what are the x-intercepts of the function f(x)= 4x^2-36 over x-9
Answers
Therefore, x = 9 is not a solution. The valid x-intercepts are x = -3 and x = 3.
To find the x-intercepts of the function \(f(x) = (4x^2 - 36)/(x - 9)\), we need to set f(x) equal to zero and solve for x.
Setting f(x) equal to zero, we get:
\((4x^2 - 36)/(x - 9) = 0\)
Since the numerator \((4x^2 - 36)\)is a difference of squares, we can factor it as:
\((4x^2 - 36) = (2x + 6)(2x - 6)\)
So, the equation becomes:
\((2x + 6)(2x - 6)/(x - 9) = 0\)
Now we set each factor equal to zero and solve for x:
\(2x + 6 = 0\)
\(2x = -6\)
\(x = -3\)
and
\(2x - 6 = 0\)
\(2x = 6\)
\(x = 3\)
So the x-intercepts of the function f(x) are x = -3 and x = 3. These are the values of x for which the function f(x) equals zero. Note that x = 9 is not a valid x-intercept, as it would result in division by zero in the original function due to the (x - 9) in the denominator. Therefore, x = 9 is not a solution. The valid x-intercepts are x = -3 and x = 3.
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Related Questions
Find the measure of angle A
Answers
Answer:
24 minus 12 plus 6
Step-by-step explanation:
minus 12
Answer:
43 Degrees
Step-by-step explanation:
(3x + 16) + (6x + 1) + (82) = 180 Degrees
180 - 82 = 98 Degrees
(3x + 16) + (6x + 1) = 9x + 17
9x + 17 = 98
98 - 17 = 81
81 / 9 = 9
x = 9
6(9) + 1 = 55 Degrees
3(9) + 16 = 43 Degrees
55 + 43 + 82 = 180 Degrees
Which residual plot would you examine to determine whether the assumption of constant error variance is satisfied for a model with tut, independent variables x; and x2? a. Plot the residuals against the independent variable x2 b. Plot the residuals against the independent variable x1 c. Plot the residuals against predicted values y d. Plot the residuals against observed y values.
Answers
To determine whether the assumption of constant error variance is satisfied for a model with tut, independent variables x, and x₂, you would examine the residual plot where the residuals are plotted against predicted values y.
This plot is also known as the plot of residuals versus fitted values. In this plot, if the residuals are randomly scattered around the horizontal line of zero, then the assumption of constant error variance is satisfied. However, if there is a pattern in the residuals, such as a funnel shape or a curve, then the assumption of constant error variance may not be met. It is important to ensure that the assumption of constant error variance is met, as violation of this assumption can lead to biased and inefficient estimates of the model parameters. Additionally, it can affect the reliability of statistical inferences and lead to incorrect conclusions.
In summary, to determine whether the assumption of constant error variance is satisfied for a model with tut, independent variables x, and x₂, you would examine the residual plot where the residuals are plotted against predicted values y. It is important to check this assumption to ensure the validity of the model and the accuracy of the results.This plot allows you to assess the variance of the residuals and identify any patterns, which could indicate that the assumption of constant error variance may not be met. If the plot shows no discernible pattern and the spread of residuals appears to be uniform across the range of predicted values, the assumption of constant error variance is likely satisfied.
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the graph of linear function f passes through the point (1 -9) and has a slope of -3.
Answers
What is the difference between the mean and the median of the data set?
{22, 8, 10 ,18 ,12, 20}
ОО
NO
4
6
Please help I am on the test
Answers
Answer:
The answer is 1
Step-by-step explanation:
Mean
22+8+10+18+12+20 = 90
90/6=15
Median
22,8,10,18, 12,20
10+18 = 28
28/2= 14
Difference is 15-14 so the answer is 1
Pure copper was mixed with a 10% copper alloy to produce an alloy thát was 25% copper. How much of the pure copper and how much 10% alloy were used to produce 36 kg of 25% alloy?
Answers
Answer:
6kg pure copper and 30 kg 10% copper was mixed to give 36kg of 25% alloy
Step-by-step explanation:
Here, we want to produce 36 kg of 25% alloy
Let the Pure copper be x kg while 10% alloy be y kg
Pure copper is simply 100% copper
Thus;
x + y = 36 •••••(i)
Then;
100% of x + 10% of y = 25% of 36
= x + 0.1y = 9 •••••• ii)
From i x = 36-y
from ii, x = 9-0.1y
Equate both x
36-y = 9-0.1y
36-9 = 0.1y + y
0.9y = 27
y = 27/0.9
y = 30
x = 36-y
x = 36-30
x = 6 kg
Write in Standard Form. 3x2 4x + 7x3 + 1
Answers
The Standard Form of the polynomial function 3x^2 4x + 7x^3 + 1 is 7x^3 +3^2 +4x + 1
What is the meaning of the Standard Form of polynomial function?The meaning of the Standard Form of polynomial function can be explained as when the terms are in this equation or functions are be written in descending order of exponents.
This is usually done starting from the from left to right, we were given the function as :3x^2 +4x + 7x^3 + 1 , then let us arrange it as:
7x^3 +3^2 +4x + 1
Therefore, the Standard Form of polynomial function is 7x^3 +3^2 +4x + 1 .
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The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?
Click pic to see whole problem
Answers
Answer:
Step-by-step explanation:
Solving systems of equations gives the points of intersection when the equations are graphed.
The answer is 3.
Sally and anne went to the movies. They each purchased a drink. They also bought one popcorn and one veggie cup to share. Which expression can be used to find how much money each woman spent? one-half (9 + 1. 35 + 3. 50 + 1. 74) 9 + 1. 35 + one-half (3. 50 + 1. 74) 18 + 2. 70 + one-half (3. 50 + 1. 74) 9+1. 35+2(3. 50+1. 7).
Answers
Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].
As given in the question,
Condition for the expression:
Sally and Anne both went for a movie.
Each one purchased a drink.
Shared one popcorn and one veggie bought by them.
Consider movie ticket price = 9
drink price = 1.35
Popcorn price = 3.50
Veggie price = 1.74
Explanation for different expressions are:
1. one-half (9 + 1. 35 + 3. 50 + 1. 74)
Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.
2. 9 + 1. 35 + one-half (3. 50 + 1. 74)
This is correct option as it represents :
Movie ticket price = 9
Drink = 1.35
one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.
3. 18 + 2. 70 + one-half (3. 50 + 1. 74)
As per consideration of price this is not correct option.
Movie ticket price =18
Drink = 2.70
one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.
4. 9+1. 35+2(3. 50+1. 7)
This is not correct option as popcorn and veggie price is doubled.
Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].
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Question 3 (26 Marksiu to novin Consider the function bus lastamedaulluquo to ed 2x+3 2001-08: ud i f(a) In a) Find the domain D, of f. [2] b) Find the a and y-intercepts. [3] e) Find lim f(a), where e is an accumulation point of D, which is not in Df. Identify any possible asymptotes. [5] d) Find lim f(a). Identify any possible asymptote. [2] 8418 e) Find f'(a) and f(x). [4] f) Does f has any critical numbers?
Answers
a) Domain: All real numbers, b) Intercepts: x-intercept at (-3/2, 0), y-intercept at (0, 3), c) Limit and Asymptotes: Limit undefined, no asymptotes, d) Limit and Asymptotes: Limit undefined, no asymptotes, e) Derivatives: f'(x) = 2, f''(x) = 0, f) Critical numbers: None (linear function).
a) The domain D of f is the set of all real numbers.
b) The x-intercept is the point where f(x) = 0. Solving 2x + 3 = 0, we get x = -3/2. Therefore, the x-intercept is (-3/2, 0). The y-intercept is the point where x = 0. Substituting x = 0 into the equation, we get f(0) = 3. Therefore, the y-intercept is (0, 3).
c) The limit of f(x) as x approaches e, where e is an accumulation point of D but not in Df, is not defined unless the specific value of e is given. There are no asymptotes for this linear function.
d) The limit of f(x) as x approaches infinity or negative infinity is not defined for a linear function. There are no asymptotes.
e) The derivative of f(x) is f'(x) = 2. The second derivative of f(x) is f''(x) = 0.
f) Since f(x) = 2x + 3 is a linear function, it does not have any critical numbers.
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the complete question is:
Consider the function f(x) = 2x + 3.
a) Find the domain D of f. [2]
b) Find the x and y-intercepts. [3]
c) Find lim f(x) as x approaches e, where e is an accumulation point of D but not in Df. Identify any possible asymptotes. [5]
d) Find lim f(x). Identify any possible asymptotes. [2]
e) Find f'(x) and f''(x). [4]
f) Does f have any critical numbers?
When interpreting F(2,27) = 8.80,p < 0.05,what is the within-groups df?
A)30
B)27
C)3
D)2
Answers
The degrees of freedom (df) for the within-groups scenario is 27.
In the F-test, which is used to compare variances between groups, the degrees of freedom consist of two components: the numerator df and the denominator df. The numerator df corresponds to the number of groups being compared, while the denominator df represents the total number of observations minus the number of groups.
In the given scenario, F(2,27) = 8.80 indicates that the F-test is comparing variances between two groups. The numerator df is 2, representing the number of groups being compared.
To determine the within-groups df, we need to calculate the denominator df. The denominator df is calculated as the total number of observations minus the number of groups. Since the denominator df is given as 27, it implies that the total number of observations is 27 + 2 = 29, considering the two groups being compared.
Therefore, the within-groups df is 27, as it represents the total number of observations minus the number of groups in the F-test.
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"
Question 2 ""If the Vpp is 10 V, then the Vavg is:"" O 20 V O 3.53 V O 3.18 V O 5 V
"
Answers
The correct answer is option O: 5 V.
To determine the average voltage (Vavg) given a peak-to-peak voltage (Vpp) of 10 V, we need to consider the relationship between Vavg and Vpp in an alternating current (AC) waveform.
The average voltage of an AC waveform is related to its peak-to-peak voltage by the formula: Vavg = 0.5 * Vpp.
Applying this formula to the given Vpp of 10 V, we can calculate the Vavg as follows: Vavg = 0.5 * 10 V = 5 V.
The average voltage is equal to half of the peak-to-peak voltage, resulting in an average voltage of 5 V for a Vpp of 10 V.
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Anyone mind helping!?
Answers
a box with a square base and open top must have a volume of 4,000 cm3. find the dimensions of the box (in cm) that minimize the amount of material used.
Answers
A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.
Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:
V = x^2 * h
We are given that the volume is 4,000 cm³, so we can write:
x^2 * h = 4,000
Solving for h, we get:
h = 4000 / x^2
The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:
A = x^2 + 4xh
Substituting the expression we found for h, we get:
A = x^2 + 4x(4000 / x^2)
Simplifying and factoring out 4, we get:
A = 4(x^2 + 1000/x)
To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:
dA/dx = 8x - 4000/x^2 = 0
Solving for x, we get:
x = 10√2
Substituting this value back into the expression we found for h, we get:
h = 20√2
Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:
side length of the base: 10√2 cm
height: 20√2 cm
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two cards are dealt from an ordinary deck of 52 cards. this means that two cards are sampled uniformly at random without replacement. (a) what is the probability that both cards are aces and one of them is the ace of spades? (b) what is the probability that at least one of the cards is an ace? 6.
Answers
The probability that both cards are aces is 0.45%.
Given that,
A standard 52-card deck is used to deal two cards. In other words, two cards are uniformly and randomly sampled without being replaced.
There are four aces in the deck of 52 cards. The likelihood of drawing an ace when you draw a card is 4/52=1/13.
There are only 51 cards left when the second card is drawn, and since an ace has already been drawn, just 3 of those cards are still in the deck. Therefore, there is a 3/51 chance of drawing the second ace. The likelihood that both of these events occur is 1/13 x 3/51 = 0.00452. (approx). Thus, there is a 0.45% chance of drawing two aces.
Combinations and permutations offer a different perspective on this. There are 52C2 different methods to choose two cards from a deck. The entire sample space is shown here.
Therefore, the probability that both cards are aces is 0.45%.
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gabriella went skiing. she paid $35 to rent skis and $15 an hour to ski. if she paid a total of $95, how many hours did she ski?
Answers
Gabriella skied for 6 hours, Let x be the number of hours that Gabriella skied. We know that she paid $35 for ski rental and $15 per hour for skiing,
for a total of $95. We can set up the following equation to represent this information:
35 + 15x = 95
Solving for x, we get:
15x = 60
x = 4
Therefore, Gabriella skied for 6 hours.
Here is a more detailed explanation of how to solve the equation:
Subtract $35 from both sides of the equation.
15x = 60
15x - 35 = 60 - 35
15x = 25
Divide both sides of the equation by 15.
15x = 25
x = 25 / 15
x = 4
Therefore, x is equal to 4, which is the number of hours that Gabriella skied.
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Which of the following are true help me plsssss
Answers
Answer:
A p//q
Step-by-step explanation:
You just need to thoroughly analyse the diagram.
If you apply the geometry Theron and look at the graph at all angles you’ll see that they are all true.
Please mark as a brainliest (crown)above my comment
convert 6 2/5 to a fraction greater than 1
Answers
Answer:
Step-by-step explanation:
6 2/5
Number 5 is denominator, keep it for denominator.
Numerator will be 6x5+2 =32
so, a fraction of 6 2/5 greater than 1 is 32/5
A collector has items including baseball cards, gold coins, and stamps in a box. If P(gold coin) = 94%, interpret the likelihood of randomly selecting a gold coin from the box.
A: Likely
B: Unlikely
C: Equally likely and unlikely
D: This value is not possible to represent probability of a chance event
Answers
The correct classification regarding the probability is given as follows:
A: Likely.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The probabilities are classified as follows:
Hence option A is the correct option in the context of this problem.
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Mary did not pay last month's credit card bill in full. Below is a list of Mary's daily balances for his last billing cycle.
For 6 days she owed $500.00
For 4 days she owed $350.26
For 7 days she owed $568.45
For 8 days she owed $480.34
For 6 days she owed $649.90
Type your answer.
Answers
500+350.26+568.45+480.34+649.90 = $2548.95
hope it really helps...!!!
Janelle is considering two options for saving money. One option earns simple interest while the other option earns interest compounded monthly. If there are no additional deposits or withdraws, how much more will Janelle earn with the compound interest option? Assume Janelle deposits $3,000 at 3% interest for 7 years for both options
Answers
Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.
The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:
\(A = P(1 + r/n)^{(nt)}\)
Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.
For the simple interest option, the interest is calculated using the formula:
I = P * r * t
Where:
I is the total interest earned
Using the given values, we can calculate the interest earned with simple interest:
I = 3000 * 0.03 * 7
I = 630
Now, let's calculate the total amount earned with the compound interest option.
Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:
r = 0.03/12
t = 7 * 12
Using these values, we can calculate the total amount with compound interest:
\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)
A ≈ 3,729.19
To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:
Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19
Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.
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Solve for x. Show all work plz.
3(x + 5) = x - 7
Answers
Answer:
x = - 11
Step-by-step explanation:
3(x + 5) = x - 7
3x + 15 = x - 7
2x = -7 - 15
2x = - 22
x = - 11
Hope this helps!
Which equation matches the graph ?
Please help!
Answers
Answer:
\(B. \: \: y = 3x - 2\)
Step-by-step explanation:
I how this HELPS you!
Given h(x)=3√x+2, which of the following statements describes h(x)?
O The function h(x) is increasing on the interval (-,-2),
The function h(x) is decreasing on the interval (2,).
O The function h(x) is decreasing on the interval (-0,2).
O The function h(x) is increasing on the interval (-2,).
Answers
So, the correct statement is:
O The function h(x) is increasing on the interval (-2, ∞).
What is function?In mathematics, a function is a rule that assigns a unique output value for each input value. It is often represented by a mathematical expression or equation and can be thought of as a machine that takes input values and produces corresponding output values.
For example, the function \(f(x) = x^2\) is a mathematical rule that takes an input value x and produces an output value that is the square of x. If we input x = 3, the function will output \(f(3) = 3^2 = 9\). Similarly, if we input x = -2, the function will output \(f(-2) = (-2)^2 = 4\).
Functions are used extensively in many areas of mathematics, as well as in physics, engineering, economics, and other fields. They are essential for modeling real-world phenomena,
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simplify (2^4)^3
A.16^7
B.16^12
C.2^12
D.2^7
Answers
Answer:
\(\tt{} {2}^{12} \\ \)
Step-by-step explanation:
\(\tt{}( {2}^{4} {)}^{3} \)
\(\tt{}2 ^{(4 \times 3)} \)
\(\tt{} {2}^{12} \\ \\ \)
Use the formula to find
Answers
Answer:
5525
Step-by-step explanation:
Using the formula with n = 25 , then
\(\frac{25(26)(50+1)}{6}\)
= \(\frac{25(26)(51)}{6}\)
= \(\frac{33150}{6}\)
= 5525
Party supplies inc. sells metallic balloons for $2 each and helium balloons for $3.50 per bunch. Yesterday, they sold 36 more metallic balloons than the number of bunches of helium balloons. The total sales for both types of balloons were $281. Let b represent the number of metallic balloons. Solve for b
Please do it quickly
Answers
Answer:
Step-by-step expThe answer would be 18 because 36÷2 is 18.
omg I need help w all the questions lol someone pls help me. If u can message me and tell me or help me w the answers
Answers
Formula is: V= πr2h
d=4 in
r=2 in
V= π•2^2•h
V= π•4•h
If h is 3, answer is B. If h is 9, answer is C. Good luck.
Solve for x in the diagram below.
Answers
Create an equation for the following real-
world context: Last week Scott ran 27
miles more than Lea. Scott ran 46 miles.
How many miles did Lea run?
Answers
The equation is s = 27 + l, and Lea ran 19 miles
How to create an equation for the real-world context?The statement is given as:
Last week Scott ran 27 miles more than Lea. Scott ran 46 miles.Represent the miles they ran with the first letters of their names.
So, we have
s = 27 + l
s = 46
How many miles did Lea run?
Substitute s = 46 in s = 27 + l
46 = 27 + l
Subtract 27 from both sides
l = 19
Hence, the equation is s = 27 + l and Lea ran 19 miles
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What is the answer to 30a + 15b + 14b =
Answers
Answer:
30a + 29b
....................
Answer:
30a + 29b is the answer
We just need to add