Given the following function
\(f(x)=x^4-x^3+7x^2-9x-18\)We want to find its roots. Since we already know that (x + 1) and (x - 2) are factors of this polynomial, we can divide our polynomial by those factors and factorize the result to get the other roots.
Let's start by dividing by the first factor
\(\frac{x^4-x^3+7x^2-9x-18}{x+1}\)To divide a polynomial by other, we start by dividing the leading term of the dividend by the leading term of the divisor(this will be the first term of our result)
\(\frac{x^4}{x}=x^3\)Then, we ultiply it by the divisor
\(x^3(x+1)=x^4+x^3\)Subtracting this result from the dividend, we have
\((x^4-x^3+7x^2-9x-18)-(x^4+x^3)=-2x^3+7x^2-9x-18\)This means that our division is
\(\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3+\frac{-2x^3+7x^2-9x-18}{x+1}\)Repeating the whole process of division with the second term, we have
\(\begin{gathered} x^3+\frac{-2x^3+7x^2-9x-18}{x+1}=x^3-2x^2+\frac{9x^2-9x-18}{x+1} \\ \Rightarrow\frac{x^4-x^3+7x^2-9x-18}{x+1}=x^3-2x^2+9x-18 \end{gathered}\)From this result, we can rewrite our function as
\(x^4-x^3+7x^2-9x-18=(x+1)(x^3-2x^2+9x-18)\)Repeating this same process with the other know factor, the other division we have to solve is
\(\frac{(x^3-2x^2+9x-18)}{x-2}=x^2+9\)Then, our function is
\(f(x)=(x^4-x^3+7x^2-9x-18)=(x+1)(x-2)(x^2+9)\)Then, to find the roots we need to solve the following equation
\((x+1)(x-2)(x^2+9)=0\)Since we have a product of 3 terms, the result will be zero if and only if one of the terms is zero. This means that the roots can be found by assuming each one is zero. The solutions for this equation are the same solutions for the following system
\(\begin{cases}x+1=0 \\ x-2=0 \\ x^2+9=0\end{cases}\Rightarrow\begin{cases}x=-1 \\ x=2 \\ x=\pm\sqrt[]{-9}=\pm3i\end{cases}\)And those are the roots for our function. x = -1, 2, +-3i.
Write 0.0065 in standard form.
Answer:
It is just 65.
Step-by-step explanation:
Which of the following statement(s) is (are) true?
I. The set of all second-degree polynomials with the standard operations is a vector space. II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space. III. The set of second quadrant vectors with the standard operations is a vector space A) 1 B) II and III C) II and III D) 11
The true statement is; II. Option D
How to determine the correct statementsFrom the information given, we have that;
I. The set of all second-degree polynomials with the standard operations is a vector space
II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space
III. The set of second quadrant vectors with the standard operations is a vector space
Note that;
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Convert the decimal 0.875 to a percent.
Question 1 options:
0.875%
8.75%
875%
87.5%
Answer: 87.5%
hope this helps! :)
Answer:
A
Step-by-step explanation: i just did the test
Pleaseee help I need a visual to do this. I'll really appreciate it
The visual that can help you in creating a 3D structure using rectangular prism and others is given in the image attached.
What is the 3D structure creation?3D structure creation is the method of planning and building three-dimensional structures or objects utilizing various materials and methods. This may make use of physical development with the use of materials such as wood, metal, and plastic, as well as virtual development utilizing computer program programs.
In virtual 3D structure creation, creators make use of program to make 3D models of structures or objects. These models can be seen and controlled in virtual space, and can be utilized to reenact how the structure will see and work within the real world.
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See text below
1. Start by creating a rectangular prism
as the base of your structure. This will
be the main structure that includes
the walls and interior rooms.
2. Add a cylindrical tower to one corner of the rectangular prism. Adjust the size and height to your liking.
3. Add another cylindrical tower to the opposite corner of the rectangular
prism. Again, adjust the size and
height to your liking.
4. Add a pyramid-shaped roof to one of the cylindrical towers, and a cone-
shaped roof to the other cylindrical tower.
5. Add a second rectangular prism on top of the first one, with a different orientation or size. This can serve as an additional room or tower.
6. Add a pyramid-shaped roof to the second rectangular prism, and a cone-shaped roof to the cylindrical tower that does not have one yet.
7. Add a rectangular prism
perpendicular to the main structure,
creating an L-shape. This can be a
separate building or an extension of
the main structure.
8. Add a pyramid-shaped roof to the new
rectangular prism, and a cone-shaped roof to the cylindrical tower on the
opposite side of the main structure. 9. Finally, add spheres as decorative
elements to the walls and towers. You can also add other shapes, such as additional rectangular prisms,
pyramids, or cones, as long as you have at least 2 of each of the 5
required shapes.
Which ordered pair is a solution of the equation shown? A.-3/4,- 1/2 B. 0,3/4 C.4/3, 1/2 D. 4, 3/2
pls hurry = 50 point
Answer:
the answer is b, c, d, a, respectively
A DJ charges a $350 booking fee, plus an hourly rate of $45. The Martins want to book the DJ for a party that will last 5 hours. How much will the DJ charge them? answer
The DJ will charge them $575.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given that,
Booking fee for DJ = $350
Rate for an hour = $45
Let x be the number of hours DJ is lasting.
Expression to find the total charge for x hours is 350 + 45x.
The Martins want to book the DJ for a party that will last 5 hours.
Cost for the DJ party for Martins = 350 + (45 × 5) = $575
Hence the cost for the DJ party booked by Martins is $575.
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A carpenter needs to cut a small triangular pice of wood for part of a jewelry box. He knows the dimension shown and that 0=68°. What is the length of a to the nearest tenth of a centimeter?
Answer:
36.0 cm
Step-by-step explanation:
use cosine to find the value of a
cos(68) = a/96 Multiply both sides by 96
a = cos (68) * 96
a = 35.96
Round to nearest tenth: 36.0 cm
Answer:
36.0 cm
Hope this helped have an amazing day!
What is the approximate area of the circle shown below
Answer:
the approximate area of corcle is 3848
\(diameter = 70in \\ radius = \frac{70}{2} \\ = 35in \\ area = \pi \: r {}^{2} \\ = \pi \: 35 {}^{2} \\ = 3848.45in {}^{2} \)
11
Y1
0
4
1
12
2
36
3
108
Write an explicit function
56566965577553666645556566667
Solve me the question
The mean, mean deviation mode, median standard deviation, and coefficients of variation, CV, are as follows;
1. The mean deviation about the mean, median mode are;
2.653, 3.709, and 3.709, respectively
The coefficients of variation are;
0.364, 0.337, 0.337, respectively
The variance is about 9.462
The standard deviation is about 3.076
2. Section A has a higher relative dispersion than section B
3. City 2
4. a. Mean ≈ 43.85
b. Mode 40 - 54 inches
c. Median ≈ 45.16
The variance ≈ 125.8056
Standard deviation ≈ 11.216
Coefficient of variation ≈ 0.268
What is a coefficient of variation?The coefficient of variation of a data quantifies or is a measure of the variability of the values in the set of data.
The mean for the data can be calculated as follows;
Mean = (3×10 + 6×15 + 11×25 + 2×6 + 4×4 + 10×3 + 5×2 + 7×8 + 8×9 + 9×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 7.29
The median is the 86/2 value = 43rd value
10 + 15 + 25 = 50
Therefore, the median is in the class with a frequency of 25, which is 11
The mode of the data, which is the value with the highest frequency in the data set is 11
The mean deviation from the mean is therefore;
(|3 - 7.29|×10 + |6 - 7.29|×15 + |11 - 7.29| ×25 + |2 - 7.29| ×6 + |4 - 7.29| ×4 + |10 - 7.29| ×3 + |5 - 7.29| ×2 + |7 - 7.29|×8 + |8 - 7.29| ×9 + |9 - 7.29| ×4)/(10+15+25+6+4+3+2+8+9+4) ≈ 2.653
The coefficient for the mean deviation about the mean is therefore; 2.653/7.29 ≈ 0.364
The mean deviation about the median is therefore;
(|3 - 11|×10 + |6 - 11|×15 + |11 - 11| ×25 + |2 - 11| ×6 + |4 - 11| ×4 + |10 - 11| ×3 + |5 - 11| ×2 + |7 - 11|×8 + |8 - 11| ×9 + |9 - 11| ×4)/(10+15+25+6+4+3+2+8+9+4)
The mean deviation about the median = 319/86 ≈ 3.709
The coefficient ≈ 3.709/11 ≈ 0.337
The median = The mean deviation about the mode ≈ 3.709
The coefficient is about 0.337
The variance = (10×(3 - 7.29)² + 15×(6 - 7.29)² + 25×(11 - 7.29)² + 6×(2 - 7.29)² + 4×(4 - 7.29)² + 3×(10 - 7.29)² + 2×(5 - 7.29)² + 8×(7 - 7.29)² + 9×(8 - 7.29)² + 4×(9 - 7.29)²)/(10+15+25+6+4+3+2+8+9+4) ≈ 9.462
The standard deviation, s ≈ √(9.462) ≈ 3.076
2. The coefficient of variation, CV, can be used to compare the variability of the datasets comprising of different scales as follows;
CV = Standard deviation/( The mean of the data)
Therefore; CV for section A = 23/79 ≈ 0.2911
CV for section B = 11/64 ≈ 0.172
The higher CV value for section A indicates that the scores of section A have a higher relative dispersion than the scores for the section B
3. The consistency values can be obtained by finding the standard deviation for the values in the data for each city, using a web based tool as follows;
City 1; Mean = 23
Variance = 50/4
Standard deviation, City 1 = (√(50))/2 = 5·√2/2
City 2; Mean = 21.8
Sample variance = 2.2
Standard deviation, City 2 = √(2.2) ≈ 1.483
City 3; Mean = 29.2
Sample variance = 18.7
Standard deviation, City 3 = √(18.7) ≈ 4.324
The standard deviation of city 2, which is the smallest compared tom the other cities, indicates that the City 2, has the most consistent temperature
4. The mean of the data obtained from the data using the midpoint of the data, is; Mean = ∑fx/∑f
Therefore; The mean obtained using an online tool is; 43.85
The mode is the data that occurs most frequently, which is the data with the value; 40 - 54 inches
The median is the value at the middle of the data set, which is the value with a frequency of 53, and in the interval 40 - 54 inches
The median is; 39.5 + (54.5 - 39.5) × (50 - 30)/53 ≈ 45.16
The standard deviation found for the grouped data, using an online tool is as follows;
Variance, σ² ≈125.8056
The standard deviation, σ ≈ √(125.8056) ≈ 11.216
The coefficient of variation is; 11.216/41.83 ≈ 0.268
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If the standard deviation of returns on the market is 20 percent, and the beta of a well-diversified portfolio is 1.5. Calculate the standard deviation of this portfolio.
a. 30 percent.
b. 20 percent.
c. 15 percent.
d. 10 percent.
Answer:
a. 30 percent.
Step-by-step explanation:
Given that:
The standard deviation of returns = 20 percent
Beta = 1.5
Beta=Standard deviation of portfolio × correlation/Standard deviation of market × Correlation
Since Correlation with the market will be +1;
Then;
The Standard deviation of portfolio = 1.5 × 20%
The Standard deviation of portfolio = 30.00%
Which of the following graphs have hamiltonian circuits?
Answer:
D
Step-by-step explanation:
The image
shown at the right contains many triangles.
Describe the different types of triangles found in
the image.
Answer:
Cna you please put a image, I would like that so much so I can help you?
Step-by-step explanation:
WHO EVER ANSWERS FIRST GETS BRAINLIEST I REALLY NEED HELP!!!
simplify... (3/8)^-2(1/3•3/8)^3(1/3)^4
Answer:
i awnsered 4.2^(-3)*5.1^(2)*4.2^(4)*5.1^(3)
Step-by-step explanation:
14491.060542
A past survey of 1, 068,000 students taking a standardized test revealed that 8.9% of the students were planning on studying engineering in college.
In a recent survey of 1, 476,000 students taking the SAT. 9.2% of the students were planning to study engineering.
Construct a 95% confidence interval for the difference between proportions ^p1−^p2 by using the following inequality. Assume the samples are random and independent.
(^p1−^p2)−zc√^p1^q1n1+^p2^q2n2
The confidence interval is _____
Complete Question
The complete question is shown on the first uploaded image
Answer:
The interval is \(-0.0037 < p_1-p_2<-0.0023\)
Step-by-step explanation:
From the question we are told that
The first sample size is \(n _1 = 1068000\)
The first sample proportion is \(\r p_1 = 0.089\)
The second sample size is \(n_2 = 1476000\)
The second sample proportion is \(\r p_2 = 0.092\)
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
\(\alpha = (100 - 95 )\%\)
\(\alpha = 0.05\)
Next we obtain the critical value of \(\frac{\alpha }{2}\) from the normal distribution table
The value is
\(Z_{\frac{\alpha }{2} } =z_c= 1.96\)
Generally the 95% confidence interval is mathematically represented as
\((\r p_1 - \r p_2 ) -z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}} < (p_1 - p_2 ) < (\r p_1 - \r p_2 ) +z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}}\)
Here \(\r q_1\) is mathematically evaluated as \(\r q_1 = (1 - \r p_1)= 1-0.089 =0.911\)
and \(\r q_2\) is mathematically evaluated as \(\r q_2 = (1 - \r p_2) = 1- 0.092 = 0.908\)
So
\((0.089 - 0.092 ) -1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}} < (p_1 - p_2 ) < (0.089 - 0.092 ) +1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}}\)
\(-0.0037 < p_1-p_2<-0.0023\)
On the first day of a song's release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day? Round to the nearest million.
27 million
35 million
37 million
38 million
Answer:
35 million
Step-by-step explanation:
20000000×70%=35million
Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. The correct option is D, 38 millon.
What is compounding?Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
A = P(1+r)ⁿ
where, A is the value after n period of time, P is the initial amount, and,
r is the rate of increment or decrement.
Given that On the first day of a song's release, it had 20 million streams. Also, the number of streams increases by 10% per day. Therefore, it can be said that the number of streams is compounding. Thus, the number of streams on the seventh day will be,
Number of streams = 20 (1+0.10)⁷ million
= 20 × 1.9487 million
= 38.974 million
= 38 million
Hence, the number of streams there will be on the seventh day is 38 million.
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what is 15/4 + (−4/13) as a fraction in simplest form.
Step-by-step explanation:
15/4 + (−4/13) can be rewritten as 15/4-4/13.
15/4-4/13
15 x13
4 x13
195/52
4 x4
13 x4
16/52
195/52-16/52=179/52 or 3 23/52
hope it helps!
A machine costing N$200 000 has effective life of 7 years and its scrap value is N$30000. What amount should
the company deposit annually into a sinking fund earning 5% per annum so that it can replace the machine
after its useful life? Assume that a new machine will cost N$300 000 after 7 years
The company should deposit approximately N$46,601.03 annually into the sinking fund to replace the machine after its useful life.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
To replace the machine after its useful life, the company needs to accumulate an amount equal to the difference between the cost of the new machine and the scrap value of the old machine, which is N$300,000 - N$30,000 = N$270,000.
Using the sinking fund approach, the annual deposit required can be calculated as follows:
PV = PMT x [(1 - \((1+i)^{-n}\) / i]
where:
PV = present value of the accumulated sinking fund
PMT = annual deposit
i = interest rate per period
n = number of periods
In this case, the interest rate is 5% per annum, and the number of periods is 7 years. Therefore:
PV = N$270,000
i = 5% per annum
n = 7 years
Plugging in these values, we can solve for PMT:
N$270,000 = PMT x [(1 - (1 + 0.05)^-7) / 0.05]
N$270,000 = PMT x 5.791
PMT = N$270,000 / 5.791
PMT ≈ N$46,601.03
Therefore, the company should deposit approximately N$46,601.03 annually into the sinking fund to replace the machine after its useful life.
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What is the allusion:
"I don't know if this store carries shoes in your size, Sasquatch," my dad joked when we went shopping for another new pair of shoes, my second pair in two
months.
Shoes
Dad
Sasquatch
Two Months
The allusion in this statement is "Sasquatch," referencing a legendary creature known for its large size and used humorously to imply the person's abnormally large shoe size.
The allusion in the given statement is "Sasquatch." Sasquatch, also known as Bigfoot, is a legendary creature often depicted as a large, hairy, and elusive humanoid. In this context, the reference to Sasquatch is used metaphorically to humorously imply that the person's shoe size is abnormally large.
The mention of Sasquatch adds a playful and exaggerated tone to the conversation about shopping for shoes. It serves as a lighthearted way for the dad to comment on the frequency of buying new shoes, suggesting that the person's feet grow rapidly or that they have a high shoe consumption rate.
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math math math math math math math
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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I need Help please!!!
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
3. The object has the shape of a rectangular prism, but part of a face is missing.
Find the surface area of the object and show your work.
a)
Find the surface area of the complete prism.
5 cm
30 cm
20 cm
10 cm
15 cm
I need an answer
Determine if 2 functions are invertable algebraically why or why not
The two functions f and g are inverses of each other. Correct option is A. Yes
What is Inverse Function?Inverse functions are functions which can be reversed in to another function.
Two functions f and g are inverses of each other if the composition of functions,
f (g(x)) = x and g(f(x)) = x
Given f(x) = 9x + 12 and g(x) = \(\frac{x-12}{9}\)
First, plug g(x) into f(x).
f [g(x) ] = f [ \(\frac{x-12}{9}\)]
= 9 ( \(\frac{x-12}{9}\)) + 12
= x - 12 + 12
= x
Now plug f(x) into g(x).
g [f(x) ] = g [9x + 12]
= \(\frac{9x+12-12}{9}\)
= 9x / 9
= x
Hence f and g are inverses of each other.
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Find the value of each variable. (x and y)
Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)
Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).
To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due
north. To get from home to his friend Cooper's house, Jaden would have to walk 6.3
kilometers due east. What is the straight-line distance between Akira's house and Cooper's
house? If necessary, round to the nearest tenth.
The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)
Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)
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If you draw a card from a standard deck of 52 playing cards, what is the probability that it is a heart or a diamond?
Answer:
1/2
Step-by-step explanation:
In a deck of cards, there are 13 hearts and 13 diamonds
13+13 = 26 hearts or diamonds
P( hearts or diamonds) = numbers of hearts or diamonds / total
=26/52
= 1/2
1.3.1 1.3.2 1.3.3 1.3.4 Government receives income from various sources, like tax and loans. This income is then distributed to the different sectors. TABLE 3 below shows the source of the income and the expenditure for the 2019/20 tax year. SOURCE Tax INCOME Loans ASC QP Other income Non-tax income AMOUNT (in billion rand) 1370 242.7 180.3 31.5 EXPENDITURE SECTOR Social Development Basic Education Health Peace and safety Economic development Community Development Debt service cost AMOUNT (in billion rand) Further Education and Training Other 278.4 262.4 222.6 211.0 209.2 208.5 202.2 APRIL 2021 112.7 B 1823.72 TOTAL A Write the amount received from loans as a number in millions (1) (3) (3) Calculate the missing value A Calculate the missing value B. Show ALL calculations. Determine the amount allocated for Community Development as a percentage of the total expenditure. (4)
The amount received from loans as a number in millions is 242,700 million rand.
How to calculate the valueDeducing value A requires computation of collective income sources, for which the following summation suffices:
Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A
In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.
Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:
Total Income - Total Expenditure = B
(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B
Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.
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A tire shop counted 80 invoices at the end of the month. They charge $325 for a set of new tires and $50 for a set of used tires. The total dollar amount of the invoices was $6,750. Let x represent the number of sets of new tires and y represent the number of sets of used tires. Which system of equations represents the situation?
a. x+y=80
325z=50y + 6,750
b. z+y=80
325x=-50y+6750
c. x+y=80
325x=-50y-6750
d. x+y=80 -325z=-50y + 6,750
Answer:
\(x+y = 80\\325x+50y = 6, 750\)
Step-by-step explanation:
Le x represents the set of new tires
Let y be the set of used tires
If a tire shop counted 80 invoices at the end of the month, then the equal that represents the total amount of invoices counted at the end of the month is:
\(x+y = 80 ............ 1\)
If they charge $325 for a set of new tires, the total amount charged for new tires will be:
\(325 \times x \\325x\)
If they charge $50 for a set of used tires, the total amount charged for used tires will be:
\(50 \times y\\50y\)
If the total dollar amount of the invoices was $6,750, then the expression that models the amount generated on tickets will be:
\(325x+50y = 6,750 .............. 2\)
Hence the system of equations represents the situation is:
\(x+y = 80\\325x+50y = 6, 750\)
Answer:
x + y = 80
325x = -50y + 6,750
Step-by-step explanation:
Pls tell me I really need help
Answer:
The answer is C or 44/12
Step-by-step explanation:
1/2 is equivalent to 3/6
1 4/6 is equivalent to 1 4/6 or 10/6
1 2/4 is equivalent to 1 3/6 or 9/6
When you add all of these together you get 22/6
Then you multiply 22/6 by 2 to get 44/12
ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°.
The length of side AB in right angled triangle ABC will be 48 cm.
What is a right angled triangle?Every triangle with one 90° angle is said to have a right angle. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees.The longest side of a right angle is known as the hypotenuse, and it is opposite the right angle.
Given,
∠B= 90°, AC = 96 cm, ∠C = 30°
Now, we know, Trignometric ratio sin θ in triangle can be given by-:
sin θ = \(\frac{perpendicular}{hypotenuse}\)
From given figure,
Perpendicular= AB= ?
and Hypotenuse= AC = 96
and θ= 30°
Hence,
sin 30° =\(\frac{perpendicular}{hypotenuse}\)= \(\frac{AB}{96}\)
\(\frac{1}{2} = \frac{AB}{96}\) (∵ sin 30°= 1/2)
\(AB=\frac{96}{2}\)
\(AB= 48 cm\)
Thus, AB= 48 cm
Learn more about right angled triangle here:
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Correct Question:ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB = ?