Answer:
a) C) The system has no solutions only when h=3 and k is any real number.
b) D) The system has a unique solution when \(h=(-\infty,3)U(3,\infty)\) and k is any real number.
c) The system has may solutions when h=3 and k=15
Step-by-step explanation:
a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:
\(x_{1}+hx_{2}=3\)
so
\(x_{1}=3-hx_{2}\)
Next we can substitute this into the second equation so we get:
\(5(3-hx_{2})+15x_{2}=k\)
We distribute the 5 into the first parenthesis so we get:
\(15-5hx_{2}+15x_{2}=k\)
and group like terms:
\(-5hx_{2}+15x_{2}=k-15\)
we factor x2 so we get:
\(x_{2}(-5h+15)=k-15\)
and solve for x2:
\(x_{2}=\frac{k-15}{-5h+15}\)
this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:
\(-5h+15= 0\)
and solve for h:
\(-5h= -15\)
\(h=\frac{-15}{-5}\)
\(h= 3\)
so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.
b)
For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.
So we take the second equation and factor it:
\(5x_{1}+15x_{2}=k\)
we start by factoring a 5 from the left side of the equation so we get:
\(5(x_{1}+3x_{2})=k\)
Next, we divide both sides of the equation into 5 so we get:
\(x_{1}+3x_{2}=\frac{k}{5}\)
we now compare it to the first equation:
\(x_{1}+hx_{2}=3\)
\(x_{1}+3x_{2}=\frac{k}{5}\)
In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and \(\frac{k}{5}=3\)
when taking the second condition and solving for k we get that:
\(k=3(5)\)
so
k=15
Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:
D) The system has a unique solution when and k is any real number.
c)
We have already solved part c on the previous part of the problem, so the answer is:
The system has many solutions when h=3 and k=15
teri wants to buy as many pencils and pens as possible. she wants three pencils for every pen. each pencil costs $0.15 and each pen costs $0.20. she cannot spend more than $6.50
The maximum number of pens and pencils she can purchase is 10 pens and 30 pencils. The result is obtained by using substitution method on inequality problem.
How to find the maximum value in inequality?The most important thing in inequality problem is the inequality symbol. The symbols are:
">" = greater than"<" = less than"≤" = at least/no more than"≥" = greater than or equal toTeri wants to buy as many pencils and pens as possible by spending no more than $6.50. She wants three pencils for every pen. Each pencil costs $0.15 and each pen costs $0.20.
Find the maximum number of pens and pencils she can purchase?
Let's say:
x = number of pencilsy = number of pensThe money spent is no more than $6.50. It means the maximum money spent is $6.50. We got the inequality.
0.15x + 0.20y ≤ 6.50
She wants 3 pencils for 1 pen. We have x = 3y.
Substitute x with 3y!
0.15(3y) + 0.20y ≤ 6.50
0.45y + 0.20y ≤ 6.50
0.65y ≤ 6.50
y ≤ 10
x = 3y = 3(10) = 30
Hence, Teri can purchase 10 pens and 30 pencils with the money she can spend.
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Raul earned $3,600 in one month. He paid $828 in income tax that month. What decimal represents the income tax rate?
Answer:
0.23
Step-by-step explanation:
A formula I like to use to find the answer to these types of questions is
\(\frac{828}{3600} =\frac{x}{100}\)
first, multiply 828×100=82,800
now divide 82800÷3600=23
so your answer is 23%=\(\frac{23}{100}\)=0.23
Solve the proportion. 8/11 = 4/y + 2
Answer:
\(y=-\frac{22}{7}\)
Step-by-step explanation:
QUESTION 6 1 POINT
Using the table, what is the average daily balance of the credit card for the August 1 through August 31 billing period?
Round your answer to the nearest dollar.
Provide your answer below:
Day
1
8
16
24
Activity
Payment
Purchase
Purchase
Adjustment Closing Balance
-550
4
+200
+150
850
300
500
650
Rounded to the nearest dollar, the average daily balance of the credit card for the August 1 through August 31 billing period is $74.
To find the average daily balance of the credit card for the August 1 through August 31 billing period, we need to calculate the sum of the daily balances and divide it by the number of days in the billing period.
Let's calculate the daily balances for each day:
Day 1: Closing Balance = $850
Day 8: Closing Balance = $300
Day 16: Closing Balance = $500
Day 24: Closing Balance = $650
To calculate the daily balances, we need to consider the activities that occurred on each day.
On Day 1, there was no activity recorded, so the closing balance remains at $850.
On Day 8, a payment of $550 was made. Therefore, the closing balance is $850 - $550 = $300.
On Day 16, a purchase of $200 was made. Therefore, the closing balance is $300 + $200 = $500.
On Day 24, a purchase of $150 was made and an adjustment of $4 was applied. Therefore, the closing balance is $500 + $150 - $4 = $650.
Now, let's calculate the average daily balance:
Sum of daily balances = $850 + $300 + $500 + $650 = $2300
Number of days in the billing period = 31
Average daily balance = Sum of daily balances / Number of days = $2300 / 31 ≈ $74.19
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A gallery is using glass display cases to display artifacts. They need to cover each display case with a sheet of clear protective film to protect the glass on every side. This net represents a single display case.
How much film is needed to cover each display case?
Enter your answer in the box.
in²
Answer:
88.31 in ²
Step-by-step explanation:
multiply them all then get the square root of the answer.
its 2420
i just took the quiz and passed anyways good luck
make r the subject in the relation; rv= h
Answer:
step by step
take v to divide
r=h/v
Which expression does not belong with the other three? explain
The only expression that does not belong to the other 3 is the one that is a binomial.
How to identify the type of algebraic expression?A monomial is defined as an algebraic expression that has only one non- zero term. Examples of a monomial expression are x, 7xy²
A binomial is defined as an algebraic expression that has two non-zero terms. Examples of a binomial expression: x² + 2y
A trinomial is defined as an algebraic expression that possesses three non-zero terms. Examples of a trinomial expression: a + b + c
A polynomial is defined as an algebraic expression that has one, two or more terms.
The only expression that does not belong to the other 3 is (b - 2⁻¹) because it is the only binomial.
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This answer in a fraction
The experimental probability that the next student will register for German is 9/79.
What is probability?
To find the experimental probability that the next student will register for German, we need to divide the number of students who have registered for German by the total number of students who have registered so far:
P(German) = number of students who have registered for German / total number of students who have registered
P(German) = 108 / (108 + 360 + 21 + 459) [Adding all the students who registered for each language]
P(German) = 108 / 948
P(German) = 9/79
Therefore, the experimental probability that the next student will register for German is 9/79.
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10) Determine which point is a solution of the linear inequality.
92 + 3y < 6
O (1, -1)
O (2, -2)
• (1,1)
• (1,3)
Step-by-step explanation:
To determine which point is a solution of the linear inequality 92 + 3y < 6, we can substitute the values of each point into the inequality and check if the inequality holds true.
Let's evaluate the inequality for each point:
1. Point (1, -1):
92 + 3(-1) < 6
92 - 3 < 6
89 < 6
The inequality is not true for this point.
2. Point (2, -2):
92 + 3(-2) < 6
92 - 6 < 6
86 < 6
The inequality is not true for this point.
3. Point (1, 1):
92 + 3(1) < 6
92 + 3 < 6
95 < 6
The inequality is not true for this point.
4. Point (1, 3):
92 + 3(3) < 6
92 + 9 < 6
101 < 6
The inequality is not true for this point.
None of the given points satisfy the inequality. Therefore, none of the points (1, -1), (2, -2), (1, 1), or (1, 3) are solutions to the linear inequality 92 + 3y < 6.
what is the answers to this question
By evaluating the quadratic equation, we will see that the values of the expressions are:
f(-1) + f(4) = 27
f(-1) - f(4) = -35
How to evaluate the given expressions?Here we need to work with the quadratic function:
f(x) = x^2 + 6x + 1
First, we want to find the value of the expression:
f(-1) + f(4)
To get that, we need to evaluate the quadratic equation:
f(-1) = (-1)^2 + 6*(-1) + 1
f(-1) = 1 - 6 + 1 = -4
f(4) = 4^2 + 6*4 + 1
f(4) = 16 + 24 + 1 = 31
Then the first expression is:
f(-1) + f(4) = -4 + 31 = 27
The second expression is:
f(-1) - f(4)
We already know these values, we can replace these to get:
f(-1) - f(4) = -4 - 31 = -35
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Solve the problem below:
6315*41=
Show your work
The value of 6315 ×41 is 260391.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We have to find the product of 6315 times of forty one
6351
× 41
_______
6351
25404+
__________
260391
Hence, the value of 6315 ×41 is 260391.
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In October , Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than ounces, it was about lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of hours (The Wall Street Journal, October , ). Assume that battery life of the iPad Mini is uniformly distributed between and hours.a. Give a mathematical expression for the probability density function of battery life.A.B.C.The correct answer is:- Select your answer -b. What is the probability that the battery life for an iPad Mini will be hours or less (to 4 decimals)
Answer:
a. Probability density function for the battery life
\(f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}\)
b. P(x<11) = 0.7143
Step-by-step explanation:
The question is incomplete
In October, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a. Give a mathematical expression for the probability density function of battery life.
b. What is the probability that the battery life for an iPad Mini will be 11 hours or less (to 4 decimals).
a. We model the battery life as random variable with an uniform distribution with parameters a (min. value)=8.5 hours and b (max. value)=12 hours.
The probability that the battery life takes any value between 8.5 and 12 is constant. Also, the probability that takes any value outside the interval (8.5, 12) is 0.
We can express that as:
\(f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}\)
The last is the probability density function for the battery life.
b. We can calculate P(x<11) using the cumulative density function or integrating the density function between x=0 (or x=a=8.5) and x=11.
\(P(x<11)=\int\limits^{11}_{8.5} \dfrac{1}{3.5} \, dx=\dfrac{1}{3.5}(x_2-x_1)=\dfrac{1}{3.5}(11-8.5)=\dfrac{2.5}{3.5}= 0.7143\)
4. A circle has a radius of 4 inches. What is the circumference of the circle?
A.4 π inches
B.8 π inches
C.12π inches
D.16π inches
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Beginning inventory is &12,000 the purchase are $20,000 the ending inventory is $14,000 and other credits are $2,000 what is the actual food cost
Answer:
the actual food cost is $20,000.
Step-by-step explanation:
To calculate the actual food cost, we need to use the following formula:
Actual Food Cost = Beginning Inventory + Purchases - Ending Inventory + Other Credits
Substituting the given values in the formula, we get:
Actual Food Cost = $12,000 + $20,000 - $14,000 + $2,000
Actual Food Cost = $20,000
Therefore, the actual food cost is $20,000.
Find an autonomous differential equation with all of the following properties:
equilibrium solutions at y=0 and y=3,
y' > 0 for 0
y' < 0 for -inf < y < 0 and 3 < y < inf
dy/dx = ______
dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.
The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.
To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.
Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.
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determine the maximum and minimum values of the function, at what values of x are they achieved? (without using a derivative)
\(y=\sin^3x-\sin^6x\)
The maximum and minimum values of the function is solved
Given data ,
We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.
y = (sin x)³ - (sin x)⁶
y' = 3(sin x)² cos x - 6(sin x)⁵ cos x
Setting y' equal to zero:
0 = 3(sin x)² cos x - 6(sin x)⁵ cos x
0 = 3(sin x)² cos x (1 - 2(sin x)³)
sin x = 0 or (sin x)³ = 1/2
If sin x = 0, then x = kπ for any integer k.
If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.
To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.
y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x
y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)
For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.
For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.
Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3
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Answer:
maximum: 0.25minimum: -2Step-by-step explanation:
You want the maximum and minimum values of the function ...
y = sin³(x) -sin⁶(x)
SolutionWhen we substitute sin³(x) = z, we have the quadratic expression ...
y = z -z² . . . . . a quadratic function
Adding and subtracting 1/4, we can put this in vertex form:
y = -(z -1/2)² +1/4
MaximumThis version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.
The maximum value of y is 1/4.
MinimumThe sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...
y = (-1) -(-1)² = -1 -1 = -2
The minimum value of y is -2.
__
Additional comment
The range of y is confirmed by a graphing calculator.
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Each week Julie spends 5 hours reading, 6 hours watching television, and 4 hours playing outside.Use the Associative Property of Addition to write two equivalent expressions that show the totalnumber of hours Julie spends reading, watching television, and playing outside.Choose the correct answer below.
Hours spent on reading = 5
Hours spent on watching tv= 6
Hours spent on playing outside = 4
let R represent hours spent on reading
let W represent hours on watching tv
let P represent hours spent playing outside
Using associative property
R + (W + P) = (R + W ) + P
=>
5 + (6 + 4) = (5 + 6) + 4Ho
Ed needed to extend the string on his kite. The current string was nine and three fourths feet. He cut a piece of string that measured 2.5 feet and added it to the existing string. What is the new length of the string?
twelve and one fourth feet
eleven and three fourths feet
seven and one half feet
seven and one fourth feet
Answer:
Twelve and one fourth feet
Step-by-step explanation:
9 and 3/4 feet =9.75
2 and 2/4 feet =2.50
9.75 + 2.50
= 12.25/12 and 1/4 feet
Lauren's mother gave Lauren $15.00 to buy some things at the store. Lauren has spent $12.79 and still needs to stop at the fruit stand to buy some grapes that are on sale for $0.89 per pound. Lauren uses the following inequality to determine how many pounds of grapes to buy. 0.89g + 12.79 < 15.00 Which could be the number of pounds of grapes that Lauren can purchase? Select all that apply,
2.45
2.5
2.49
2.4
2.39
The number of pounds of grapes that can be purchased are 2.45, 2.4, 2.39.
The total amount Lauren's mother can spend has to be less than $15. This is why the inequality sign used is the less than sign - <.
Given this equation: 0.89g + 12.79 < 15.00 , in order to determine the pounds of grapes that can be used, take the following steps:
Combine similar terms
0.89g < 15 - 12.79
Add similar terms
0.89g < 2.21
Divide both sides of the equation by 0.89
g < 2.48g
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Read The Question in the PNG
9514 1404 393
Answer:
A. dollars = euros × 0.75
B. the exchange rate is the slope of the graph
Step-by-step explanation:
A. The graph indicates 1 euro will be exchanged for 0.75 dollars, or 4 euros for 3 dollars.
__
B. This exchange rate is the slope of the line on the graph: 0.75 dollars per euro.
HELPPPP PLEASEEEE ASAPPPP
Answer:
13) 3/4
14) 3/5
15) 73/100
16) 1/10
17) 8.52
18) 0.9
19) 2.66
20) 5.19
Step-by-step explanation:
13) 75% = 75/100 = 3/4
14) 60% = 60/100 = 6/10
15) 73% = 73/100
16) 10% = 10/100 = 1/10
Janna’s average score on five 100-point tests was 80. Her score on the sixth test raised her mean score two points. How many points did she score on the sixth test?
The point that Janna scores on the 6th test is 92.
How to calculate the value?Since Janna’s average score on five 100-point tests was 80. The total score will be:
= 5 × 80
= 400
Since the score on the sixth test raised her mean score two points, the total score will be:
= (80 + 2) × 6
= 82 × 6
= 492
The points that she had on the sixth score will be:
= 492 - 400
= 92
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5x+4y=-12 Y=-2x-9 What is x
Answer:
X = -16
Step-by-step explanation:
5x+4y=-12 Y=-2x-9
substitute the value of y
5x + 4(-2x - 9)=12
solve the equation
x=-16
what is 4x+3y-x-4y? please help-
Answer:
3x-1y
Step-by-step explanation:
i think that Is that
Answer:
what is 4x+3y-x-4y?
Simplify the expression.
Final answer: 4x+3y-x-4y = 3x-y
Step-by-step explanation:
I hope that this answer helps you to understand your question more thoroughly. If you have any other questions, please put them below.
Have a great rest of your day/night!
Need help I can’t fail this assignment. Answer asap!
Answer:
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes
6x + 5y = 10
5y = -6x + 10
y = (-6/5)x + 2
so a perpendicular line has slope 5/6
y = (5/6)x + b
plug in our desired point
3 = (5/6)6 + b
b = -2
y = (5/6)x - 2
I might be able to help you pass this assignment, but better learn it yourself as I cannot assure you will pass the class.
One of those "Win the battle but lose the war" type situations.
Name and define the two areas of statistics.
Answer:The two major areas of statistics are known as descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions.
4.4 cm3.4 cmWhat is the surface area of the square pyramid, in squarecentimeters?Answer: AcmSubmit Answer
The surface area is the sum of the area of the square plus the area of the 4 equal triangles. So, we need to find the area of one triangle multiply by 4 and add the area of the square.
Then, the area of one triangle is
\(\begin{gathered} A_T=\frac{1}{2}(3.4)(4.4) \\ A_T=7.48cm^2 \end{gathered}\)and the area of the square is
\(\begin{gathered} A_S=(3.4)^2 \\ A_S=11.56cm^2 \end{gathered}\)Then, the surface S is
\(\begin{gathered} S=4\times A_T+A_S \\ S=4\times7.48+11.56 \\ S=41.48cm^2 \end{gathered}\)And the answer is 41.48 centimeters squared.
A box contains four blue and eight red balls. Jim and Jack start drawing balls from the box, respectively, one at a time, at random, and without replacement until a blue ball is drawn. What is the probability that Jack draws the blue ball?
Answer:
the probability that Jack draws the blue ball is 0.38539
Step-by-step explanation:
Given the data in the question;
box contains
blue balls = 5
red balls = 8
Jim and Jack start drawing balls from the box, respectively, one at a time, at random, and without replacement
Now,
on the first attempted;
⇒ ( 8/13) × ( 5/12) = 10/39
on the second attempt;
⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) = 14/143
on the third attempt;
⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) ( 4/9 ) ( 5/8 ) = 35/1287
on the fourth attempt;
⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) ( 4/9 ) ( 3/8 ) ( 2/7 ) ( 5/6 ) = 5/1287
so we add everything;
⇒ 10/39 + 14/143 + 35/1287 + 5/1287
= 0.38539
Therefore, the probability that Jack draws the blue ball is 0.38539
Scott invested $1600 into a retirement account that earns 2.4% interest compounded monthly. What will the balance of the account be after 30 years? Round answer to the nearest hundredth
Answer:
Step-by-step explanation:
\(V=P\left(1+\ frac{r}{c}\right)^{ct}\\ \\ V=1600\left(1+\frac{0.024}{12}\right)^{12(30)}\\ \\ V=\$ 3284.73\)
Answer:
The interest is $13824 and the amount is $15424.
Step-by-step explanation:
i did 2.4% of 1600 which is 38.4 then i took that number and multiplied it by 12 (months in a year) and got 13824
I am not sure if you are supposed to add in the original amount, and if you are, it would be 15424
Hope this helped!