total Assets.
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To show that NMQ ≈ QPN by SAS, what must be the value or x?
I need help with this please help me
Answers
Answer:
x = 3
Step-by-step explanation:
You want to know the value of x, given that NM = 5x-1 and QP = 3x+5 in congruent triangles NMQ and QPN.
CPCTCCorresponding parts of congruent triangles are congruent, so we have ...
NM = QP
5x -1 = 3x +5
2x = 6 . . . . . . . . . . add 1-3x
x = 3 . . . . . . . . . . divide by 2
Write the expression as a decimal number 2 x 0.1 + 5 x 0.001 =
Answers
The measure of decimal number is 2 tenths + 5 thousandths is 0.205.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given expression
2 x 0.1 + 5 x 0.001
the expanded form is 2 tenths + 5 thousandths
= 2/10 + 5/1000
multiply and divide by 100 in 2/10
we get 200/1000
now 200/1000 + 5/1000 = 205/1000 = 0.205
Hence value of expression is 0.205.
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Ann's car can go 210 miles on 6 gallons of gas. During a drive last weekend, Ann used 7 gallons of gas. How far did she drive?
Answers
Answer:
245 miles
Step-by-step explanation:
210 = 6 gallons
210/6 = how far you can travel with one gallon
210/6 = 35
7*35 = how far you can travel with 7 gallons
7*35 = 245
Answer:
Ann drove 245 miles during her drive last weekend.
Step-by-step explanation:
If Ann used 7 gallons of gas during her drive last weekend, we can use the car's MPG to find out how far she drove by multiplying the number of gallons used by the MPG:
7 gallons * 35 miles/gallon = 245 miles
17v = 62 (exponential equations with logarithms, solve)
Answers
Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.
Define log(Logarithm).The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
What is a function?A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).
Given the equation 17v = 62, we can take the logarithm base 17 of both sides:
log(17^v) = log(62)
v*log(17) = log(62)
Dividing both sides by log(17) gives us:
v = log(62) / log(17)
This is the solution for v, the unknown variable in the equation.
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It took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, what was Luca's average trip?
-process
Answers
Luca's average trip will be 58 miles per hour.
How to calculate the speed?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.
In this case, it took Luca 8 hours to drive 464 miles from Richmond VA to Cleveland, OH. In miles per hour, Luca's average trip will be:
= Distance / Time
= 464 / 8
= 58 miles per hour.
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Estthe product silve using an area model and the standard algorithm 1.7x55=
Answers
The expression 1.7 x 5.5 can be an area model of the rectangle where the length is 1.7 and the width is 5.5
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The expression 1.7 x 55 is an area model.
Area of rectangle = length x width
Now,
Length = 1.7
Width = 55
Area = 1.7 x 5.5
Thus,
The expression 1.7 x 5.5 can be an area model.
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Can someone pls help answer this asap!! I’d really appreciate it!
Answers
Answer:
124 degrees
Step-by-step explanation:
Since they are congruent the corresponding angles will be equal. There is only one obtuse in each triangle, Angles Y and N. N is measured to be 124 degrees so Y is also 124 degrees.
What is the value of 7/8+ (-2/3) - (-4)?
Answers
The value of fraction will be;
⇒ 101/24
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The expression is,
⇒ 7/8+ (-2/3) - (-4)
Now,
Since, The expression is,
⇒ 7/8+ (-2/3) - (-4)
Simplify as;
⇒ 7/8 - 2/3 + 4
⇒ (21 - 16)/24 + 4
⇒ 5/24 + 4
⇒ (5 + 96) / 24
⇒ 101/24
Thus, The solution is,
⇒ 101/24
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Determine the value of x.
A) 2√3 B) 6√3 C) 12 D) 12√3
Answers
Sin60=6/hyperbola
•hyperbola=6/sin60
•hyperbola=4 √3
Now,
We know,
Hyperbola^2= Base ^2 +Perpendicular ^2
•Base(x)= √(Hyperbola^2-Perpendicular ^2)
•Base(x)=2√3
So Value of X is 2√3 (Ans.)
Correct Option: A) 2√3
Nevaeh has $0.80 worth of nickels and dimes. She has a total of 11 nickels and dimes altogether. Graphically solve a system of equations in order to determine the number of nickels, x,x, and the number of dimes, y,y, that Nevaeh has.
Answers
Solve on the interval [0, 2pi): 4csc x +6=-2
Answers
By solving the interval : [0,2pi] 4 csc x +6=-2 is 7pi/6 , 11pi/6
What are Trigonometric identities?Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These are identities that, geometrically speaking, involve certain functions of one or more angles. defining sine and cosine in terms of tangent, cotangent, secant, and cosecant interactions. The sine and cosine formula according to Pythagoras. This trig identity is arguably the most significant.[tex]& 4 \csc x+6=-2 \\[/tex]
[tex]& 4 \csc x=-8 \\[/tex]
Simplifying,
[tex]& \csc x=-2 \\[/tex]
[tex]& \frac{1}{\sin x}=-2 \\[/tex]
[tex]& \sin x=-\frac{1}{2} \\[/tex]
We get,
[tex]& x=\frac{7 \pi}{6}, \frac{11 \pi}{6}[/tex]
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