The final result of algebra is: (6x^3 - x^2 - 14x + 5) : (2x - 1) = 3x^2 - x - 7 + 5/(2x-1)This is the simplified form of the given expression.
What is simplification?Simplification is the process of making an expression or equation simpler and easier to understand or work with. In mathematics, simplification often involves combining like terms, removing unnecessary operations, or reducing the number of terms in an expression. The goal of simplification is to obtain an equivalent expression that is clearer, more manageable, and easier to interpret.
Here ,
is the step by step process:
(6x ^ 3 - x ^ 2 - 14x + 5):(2x - 1)
Step 1: Divide 6x^3 by 2x and write the quotient 3x^2.
Step 2: Multiply the denominator (2x - 1) by the quotient (3x^2)
Step 3: Subtract the result from the numerator and bring down the next term of the numerator ( x^2)
Step 4: Repeat the process by dividing the x^2 by 2x and write the quotient -x.
Step 5: Multiply the denominator (2x - 1) by the quotient (-x)
Step 6: Subtract the result from the numerator and bring down the next term of the numerator ( -14x)
Step 7: Repeat the process by dividing the -14x by 2x and write the quotient -7
Step 8: Multiply the denominator (2x - 1) by the quotient (-7)
Step 9: Subtract the result from the numerator and bring down the next term of the numerator (5)
Step 10: We can see that the degree of the remainder is less than the degree of the denominator so we can write the remainder as 5/(2x-1)
So the final result is:(6x^3 - x^2 - 14x + 5) : (2x - 1) = 3x^2 - x - 7 + 5/(2x-1)
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using the factor theorem which of the following is a factor of the polynomial below x^3 + 7x^2 + 4x -12
A.
x-6
B.
x-3
C.
`X+4
D.
X-2
Using the Factor Theorem, it is found that none of these options represent a linear factor of f(x) = x³ + 7x² + 4x - 12.
How to verify if a term is a factor of the polynomial?The Factor Theorem states that if x - a is a factor of the polynomial y = f(x), then f(a) = 0.
The polynomial for this problem is defined as follows:
f(x) = x³ + 7x² + 4x - 12.
The numeric values for each of the options are given as follows:
f(6) = 6³ + 7(6)² + 4(6) - 12 = 480.f(3) = 3³ + 7(3)² + 4(3) - 12 = 90.f(-4) = (-4)³ + 7(-4)² + 4(-4) - 12 = 20.f(2) = 2³ + 7(2)² + 4(2) - 12 = 32.As none of the values of a have f(a) = 0, none of these terms are linear factors of the polynomial x³ + 7x² + 4x - 12.
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Monty works for a company that distributes multiple alcoholic beverages in the United States. Due to multiple events going on around the world, Monty has started wondering about the perceived home location of certain spirits. He takes a random sample of 135 people and find that 82 of them say that “Smirnoff” is produced in Russia. Monty takes a second random sample of 127 people and find that 74 of them say that “Stoli” is produced in Russia. At the .05 level of significance, is there a difference in the proportion of people who think Smirnoff is produced in Russia and the proportion of people who think Stoli is produced in Russia?
There is no evidence to reject the claim that there a difference in the proportion of people who think Red label is produced in Russia.
How to explain the critical value?It should be noted that we want to test the claim at 5% level of significance. The z critical value at 5% level of significance for two tailed test is 1.96.
The test statistic is 0.5. Since the z critical value is greater than the test statistic we do not reject the null hypothesis at 5% level of significance.
Therefore, we do not have enough evidence to reject the claim that there a difference in the proportion of people who think Red label is produced in Russia and the proportion of people who think Hennessy is produced in Russia.
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The function fis defined for f(x)= cos x+sinx for 0≤x≤ 2. What is the x-coordinate of the point of inflection where
the graph of fchanges from concave down to concave up?
The maximum and minimum x-coordinates at the point of inflection are, respectively,[tex]$\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$[/tex] and [tex]$\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$[/tex], and the function f is defined as f(x)=cos x+sin x for 0≤x≤ 2.
What is meant by x-coordinate of the point of inflection ?[tex]$\frac{d}{d x}(\cos (x)+\sin (x))$[/tex]
Continuity of [tex]$\cos (x)+\sin (x): \quad 2 \pi$[/tex]
Domain of [tex]$\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]
Range of [tex]$\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\sqrt{2} \leq f(x) \leq \sqrt{2} \\ \text { Interval Notation: } & {[-\sqrt{2}, \sqrt{2}]}\end{array}\right]$[/tex]
Axis points of interception [tex]$\cos (x)+\sin (x)$[/tex] [tex]: X Intercepts: $\left(\frac{3 \pi}{4}+2 \pi n, 0\right),\left(\frac{7 \pi}{4}+2 \pi n, 0\right)$,[/tex]
The Y intercept: (0,1)
the asymmetrical [tex]$\cos (x)+\sin (x)$[/tex] : None
Excessive Points of [tex]$\cos (x)+\sin (x): \quad$[/tex] Maximum [tex]$\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$[/tex] , Minimum [tex]$\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$[/tex]
We put the second derivative of the function equal to zero to get the x-coordinate of the point of inflection. Re-inserting the x-coordinate into the initial function yields the point's y-coordinate.
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Which simplified ratio correctly compares 12 yards to 20 feet?
Responses
3:5
3 colon 5
9:5
9 colon 5
5:9
5 colon 9
5:3
Answer:3:5
Step-by-step explanation:
12/4 is 3 and 20/4 is 5
so 3:5
Answer:9 and 5
Step-by-step explanation:k12
Need Help
Let ={x∈ℕ:2≤<19} and ={x∈ℕ: x is even}.
A: Find A ∩ B.
B: Find A∖B.
A: To find the intersection of the sets A and B, we need to find the elements that are common to both sets.
A = {x ∈ ℕ : 2 ≤ x < 19}
B = {x ∈ ℕ : x is even}
The intersection of the sets A and B is {x ∈ ℕ : 2 ≤ x < 19, x is even}
∩ = {4,6,8,10,12,14,16,18}
B: To find the difference of the sets A and B, we need to find the elements that are in set A but not in set B.
A = {x ∈ ℕ : 2 ≤ x < 19}
B = {x ∈ ℕ : x is even}
The difference of the sets A and B is {x ∈ ℕ : 2 ≤ x < 19, x is not even}
∖ = {3,5,7,9,11,13,15,17}
So the solution for A is ∩={4,6,8,10,12,14,16,18} and for B is ∖={3,5,7,9,11,13,15,17}
A garage charges $55 per tire and $30 per hour of labor. If you need two tires and it takes half an hour to install, how much do you pay?
Answer: $125
Step-by-step explanation:
$55 per tire (2)
$30 per hour of labor (0.5)
$55(2)+30(0.5)=$125
Answer:
$125
Step-by-step explanation:
2 tires =$110 ($55 each tire)
half an hour of labor=$15
Ray Rice, Adrian Peterson, Tom Brady,
and Ezekiel Elliot were suspended by the NFL.
Did the NFL succeed in upholding these suspen-
sions in arbitration and in court? Were the
decisions fair? Did the decisions to suspend
these players enhance or hurt the leagues
image. Does the commissioner of the NFL have
too much power in these cases, or is this type
of authority necessary to police the actions of
athletes and employees in the league?
Solving by function The NFL punished Ray Rice, Adrian Peterson, Tom Brady, and Ezekiel Elliott for a variety of reasons, but each of those reasons had to do with their personal lives.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.
By function
f(x) = 23x 243.2y + 23.2xy
we have Ray Rice struck his future wife. Adrian Peterson took part in kidnapping. In accordance with the NFL's Personal Conduct Policy, all of these players were suspended.
Also, both in arbitration and court, the NFL was successful in upholding these punishments.
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An ice rink charges hockey teams for ice time to practice. The ice rink charges $10 for the first hour
and $12 for each additional hour. Write a function that represents the charges for up to 5 hours.
The function that represents the charges is [tex]t_{n}=[/tex] 10 + (n- 1 )12
What is the function representing the charges ?Here, let us apply Arithmetic sequence Let the charges for the first hour = a = $10 Let the common difference = d = $12The formula for the nth term is given by
[tex]t_{n}=[/tex] a +(n-1)d
The function that represents the charges is given by,[tex]t_{n}=[/tex] a +(n-1)d
[tex]t_{n}=[/tex] 10 + (n- 1 ) 12
a ) First hour
n = 1
[tex]t_{1 }=[/tex] 10 + (1- 1 ) 12
= 10
b ) Second hour
n = 2
[tex]t_{2 }=[/tex] 10 + (2- 1 ) 12
= 10 + 12
= 22
c ) Third hour
n = 3
[tex]t_{3}=[/tex] 10 + (3- 1 ) 12
= 10 + 24
= 34
d ) Fourth hour
n = 4
[tex]t_{4 }=[/tex] 10 + (4- 1 ) 12
= 10 + 36
= 46
e ) Fifth hour
n = 5
[tex]t_{4 }=[/tex] 10 + (5- 1 ) 12
= 10 + 48
= 58
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The real numbers greater than or equal to 5 or less than or equal to -5
Answer:
x <= -5 or x >= 5.
Step-by-step explanation:
The boundary values (-5) and (5) contain closed circles to show that these values are included in the solution sets for the given inequalities.
Had our given compound inequality been:
x < -5 or x > 5
Then the boundary values (-5) and (5) would have contained open circles to show that these values are not included in the solution sets for these inequalities.
Jasmine went for a run. She started running at 06:55 and finished at 08:15. How long was she running for?
Answer:
Step-by-step explanation:
6:55 to 7 o'clock is 5 minutes.
from 7 to 8 is 60 minutes
from 8 to 8: is 15 minutes.
So, 5+60+15=80 minutes, also calls one hour and 20 minutes.
she ran for 3hours
06:55
08:15
14:60 therefore 14 is 2hours and 60 is 1hour
what rule about overtime does the fair labor standards act establish?
Answer: The Fair Labor Standards Act (FLSA) establishes a rule about overtime that requires covered employers to pay their employees a premium rate for any hours worked over 40 in a workweek. The premium rate is one and a half times the regular rate of pay for the employee. This overtime rule applies to all non-exempt employees, meaning those who are eligible for overtime pay.
Write an equation that has a solution of 4.
Use the variable n and multiplication. Example: ( 5 x n = 40)
On solving the provided question, we can say that equation that has a solution of 4 is -8+16=0
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
If we solve -8+16=0, we get
-4-4n+16=0
(-4)-4(-4)=0
(-4)(-4)=0
which give -4=0
=4
Hence, the equation -8+16=0 has solution =4.
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Jaxson earns $62 for 4 hours of work. If he makes a constant hourly wage, which
table represents the relationship between the number of hours he works and his total
earnings?
A
C
Time
(hours)
1
2
3
Time
(hours)
4
5
6
Pay
$15.50
$16.50
$17.50
Pay
$62
$77.50
$93
B
D
Time
(hours)
4
8
12
Time
(hours)
1
11
21
Pay
$62
$66
$70
Pay
$15.50
$25.50
$35.50
If Jaxson makes a constant hourly wage (unit rate) and earns $62 for 4 hours of work, the table representing the relationship between the number of hours he works, and his total earnings is C. as follows:
Time Pay
(Hours)
4 $62.00
5 $77.50
6 $93.00.
What is the unit rate?The unit rate is the ratio of two values.
The unit rate is the average of the total value divided by the total units.
We can also describe the unit rate as the constant rate of change, the variable cost per unit, or the slope in a linear equation.
Time Pay Unit
(Hours) Rate
4 $62.00 $15.50 ($62/4)
5 $77.50 $15.50 ($77.50/5)
6 $93.00 $15.50 ($93/6)
Thus, the unit rate of $15.50 is constant across all time hours that Jaxson works, making Option C to be correct.
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Answer:
Step-by-step explanation:
i dont know either
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer: yo wyd ?
Step-by-step explanation: pull up
Find the common difference of the arithmetic
Answer:
4
Step-by-step explanation:
9 , 13, 17, 21
9 + 4 = 13
13 + 4 = 17
17 + 4 = 21
The closing stock price of MNM Corporation for the last 7 trading days is shown below.
Day Stock Price
O 84
O 87
O 84
O 88
O 85
O 90
O 91
The mode is
The mode is 2.
The mode is the value that appears often in a set of data values.
The mode is a way of expressing, in a single number, important details about a random variable. The numerical value of the model is the alike as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.
Given Data :
84, 87,84,88,85,90,91
First, arranging the data in ascending order :
84, 84, 85, 87, 88, 90,91
Now, we have to find how many times this number occurs :
⇒ 84 occurs 2 times
⇒ 85 occurs 1 time
⇒ 87 occurs 1 time
⇒ 88 occurs 1 time
⇒ 90 occurs 1 time
⇒ 91 occurs 1 time
So, the mode is 2.
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Given
w (x) = x² + 4x − 3
and
z (x) = x + 5
what is the value of
w (z (7))
Answer:
[tex]w(z(7))=189[/tex]
Step-by-step explanation:
[tex]z(7)=7+5=12 \\ \\ w(z(7))=w(12)=12^2+4(12)-3=189[/tex]
Explain why multiplying by 8/3 gives the same result as first multiplying by 8 and then multiplying by 1/3
The outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.
Explain multiplication of fraction?The two fractions that want to multiply come first when multiplying fractions.
You multiply both denominators (the lower numbers) by the sum of the numerators (this same top numbers). Finding the sum of two or maybe more fractions is known as multiplying fractions. When multiplying fractions, a different approach is taken than when adding and subtracting fractions.For the stated number.
The number given is 8/3.
Other set of numbers are-
Multiplying 1/3 with 8.
= 1/3*8
= (1*8)/3
= 8/3, which is equal to the stated number.
Thus, the outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.
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13. A 66 lb. child is to receive 1 mEq/kg of a drug. The drug is available in 2 meq/4 ml. How many ml will be given?
A child can receive 0.5 kg /ml of drug.
What is density?
It is the quantity of a substance per unit volume. A quantity of mass is divided by volume, and we get a density of a particular substance.
How many ml drug will be given?
A 66 lb. child can receive 1 meq/ kg of drug.
but the drug is available in 2 meq/ 4ml.
we need to divide kg by ml to estimate how much quantity is suitable.
From the standard unit, if we divide the quantity in kg by the quantity in ml we achieve a density of drug.
(1 meq / kg) / (2 meq/ 4ml) = 2 ml / kg
the above value is inversed, and we get a density.
the density of drug = 0.5 kg / ml
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Rewrite the ratio 15:42 as an equivalent ratio of the form 1:n.
Equalizing ratios refer to two ratios with the same value.Multiply or divide both values by the same number to arrive at an equivalent ratio. The ratio 1: 3.5 will be the equivalent of the ratio 8: 28.
What does ratio mean?A ratio shows how many of one number there are of another.Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.
where each of the two variables, x and y, is a separate quantity.Additionally, the combined total is given as x + y.
Knowing that;
is the ratio;
8 : 28
And the ratio has the following equivalent form: 1: n.
Now,
The ratios 8: 28 and 1: n are identical, thus.
in order to formulate;
8 : 28 = 1 : n
Calculate n as;
8 / 28 = 1 / n
n = 28 / 8
n = 3.5
As a result, 1: 3.5 will be the ratio that the ratio 8: 28 corresponds to.
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exercise 1.1.14 in each case either show that the statement is true, or give an example showing it is false. (a) If a linear system has n variables and m equations, then the augmented matrix has n rows. quations • (b) A consistent linear system must have infinitely many solutions. . (c) If a row operation is done to a consistent linear system, the resulting system must be consistent. (d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.
The statements are:
(a) If a linear system has n variables and m equations, then the augmented matrix has n rows equations = False
(b) A consistent linear system must have infinitely many solutions. = False
(c) If a row operation is done to a consistent linear system, the resulting system must be consistent = True
(d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent = True
(A) An equation with n variables. Order of the matrix is m*m=. enhanced matrix Instead of (m+1) rows, this matrix has m rows. Thus, the claim is false.
(b) Either a singular or infinite linear system that is consistent. This technology is reliable and offers a distinctive solution. Therefore, statement (c) is false. If a consistent linear system is subjected to a row operation, the new system must also be consistent. We are aware that the matrix's rank remains unchanged after conducting a row action. So, it is accurate.
(d) The initial system is inconsistent if a succession of row operations on a linear system yields an inconsistent system. We are aware that the resulting system is identical to the original system of linear equations after conducting a sequence of row operations. So, it is true.
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Brooklyn is trying to pick out an outfit for the first day of school. She can
choose from 6 pairs of pants, 8 t-shirts, 3 sweaters or hoodies, and 5 pairs of
shoes. How many different outfits does Brooklyn have to choose from?
Therefore , the solution to the given problem of combination comes out to be thus, we might deduce that Brooklyn has 720 options from which to choose.
What is the Combination?Combinations are mathematical procedures that count the number of possible configurations from a set of things, where the ordering of the selection of the elements is not important. You can select any set of items in any arrangement. Combinations and permutations are frequently wrong.
Here,
For the predicament,
six pants pairs
8 t-shirts
5 pairs equal 1 pair.
hoodies= 3
The formula to determine how many ways there are in a combination is = C. (n,r)
The number of possible outfit combinations is equal to C(n,r)* C(n,r)* C(n,r)* C (n,r)
=> C(6,1)*C(8,1)* C(5,1)* C(3,1) (3,1)
=> 6*8*5*3
=> 720
Therefore , the solution to the given problem of combination comes out to be thus, we might deduce that Brooklyn has 720 options from which to choose.
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Answer:
720
Step-by-step explanation below:
Brainly pls
Solve the following equation for x 5x+3y=15
Answer:
x=3-3/5y
Step-by-step explanation:
5x+3y=15
5x=15-3y
x=(15-3y)/5
x=3-3/5y
Answer:
x= 3 y=5
Step-by-step explanation:
solving for x
5x + 3y = 15 Zero out the substitute
5x +( 3y * 0) = 15
5x + 0 = 15 Adding by zero can be ommited
5x = 15 Divide both side by 5
x = 3
if solving for y
5x + 3y = 15
(5x*0) + 3y = 15 zero out the substitute
0 + 3y = 15
3y = 15 devide by the number in front of x
y= 5
Taub goes out to lunch. The bill, before tax and tip, was $11.85. A sales tax of 3% was added on. Taub tipped 24% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
The value of the sales tax applied to the bill is $0.36
How much was the sales tax?If we have an initial value A, and we increase it by a percentage X, then the new value (after the increase) is given by:
A' = A*(1 + X/100%).
Here we know that the bill before the tax and the tip (it will be the initial value) is:
A = $11.85
And a sales tax of 3% is applied to that bill, then the new amount is:
A' = $11.85*(1 + 3%/100%)
A' = $11.85*(1 + 0.03) = $12.21
The sales tax is equal to the difference between the amount above and the initial value of the bill.
tax = $12.21 - $11.85 = $0.36
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Please answer this question and explain how you got it
1000 ml of sodium silicate is used to make 10 liters soap
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the amount of sodium silicate in x ml of liquid soap.
From the graph, using the points (1000, 100) and (3000, 300):
y - 100 = [(300 - 100)/(3000 - 1000)](x - 1000)
y - 100 = 0.1(x - 1000)
y = 0.1x
For 10 L (10000 ml)of soap:
y = 0.1(1000) = 1000 ml
1000 ml of sodium silicate is used to make the soap
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NEED HELPS ASAP PLS AND THX PIS IS ATTACHED
The reasons are When two lines intersect, the angles formed opposite to each other are termed as vertical angles
what is right angle congruence theorem?Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle.In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.Regarding right triangles, there are four theorems that prove congruence. They are the leg-leg theorem, the hypotenuse-leg theorem, the hypotenuse-angle theorem, and the leg-angle theorem Two right triangles can have all the same angles and not be congruent, merely scaled larger or smaller. If all the side lengths are multiplied by the same number, the angles will remain unchanged, but the triangles will not be congruent.To learn more about right angle congruence theorem refers to:
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y= "-2x+4" y=2x How many solutions does the system of equations have? • One solution * Infinitely many solutions * No solution
Answer: one solution
Step-by-step explanation:
y=-2x+4 y=2x
2x=-2x+4
4x=4
x=1
Answer:
Step-by-step explanation:
one
A cone with diameter 20 ft and a height of 20
ft.
Answer:
Volume = 2094.40 ft³ (2 d.p.)
Surface area = 1016.64 ft² (2 d.p.)
Step-by-step explanation:
If the diameter of a cone is 20 ft, then its radius is 10 ft since d = 2r.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
r = 10h = 20Substitute the given values of r and h into the formula for the volume of a cone and solve for V:
[tex]\implies V=\dfrac{1}{3} \pi \cdot 10^2 \cdot 20[/tex]
[tex]\implies V=\dfrac{1}{3} \pi \cdot 100 \cdot 20[/tex]
[tex]\implies V=\dfrac{1}{3} \pi \cdot 2000[/tex]
[tex]\implies V=\dfrac{2000}{3} \pi[/tex]
[tex]\implies V=2094.40\;\rm ft^3\;\;(2\;d.p.)[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Surface Area of a cone}\\\\$SA=\pi r \left(r+\sqrt{h^2+r^2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
r = 10h = 20Substitute the given values of r and h into the formula for the surface area of a cone and solve for SA:
[tex]\implies SA=10\pi \left(10+\sqrt{20^2+10^2}\right)[/tex]
[tex]\implies SA=10\pi \left(10+\sqrt{400+100}\right)[/tex]
[tex]\implies SA=10\pi \left(10+\sqrt{500}\right)[/tex]
[tex]\implies SA=10\pi \left(10+\sqrt{100\cdot 5}\right)[/tex]
[tex]\implies SA=10\pi \left(10+10\sqrt{5}\right)[/tex]
[tex]\implies SA=100\pi +100\sqrt{5}\: \pi[/tex]
[tex]\implies SA=1016.64\; \rm ft^2\;\;(2\;d.p.)[/tex]
Please actually answer this for me please will mark brainiest
Answer:
[tex]\dfrac{155}{18} \pi \textrm{ cm}[/tex]
Step-by-step explanation:
This problem asks us to find the length of an arc ACB on the circumference of a circle with center O and a radius of 5 cm.
We first must solve for the total circumference (perimeter) of the circle. This is represented by the formula C = 2πr. Hence, the circumference of this circle is:
C = 2π(5) cm
C = 10π cm
Next, we have to find what fraction of 360º the major arc ACB is in order to deduce how much of the circle's total circumference the arc takes up.
[tex]\dfrac{(360 - 50)\textdegree}{360\textdegree} = \dfrac{31}{36}[/tex]
Finally, we can multiply the amount of circumference that arc ACB takes up by the length of the whole circumference to get the length of arc ACB.
[tex]\textrm{Length of arc } ABC = \dfrac{31}{36} \cdot 10\pi[/tex]
[tex]= \dfrac{310}{36} \pi[/tex]
[tex]= \dfrac{155}{18} \pi \textrm{ cm}[/tex]
Answer:
[tex]\textsf{Length of major arc $\overset{\frown}{ACB}$}: \;\; \boxed{\dfrac{155}{18}\pi\; \sf m}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $= \pi r\left(\dfrac{\theta}{180^{\circ}}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]
Angles around a point sum to 360°. Therefore:
[tex]\begin{aligned}\implies m \angle BOA&=360^{\circ}-m \angle AOB\\&=360^{\circ}-50^{\circ}\\&=310^{\circ}\end{aligned}[/tex]
Therefore, the given values are:
r = 5 mθ = m∠BOA = 310°To find the length of the major arc ACB, substitute the given values into the arc length formula:
[tex]\begin{aligned}\implies \overset{\frown}{ACB}&=\pi \cdot 5 \cdot \left(\dfrac{310^{\circ}}{180^{\circ}}\right)\\\\&=5\pi \cdot \dfrac{31}{18}\\\\&=\dfrac{155}{18}\pi\; \sf m\end{aligned}[/tex]
A factory sells backpacks for
$
40.00
$40.00 each. The cost to make
1
1 backpack is
$
10.00
$10.00. In addition to the costs of making backpacks, the factory has operating expenses of
$
12
,
000
$12,000 per week. The factory's goal is to make a profit of at least
$
980
$980 each week. Which inequality represents the number of backpacks,
x
x, that need to be sold each week for the factory to meet this goal? How many backpacks must the factory sell to meet its weekly goal?
Select the inequality that represents this situation and select the correct statement.
The inequality which represents the number of backpacks need to be sold is 40x - (10x + 12,000) ≥ 980. Factory should sell at least 433 backpacks in a week.
What are Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Selling price of 1 backpack = $40
Cost to make 1 backpack = $10
Operating expense per week = $12,000
Let x be the number of backpacks which are sold in a week.
Total revenue per week = 40x
Total expense per week = 10x + 12,000
Profit = Revenue - Expense
= 40x - (10x + 12,000)
Factory's goal is to make a profit of at least $980 each week.
40x - (10x + 12,000) ≥ 980
This is the inequality that represents the number of backpacks need to be sold.
Solving the inequality,
40x - (10x + 12,000) ≥ 980
40x - 10x - 12,000 ≥ 980
30x ≥ 980 + 12,000
30x ≥ 12,980
x ≥ 432.67 ≈ 433
Hence factory must at least a total of 433 backpacks to meet it's weekly goal of $980.
Learn more about Inequalities here :
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