The polynomial in factored form is: (x-5)(x+6)(x-(3-2i))(x-(3+2i))
Since complex roots always come in conjugate pairs, we know that if 3-2i is a root, then 3+2i must also be a root. Therefore, we can write the polynomial in factored form by multiplying together the factors (x-5), (x+6), (x-(3-2i)), and (x-(3+2i)).
Alternatively, we can write the polynomial in factored form using the formula for a polynomial with complex roots:
p(x) = (x-r1)(x-r2)(x-r3)(x-r4)
where r1, r2, r3, and r4 are the roots of the polynomial. In this case, r1 = 5, r2 = -6, r3 = 3-2i, and r4 = 3+2i. Substituting these values into the formula gives us:
p(x) = (x-5)(x+6)(x-(3-2i))(x-(3+2i))
Therefore, the polynomial in factored form is written in the following form: (x-5)(x+6)(x-(3-2i))(x-(3+2i)).
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2(3a+2b−7) what is the equivalent expression to the given expression?
For an expression 2(3a+2b−7), an equivalent expression is 6a + 4b - 14
The correct answer is an option (D)
Consider an expression 2(3a+2b−7)
We simplify this expression.
2(3a+2b−7)
To simplfy this expression, multiply each term of (3a+2b−7) by 2
2(3a+2b−7)
= 2 × (3a + 2b - 7)
= (2 × 3a) + (2 × 2b) - (2 × 7)
= 6a + 4b - 14
So, we get 2(3a+2b−7) = 6a + 4b - 14
Therefore, 6a + 4b - 14 is an equivalent expression to 2(3a+2b−7)
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The complete question is:
Which expression is equivalent to the given expression? 2(3a+2b−7)
A 5a+4b−5
B 6a+2b−7
C 6a+4b−7
D 6a+4b−14
A certain disease has an incidence rate of 0.8%. If the false negative rate is 8% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.
The probability that a person who tests positive actually has the
the disease is, 10%.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, A certain disease has an incidence rate of 0.8%.
Therefore, The probability that a person who tests positive actually has the disease is,
= (8/0.8)%.
= 10%.
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how many possible meals can be made by choosing a dinner from 6 main courses, 4 vegetables, 2 salads, and 3 beverages
Just multiplying the amount of possibilities in each category together will give us the total number of meals that can be made using the options provided.
This is known as the Fundamental Counting Principle. Using this principle, the total number of possible meals is:
6 main courses × 4 vegetables × 2 salads × 3 beverages = 144 possible meals
Therefore, there are 144 possible meals that can be made by choosing from the given options.
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x^3+x^2y-4y-4x write as a product
Answer: x^3+x^2y–4y–4x = (x-2)(x+2)(x+y)
I WILL GIVE BRAINLIEST TO WHOEVER ANSWER ALL 3 QUESTIONS RIGHT AND MANY POINTS I BEG PLEASE
In theory think about how many sides are on a dice and the numbers that are shown on each side.
it is a six sided dice
In an experiment the dice is rolled 20 times and lands on 1 two times and on 5 four times.
Find each experimental and theoretical probability.
a) landing on 5
Experimental:
Theoretical
b) not landing on 1
Experimental:
Theoretical:
c) landing on 1
Experimental:
Theoretical:
(please help)
Answer:
a) experimental : 4 ÷ 20 = 1/5 or 20%
Theoretical : 1/6
b) experimental: 18÷20= 9/10 or 90%
Theoretical : 5/6 or 83%
c) experimental: 2÷20 = 1/10 or 10%
Theoretical : 1/6
Natalie mowed 3 lawns in 18 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answer: See attached.
Step-by-step explanation:
First, we will find the unit rate by dividing.
18 hours / 3 lawns = 6 hours per lawn
Then, we can fill out the other values using this unit rate.
1 lawn * 6 hours = 6
12 hours / 6 hours = 2
Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.
It costs an appliances company an initial flat rate of $25.70 to
request a shipment of products, with an additional $2.30 charged
per item. Write an equation in slope-intercept form where x
represents the number of items manufactured, and y represents the
total cost of the appliances.
Answer: The flat rate cost is $25.70 and the cost per item is $2.30, so the total cost (y) can be represented as:
y = 2.30x + 25.70
This is in slope-intercept form, where the slope is 2.30 and the y-intercept is 25.70.
Step-by-step explanation:
Kimani can paddle her kayak 7 miles per hour in still water. It takes her as long to paddle 17.5 miles upstream as it takes her to travel 31.5 miles downstream. Determine the speed of the river's current. Enter an equation with the following properties: 1. It uses the variable c to represent the speed of the river's current in miles per hour. 2. It uses the information as it is given above. 3. It can be solved to answer the question. Equation: How fast is the river's current? σ* miles per hour
a)c = (31.5 - 17.5)/(31.5/7 + 17.5/7)
b)4 mph.
The equation to solve for the speed of the river's current is c = (31.5 - 17.5)/(31.5/7 + 17.5/7) = 4 mph. Therefore, the speed of the river's current is 4 miles per hour.
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4. For the system of equations \[ \begin{array}{r} 2 x_{1}-2 x_{2}+5 x_{3}+7 x_{4}=0 \\ x_{1}+5 x_{2}+6 x_{3}+9 x_{4}=0 \\ x_{1}+17 x_{2}+13 x_{3}+20 x_{4}=0 \\ 3 x_{1}-2 x_{2}+4 x_{3}=0 \end{array} \
$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.
To solve this system of equations, first use the array method to organize the equations.
Array Method:
\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 1 & 17 & 13 & 20 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]
Now, use row operations to solve the system. Begin by combining the first and third equations by adding them together.
\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 1 & 5 & 6 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]
Next, combine the second and fourth equations by subtracting the fourth equation from the second equation.
\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 7 & 2 & 9 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]
Then, combine the second and third equations by adding the second equation to the third equation.
\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 12 & 12 & 27 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]
Now, combine the first and third equations by subtracting the third equation from the first equation.
\[ \begin{array}{cccc|c} 2 & -2 & 5 & 7 & 0 \\ 0 & 0 & 14 & 36 & 0 \\ 0 & 0 & -2 & -9 & 0 \\ 3 & -2 & 4 & 0 & 0 \end{array} \]
Finally, use back substitution to solve for the variables. Starting with $x_4$, use the fourth equation to solve for it:
$x_4 = \frac{9}{2}$
Then, use the third equation to solve for $x_3$:
$x_3 = -\frac{1}{2}$
Continuing this process, we can also solve for $x_2 = \frac{11}{2}$ and $x_1 = \frac{7}{2}$.
Therefore, the solution to the system is:
$x_1 = \frac{7}{2}, \ x_2 = \frac{11}{2}, \ x_3 = -\frac{1}{2}, \ x_4 = \frac{9}{2}$.
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The diagram shows a quarter circle of radius 12 cm
12 an
Work out the area of the shape,
Answer
Not drawn
accurately
cm²
[2 marks]
In response to the supplied query, we may state that Therefore, the area of the circle is approximately 113.1 cm² (rounded to one decimal place).
What is circle?A circle is created in the plane by each point that is a specific distance from another point (center). Hence, it is a curve made up of points that are separated from one another by a defined distance in the plane. Moreover, it is rotationally symmetric about the centre at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "centre." A circular symmetry line is made by drawing a line through the circle. Moreover, it is rotationally symmetric about the centre at every angle.
We must make certain assumptions because the diagram was not created precisely. Assume that the quarter circle is a perfect quarter circle and that its radius is 12 cm (as given in the question).
A = r2, where r is the radius, is the formula for calculating a circle's surface area. Due to the fact that we only have a quarter of a circle, we must divide the outcome by 4. Hence, the quarter circle's area is:
[tex]A = (1/4)\pi r^2\\A = (1/4))\pi(12^2)\\A = (1/4))\pi(144)\\A = 36)\pi[/tex]
Therefore, the area of the shape is approximately 113.1 cm² (rounded to one decimal place).
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Only datasets having a linear relationship between variables can be assessed using regression analyses. A. True B. FALSE
The statement, "Only datasets having a linear relationship between variables can be assessed using regression analyses" is False, because Non-Linear relationships also can be assessed, the correct option is (b)False.
The Regression Analysis can be used to assess the relationship between variables, including non-linear relationships.
There are various types of regression models that can capture non-linear relationships, such as polynomial regression, exponential regression, and logarithmic regression.
The interpretation of the regression coefficients and other statistics may be different in non-linear regression models compared to linear regression models.
Therefore, the given statement is (b)False.
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read the ss
PLS HELP
Answer:
(0,4)
Step-by-step explanation:
Your coordinates of your Y-intercept is where the line crosses over the Y line (the vertical line). This means your x (x,y) is always going to be 0 and your y is going to be the number in which the line crosses over your Y-line.
Rewrite the expression in terms of ln 3 and ln 4.
ln(144)
ln(144) can be written in terms of ln(3) and ln(4) as:
ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)
We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).
First, we can find the prime factorization of 144:
[tex]144 = 2^4 * 3^2[/tex]
Using the property above, we can rewrite ln(144) as:
[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]
Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):
ln(144) = 4 ln(2) + 2 ln(3)
Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:
ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)
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James invests $5,980 in a retirement
account with a fixed annual interest rate of
5.61% compounded continuously. What
will the account balance be after 17 years?
Answer:
the account balance will be $15, 485.41
Step-by-step explanation:
Compound interest, can be calculated using the formula FV = P*(1+R/N)^(N*T), where FV is the future value of the loan or investment, P is the initial principal amount, R is the annual interest rate, N represents the number of times interest is compounded per year, and T represents time in years.
5890*(105.61/100)*17
=15485.41
Ordering of Rock Layers
I did not mean to put math
The number from oldest to youngest is - 5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3 , the layer 5 is older than the layer 3 and line "B" represent - Fault .
How to do ordering of rock layers ?
Ordering of rock layers, also known as stratigraphy, is a process of arranging rock layers in a specific order based on their age and location. There are several principles that geologists use to determine the relative ages of rock layers:
Law of superposition: In an undisturbed sequence of rocks, the oldest rocks are at the bottom and the youngest rocks are at the top.
Principle of original horizontality: Layers of sediment are originally deposited horizontally, and any deformation of these layers must have occurred after deposition.
Principle of cross-cutting relationships: Any feature that cuts across a rock or rock layer is younger than the rock or layer that it cuts across.
Principle of inclusions: Any rock fragments included in another rock layer must be older than the rock layer that contains them.
Ordering of given rock layers :
The number from oldest to youngest is given below -
5 - 4 - 2 - Fault B- Unconformity A - 6 - 1 - 3
The age of layer 5 is older than the layer 3 .
The line "B" represent - Fault . A fault in rock is a fracture or break in the Earth's crust where rock on either side has moved relative to the other side.
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1. A graduate student from the Catholic University of Puerto Rico carried out a research project on how the adult population in Puerto Rico communicates with the objective of estimating the percentage of adults who prefer postal mail to electronic mail. She started with a survey that she mailed to 600 of the adults she knew. She asked them to send her the answer to this question: Do you prefer to use email or the postal service? Upon receiving the responses, 250 adults indicated their preference for the postal service. After completing her study, the student concludes that 48% of adults in Puerto Rico prefer the postal service to email.
a. the variable
b.population
c.population
d.parameter
e. sample
a. The variable is the type of communication preference: postal service or email.
b. The population is the adult population in Puerto Rico.
c. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.
d. The parameter being estimated is the percentage of adults who prefer postal mail to electronic mail.
e. The sample is the 600 adults that the graduate student surveyed.
a. The variable in this research project is the preferred method of communication for adults in Puerto Rico (postal mail or email).
b. The population in this research project is the adult population in Puerto Rico.
c. The sample in this research project is the 600 adults that the graduate student surveyed.
d. The parameter in this research project is the percentage of adults in Puerto Rico who prefer postal mail to email.
e. The statistic in this research project is the 250 adults who indicated their preference for the postal service out of the 600 adults surveyed. This statistic was used to estimate the parameter of 48% of adults in Puerto Rico preferring the postal service to email.
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Yolanda wants to rent a boat and spend at most $39. The boat costs $7 per hour, and Yolanda has a discount coupon for $3 off. What are the possible numbers of hours Yolanda could rent the boat? Can someone please help me!! ALKES IS A LOT! PLEASE HELP ME!!
The possible numbers of hours Yolanda could rent the boat is 6 hours.
What is inequality?The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().
Here the given boat cost per hour = $7.
Offer he gets = $3.
Now writing a inequality then, t represent number of hours,
=> 7t-3[tex]\le[/tex]39
Now solving this inequality for t then,
=> 7t[tex]\le[/tex]39+3
=> 7t[tex]\le[/tex]42
=> t[tex]\le[/tex]42/7
=>t[tex]\le[/tex]6
Hence the possible numbers of hours Yolanda could rent the boat is 6 hours.
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Which value of x makes the equation true?
2x - 22 = 12
Group of answer choices
A. 30
B. -6
C. 17
D. 6
Answer: C (17)
Step-by-step explanation: We need to make the equation true so we take
2x times 17 to get 34 and so 34-22=12
Suppose that the augmented matrix of a system of linear eq [[1,0,5,-(11)/(3)],[-4,1,-23,(68)/(3)],[5,0,25,-(43)/(3)]]
The solution to this system of linear equations is x = 11/3, y = -3/13, and z = 1/12.
The augmented matrix of a system of linear equations is [[1,0,5,-(11)/(3)],[-4,1,-23,(68)/(3)],[5,0,25,-(43)/(3)]]. To solve this system, we can use the process of elimination.
Step 1: Add 4 times row 1 to row 2.
[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[5,0,25,-(43)/(3)]]
Step 2: Subtract 5 times row 1 from row 3.
[[1,0,5,-(11)/(3)],[0,1,-13,(39)/(3)],[0,0,15,-(32)/(3)]]
Step 3: Divide row 2 by -13.
[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,15,-(32)/(3)]]
Step 4: Add 3 times row 2 to row 3.
[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,12,-(1)/(13)]]
Step 5: Divide row 3 by 12.
[[1,0,5,-(11)/(3)],[0,1,1,-(3)/(13)],[0,0,1,(1)/(12)]]
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Perform long division, please clearly show work of remainders
and arrows, where numbers pass down.
Thanks
1. 32.156 / 100
2. 174.787 / 0.01
There are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.
To perform long division, we need to follow these steps:
Set up the long division problem with the dividend on the inside and the divisor on the outside of the division symbol.
Determine how many times the divisor can go into the first digit or group of digits of the dividend.
Write the result above the division symbol and multiply it by the divisor.
Subtract the result from the first digit or group of digits of the dividend.
Bring down the next digit or group of digits from the dividend and repeat the process until there are no more digits to bring down.
The final result is the quotient with any remainders.
For the first problem, 32.156 / 100, we can set it up like this:
```
100 | 32.156
```
Since 100 cannot go into 32, we need to bring down the next group of digits, which is 156. Now we have:
```
100 | 3215.6
```
100 can go into 3215 a total of 32 times, so we write 32 above the division symbol and multiply it by 100:
```
32
100 | 3215.6
-3200
-----
15.6
```
Now we bring down the next group of digits, which is 6:
```
32.1
100 | 3215.6
-3200
-----
156
```
100 can go into 156 a total of 1 time, so we write 1 above the division symbol and multiply it by 100:
```
32.16
100 | 3215.6
-3200
-----
156
-100
-----
56
```
Since there are no more digits to bring down, we are left with a remainder of 56. So the final result is 32.156 with a remainder of 56.
For the second problem, 174.787 / 0.01, we can set it up like this:
```
0.01 | 174.787
```
Since 0.01 cannot go into 174, we need to bring down the next group of digits, which is 787. Now we have:
```
0.01 | 17478.7
```
0.01 can go into 17478 a total of 1747800 times, so we write 1747800 above the division symbol and multiply it by 0.01:
```
1747800
0.01 | 17478.7
-17478
-----
0.7
```
Since there are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.
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How many different two-digit numbers can be formed using the
digits 3,9,4,7,6,1,2 and 8 with repetition?
There are 64 different two-digit numbers that can be formed using the digits 3,9,4,7,6,1,2 and 8 with repetition.
To see why, note that there are 8 possible choices for the first digit (any of the 8 given digits can be used) and 8 possible choices for the second digit (again, any of the 8 given digits can be used). Therefore, by the multiplication principle of counting, there are 8x8=64 possible two-digit numbers that can be formed.
To find all possible two-digit numbers, simply list all possible combinations of the given digits, allowing repetition. One example would be: 11, 12, 13, ..., 98, 99.
Alternatively, you can use the formula for counting with repetition, which is n^k where n is the number of choices for each digit and k is the number of digits. In this case, n=8 (since there are 8 possible digits) and k=2 (since we want two-digit numbers). Therefore, the total number of possible two-digit numbers is 8^2=64.
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Math is not my thing helpppppppppppppppppp
Answer: 3, 5, and 7
Step-by-step explanation:
Vertical angles, corresponding angles, and alt. ext. angles
The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to miles. What are these speed limits in miles per hour?
Using the conversion formula,
In Australia on the country roads the speed is 60mph and on the motorways is 66mph.
In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.
In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.
In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.
How do you translate a speed in kilometres per hour to miles per hour?To translate the number to miles per hour, we must multiply it by the conversion factor of 0.6214. As an illustration, 50 km/h is equivalent to 31.07 mph.
In the question,
By multiplying each speed limits with the conversion factor = 0.6214,
we can get the speed limits in miles per hour.
Therefore,
In Australia on the country roads the speed is 60mph and on the motorways is 66mph.
In South Africa on the country roads the speed is 60mph and on the motorways is 72mph.
In Great Britain on the country roads the speed is 58mph and on the motorways is 67mph.
In Turkey on the country roads the speed is 54mph and on the motorways is 54mph.
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The complete question is:
The table at right shows speed limits in some foreign countries in kilometers per hour. One kilometer is equal to miles. What are these speed limits in miles per hour?
How can you use place value to find the quotient of a multiple of Value 10 and a number?
By following the 6 steps explained, you can find the quotient of a multiple of 10 and any number.
How to use place value to find quotient?
To use place value to find the quotient of a multiple of 10 and a number, you can use the following steps:
Write down the multiple of 10 and the number being divided.Determine how many times the number being divided goes into the first digit of the multiple of 10.Write down that digit as the first digit of the quotient.Subtract the product of that digit and the number being divided from the first digit of the multiple of 10 to get the remainder.Bring down the next digit of the multiple of 10 to the remainder to form a new dividend.Repeat steps 2-5 until all digits of the multiple of 10 have been used.Learn more about place value here: https://brainly.com/question/25137147
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Aidan and Godwin like saving money when grocery shopping by sharing the costs. Aidan buys 10 cans of soup for $8.69 and a case of (24 cans) of chili for $19.20. Godwin takes 4 cans of soup and 12 cans of chili. Not including sales tax, how much does Godwin owe Aidan?
Calculate the unit rate of the soup
What is the unit rate of the soup?
Calculate the unit rate of the chili
What is the unit rate of the chili?
How much does Godwin owe Aidan?
Answer: To find how much Godwin owes Aidan, we first need to calculate the total cost of the items Aidan purchased:
10 cans of soup for $8.69, so the cost per can of soup is $8.69/10 = $0.869 per can.
1 case of chili for $19.20, so the cost per can of chili is $19.20/24 = $0.80 per can.
Godwin takes 4 cans of soup at $0.869 per can, which is a total of 4 x $0.869 = $3.476 for the soup.
Godwin takes 12 cans of chili at $0.80 per can, which is a total of 12 x $0.80 = $9.60 for the chili.
Therefore, Godwin owes Aidan $3.476 + $9.60 = $13.076.
The unit rate of the soup is $0.869 per can.
The unit rate of the chili is $0.80 per can.
Step-by-step explanation:
(73) If you insert number of arithmetic means between - 65 and 125 and the twelveths mean = - 113 , then the number of means = .. (a) 12 (b) 13 (c) 14 (d) 15
The number of means is 13. Option B
How to find the number of meansWe can use the formula for the nth term of an arithmetic sequence to solve the problem. Let d be the common difference and n be the number of terms between -65 and 125.
Then we have:
a + (n-1)d = 125 (1)
a + nd = -113 (2)
Subtracting equation (2) from equation (1), we get:
(n-1)d + 238 = 0
Solving for d, we get:
d = -238/(n-1)
Using the formula for the twelfth term, we have:
a + 11d = -113
Substituting the expression for d, we get:
a - 11(238/(n-1)) = -113
Multiplying both sides by n-1, we get:
a(n-1) - 11(238) = -113(n-1)
Substituting a = -65 and simplifying, we get:
n = 13
Therefore, the number of means is 13
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What is the first step in solving this system by elimination if we want to eliminate
the x variable first?
5x + y = 9
10x - 7y = -18
multiple choice
1. Add both equations together
2.Divide the bottom equation by 5
3.Subtract the bottom equation from the top
4.Multiply top equation by 2
The first step in solving by elimination is (4) Multiply top equation by 2
How to determine the first step in solving by eliminationFrom the question, we have the following parameters that can be used in our computation:
5x + y = 9
10x - 7y = -18
To eliminate x the coefficient of x in both equations muet be the same i.e 10
Using the above as a guide, we have the following:
Multiply (1) by 2
So, we have
10x + 2y = 18
10x - 7y = -18
Hence, the first step is (4)
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For what values of a will the quadratic y=ax^(2)-6x+3 have no real zeroes? (1) a=1 (3) a=-5 (2) a=-2 (4) a=7
For a=7 the quadratic equation have no real roots. (4)
For a quadratic equation y=ax^(2)-6x+3 to have no real zeroes, the discriminant of the equation must be less than zero. The discriminant of a quadratic equation is given by the formula b^(2)-4ac, where a, b, and c are the coefficients of the equation. In this case, a=a, b=-6, and c=3.
Plugging these values into the formula for the discriminant, we get:
(-6)^(2)-4(a)(3)<0
36-12a<0
12a>36
a>3
Therefore, the values of a that will make the quadratic equation have no real zeroes are those that are greater than 3. This means that the correct answer is (4) a=7, since this is the only value of a that is greater than 3.
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g in the axis of symmetry ng quadratic function by finding the key features. f(x)=x^(2)-2x-24 Axis of Symmetry:
The axis of symmetry of a quadratic function can be found by taking the negative of the coefficient of the x term, and then dividing it by 2. In this case, the coefficient of the x term is -2, so the axis of symmetry is located at x = -1.
The key features of the quadratic function are the vertex, the y-intercept, and the x-intercepts. To find the vertex, substitute the x-value for the axis of symmetry into the equation. In this case, the vertex is located at (x, y) = (-1, 27).
The y-intercept is found by setting x = 0 and solving for y. This gives us y = -24, so the y-intercept is located at (0, -24).
To find the x-intercepts, set y = 0 and solve for x. In this case, the x-intercepts are located at (2, 0) and (6, 0).
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Perform the multiplication or division and simplify
x2 + 2xy + y2
x2 − y2
·
3x2 − xy −
2y2
2x2 − xy −
3y2
After performing multiplication or division and simplify we get 2x2 − xy − 3y2 as the answer of this question.
The question is asking you to perform the multiplication or division and simplify:
x2 + 2xy + y2 ÷ x2 − y2 =
(x2 + 2xy + y2)(3x2 − xy − 2y2) ÷ (x2 − y2) =
3x4 − x3y − 2x2y2 − 3xy2 + 2xy3 + 2y4 ÷ (x2 − y2) =
3x4 − x3y − 2x2y2 − 2y4 ÷ (x2 − y2)
= 2x2 − xy − 3y2
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