The required mass of the paper clips in the box is = 61.44 mg.
Given that,
mass of a paperclip = 8.0 × 10⁻⁴
Number of paperclip in the box = 7.68 × 10⁴
The total mass of the paper clips is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Mass of paperclips = 8.0 × 10⁻⁴ x 7.68 × 10⁴
Mass of paperclips = 61.44 * 10 ⁻⁴⁺⁴
Mass of paperclips = 61.44 * 10 ⁰
Mass of paperclips = 61.44 * 1
Thus, the required mass of the paper clips in the box is = 61.44 mg.
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Use the Distance Formula to find the distance between the pair of points.
M(1,-2), N(9,13)
Using the distance formula, the distance between the points M(1,-2) and N(9,13) is 17 units
Given,
The points = M(1,-2) and N(9,13)
We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values in the equation
[tex]=\sqrt{(9-1)^{2}+(12--3)^{2} } \\=\sqrt{8^{2}+15^{2} } \\=\sqrt{64+225}\\ =\sqrt{289}[/tex]
=17 units
Hence, Using the distance formula, the distance between the points M(1,-2) and N(9,13) is 17 units
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You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?b. Identify your formula as explicit or recursive.
Money received in tenth month: $104, as found by the formula of arithmetic progression.
The formula used here is recursive.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given: Money received in first four months: $50, $52, $55, %59.
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+d[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
The formula so used is recursive, as the consequent values of the given arithmetic sequence are obtained from the preceding values.
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What is the standard form of the following equation?
y = -2/5x + 4
Use integers for A, B, and C. Enter your answer in the box.
____ x +
____ y =
____
The standard form of the given equation is y = -2/5(x + 10).
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
y = -2/5x + 4
We know that the given equation is of parabola.
Thus, converting it to the standard form of parabola,
y = a(x-h)^2 + k
where (h, k) is the vertex .
Now we have,
y = -2/5x + 4
Thus, multiplying both the side the given equation by 5 we get,
5y = (-2/5x + 4)*5
Expanding the brackets we get,
5y = -2*5/5x + 4*5
Solving we get
5y = -2x + 20
Now factoring R.H.S we get,
5y = -2x + 2*10
Taking common we get,
5y = -2(x + 10)
Dividing both the side by 5 we get,
5y/5 = -2(x + 10)/5
Solving we get,
y = -2/5(x + 10)
thus is the required standard form of the given equation.
Thus, the standard form of the given equation is y = -2/5(x + 10).
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find the values of x and y
Answer:
x=46 and y=42
Step-by-step explanation:
make 2y+6 equal to 8y-102 to solve for y as they are vertically oppisate angles which make them equal.
then substitute the new value for y into either expression and solve x using the rule a straight line is equal to 180.
Malik bought 0.8 pounds of turkey and 1.45 pounds of ham from deli. if turkey costs $6.45 per pound and ham costs $4.80 per pound, find the total cost.
On solving the equations, the total cost is 25.86.
The cost of ham is $4.80 a pound.
The cost of cheese is $6.3 for a pound.
Cheese weighing pounds was provided for $14.76.
Let "a" represent the cost of a pound of ham, and "b" represent the cost of a pound of cheese.
Given the available information,
1.3a + 0.8b = 11.28 —— (1)
1.50 +1.2b = 14.76 —— (2)
From the equation now (1).
11.28 -0.8b 1.3 (3)
Now, using equations (2) and (3), we obtain the following: 11.28 0.8 b. 1.3)+1.2 b. 14.76. 12.97 0.92 b+1.2 b. 14.76 0.28 b. 1.79 b. 6.3
The result of adding the value of b to equation (3) is 11.28 0.8. (6.3)
1.3 a = 4.8
The cost of ham is $4.80 a pound.
The cost of cheese is $6.3 for a pound.
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A plastic pipe 5m long is divided into ten equal parts. What is the length of each part?
Answer:
each part will be half a meter or fifty centimeters
Step-by-step explanation:
divide the total length by ten to find the individual part.
Every year, the Rock and Roll Hall of Fame and Museum inducts legendary musicians and musical acts to the Hall. The table shows the number of inductees for each year.
What are the domain and range of this relation?
Range - { 6, 7, 8,9 ,10, 11 } is the domain and range of this relation.
What is domain and range in math?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.How are the domain and range determined?
In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).the domain and range of this relation -
Domain - { 1 , 2, 3, 4, 5, 6 }
Range - { 6, 7, 8,9 ,10, 11 }
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1. A point is 5 units to the left of the y-axis
and 8 units up from the x-axis. Which
quadrant contains the point?
(-5,8) would be in quadrant 1
- How does writing the weight for potatoes in expanded form show why
the same digit can have different values?
What is the relationship between the values of the two 4s in the weight
of the potatoes?
Suppose the given number is 3.441
The first 4 is in the tenth place that is written like or 0.4
The second 4 is in the hundredth place that is written like or 0.04
We can see that the second 4 is one tenth times the first 4.
This is shown like,
1/10 x 1/10 = 1/100
Or we can say the opposite that the first 4 is ten times the second 4.
Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that children understand that while a digit can be the same, its value depends on where it is in the number.Place Value is important because it provides the foundation for regrouping, multiple-digit multiplication, and more in the decimal system, as well as a starting point for the understanding of other base systems.Place value helps us make decisions that are used in our daily lives ex) costs, weight, distances, time etc. Our number system is based on a Base Ten system. Base ten means our number system has a base of ten.A place value chart is a table that is used to find the value of each digit in a number based on its position, as per the numeral systemto know more about place value;
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a. Evaluate the expression 2(2x² - x) - 3(x² - x) + x² - x for x=3 . Do not simplify the expression before evaluating it.
The value of the expression 2(2x²-x)-3(x²-x)+x²-x at x=3 is 18.
An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).
According to the question
2(2x²-x) - 3(x²-x) + x²-x
Since we do not have to simplify the expression before evaluating it we will substitute the value of x=3 in the above expression .
=2(2*3² -3)-3(3² -3)+3²-3
=2(2*9-3)-3(9-3)+9-3
=2(18-3)-3(6)+6
Simplifying further we get
=2(15)-18+6
=30-18+6
=36-18
=18
Therefore , the value of the expression 2(2x²-x)-3(x²-x)+x²-x for x=3 is 18.
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When jorge arranges his pennies into a rectangle with two equal rows, three equal rows, or five equal rows, he has one leftover penny. when he arranges his pennies into a rectangle with four equal rows, he has three leftover pennies. how many pennies could jorge have?
Using common multiple, Jorge could have 31 pennies.
A common multiple is defined as a whole number, a shared multiple of each set of numbers. The common multiples of two or more prime numbers is the multiples of their product.
"when Jorge arranges his pennies into a rectangle with two equal rows, three equal rows, or five equal rows, he has one leftover penny"
Find the common multiples of 2, 3, and 5, and add 1.
Since 2, 3, and 5 are prime numbers, their common multiples are the multiples of their product.
Common multiples : 30, 60, 90, . . .
n = possible number of Jorge's pennies = 31 or 61 or 91 . . .
"when he arranges his pennies into a rectangle with four equal rows, he has three leftover pennies"
Find the common multiples of 4 and add 3.
multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, . . .
n = possible number of Jorge's pennies = 7, 11, 15, 19, 23, 27, 31, 35, . . .
31 ÷ 2 = 15 r 1
31 ÷ 3 = 10 r 1
31 ÷ 5 = 6 r 1
31 ÷ 4 = 7 r 3
Hence, Jorge could have 31 pennies.
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Write an equation of each line in slope-intercept form.slope 1/2 , through (2,3)
y = 1/2x + 2 is an equation in slope-intercept form for the slope 1/2 , through (2,3).
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
As we have slope and x and y we can write the given data in point-slope form, that is,
y - 3 = 1/2(x - 2)
And now we can distribute to convert it to slope-intercept form
y - 3 = 1/2(x - 2)
y = 1/2x -1 + 3
y = 1/2x + 2
So, y = 1/2x + 2 is in lope-intercept form for the slope 1/2 , through (2,3)
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-QS is a diameter of ®V . Find the measure.
m PQR
The measure of m∠RQS and m∠PQR is the line QS bisects ∠PQR and m∠PQS=63° are 63 and 126 degrees.
What is an angle bisector?The line or line segment that divides an angle into two equal pieces is known as the bisector of an angle, also known as the internal angle bisector. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
If line QS bisects ∠PQR, then;
<PQS = <RQS
WE have Given the following parameter;
m∠PQS=63°
Hence <PQS = <RQS = 63 degrees
Also,
<PQR = <PQS + <RQS
<PQR = 63 + 63
<PQR = = 126 degrees
The measure of m∠RQS and m∠PQR is the line QS bisects ∠PQR and m∠PQS=63° are 63 and 126 degrees respectively
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Write and solve a system of equations for each situation. Check your answers.A shop has one-pound bags of peanuts for 2 and three-pound bags of peanuts for 5.50 . If you buy 5 bags and spend 17 , how many of each size bag did you buy?
I bought 3 one-pound bags of peanuts and 2 three-pound bags of peanuts.
Firstly forming the equation according to the given information in question. Let us represent one-pound bags of peanuts with x and three-pound bags of peanuts with y.
Equation based on number of bags bought -
x + y = 5 - Equation 1
Rearranging equation 1 according to x
x = 5 - y - Equation 2
Equation based on cost of bags -
2x + 5.5y = 17 - Equation 3
Keep the value of x from Equation 2 in Equation 3
2 (5 - y) + 5.5y = 17
Performing multiplication of brackets
10 - 2y + 5.5y = 17
Rearranging the equation and performing subtraction
3.5y = 7
Shifting 3.5 to denominator on Right Hand Side of the equation
y = 7 ÷ 3.5
Performing division
y = 2
Calculating value of x by keeping value fo y in Equation 2
x = 5 - 2
x = 3
Thus, I bought 3 one-pound bags of peanuts and 2 three-pound bags of peanuts.
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11. (01.07 MC)
What is the value of x if log₂√x-1-2? (5 points)
82
O 65
O 19
O-8
Answer: 65
Step-by-step explanation:
Answer:
82
Step-by-step explanation:
65 because the other guy said it and im taking the test rn and i put that as my answer. and im answering this now cause i know i wont get back to it
omg jk its 82
wow im glad i actually tried to solve it..
but yeah
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
x=82
thats the best i can do to explain cause im lazy
Good luck
Four birds are sitting on a telephone wire. What is the probability that a fifth bird landing at a randomly selected point between birds 1 and 4 will sit at some point between birds 3 and 4?
Probability that a fifth bird landing at a randomly selected point between birds 1 and 4 will sit at some point between birds 3 and 4 is 1/3.
As given,
Total number of birds sitting on a telephone wire=4
Possible sitting arrangement is
Bird1__Bird2 __Bird3___Bird4
Total possible number of space between birds 1 to 4=3
Possible favourable outcomes (between 3 and 4)=1
Probability fifth bird sitting between point 3 and 4
= (Number of favourable outcomes)/ Total number of outcomes
= 1/3
Therefore, probability of a fifth bird sitting at some point between birds 3 and 4 is 1/3.
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is 4 2/5 greater than the square root of 19
Answer:yes
Step-by-step explanation:
because 4 2/5 is 4.4
and the square root of 19 is 4.358
Answer:
yes, 4 2/5 > √19
Step-by-step explanation:
You want to know if 4 2/5 is greater than √19.
ComparisonThere are several ways you can determine the relationship between these numbers. If you have a calculator, you can simply subtract one from the other. The sign of the result will tell you which is greater:
4 2/5 -√19 ≈ 0.0411 > 0 . . . . . . 4 2/5 is larger
Even without a calculator, you can square both numbers. Squaring positive numbers does not change their order, so ...
(4 2/5)² = 19.36 . . . . . . . . . . . . 4 2/5 is larger than √19
(√19)² = 19
Your calculator can tell you the decimal value of the two numbers, so you can compare their values yourself (as opposed to using subtraction).
4 2/5 = 4.400 . . . . . . . . . . . 4 2/5 is larger than √19
√19 ≈ 4.359
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Apply it! A regular 92-sided figure has ___ lines of symmetry.
Answer:
I think the answer is 92 lines because of the regularity of the figure
Write –0.67 as a fraction.
I need help please
Answer:
[tex]-\frac{67}{100}[/tex]
Step-by-step explanation:
Answer:
67/100
Step-by-step explanation:
0.67/1×100/100=67/100
if wrong i tried T^T
Pls pls help whoever gets it right gets a crown
x⁴y² - 6x³y³
x⁴ = x² × x²
y² = y²
x³ = x² × x¹
y³ = y² × y¹
x²y²(x²-6xy) Ans.Sherman bought a new house. Over a 5 month period, he has paid $350 to his neighborhood homeowners association in monthly fees. Which representation shows the relationship between x, the number of months, and y, the fees Sherman has paid to the homeowners association?
The proportional relationship between the fees paid and the number of months is given by:
y = 70x.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:
y = kx
In the case of an inverse relationship, we have that:
y = k/x.
k is the constant of proportionality for both cases.
For this problem, the time and the fees are direct proportional, that is, the fee increases as the number of months increase.
Over a 5 month period, he has paid $350 to his neighborhood homeowners association in monthly fees, hence the constant is found as follows:
k = 350/5 = 70.
Hence the proportional relationship between the fees paid and the number of months is given by:
y = 70x.
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Answer:
Step-by-step explanation:
y]yyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
6^5x1/6^5 =_______.
What
Answer:
1
Step-by-step explanation:
6^5x1/6^5
6^5 = 6*6*6*6*6 = 7776
7776x1/6^5 7776x1 = 7776
7776/7776= 1
I need help ASAP pls someone help and hurry
The solution to given equation 2(5 - 10x) + 8x = -19x + 52 is x = 2
In this question, we have been given an equation:
2(5 - 10x) + 8x = -19x + 52
We need to solve given equation for x.
2(5 - 10x) + 8x = -19x + 52 ................(Given equation)
10 - 20x + 8x = -19x + 52 ................(Evaluate the bracket )
10 - 12x + 19x = 52 ...............(Add 19x on each side)
10 + 7x = 52
7x = 52 - 10 ...............(Subtract 10 from each side)
7x = 42
x = 42/7 ..............(Divide each side by 7)
x = 6
Therefore, the solution to given equation 2(5 - 10x) + 8x = -19x + 52 is x = 2
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F(x)=|x|+5 horizontal shrink of factor 3 Please help
The function f(x) = |x| + 5 undergoes horizontal shrinking by a factor of 3 to get; f(x) = |¹/₂x| + 5
How to interpret Shrinking Transformation?There are different ways of transforming a function such as dilation, translation, reflection, stretching, shrinking e.t.c
Now, To stretch or shrink the graph in the y direction, what needs to be done is to multiply or divide the output by a constant. Now, f(2x) simply means that the function f(x) is stretched in the x direction by a factor of 2,. Meanwhile, f(¹/₂x) means that the function f(x) is shrunk in the x direction by a factor of 2 (or stretched by a factor of ¹/₂).
Now, we are told that the function f(x) = |x| + 5 undergoes horizontal shrinking by a factor of 3. Applying the above rule for shrinking gives us;
f(x) = |¹/₂x| + 5
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help me.............................................,.
Answer:
Step-by-step explanation:
a. 0.5+0.3 = 0.8
b. 2.7+28.2 = 30.9
c. 3.1+2.4+9.9 = 15.4
d. 15.2+1.4+0.8 = 17.4
e. 39.2+2.5+0.9 = 42.6
write an equation for an polynomial function whose graph intercepts the horizontal axis at -7, 8, and 15
The equation of the polynomial is -
f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex].
We have a polynomial function whose graph intercepts the horizontal axis at -7, 8, and 15.
We have to identify the polynomial.
What is Polynomial ?A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
According to the question -
x = -7, 8, 15 are the horizontal or the x - axis intercepts of the graph of the polynomial.
This means for -
x = -7
x = 8
x = 15
the polynomial (say f(x)) is equal to 0.
Therefore, x = -7 , x = 8 and x = 15 are the solutions of the polynomial f(x).
Then -
(x + 7) , (x - 8) and (x - 15) are the factors of this polynomial. Therefore -
f(x) = (x + 7)(x - 8)(x - 15)
f(x) = [tex](x^{2} -x-56)(x-15)\\[/tex]
f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex]
Hence, the equation of the polynomial is -
f(x) = [tex]x^{3} - 16x^{2} -41x+840[/tex]
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Solve each equation. Check each solution. 1/4 - x = x/8
The value of x for the equation 1/4 - x = x/8 is x = 2/9.
According to the given question.
We have an equation 1/4 - x = x/8.
As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Here, we have to find the solution of the equation 1/4 - x = x/8 for x.
So, the solution of the given equation 1/4 - x = x/8 for x is given by
1/4 - x = x/8
⇒ 1/4 = x/8 + x (adding x both the sides)
⇒ 1/4 = x + 8x/8
⇒ 1/4 = 9x/8
⇒ (1/4)(8) = 9x
⇒ 2 = 9x
⇒ x = 2/9 (dividing both the sides by 9)
Hence, the value of x for the equation 1/4 - x = x/8 is x = 2/9.
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I need help with this question
168>= 7x+4y
I need to solve for Y
Two expressions with an equal sign in between is Equation, The given equation is 168>= 7x+4y, when we solve it for y we get y<=42-7x/4..
What is Equation?
Two expressions with an equal sign in between is called as Equation.
The given equation is
168>= 7x+4y
Now we need to make y as independent variable.
Subtract 7x on both the sides
168-7x>=7x-7x+4y
168-7x>=4y
Now divide both side by 4.
42-7x/4>=y
Therefore the value of y is 42-7x/4, y<=42-7x/4.
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Write the following expression using the fewest possible terms.
(−3x − 12) + (16 + 8x)
A. 5x + 4
B. 5x + (−4)
C. 11x + 28
D. 11x + (−4)
The simplified expression of (−3x − 12) + (16 + 8x) is 5x + 4 (option A).
What is the simplified expression?A mathematical expression is when numbers and variables are combined together using mathematical symbols. A mathematical expression does not have an equal to sign.
To simplify an expression means to use the fewest possible terms. In order to simplify the expression, the BODMAS rule would be made use of. The BODMAS rule provides the procedure for solving mathematical expressions. According to the rule, terms in the bracket would be solved first.
Addition is the process of determining the sum of numbers. The sign used to represent addition is +. Subtraction is the process of calculating the difference between two or more numbers. The sign used to represent subtraction is -.
(−3x − 12) + (16 + 8x)
The first step is to combine similar terms together: (-3x + 8x) (-12 + 16)
Add similar terms together: 5x + 4
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An online furniture store sells chairs for $200 each and tables for $800 each. Every day, the store can ship at most 19 pieces of furniture and must sell a minimum of $8000 worth of chairs and tables. If 7 chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.
Answer must be in this form (,)
Tables cost $800 each, while chairs go for $200 each in an online furniture retailer. The store must sell at least $8000 worth of chairs and tables each day and can only ship a maximum of 19 pieces of furniture per day. Find the bare minimum of tables that the shop must sell to satisfy the requirements if 7 chairs were sold.
If chairs were sold, the minimum number of tables that the store must sell in order to meet the requirements is 4 tables.
Let x be number of chairs
y be number of tables
Given every day, the store can ship at most 19 pieces of furniture
Then we can write x+y=19--------->equation(1)
Given an online furniture store sells chairs for $200 each and tables for $800 each.
200x is the revenue of number of chairs.
800y is the revenue of number of tables.
And given must sell a minimum of $8000 worth of chairs and tables.
Then we can write 200x+800y=8000---------->equation(2)
We have to find out If 7 chairs were sold, determine the minimum number of tables that the store must sell in order to meet the requirements.
When x=7 what is y=?
By substituting x=7 in equation (1)
7+y=19
y=19-7
y=12
Now, substitute the x=7 in equation(2)
200(7)+800y=8000
1400+800y=8000
800y=8000-1400
800y=6600
y=[tex]\frac{6600}{800}[/tex]
y=8.25
y=9
We got 2 required values when x=7.
They are y=9 and y=12.
Therefore, the possible values we get are y=9,10,11,12.
If chairs were sold, the minimum number of tables that the store must sell in order to meet the requirements is 4 tables.
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