The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645
In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:
x²
When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -
x² = 3 -
When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x
x² = 3 - 4x
Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0
Where:
a= 1b= 4c= -3Solving the quadratic question we get the values for the (x) number
x= {- b ± √ [b² - (4* a*c)]} / (2 *a)
x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)
x= {- 4 ± √ (16 + 12)} / 2
x= {- 4± √ 28} / 2
x= (- 4 ± 5.29 ) / 2
x1= (- 4 + 5.29 ) / 2
x1= (1,29) / 2
x1= 0.645
x2= (- 4 - 5.29 ) / 2
x2= (9.29) / 2
x2= -4.645
We can check the values, replacing them into the equation:
(x1)² = 3 - 4(x1)
(0.645)² = 3 - 4*(0.645)
0.42 = 0.42
(x2)² = 3 - 4(x2)
(-4.645)² = 3 - 4*(-4.645)
21.58 = 21.58
What is a quadratic equation?It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:
ax²+ bx + c = 0
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Reece and sarah share some money in the ratio 9:16
reece says that sarah gets more than 60% of this money
show that reece is correct (3marks)
Hence it is proved that Reece is correct.
What is meant by percentage?
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Given that Reece and Sarah share some money at a ratio of 9:16
Let the total money be x.
Then, Sarah's share = x*16/25 = 0.64*x
That is 64% of the total money.
Which is greater than 60% of the total money.
Therefore, Reece is correct.
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Graph the rational function
by identifying its key features.
The graph of the rational function is shown below
Graph of rational functionsFrom the question, we are to graph the given rational function
To determine the graph that corresponds to the given rational function,
First, we will graph the given rational function.
The given rational function is
x²+3x-1/x+1
The graph of the rational function is shown below
Now, we will compare each of the rational graphs in the provided options with the attached graph
The graph that corresponds to the given rational graph in the attachment below is the graph that represents the given rational function.
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A cylinder has a base diameter of 4 centimeters and a height of 4 centimeters. What is its volume in cubic centimeters, to the nearest tenths place
Answer:
50.3 cm³
Step-by-step explanation:
Use the cylinder volume formula:
V = \(\pi\)r²h, where r is the radius and h is the height.
Since the radius is half of the diameter, and the cylinder has a diameter of 4 cm, this means the radius is 2 cm.
Plug in the radius and height into the equation:
V = \(\pi\)r²h
V = \(\pi\)(2²)(4)
V = 16\(\pi\)
V = 50.3 cm³
Answer:
50.3 cm³
Step-by-step explanation:
Use the cylinder volume formula:
V = r²h, where r is the radius and h is the height.
Since the radius is half of the diameter, and the cylinder has a diameter of 4 cm, this means the radius is 2 cm.
Plug in the radius and height into the equation:
V = r²h
V = (2²)(4)
V = 16
V = 50.3 cm³
help, please the question and thank you
Answer:graph D its the only one that reflects across the X AXIS correctly
Step-by-step explanation:
6. Solve for x!! please help!
x/2 = -7
=> x = -7 × 2
=> x = -14
Answer:
x=-14
Step-by-step explanation:
\(\frac{x}{2} =-7\\\\x=-14\\\)
I need help with this question
The length of the legs of the right triangle are 2.83 units.
How to find the side of a right triangle?A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the legs of the triangle can be found using trigonometric ratios.
Hence,
sin 45 = opposite / hypotenuse
sin 45 = a / 4
cross multiply
a = 4 × 0.70710678118
a = 2.83 units
Therefore,
cos 45 = b / 4
cross multiply
b = 0.70710678118 × 4
b = 2.82842712475
b = 2.83 units
Therefore, the legs are 2,83 units
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randy is a car salesman who earns a base pay of $39,800 and is a paid commission of 18% for each car he sells. if x represents total sales in dollars, which equation best represents randys total pay in dollars
Answer:
39,800+x0.18= his total pay
Your Welcome
Biffy Out!!!
In a right triangular prism, the area of the triangular base is 50 square feet. The height of the prism is 12 feet. What is the volume of the prism
The volume of the is right triangular prism is 600 cubic feet.
In a right triangular prism, the area of the triangular base is 50 square feet, and the height of the prism is 12 feet. To find the volume of the prism, we can use the formula:
Volume = Base Area × Height
Step 1: Identify the base area, which is given as 50 square feet.
Step 2: Identify the height of the prism, which is given as 12 feet.
Step 3: Multiply the base area by the height to find the volume.
Volume = 50 square feet × 12 feet = 600 cubic feet
So, the volume of the right triangular prism is 600 cubic feet.
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I need help finding the midpoint
Answer:
(0,3)
Step-by-step explanation:
This is the middle of the graph.
Have a great day!!
What is the end behavior of the polynomial
Answer:
As x --> ∞, then y --> - ∞
Step-by-step explanation:
As the value of x increases(as the graph goes right), the graph seems to go down, meaning the y-values are getting more an more negative. This means that as x approached infinity, the y values approach negative infinity ( x --> ∞, y --> - ∞ ).
As the value of x decreases(going to the left), the graph seems to go higher and higher. Therefore, as x approaches negative infinity, the y-value approach infinity. ( x --> - ∞, y --> ∞ )
Out of the options given, the one As x --> ∞, then y --> - ∞ is true.
Is dividing by 0.5 the same as dividing by 2?
The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers .
Let us understand the Division with the help of example ;
let the number be 10 ;
first we divide the number 10 by 0.5 ;
this can be written mathematically as ⇒ \(\frac{10}{0.5}\) ;
⇒ \(\frac{10}{\frac{1}{2} }\) = \(10\times2\) = 20 ;
So , on dividing 10 by 0.5 , we get the answer as 20 .
Second , the number 10 is divided by 2 ;
this can be written mathematically as ⇒ \(\frac{10}{2}\) ;
⇒ \(\frac{10}{2 }\) = 5 ;
So , on dividing 10 by 2 , we get the answer as 5 .
Therefore , dividing by 0.5 is not same as dividing by 2 .
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Mr.McMahon pays $880 for a $1000 bond paying bond interest at 9% compounded semi- annually and redeemable at $1000 in 20 years. If his desired yield was 8% compounded semi-annually, what semi-annual probability of default did he expect?
Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.
How to solve?
To solve this problem, we can use the formula for the present value of a bond:
PV = (C/r) ×[1 - 1/(1+r)²n] + F/(1+r)²n
where PV is the present value of the bond, C is the semi-annual coupon payment, r is the semi-annual yield rate, n is the number of semi-annual periods, and F is the face value or redemption value of the bond.
We know that Mr. McMahon paid $880 for a $1000 bond, so the present value of the bond is PV = $880. The redemption value of the bond is F = $1000, and the yield rate that he desired was r = 8% per year, compounded semi-annually. Therefore, the semi-annual yield rate is:
i = 0.08/2 = 0.04
We can use the formula to solve for the number of semi-annual periods:
PV = (C/i) ×[1 - 1/(1+i)²n] + F/(1+i)²n
$880 = ($45/i) ×[1 - 1/(1+0.04)²(220)] + $1000/(1+0.04)²(220)
Solving for i gives:
i = 0.0517 or approximately 5.17%
This is the semi-annual yield rate that Mr. McMahon actually received on the bond. To find the semi-annual probability of default that he expected, we can use the formula for the expected yield rate of a bond:
yield = (1 - probability of default) ×(yield rate on the bond) + (probability of default) ×(recovery rate)
where the recovery rate is the percentage of the face value that would be recovered in the event of default.
Assuming that the recovery rate is zero (meaning that in the event of default, Mr. McMahon would receive nothing), we can solve for the probability of default:
0.08 = (1 - p) ×0.0517 + p ×0
Solving for p gives:
p = 0.357 or approximately 35.7%
Therefore, Mr. McMahon expected a semi-annual probability of default of 35.7% on the bond.
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no member of the green party voted for the tax cut. p2) mr jacobs did not vote for the tax cut. c) mr jacobs is a member of the green party.
Answer:
Mr Jacobs did not vote for the tax cut. C - Mr Jacob is a member of the Green Party. Invalid.
Step-by-step explanation:
If afc is $8 at a quantity of output of 1,000 units, and atc is $12 at the same level of output, it follows that:_______.
The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.
To determine the relationship between average fixed cost (AFC) and average total cost (ATC) at a quantity of output of 1,000 units, we need to understand the formulas for AFC and ATC.
AFC is calculated by dividing total fixed cost (TFC) by the quantity of output (Q). ATC is calculated by dividing total cost (TC) by the quantity of output (Q). Mathematically, we have:
AFC = TFC / Q
ATC = TC / Q
Given that AFC is $8 at a quantity of output of 1,000 units, we can substitute the values into the AFC formula:
$8 = TFC / 1,000
Multiplying both sides of the equation by 1,000, we find:
TFC = $8,000
Now, we are given that ATC is $12 at the same level of output. Substituting the values into the ATC formula, we have:
$12 = TC / 1,000
Multiplying both sides of the equation by 1,000, we find:
TC = $12,000
To summarize:
Total fixed cost (TFC) = $8,000
Total cost (TC) = $12,000
Therefore, it follows that the difference between AFC and ATC lies in the variable cost component. The AFC represents the fixed portion of the total cost, while the difference between ATC and AFC represents the variable cost per unit.
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Compare the budgets of Hong Kong, United States of America, and
Korea based on your definition of a budget, in terms of contents,
formats, advantages, and disadvantages, etc.
The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.
A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:
Hong Kong Budget:United States Budget:
Contents: The US budget comprises revenue, expenditures, and deficit or surplus. It includes an analysis of taxes, social security, and Medicare.Format: The US budget is presented in a complex and lengthy format, including tables, graphs, and other financial documents.Advantages: The budget provides detailed information on tax expenditures and encourages public participation in the budget process.Disadvantages: The budget can be challenging to understand due to its complexity, and it may not provide an accurate depiction of federal spending.Korean Budget:
Contents: The Korean budget comprises revenue, expenditures, and surplus or deficit. It includes detailed information on taxes, social security, and public welfare.Format: The Korean budget is presented in a clear and concise format, including tables and charts to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability. It also provides detailed information on social welfare expenditures.Disadvantages: The budget may not provide an accurate depiction of government spending, and it may not include information on hidden expenditures.Learn more about Budget:
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A 4. What is the measurement of this angle?
• 130
• 120
• 140
• 100
Answer:
120 deg
Step-by-step explanation:
I put an image of 120 deg down below.
Try comparing those two
Answer:
It is 120 degrees compare from picture
Step-by-step explanation:
Kenji earned the test scores below in English class 79, 91, 93, 85, 86, and 88 is next after his next test, his mean and median scores both changed to 88 how much does he earn on his test
The mean of the numbers will be 87 and the median is also 87.
What are the mean and median?The mean of the number is defined as the average of the numbers that is the ratio of the sum of the numbers to the total count of the numbers.
The median of the numbers is defined as the first arranging the numbers in increasing order and then the middle most value of the numbers will be the median.
Given that Kenji earned the test scores below in English class 79, 91, 93, 85, 86, and 88 is next after his next test, his mean and median will be calculated as:-
Mean = ( 79 + 91 + 93 + 85 + 86 + 88 ) / 6 = 87
Median:- 79,85,86,88,91,93
Median = ( 86 + 88 ) / 2 = 87
Therefore, the mean of the numbers will be 87 and the median is also 87.
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if there are 60 songs on a mp3 and 21 are rock. what is the ration of rock songs not being played at all
Answer:
rock: not rock
7:13
Step-by-step explanation:
First determine how many songs are not rock
60-21 = 39
There are 39 songs that are not rock
ratio of rock to not rock
rock: not rock
21:39
We can divide by 3
21/3:39/3
7 : 13
8 Factorise 3x² - 2x - 8
Answer:
(3X +4) x (X-2)
Step-by-step explanation:
NEED HELP FAST:
Which mixed number is equivalent to the improper fraction?
35/6
A. 5 1/5
B. 5 5/6
C. 5 1/6
D. 6 5/6
Answer:
B- 5 5/6
Step-by-step explanation:
35 divided by 6 is 5 meaning there are 5 whole numbers in the fraction you then figure out how many 6 the remaining amount is which in this case is 5 so the answer is 5 5/6 hope this helps!
Excel: Starbucks Data 1. Consider using a simple moving average model. Experiment with models using five weeks' and three weeks' past data. The past data in each region are given below (week \( -1 \)
1. For the simple moving average model, evaluate forecasts using mean absolute deviation, mean absolute percent error, and tracking signal based on five weeks' and three weeks' past data.
2. For the simple exponential smoothing model, test alpha values of 0.2 and 0.4. Assume the forecast for week 1 based on the past three-week or five-week average.
3. Analyze the accuracy of the forecast for aggregated demand across all regions using the best model from questions 1 and 2. Evaluate using mean absolute deviation, mean absolute percent error, and tracking signal.
4. Advantages of aggregating demand: Simplified supply chain, potential cost savings, improved inventory management. Disadvantages: Reduced regional responsiveness, increased transportation costs. Consider customer preferences, lead time, and overall supply chain strategy.
1. Simple Moving Average Model:
Experiment with five weeks' and three weeks' past data.
Calculate forecasts for 13 weeks using the selected model.
Evaluate forecasts using mean absolute deviation (MAD), mean absolute percent error (MAPE), and tracking signal.
Simple Exponential Smoothing Model:
Test alpha values of 0.2 and 0.4.
Assume forecast for week 1 based on past three-week average (alpha = 0.2) or past five-week average (alpha = 0.4).
Evaluate forecasts using MAD, MAPE, and tracking signal.
2. Supply Chain Simplification:
Consider supplying the coffeemaker from a single location instead of five distribution centers.
Aggregate demand across all regions.
Use the best model from previous analysis to generate forecasts.
Evaluate the accuracy of the new forecast using MAD, MAPE, and tracking signal.
Advantages and Disadvantages of Aggregating Demand:
Advantages:
Simplification of supply chain operations and logistics.
Potential cost savings through consolidation of distribution centers.
Improved inventory management and reduced complexity.
Disadvantages:
3. Reduced flexibility and responsiveness to regional demand variations.
Increased transportation costs to deliver products from a single location.
Higher risk of supply disruptions if the single location experiences issues.
Other Considerations:
4. Customer preferences and regional differences in demand patterns.
Lead time and order fulfillment requirements.
Distribution center capacities and capabilities.
Overall supply chain strategy and long-term business goals.
In conclusion, analyzing different forecasting models and evaluating their performance based on accuracy metrics helps in selecting the most suitable approach. Aggregating demand from multiple distribution centers to a single location can offer cost advantages but may sacrifice regional responsiveness. Consideration of customer needs, supply chain dynamics, and strategic objectives is crucial when making decisions regarding supply chain simplification.
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Question
Excel: Starbucks Data 1. Consider using a simple moving average model. Experiment with models using five weeks' and three weeks' past data. The past data in each region are given below (week −1 is the week before week 1 in the table, −2 is two weeks before week 1, etc.). Evaluate the forecasts that would have been made over the 13 weeks using the overall (at the end of the 13 weeks) mean absolute deviation, mean absolute percent error, and tracking signal as criteria. 2. Next, consider using a simple exponential smoothing model. In your analysis, test two alpha values, 0.2 and 0.4. Use the same criteria for evaluating the model as in question 1. When using an alpha value of 0.2, assume that the forecast for week 1 is the past three-week average (the average demand for periods −3,−2, and −1 ). For the model using an alpha of 0.4, assume that the forecast for week 1 is the past five-week average. 3. Starbucks is considering simplifying the supply chain for their coffeemaker. Instead of stocking the coffeemaker in all five distribution centers, they are considering only supplying it from a single location. Evaluate this option by analyzing how accurate the forecast would be based on the demand aggregated across all regions. Use the model that you think is best from your analysis of questions 1 and 2 . Evaluate your new forecast using mean absolute deviation, mean absolute percent error, and the tracking signal. 4. What are the advantages and disadvantages of aggregating demand from a forecasting view? Are there other things that should be considered when going from multiple DCs to a DC?
What is the area of this polygon
A=220 cm^2
A=242 cm^2
A=248 cm^2
A=270 cm^2
Answer:
A = 220 cm²
Step-by-step explanation:
Area of a rectangle = width x heightArea of a triangle = 1/2 x base x heightArea of the rectangle = 11 x 18 = 198 cm²
Area of the triangle = 1/2 x (18 - 7) x (15 - 11) = 22 cm²
Therefore, area of the polygon = 198 + 22 = 220 cm²
Answer:
220 is The Correct Answer
Letter Choice (A)
Step-by-step explanation:
HERE'S MY PROOF AND MY RESEARCH
Area of a rectangle = width x height
Area of a triangle = 1/2 x base x height
Area of the rectangle = 11 x 18 = 198 cm²
Area of the triangle = 1/2 x (18 - 7) x (15 - 11) = 22 cm²
Therefore, area of the polygon = 198 + 22 = 220 cm²
A temperature change of 20 C° corresponds to a Fahrenheit temperature change of A) 11 F°. B) 36 F°. C) 68 F°. D) 18 F°.
A temperature change of 20°C corresponds to a Fahrenheit temperature change of 36°F. The Fahrenheit scale has a different conversion formula than the Celsius scale, resulting in a larger change in degrees for the same temperature difference.
To convert from Celsius to Fahrenheit, we use the formula: F = (C * 9/5) + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.
In this case, the temperature change is given as 20°C. To find the corresponding Fahrenheit temperature change, we apply the conversion formula: F = (20 * 9/5) + 32 = 36 + 32 = 68°F.
Therefore, a temperature change of 20°C corresponds to a Fahrenheit temperature change of 68°F. Among the given answer choices, the closest option is 36°F.
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1.70p−0.34q 0.17(q 1)−0.85(p−1) =0 =0 consider the system of equations above. how many (p, q)(p,q)left parenthesis, p, comma, q, right parenthesis solutions does this system have?
The system has exactly one solution, which is (p, q) = (-0.2118, -8.0).
We are given the system of equations:
1.7p - 0.34q = 0
0.17(q+1) - 0.85(p-1) = 0
We can simplify the second equation by distributing the 0.17 and 0.85 terms:
0.17q + 0.17 - 0.85p + 0.85 = 0
0.17q - 0.85p = -0.72
Now we have two equations in two variables, which we can solve using substitution or elimination. We will use elimination here.
Multiplying the first equation by 5, we get:
8.5p - 1.7q = 0
Multiplying the second equation by 2, we get:
0.34q - 1.7p = -1.44
Adding these two equations, we get:
6.8p = -1.44
p = -0.2118
Substituting this value of p into either of the original equations, we get:
1.7(-0.2118) - 0.34q = 0
q = -8.0
So the system has exactly one solution, which is (p, q) = (-0.2118, -8.0).
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Given the discrete uniform population: 1 fix} = E El. elseweltere .x=2.4ifi. Find the probability that a random sample of size 511, selected with replacement, will yield a sample mean greater than 4.1 but less than 4.11. Assume the means are measured to the any level of accuracy. {3 Points}.
The probability of obtaining a sample mean between 4.1 and 4.11 in a random sample of size 511 is 0.
To calculate the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in a discrete uniform population with x = 2.4, we can use the properties of the sample mean and the given population.
In a discrete uniform population, all values are equally likely. Since the mean of the population is x = 2.4, it implies that each value in the population is 2.4.
The sample mean is calculated by summing all selected values and dividing by the sample size. In this case, the sample size is 511.
To find the probability, we need to calculate the cumulative distribution function (CDF) for the sample mean falling between 4.1 and 4.11.
Let's denote X as the value of each individual in the population. Since X is uniformly distributed, P(X = 2.4) = 1.
The sample mean, denoted as M, is given by M = (X1 + X2 + ... + X511) / 511.
To find the probability P(4.1 < M < 4.11), we need to calculate P(M < 4.11) - P(M < 4.1).
P(M < 4.11) = P((X1 + X2 + ... + X511) / 511 < 4.11)
= P(X1 + X2 + ... + X511 < 4.11 * 511)
Similarly,
P(M < 4.1) = P(X1 + X2 + ... + X511 < 4.1 * 511)
Since each value of X is 2.4, we can rewrite the probabilities as:
P(M < 4.11) = P((2.4 + 2.4 + ... + 2.4) < 4.11 * 511)
= P(2.4 * 511 < 4.11 * 511)
Similarly,
P(M < 4.1) = P(2.4 * 511 < 4.1 * 511)
Now, we can calculate the probabilities:
P(M < 4.11) = P(1224.4 < 2099.71) = 1 (since 1224.4 < 2099.71)
P(M < 4.1) = P(1224.4 < 2104.1) = 1 (since 1224.4 < 2104.1)
Finally, we can calculate the probability of the sample mean falling between 4.1 and 4.11:
P(4.1 < M < 4.11) = P(M < 4.11) - P(M < 4.1)
= 1 - 1
= 0
Therefore, the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in the given discrete uniform population is 0.
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How do you sum a column in Excel on a Mac?
To see the steps of sum a column in Excel on a Mac.
Now, According to the question:
1. Click the first empty cell below a column of numbers.
2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...
3. Press RETURN .
How do you sum cells on a Mac?
Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.
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Using the Distributive Property, the expression 9.78(4.3x + 5.15) simplifies to what?
Answer:
Step-by-step explanation:
1. 9.78 x 4.3x
2. 9.78 x 5.15
3. 42.054x + 50.367
Solve this pls
6i<5i+3u
i < 3u
Step-by-step explanation:
6i < 5i + 3u
6i - 5i < 3u
i < 3u
Its PreCal I’ll give brainliest
Answer:
tan²x + tan x - 12 = 0 (1)
suppose: tan x = t
(1)=> t² + t - 12 = 0
a = 1 b = 1 c = -12
⇒ Δ = b² - 4ac = 1 + 48 = 49 > 0 => has 2 solutions
=> t = \(\frac{1+\sqrt{49} }{2}=\frac{8}{2}=4\)
or t = \(\frac{1-\sqrt{49} }{2}=\frac{-6}{2}= -3\)
because t = tan x => tan x = 4 or tan x = -3
because x ∈ [0;2pi) => with tan x = 4 => x = arctan(4) or x = arctan(4) + pi
with tan x = -3 => x = arctan(-3) + pi
Step-by-step explanation:
4(5c+3) and 9c+7 is it equivilent
Answer:
why are you cheating
Step-by-step explanation:
whats your reputation
Answer:
Step-by-step explanation:
Yes