Answer: X= -2
Step-by-step explanation:
A car moving at a constant speed passes the timing device at T equals 0 after 8 seconds the car has traveled 840 ft what linear function in the form y equals mx + b represents the distance in feet d, the car has traveled any number of seconds, t, after passing the timing device
Answer:
Answer
d = 840t + 0
select all of the factors of x3 5x2 2x 8 x 5 x3 x 4 x 1 x3 x 2
The all the factors of x³ + 5x² + 2x – 8 are (x+4)(x-1) and (x+2) , the correct options are (c) , (d) and (f) .
In the question ,
it is given that the equation is f(x) = x³ + 5x² + 2x – 8 ,
we have to find the factors of f(x) = x³ + 5x² + 2x – 8 .
We know that ,The Factor Theorem states if (x-t) is a factor of f(x) if and only if f(t)=0 .
So , Option(a) Let g(x) = x + 5 be a factor
that means for x = -5 , f(-5) = (-5)³ + 5(-5)² + 2(-5) – 8 = 2 ≠ 0 ,
hence it is not a factor .
In option (b) Let g(x) = x - 5 be a factor
that means For x = 3 , f(3) = (3)³ + 5(3)² + 2(3) – 8 = 70 ≠ 0 ,
hence it is not a factor .
In option (c) Let g(x) = x + 4 be a factor
that means For x = -4 , the equation is f(-4) = (-4)³ + 5(-4)² + 2(-4) – 8 = 0 ,
hence it is a factor .
In option (d) Let g(x) = x - 1 be a factor
that means For x = 1 , f(1) = (1)³ + 5(1)² + 2(1) – 8 = 0 ,
hence it is a factor .
In option (e) Let g(x) = x + 3 be a factor
that means For x = -3 , it becomes f(-3) = (-3)³ + 5(-3)² + 2(-3) - 8 = 4 ≠ 0 ,
hence it is not a factor .
In option (f) Let g(x) = x + 2 be a factor
that means For x = -2 ,the equation f(-2) = (-2)³ + 5(-2)² + 2(-2) - 8 [tex]=[/tex] 0 ,
hence it is a factor .
Therefore , the factors are (x+2) , (x - 1) and (x + 4) .
The given question is incomplete , the complete question is
Select all of the factors of x³ + 5x² + 2x – 8.
(a) x + 5
(b) x – 3
(c) x + 4
(d) x – 1
(e) x + 3
(f) x + 2
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Kendra earns $11.60 per hour working at the movie theater. Each week, she donates
1
10
of her earnings to Best Friends Animal Society, her favorite charity. If Kendra worked 8
1
2
hours last week, how much money did she donate to the charity?
$9.86, Kendra donates to the charity.
Kendra worked 8 hours and 30 minutes last week
She earns $ 11.60 per hour
She will earn money if she works for 30 minutes = $(11.60/2)
Therefore,
Total amount of money she earns last week = $((11.60×8) + (11.60÷2))
= $(92.8+5.80)
= $98.6
Kendra donates 1/10th of the total money she earns in a week
Therefore,
Amount she donate last week = total amount she earns last week * 1/10
= $(98.6× (1÷10))
=$9.86
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On January 1, Year 1, the Platte Corporation issues a 5-year note payable for $5,000. The interest rate is 5% and the annual payment of $1,156, due each December 31, includes both interest and principal. Which of the following correctly shows the effect of the issuance of the note on Platte's financial statements?
The correct effect of the note issuance on Platte's financial statements is A. Cash and Notes Payable increased by $5,000 on the balance sheet and an increase in Financing Activity on the Cash Flows Statement.
What is the journal entry to record the issuance?The journal entry to record the issuance of the 5-year note payable for $5,000 by Platte Corporation on January 1, Year 1 includes:
Debit to Cash
Credit to Notes Payable.
This entry increases the Cash account, an asset that appears on the balance sheet.
It also increases the Notes Payable, a liability on the balance sheet.
On the Cash Flow Statement, the issuance is a financing activity as cash inflow is increased by the amount.
January 1, Year 1:
Note payable = $5,000
Note period = 5 years
Interest rate = 5%
Annual payment = $1,156
Thus, the note issuance does not affect the Income Statement and will not have an effect on the Equity, but Option A is correct.
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Question Completion:Answer Options are attached.
Which set of points includes all of the solutions for y = negative four fifths times x plus two?line going through 0 comma 2 and 5 comma negative 2 a (15, 10), (0, 2), and (−10, 10) b (−10, 10), (−5, 6), (0, 2), (5, −2), (10, −6) c (x, y) for all real numbers d (x, negative four fifths times x plus two) for all real numbers
The set of points includes all of the solutions is (x, - 4/5 x + 2).
What is the solution of an equation?
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given equation is
y = - 4/5 x + 2
The value of x can be any real number.
The value of y is - 4/5 x + 2.
The solution of the equation is (x, - 4/5 x + 2).
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et p be prime. determine the number of polynomials of the form x2 ax b which are [15 pts] irreducible over zp.
We observe that there are p² polynomials of the form x² + ax + b in Zp.
Since there are p choices for each of a and b.
Now a polynomial which is reducible over Zp may be rewritten in the form
(x - c)(x - d)
where c and d are roots.
So there are p choices if c = d
and if c ≠ d then there are [tex]\frac{p(p-1)}{2}[/tex] choices, the division of 2 eliminates repeated pairs.
Therefore there are p² - ( p + [tex]\frac{p(p-1)}{2}[/tex]) polynomials irreducible over Zp.
A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. The property of irreducibly depends on the field or ring to which the coefficients are considered to belong. Irreducible polynomials appear naturally in polynomial factorization and algebraic field extension.
A polynomial expressible as the product of two or more polynomials of lower degree is known as Reducible polynomial.
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Write the equation in standard form.
2y+3=−1/3(x−2)
The given equation can be written in standard form as x + 6y + 11 = 0.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is 2y + 3 = −1/3 (x − 2).
It can be written in the standard form of ax + by + c = 0 as follows,
2y + 3 = −1/3 (x − 2)
=> 3(2y + 3) = -1(x − 2)
=> 6y + 9 = 2 - x
=> 6y + x + 9 + 2 = 0
=> x + 6y + 11 = 0
Hence, the standard form of the given equation is x + 6y + 11 = 0.
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with double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (usa today, january 23, 2004). the following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. for the purposes of this study, small companies are companies that have fewer than 100 employees. medium companies have 100 to 999 employees, and large companies have 1000 or more employees. sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies. health insurance size of company yes no total small 37 13 50 medium 64 11 75 large 88 12 100 Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05.
Compute the value of the 2 test statistic (to 2 decimals).
The p value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2
What is your conclusion?
SelectConclude health insurance coverage is not independent of the size of the companyCannot reject the assumption that health insurance coverage and size of the company are independentItem 3
The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number).
Small %
Medium %
Large %
Based on the percentages calculated above, what can you conclude?
SelectLarge companies have a higher percentage of no coverage than medium and small companiesMedium companies have a higher percentage of no coverage than large and small companiesSmall companies have a higher percentage of no coverage than large and medium companiesSmall, medium, and large companies all have roughly the same percentage of no coverage
The value of the test statistics is , χ² = 15.3902
The value of P is less than 0.005 and the conclusion which we can draw from this is that the health insurance coverage is depending on the size of the business in point a.
The percentages of employees without health insurance based on company size for small , medium and large companies is ,
Small%= 33/50= 0.66Medium%=68/75 =0.91Large%= 88/100= 0.88We established our null hypothesis and alternate hypothesis as
H0: The availability of health insurance for employees is unrelated to the size of the business
H1 :The availability of employee health insurance is depending on the size of the business.
2) The alpha level for significance is set at 0.05.
3) The H0 test statistic is
O is the measured frequency, and E is the anticipated frequency, so that 2 = (O - E)2/E
This has a chi-square distribution that is around (3-1) (2-1)= 2 d.f.
We reject the null hypothesis that employee health insurance coverage is NOT independent of the size of the company because the calculated 2 = 15.3902 falls in the critical area 2 5.99.
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-3(16x - 8)+3=123
solve for x
Four transformations of the function f(x) = 4x + 5 are given below.
For each transformation, drag the expression that shows the result of that transformation into the box under it.
The results of the transformation for f(x+3), f(x)+3, 3f(x) and f(3x) are 4(x + 3)+ 5, 4x + 3 + 5, 3 (4x + 5) and 4(3x) + 5 respectively
How to determine the expression that shows the result of the transformation?A geometric transformation is a function that maps points in a plane or space to other points in the same plane or space. Geometric transformations can be used to change the size, shape, orientation, or position of an object or image.
Given: f(x) = 4x + 5
f(x+3) = f(x+3) = 4(x + 3)+ 5
f(x) + 3 = 4x+5 + 3 = 4x + 3 + 5
3 f(x) = 3 (4x + 5)
f(3x) = 4(3x) + 5
Therefore, drag the results into the box accordingly
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A group of ten friends played a number guessing game. They were asked to pick a number
between 1 and 20. The person closest to the target number wins. The ten people made these
guesses:
The table with the absolute guessing errors should be completed as follows;
Guess 2 15 10 8 12 19 20 5 7 9
Absolute guessing error 12 1 4 6 2 5 6 9 7 5
A graph of the guess and absolute guessing error is shown in the image attached below.
Yes, the absolute guessing error is a function of the guess because every guess (input value) has one absolute guessing error (output value).
What is the margin of error?In Mathematics, the margin of error (MOE) is sometimes referred to as an absolute guessing error and it can be defined as a measure of the difference that exist between an observed value and a true value of the population parameter.
Mathematically, the absolute guessing error for the guesses made by these group of ten friends with respect to the actual number of 14 as follows;
Absolute guessing error = 14 - 2 = 12
Absolute guessing error = 14 - 15 = 1
Absolute guessing error = 14 - 10 = 4
Absolute guessing error = 14 - 8 = 6
Absolute guessing error = 14 - 12 = 2
Absolute guessing error = 14 - 19 = 5
Absolute guessing error = 14 - 20 = 6
Absolute guessing error = 14 - 5 = 9
Absolute guessing error = 14 - 7 = 7
Absolute guessing error = 14 - 9 = 5
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What is the AREA of this composite figure?
A. 134 square units
B. 72 square units
C. 234 square units
D. 102 square units
E. 132 square units
Answer:
102
Step-by-step explanation:
As we know that the area of triangle is 1/2 × base × height so A.TQ
1) finding the triangle area = 1/2 × base × height
= 6 × 5.
= 30
2) finding the area of rectangle = l×b
= 12 × 6
= 72
Now to find total area is 72 + 30 which will be 102
so the answer is = 102
T/F problem 1e. given rosebud lane's cost structure, which reimbursement method is less risky for the hospital? group of answer choices
The less risky reimbursement method for the hospital is fee for service.
Given,
Rosebud lane's cost structure;-
We have to find the lass risky reimbursement method for the hospital;
Reimbursement method;-
A system of reimbursement that pays for each time a service is rendered. A system of payment that bases compensation on the volume of services delivered rather than the number of lives covered. A fee-for-service reimbursement system that takes service costs into account
Therefore,
The best reimbursement method that suits for the hospital is fee for service which is less risky also.
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Can anyone help me graph this out. its the last question for my homework and im stuck on it
The required graph of the given function has been shown.
Given that,
To draw the graph of the composite function,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Illustrating the function on the graph for the respective domain
f(x) = 0 for x ≤ -1
f(x) = -x -1 for -1 < x ≤ 2
f(x) = -1 for x > 2
Thus, the required graph of the given function has been shown.
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The Washington Wheat Farmers Club is studying the impact of rising grain prices on their members' planting habits. The club members produce an average of 150 million bushels of wheat per year, with a standard deviation of 18 million bushels. The club takes a random sample of 35 years to create a statistical study. Identify each of the following, rounding to the nearest hundredth when necessary:
Provide your answer below: u= million bushels
a= million bushels n= 0 - million bushels
0 = LA million bushels
Sampling distribution of mean, Sampling distribution of proportion and T-distribution.
How does sampling distribution work?An example of a sampling distribution is a probability distribution of a statistic that is derived by repeated sampling of a particular population. It describes a variety of potential possibilities for a statistic, such the mean or mode of some variable in a population.
Give an example of sampling distribution.When you repeat your survey or poll for all potential samples of the population, you get the sampling distribution of a proportion. For instance, you may conduct many polls rather than asking 1000 cat owners which cat food they prefer.
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Answer:
μ = 150
σ = 18
n = 35
μx¯ = 150
σx¯ = 3.04
Step-by-step explanation:
We are given population mean μ=150 and population standard deviation σ=18, and want to find the mean and standard error of the sampling distribution, μx¯ and σx¯ for samples of size n=36.
By the Central Limit Theorem, the means of the two distributions are the same:
μx¯=μ=150
To find the Standard Deviation of the sampling distribution, we divide the population standard deviation by the square root of the sample size:
σx¯=σn−−√=1835−−√≈3.04
Which statement best describe a parallelogram a parallelogram? A.a quadrilateral with one pair of parallel sides
B.A quadrilateral with two pairs of parallel sides
C.A quadrillateral with two pairs of congruent sides. D.any four sided figure with opposites sides congruent
B.A quadrilateral with two pairs of parallel sides
How do you identify a parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
What is an example of a parallelogram?Few examples of a parallelogram are rhombus, rectangle, and square.
A quadrilateral with both pairs of opposite sides parallel is known as a parallelogram.
Additionally, a parallelogram has the following qualities:
Congruent opposite angles;
The opposing factions are in agreement;
Additional angles can be found nearby;
The diagonals cut each other in half.
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demonstrate how you would employ fourier analysis to determine the frequencies of any other particular chords at varying volumes of your own choosing
The use of Fourier analysis in the chords of varying volumes is explained below .
What is Fourier Series ?
The Fourier Series can be defined as a expansion of a periodic function f(x) in terms of infinite sum of sine and cosine .
The Fourier Series make use of orthogonality relationship of sine and cosine function.
The process in which the Fourier Series analysis helps in determine the frequencies of any other particular chords at varying volumes is :
the Fourier series convert the time-domain input signal into a frequency-domain representation which is analyzed for the intensities of specific pitches.
and the relationship between the pitches at a particular given time is then analyzed to find the chord that is being played.
Therefore , the process of Fourier series in music is explained above .
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Find Θ in radians:
(Use \large \pi=3.14 when necessary and round your final answer to the tenths.)
Θ =
Angle θ in radians is 12/5 or 2.4 radians.
Define Arc Length
Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).
Given,
radius = 5 cm
length of arc = 12 cm
We know that,
θ = length of arc / radius
Now, plug in the values
θ = 12 / 5 or 2.4 radians
Hence,angle θ in radians is 12/5 or 2.4 radians.
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Answer: 2.4
Step-by-step explanation:
radius = 5 cm
length of arc = 12 cm
θ = length of arc / radius
θ = 12 / 5 or 2.4 radians
2.4 radians
the speed (or rate) josiah travels to work is inversely proportion to time it takes to get there. if he travels 35 miles per hour it will take him 2.5 hours to get to work.
Josiah will take 1.5 hours to travel to work at the speed of 55 miles per hour.
As the speed and time are inversely proportional to each other, we can represent it as -
speed(i)/speed(f) = time(f)/time(i), where I represents initial and f represents final. Now, keep the values in formula to find the time (final).
35/55 = time(f)/2.5
Rewriting the equation according to variable time(f).
time(f) = (35×2.5)/55
Performing multiplication on Right Hand Side of the equation
time(f) = 87.5/55
Performing division on Right Hand Side of the equation
time(f) = 1.59 hours
Hence, it will take 1.59 hours.
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The complete question is -
The speed (or rate) Josiah travels to work is inversely proportional to time it
takes to get there. If he travels 35 miles per hour it will take him 2.5 hours to get to work. How long will it take him if he travels 55 miles per hour?
Let U be a Universal set with subsets A and B. U={1,2,3,4,5,6,7,8,9,10} A={1,3,5,7} B={4,5,6} Find A′. Use set roster notation. If there is more than one element in the set, list in ascending order, separated by a comma.
The complement of set A is-
A' = {2, 4, 5, 6, 7, 8, 9, 10}
What is a set? What is union of sets? What is complement of a set?A set is a collection of elements or numbers or objects, represented within the curly brackets { }. For example: {1,2,3,4} is a set of numbers.The union of two sets is a set containing all elements that are in A or in B (possibly both). For example, {1,2} ∪ {2,3} = {1,2,3}.The complement of a set is the set that includes all the elements of the universal set that are not present in the given set.We have -
U={1,2,3,4,5,6,7,8,9,10} A={1,3,5,7} B={4,5,6}A' = U - A
A' = {1,2,3,4,5,6,7,8,9,10} - {1,3,5,7}
A' = {2, 4, 5, 6, 7, 8, 9, 10}
Therefor, the complement of set A is -
A' = {2, 4, 5, 6, 7, 8, 9, 10}
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Suppose a bag of colored marbles contains 33 marbles numbered 1 to 33. If you draw one marble at a time from the bag, without replacement, how many different ways can you draw all of the marbles from the bag? Remember that "without replacement" means that the marbles are not returned to the bag after they are chosen. Write your answer in factorial notation.
The ways you can draw all of the marbles from the bag is 33! ways
How to determine the ways you can draw all of the marbles from the bag?From the question, we have the following parameters that can be used in our computation:
Total number of marbles, n = 33
Total numbers of marbles picked at a time, r = 1
From the question, the marbles are selected without replacement
This means that the number of ways the marbles can be drawn from the bag is calculated using the following factorial formula
Total = n!
Where
n = 33
Substitute the known values in the above equation
Total = 33!
Apply the factorial formula
n! = n * (n - 1) * (n - 2) * .... * 1
So, we have
Total = 33 * 32 * 31 * 30 * .... * 1
Evaluate
Total = 8.6833176e+36
Hence, the number of ways is 33!
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Use the distributive property to write an equivalent expression.
4 (w - 2r + 4)
The distributive equivalent expression of 4(w -2r + 4) is 4w -4(2r) + 4(4)
How to write the Distributive law?distributive law, also called distributive property, in mathematics, the law relating the operations of multiplication and addition, stated symbolically as a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac. From this law it is easy to show that the result of first adding several numbers and then multiplying the sum by some number is the same as first multiplying each separately by the number and then adding the products.
a(b + c) = ab + ac
using the above distributive law and comparing the expression below
4 (w - 2r + 4)
we can write it as 4w -4(2r) + 4(4)
In conclusion the equivalent expression is 4w -4(2r) + 4(4)
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In a class of students, the following data table
summarizes how many
students have a brother or a sister. What is the probability that a student
chosen randomly from the class has a sister?
Has: brother Does not have a brother
Has a sister
6
12
Does not have a sister
3
The probability that a student chosen randomly from the class has a sister is 3/5.
What is the probability of an event?The probability of an event is the fraction of the number of favorable occurrences of an event to the total occurrences of the event.
P(a) = n(a)/n(s)
where 'a' is an event.
Calculation:The given data table shows how many students have a brother or a sister in a class of students.
The number of students who have both a sister and a brother = 6
The number of students who have only a brother and do not have a sister = 3
The number of students who have only a sister and do not have a brother = 12
The number of students who do not have both a sister and a brother = 9
So, the total number of students in the class = 6 + 3 + 12 + 9 = 30
Then, the probability that a student chosen randomly from te class has a sister is
= (number of students who have a sister)/total number of students
= (6 + 12)/30
= 18/30
= 3/5
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you are examining the data with a stem-and-leaf plot. here is the start of the plot. finish the plot. 3
you are examining the data with a stem-and-leaf plot. here is the start of the plot. finish the plot. 3|6
3| 0 2 4 5 6 8 9
A stem-and-leaf plot is a type of data display that shows the frequency of data items in a set. The plot consists of two columns, a stem column and a leaf column. The stem column contains the leading digit or digits of each data item, and the leaf column contains the remaining digits.
In this case, the stem is 3 and the leaf column is 6. To finish the plot, we need to add other data items to the leaf column which have the same stem (3). So, the completed plot would look like this:
3| 0 2 4 5 6 8 9
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What term is used to name a change in the physical properties of a substance which is usually reversible?
Physical changes are those that occur when a substance's physical properties, such as appearance, texture, color, etc.
Given that,
We have to find what term is used to name a change in the physical properties of a substance which is usually reversible.
We know that,
When only the physical characteristics of a material—such as its size, shape, color, condition, or appearance—alter, this is referred to as a physical change in the substance. Its chemical makeup is unaltered. a few instances of physical change water and sugar being dissolved. wax melting.
Physical changes are those that occur when a substance's physical characteristics, such as appearance, texture, color, odor, melting and boiling temperatures, density, solubility, polarity, etc., change.
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Sofia and her children went into a grocery store that sells bananas for $0.80 each and mangos for $2 each. Sofia has $20 to spend and must buy a minimum of 12 bananas and mangos altogether. If xx represents the number of bananas purchased and yy represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.
Using graphical method to solve the system of inequality, the number of banana is 2 and mango is 10
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
In this question, we can set the unknown variables as;
x = Number of bananay = Number of Mango0.2x + 2y = 20 ...eq(i)
x + y ≥ 12 ..eq(i)
Solving x and y
This can be done graphically;
The number of banana and mango is approximately 2 and 10 respectively
Kindly find the attached graph below
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
Rob says all numbers have an even number of factors. Enrique says some numbers have an odd number of factors. Who is correct?
Answer:
Enrique
Step-by-step explanation:
9 has the factors 1, 3 and 9. That is an odd number of factors (3).
Compare the graph to the graph of f(x) = | x |. Describe the shift of g(x).
g(x) = |x+4| - 2
g(x) is shifted 4 units left and -8 units down from f(x).
How would you define a graph's shift?Shifts. A shift is similar to a stiff translation in that it does not alter the size or shape of the function's graph. The graph's placement will only change as a result of a shift. A vertical shift maintains the x-coordinate while adding or subtracting a constant from each y-coordinate.In other words, we multiply the y-coordinate of each point on the graph of f by 2 to generate the graph of g. Geometrically, a point is moved 2 units above its former location by adding 2 to its y-coordinate. It is common to refer to "moving the graph up 2 units" when adding 2 to all of the y-coordinates on a graph at once.when y=f(x)
When y = f (x + a), the function is either shifted to the right by a units (a 0) or to the left by a units (a > 0).
g(x)=(x+4)-2⇒f(x−8)
This causes f (x) to be moved by 8 units to the right.
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The members of a sewing circle are making blankets to give to shelters. This week, they made 49 twin-size blankets and 49 queen-size blankets, using a total of 441 yards of fabric. Last week, the members completed 21 twin-size blankets and 48 queen-size blankets, which required 405 total yards of fabric. How much fabric is used for the different sizes of blankets?
8 twin-size blanket , y = 1 queen-size blankets will be the fabric used
According to the given information
let
x = number of yards of fabric required to make a twin-size blanket.
y = the number of yards of fabric required to make a queen-size blanket
This week, they used 441 yards of cloth to create 49 twin-size blankets and 49 queen-size blankets:
49x + 49y = 441
The group members finished 21 queen-size blankets and 48 twin-size blankets last week, using 405 yards of cloth altogether:
48x + 21y = 405
Solving the two equations
1029x + 1029y = 9261
2352x + 1029y = 19845
hence
Solving the above two equations
We get
1323x = 10584
x = 8
Putting the value of x in above one equation
y = 1
8 twin-size blanket , y = 1 queen-size blankets will be the fabric used
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