Answers
Answer:
(a) To find the range of the function f(x), we need to consider all possible values of x in the range -7 ≤ x ≤ 7 and x ≠ -5. For each value of x, we can evaluate the function to find the corresponding value of f(x). Then, we can find the minimum and maximum values of f(x) in this range to determine the range of the function.
For example, if x = -7, then the function will return a value of 2 - 12/(-7) + 5 = 2 + 2 + 5 = 9. If x = 7, then the function will return a value of 2 - 12/7 + 5 = 2 - 1 + 5 = 6.
We can see that the minimum value of the function is 6, which is achieved when x = 7, and the maximum value of the function is 9, which is achieved when x = -7. Therefore, the range of the function is {6, 9}.
(b) To find the inverse of the function f(x), we need to switch the x and y values in the function definition to obtain a new function g(y) such that g(f(x)) = x for all values of x in the domain of the original function.
In this case, the inverse of the function f(x) is given by g(y) = (2 - y + 5)/(-12). This inverse function is defined for all values of y in the range {6, 9}, which is the range of the original function.
To find the value of f^-1(0), we can plug in 0 for y in the inverse function g(y) to obtain g(0) = (2 - 0 + 5)/(-12) = -1/12. Therefore, f^-1(0) = -1/12.
Related Questions
This morning, Kenneth took a history test. He got 42 out of 56 problems right. What percentage did Kenneth get right?
\
Answers
Answer = 75%
the accompanying data file shows the monthly closing stock price for a large technology firm for the first six months of the year.
Answers
The Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
What is a confidence interval?
A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. It is a measure of the uncertainty associated with an estimate of a population parameter, such as the mean, the proportion, or the variance.
a)
sample mean = 75.67
sample std. dev. = 3.56
b)
Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.015
[tex]CI = (xbar - tc * s/\sqrt{n} , xbar + tc * s/\sqrt{n})\\\\CI = (75.67 - 2.015 * 3.56/\sqrt{6} , 75.67 + 2.015 * 3.56/\sqrt{6})\\\\\CI = (72.74 , 78.60)[/tex]
Hence the Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
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help me with this question please
Answers
Answer:
Step-by-step explanation:
You just have to recall those rules in geometry. :/
for 1 RU = QT
the red single marks on the segment mean those are the same length
for 2 ∠T = ∠U
the red arc means they are the same angle
for 3 QT is parallel to RU
because of both red marks, same length, and same angles
for 4 RQT = SRU
because both of these angles come from the same line, and have the same length and angle below
for 5 triangle QRT = RSU
because of both red marks and starting from the same line.
• We are provided this information through the figure. The red hash marks on both corresponding sides indicate they are congruent segments.
Reason 2: Given
• Angle T and U are marked with the same angle measure red symbols, indicating they are congruent, corresponding angles.
Reason 3: Given
• Segment QT is parallel to RU, which is given at the top of question.
Reason 4: Corresponding Angles Theorem
• Because segment QT is parallel to RU, segment SQ forms a transversal. When a pair of parallel lines is intersected by a transversal, angle relationships are formed for which properties exist. In this case, the corresponding angles are congruent. This will help us prove the two triangles congruent.
Reason 5: Angle-Side-Angle (ASA)
• Lastly, we have a pair of corresponding congruent angles, a pair of corresponding congruent sides, and another pair of corresponding congruent angles. This means we can apply the ASA postulate, which states that if a pair of corresponding angles, a pair of corresponding sides, and another pair of corresponding angles are congruent, then the two triangles are congruent.
I hope this helps!
Mario's current credit card balance is $2,673.19 with a minimum payment of $102.00. Over the next month, he plans to spend $626.00. If the APR is 26.99%, what will Mario's new balance be, including
interest? (2 points)
$3,201.98
$3,269.10
$3,197.19
$3,394.68
Answers
If the APR on Mario's credit card is 26.99%, Mario's new balance, including interest will be B. $3,269.10.
What is the APR?Annual percentage rate (APR) is the annual finance charge applied to a credit balance.
The APR includes interest and other fees for borrowing credit.
Current credit card balance = $2,673.19
Minimum payment within the month = (102.00)
Purchase payments 626.00
Finance Charge $71.91 ($3,197.19 x 26.99% x 1/12)
Ending credit card balance = $3,269.10 ($3,197.19 + $71.91)
Annual percentage rate = 26.99%
Monthly percentage rate = 2.25% (26.99% ÷ 12)
Thus, Mario will end up with a credit card balance of $3,269.10 after one month with APR of 26.99%.
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Please help will mark Brainly
Answers
One glass of milk and one snacks bar have a total of 23 carbs.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Two glass of milk and Three snacks bar have a total of 56 carbs.
And, Four glass of milk and two snacks bar have a total of 72 carbs.
Now,
Let the amount of milk = x
And, The amount of snacks bar = y
So, We can formulate;
Two glass of milk and Three snacks bar have a total of 56 carbs.
⇒ 2x + 3y = 56 ..(i)
And, Four glass of milk and two snacks bar have a total of 72 carbs.
⇒ 4x + 2y = 72
⇒ 2x + y = 36
⇒ y = 36 - 2x ..(ii)
Substitute above value in equation (i),
⇒ 2x + 3y = 56
⇒ 2x + 3 (36 - 2x) = 56
⇒ 2x + 108 - 6x = 56
⇒ 108 - 56 = 4x
⇒ 4x = 52
⇒ x = 13
And, from (ii);
⇒ y = 36 - 2x
⇒ y = 36 - 2 × 13
⇒ y = 36 - 26
⇒ y = 10
Thus, One glass of milk and one snacks bar have a total of carbs
= 13 + 10
= 23
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ABC has vertices A(1, 3), B(2, 5), and C(5, 3). What are the coordinates of B′ after the transformation (x, y) ⟶ (–y, x), then translation 1 unit right and 4 units up?
Answers
Answer: we first need to apply the transformation to the x- and y-coordinates of the point individually
Step-by-step explanation:
To transform the coordinates of a point (x, y) using the transformation (x, y) ⟶ (–y, x), we first need to apply the transformation to the x- and y-coordinates of the point individually. This means that the x-coordinate becomes –y and the y-coordinate becomes x.
In the case of point B, the original coordinates are (2, 5), so the transformed coordinates are (–5, 2). This means that the x-coordinate becomes –5 and the y-coordinate becomes 2.
Next, we need to apply the translation that moves the point 1 unit right and 4 units up. To do this, we simply add 1 to the x-coordinate and add 4 to the y-coordinate. After this translation, the coordinates of B′ become (–4, 6). Therefore, the final coordinates of B′ are (–4, 6).
Which ordered pair is a solution of the equation
y = 7x-2
Answers
What is a equation in math?
Image result for What is equation?
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
What is a equation in math?
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
given:
y=7x-2
first, (3, 15)
15 = 7*3-2 = 21-2 = 19
So, (3, 15) is not the solution.
Second, (-1,-10)
-10 = 7* (-1) -2
-10 = -9
Also, (-1,-10) is not the solution.
Hence, there is no solution for y=7x-2
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Which expressions are equivalent to
5^2/5^8
Answers
ANSWER: A & C
EXPLANATION: look at the photo
• a & b both are equivalent to 5^-6
PLEASE HELP WITH THE QUESTION IN THE PICTURE
Answers
Answer:
(9.22 x 10⁻⁵) + (1.078 x 10⁻⁵)
You can take 10⁻⁵ as common from both terms and add the remaining ones.
(9.22 + 1.078) x 10⁻⁵
10.298 x 10⁻⁵
Which linear function has the greatest initial value? Which has the greatest rate of change? Use the drop-down menus to show your answer.
Answers
The linear function that has greatest initial value is function C
The linear function that has greatest rate of change is function B
Consider the function A
The y intercept = 0
Consider two points (2, 5) and (4, 10)
The slope of the line = (10-5) / 4-2
= 5 /2
The equation will be
y = 5/2x + 0
Consider the function B
y = 3x - 1
Which is in the form of slope intercept form
The slope of the line = 3
The y intercept = -1
Consider the function C
y intercept = 2
Consider the points (0, 2) and (3, 3)
The slope of the function = 3-2 / 3 -0
= 1/3
The equation is
y = 1/3x + 2
Therefore, function C has greatest initial value and function B has greatest rate of change
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2. *
In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern?
a) P=3 n
b) P=n+3
c) P=2 n+1
d) P=3-n
A
B
C
Both A andC
Answers
In a table of values for a pattern, P=3 when n=1; the equations P=3n and 2n+1 might represent the pattern. So the option d "Both A and C" is correct option.
In the given question, In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern.
a) P=3n
b) P = n+3
c) P = 2n+1
d) P = 3-n
We find the pattern we firstly observe the given diagram closely.
We firstly check which option can given P=3 when n=1.
Firstly taking the option a.
P = 3n
Now put n=1, so
P = 3
Hence, the option one is following the condition.
Now taking the option b.
P = n+3
Now put n=1, so
P = 1+3
P = 4
Hence, the option b is not following the condition.
Now taking the option c.
P = 2n+1
Now put n=1, so
P = 2(1)+1
P = 2+1
P = 3
Hence, the option c is following the condition.
Now taking the option d.
P = 3-n
Now put n=1, so
P = 3-1
P = 2
Hence, the option d is not following the condition.
Hence, the option a and c is following the condition. So the option d "Both A and C" is correct option.
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The vertex is (-4,-2) and the parabola opens up. What is the domain and range
Answers
Answer:
Domain: -∞ < x < ∞
Range: y ≥ -2
Step-by-step explanation:
The domain of a parabola graph is all real numbers, this is written as;
-∞ < x < ∞
The range of this parabola graph is all numbers greater than and equal to -2, since the parabola opens up and the vertex is at (-4, -2). This is written as;
y ≥ -2
X’(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ] X(t)X0 = [ 1234]1. (67 points) Use Theorem 1 on page 350 to solve the above system of differential equations (see section 5.6 video).2. (33points) Use your solution to show that your solution solves the original system of differential equations
Answers
To solve the system of differential equations using Theorem 1, we first need to find the eigen values and eigen vectors of the matrix X'.
The characteristic equation is given by |X' - λI| = 0, where I is the identity matrix. Solving this equation, we find the eigenvalues to be λ = -2, 0, 3, 5.
Next, we need to find the corresponding eigenvectors. For each eigenvalue, we solve the equation (X' - λI)v = 0 to find the eigenvector.
For λ = -2, the eigenvector is v = [-2 -2 -2 -2 -2 1 -2 -2 -2 -2 -2 1 -2 -2 -2 1]
For λ = 0, the eigenvector is v = [-4 1 -2 -2 4 -3 2 -2 1 -2 -5 0 1 0 4 -1]
For λ = 3, the eigenvector is v = [4 -2 -2 -2 -4 3 -2 -2 -1 -2 5 0 -1 0 -4 1]
For λ = 5, the eigenvector is v = [0 2 2 2 0 -1 2 2 2 2 0 -1 2 2 0 -1]
Using these eigen values and eigen vectors, we can use Theorem 1 to find the general solution to the system of differential equations:
X(t) = c1e^(-2t)v1 + c2e^(0t)v2 + c3e^(3t)v3 + c4e^(5t)v4
where c1, c2, c3, and c4 are constants.
To show that this solution solves the original system of differential equations, we substitute it into the given differential equation:
X'(t) = -2c1e^(-2t)v1 + 0c2e^(0t)v2 + 3c3e^(3t)v3 + 5c4e^(5t)v4
This simplifies to:
X'(t) = [-4 0 0 0 8 -3 4 0 1 0 -5 0 2 1 4 -1 ]
which is equal to the given matrix X'(t). Therefore, the solution we have found does indeed solve the original system of differential equations.
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After spending many hours studying for your math class (I am being hopeful here!) you decide to reward yourself with a case of soda. Unfortunately the store only had a warm case left (the Kent students got there first and got all of the cold ones). You buy several bags of ice and decide to chill it at home. When you get home the temperature of the soda is 76 degrees F and you proceed to pack it in ice. After ten minutes the temperature has cooled to 70 degrees F. If the soda is best served at 60 degrees F or cooler, how much longer must you wait to enjoy your soda? Note that you have not been given the temperature of the surroundings, but you should be able to figure out what that should be (you are packing it in ice that is at the freezing point of water so...).
Answers
the difference between the two temperatures as 16 degrees F. You must wait for another 6 minutes for the soda to cool down to 60 degrees F.
Since the initial temperature of the soda is 76 degrees F and the desired temperature is 60 degrees F, we can calculate the difference between the two temperatures as 16 degrees F. We also know that the temperature of the ice is at the freezing point of water which is 32 degrees F. This means that the temperature difference between the soda and the ice is 44 degrees F. Since the temperature difference between the soda and the ice is greater than the temperature difference between the desired temperature and the initial temperature, we can divide the desired temperature difference (16 degrees F) by the temperature difference between the soda and the ice (44 degrees F) and multiply it by the time elapsed (10 minutes) to calculate the remaining time needed for the soda to cool down to the desired temperature. 16/44 * 10 = 6. Therefore, we must wait for another 6 minutes for the soda to cool down to 60 degrees F.
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Which of the following is NOT one of the three main methods of inventory evaluation as described in your reading material? A. weighted average, B. straight average, C. FIFO, D. LIFO
Answers
Answer:
A or B
Step-by-step explanation:
I think it's B.. according to the people I know
If f(x) = -3x + 4, what is the value of f(-5)?
-5=-3x4
A) -4
C) 19
B) 15
D) 3
Answers
Answer:
15
Step-by-step explanation:
If f(x) = -3x + 4, then plugging in -5 for x gives f(-5) = -3(-5) + 4 = 15. Therefore, the correct answer is 15.
the perimeter of a rectangle is 124ft and the length is 5 more than twice its width, find the length and the width. note: p
Answers
Answer:
length = 43 ft ; width = 19 ft
Step-by-step explanation:
perimeter/2 = 124/2 = 62 ft
l = 2w + 5
l + w = 62
2w+5 + w = 62
3w = 62 - 5
3w = 57
w = 57/3
w = 19 ft
l = 2 · 19 + 5
l = 38 + 5
l = 43 ft
Kelly has the following income and expenses:
$200 per month paychecks
$50 cell phone
$40 gasoline
$40 Miscellaneous expenses
How much are Kelly's total planned expenses?
•
Answers
two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.
Answers
The conclusion hypothesis is to reject the null hypothesis and accept the alternative hypothesis. The z score of 0.14 is in the rejection area
What is hypothesis?
In statistics, hypothesis refers a testable statement about the relationship between two or more variables or a proposed variable.
Here we have given that two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.
And we need to find the conclusion hypothesis.
While we looking into the given question, we have identified the following values,
Sample mean: Machine 1 25 31.8 oz 2.2 oz
Sample SD: Machine 2 36 30.9 OZ 1.98 oz
So, the hypothesis is calculated as, the claim is the population mean of cereal cartons from machine 1 is larger than that from the machine 2
Null hypothesis: H0 : The population mean of cereal cartons for machine 1 and machine 2 is same
Alternative hypothesis H1: The population defines the statistical inference experiment.
So, the conclusion of hypothesis is, the critical value (cutoff point) is 2.353. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since 0.14 is less than 2.353, we reject the null hypothesis. We accept the alternative hypothesis.
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the product of 3 and a number is twice 23
Answers
x=46/3 ≈15.33
the position of a particle moving along a coordinate line is s=√(3+6t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec.
Answers
The particle's velocity at time t = 1 seconds is equal to 3 meters per seconds.
What is a position vs time graph?In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled (covered) by an object from its starting position with respect to the time when it is started moving.
Generally speaking, the position of a physical object (body) in a position vs time graph is always plotted on the y-coordinate (y-axis) while time is always plotted on the x-coordinate (x-axis).
From the information provided about this particle on a position vs time graph, we have;
s =√(3 + 6t)
Where:
s in meters.t in seconds.Substituting the given parameters into the formula, we have;
s =√(3 + 6(1))
s =√(3 + 6)
s =√9
Distance, s = 3 meters.
Now, we can determine the velocity as follows;
Velocity = distance/time
Velocity = 3/1
Velocity = 3 meters per seconds.
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the following data represent the running times of films produced by two motion-picture companies. company time (minutes) i 103 94 110 87 98 ii 97 82 123 92 175 88 118 compute a 90% confidence interval for the difference between the average running times of films produced by the two companies. assume that the running-time differences are approximately normally distributed with unequal variances
Answers
The 90% confidence interval for the difference between the average running times of films produced by the two companies ≅ (- 35.5 , 10.8)
Given that:
Company (i) :
[tex]n_{1}[/tex] = 5 , [tex]x_{1}[/tex]bar = 98.4
[tex]S_{1} ^{2}[/tex] = [tex]\frac{1 }{n_{1} - 1}[/tex] ∑ [tex](x_{i} - x_{1} bar)^{2}[/tex]
= [tex]\frac{1}{5 - 1}[/tex] [ [tex](103 - 98.4)^{2}[/tex] + [tex](94 -98.4)^{2}[/tex]+........+ [tex](98 - 98.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ [tex](4.6)^{2}[/tex] + [tex](-4.4)^{2}[/tex]+..........+[tex](0.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ 305.2]
= 76.3
Company (ii) :
[tex]n_{2}[/tex] = 7 , [tex]x_{2}[/tex] bar = 110.7143
[tex]S_{2} ^{2}[/tex] = [tex]\frac{1 }{n_{2} - 1}[/tex] ∑ [tex](xi - x_{2} bar)^{2}[/tex]
= [tex]\frac{1}{7-1}[/tex] [ [tex](97 - 110.7143)^{2}[/tex]+ [tex](82-110.7143)^{2}[/tex]+.........+[tex](118 - 110.7143)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ [tex](-13.7143)^{2}[/tex]+ [tex](-28.7143)^{2}[/tex]+.........+[tex](7.2857)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ 6125.4274]
≅ 1035.9045
For 90% confidence interval
difference between = 5+7-2 = 10, critical value is [tex]t_{c}[/tex] = 1.812.
90% confidence interval for the difference between the average running times is
[ ([tex]x_{1}[/tex] bar - [tex]x_{2}[/tex] bar) ± [tex]t_{c}[/tex] . [tex]\sqrt{\frac{S_{1}^2 }{n_{1} } } + \sqrt{\frac{S_{2}^2 }{n_{2} }}[/tex] ]
= [(98.4 - 110.7143) ± 1.812 [tex]\sqrt{\frac{76.3}{5} } + \sqrt{\frac{1035.90457}{7} }[/tex] ]
= [-12.3143 ± 23.1515]
= (- 35.4658 , 10.8372)
≅ (-35.5 , 10.8)
Therefore, 90% confidence interval for the difference between the average running times of films produced by the two companies is
≅ (- 35.5 , 10.8)
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What is the range of the set of ordered points defined below?
{(–1 , 3), (2 , 3), (4 , 5)}
Answers
Answer:
Rang is the output values or the y values.
3 and 5
Step-by-step explanation:
An ordered pair is in the form (x, y) The x is the input or the domain and the y is the output or the range.
Consider this conditional statement.
If a person is a professional athlete, then the person is a professional hockey player.
(a) Give the contrapositive of the statement.
If (Choose one)
then (Choose one)
(b) Give the converse of the statement.
If (Choose one)
then (Choose one)
(c) Give the inverse of the statement.
If (Choose one)
then (Choose one)
Answers
If a person is a professional athlete, then the person is a professional hockey player.
Given :
( a ) Give the contrapositive of the statement.
If not the person is a professional hockey player .
then not a person is a professional athlete .
( b ) Give the converse of the statement.
If the person is a professional hockey player .
then a person is a professional athlete .
( c ) Give the inverse of the statement .
If not the person is a professional hockey player.
then not a person is a professional athlete .
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What would:
2x + -2y = ?
Make?
Answers
Answer:
[tex]y=x[/tex]
Step-by-step explanation:
[tex]2(-y+x)=0\\\\-y+x=0\\\\-y=-x\\\\y=x[/tex]
It would he quite risky for you to insure the life of a 21 -year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain $\$ 1250 dollars in premiums. But if he were to die, you would lose almost \$ 100,000$. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21 -year-old men. (b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the investment. We can measure the great risk of insuring $\mathrm{u}$ single person's life in Exercise 14 by computing the standard deviation of the income $Y$ that the insurer will receive. Find or using the distribution and mean found in Exercise 14.
Answers
The standard deviation of Y can be determined which is 9708.
Given in the question that the high probability would gain in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.
According to the information, the gain around is 1250
Amount would lost in case of death is 100000.The expected value with its probability is:
E(X) = ∑x ×P(x)
=(-99750) × 0.00183 + ...+ (1250) × 0.99058
= 303.35
The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is
The standard deviation of Y can be determined as
α = under root {∑x2 × P(x) - (∑x × P(x) }
[tex]\sqrt{(-99750 - 303.3525)sq. X 0.00183 + .... + (1250 - 303.3525)sq. X 0.99058 }[/tex]
= 9708
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For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.
Hint
Examples:
f(5)=0 means (5,0) is a point on the line.
f(3)=-2 means (3,-2) is a point on the line.
How do you find the slope of the line when you have 2 points?
Answers
Answer:
f(x) = -3x + 6
Step-by-step explanation:
f(2)=0 point (2, 0)
f(4)=-6 point (4, -6)
m = slope = (y_2 - y_1)/(x_2 - x_1)
m = (-6 - 0)/(4 - 2) = -6/2 = -3
y = mx + b
y = -3 x + b
0 = -3 × 2 + b
0 = -6 + b
b = 6
y = -3x + 6
f(x) = -3x + 6
6 gallon of lemonade. how much is this in pints?
Answers
Answer:
Step-by-step explanation:
7 49999977/50000000 is gallons to pints. multiply that number by 6, which is 47 24999931/25000000.
Determine the number and type of solutions for the equation
5x^2−x−3=0
-Two different irrational-number solutions
-Two imaginary-number solutions
-One repeated rational-number solution
-One repeated irrational-number solution
-Two different rational-number solutions
Answers
The equation has one repeated rational number solution. thus Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given equation is the quadratic equation:
[tex]5x^2-x-3=0[/tex]
It is required to determine the number and type of solutions.
Noted that If the discriminant equals zero, the equation has one repeated rational number solution.
If the discriminant is positive, then the equation has two real solutions.
If the discriminant is negative, then the equation has two imaginary solutions.
If the discriminant is a perfect square, then then the equation has two real rational number solutions, it has two irrational number solutions.
Calculate the discriminant of the equation [tex]5x^2-x-3=0[/tex] by substituting a= 5, b=-1 and c= 3 into the discriminant formula:
Since the discriminant equals zero, it follows that the equation has one repeated rational number solution.
The equation has one repeated rational number solution.
Option C is correct.
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mayco, a mail-order department store, has five telephone lines available for customers who wish to contact customer service. if the probability is 1 6 that any one of the five telephone lines is engaged during business hours, find the probability that all five lines will be in use when a customer calls customer service. (round your answer to four decimal places.)
Answers
Answer:
The probability that all five lines will be in use when a customer calls customer service is 1/7776.
What is probability?
The proportion of favorable cases to all possible situations that can occur indicates how likely an event is to occur.
Step-by-step explanation:
Given that there are 5 lines and the probability for each line to be engaged in working hours is 1/6.
So, for all 5 lines to be engaged is
= 1/6 * 1/6 * 1/6 * 1/6 * 1/6
= [tex]\frac{1}{6} ^{5}[/tex]
= [tex]\frac{1}{7776}[/tex]
Therefore, the probability that all five lines are engaged is 1/7776.
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