9514 1404 393
Answer:
an extraneous solution
Step-by-step explanation:
A solution that shows up as a result of the process of solving an equation, but that does not work in the original equation, is called "an extraneous solution".
_____
Additional comment
Radical and rational expression equations can have extraneous solutions. For radical equations, they are typically ones that require a negative square root (or negative root of even index). For rational expression equations, they typically involve "excluded" values, values that make a denominator be zero.
Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions.
x1 +hx2 = 3
5x1 + 15x2 = k
a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
A. The system has no solutions only when k nothing and h is any real number.
B. The system has no solutions only when h nothing and k nothing.
C. The system has no solutions only when h nothing and k is any real number.
D. The system has no solutions only when h nothing and k nothing.
E. The system has no solutions only when h nothing and k nothing.
F. The system has no solutions only when k nothing and h is any real number.
G. The system has no solutions only when h nothing and k nothing.
H. The system has no solutions only when h nothing and k is any real number.
b. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
A. The system has a unique solution only when h and k
B. The system has a unique solution only when h =-and k is any real number.
C. The system has a unique solution only when k | and h is any real number.
D. The system has a unique solution only when h-U and k = 1
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 [tex]h=(-\infty,3)U(3,\infty)[/tex] 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:
[tex]x_{1}+hx_{2}=3[/tex]
so
[tex]x_{1}=3-hx_{2}[/tex]
Next we can substitute this into the second equation so we get:
[tex]5(3-hx_{2})+15x_{2}=k[/tex]
We distribute the 5 into the first parenthesis so we get:
[tex]15-5hx_{2}+15x_{2}=k[/tex]
and group like terms:
[tex]-5hx_{2}+15x_{2}=k-15[/tex]
we factor x2 so we get:
[tex]x_{2}(-5h+15)=k-15[/tex]
and solve for x2:
[tex]x_{2}=\frac{k-15}{-5h+15}[/tex]
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:
[tex]-5h+15= 0[/tex]
and solve for h:
[tex]-5h= -15[/tex]
[tex]h=\frac{-15}{-5}[/tex]
[tex]h= 3[/tex]
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:
[tex]5x_{1}+15x_{2}=k[/tex]
we start by factoring a 5 from the left side of the equation so we get:
[tex]5(x_{1}+3x_{2})=k[/tex]
Next, we divide both sides of the equation into 5 so we get:
[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]
we now compare it to the first equation:
[tex]x_{1}+hx_{2}=3[/tex]
[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]
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 [tex]\frac{k}{5}=3[/tex]
when taking the second condition and solving for k we get that:
[tex]k=3(5)[/tex]
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
which value of x is the solution of the equation 2/3x + 1/2 = 5/6?
Answer:
2
Step-by-step explanation:
2/3(2) + 1/2 = 5/6
If it's 2/3 * X then x is equal to 1/2.
Solve equation:7t-48=113
Answer:
The answer is 23
Answer:
t = 23
Step-by-step explanation:
find the mean of the data set 0.2 0.4 1 0.25
Answer:
.4625
Step-by-step explanation:
To find the mean, add up all the numbers, then divide by the number of terms
(0.2 +0.4+ 1+ 0.25) /4
1.85/4
.4625
Leti has just received a $15.00 gift card to Late, Late, Coffee for her birthday. Leti buys a small coffee each day. The total cost of the coffee is $1.50 including tax. The relationship between the coffee that Leti buys and the gift card can be modeled by a linear function y=15-1.50x. What is the initial value and what does it represent in the context of this problem?
Answer:
the initial value is 15 and it represents the y-intersect in the context of this problem
Step-by-step explanation:
The cost of renting a car is $20 to take the car and $4 for every hour that it is rented. The total amount Lucie paid was 546. For how many hours did Lucie have the car?
a. Define your variable.
b. Write an equation and solve.
c. Write a sentence to interpret your results.
h = time in hours
20 + 4h = 546
4h = 526
h = 131.5
131.5 hours
22 – 2(12 = 4+2*3) 3+7
Chlorofluorocarbons (CFCs) were used as propellants in spray cans until their buildup in the atmosphere started destroying the ozone, which protects us from ultraviolet rays. Since the 1987 Montreal Protocol (an agreement to curb CFCs), the CFCs in the atmosphere above the US have been reduced from a high of 1915 parts per trillion (ppt) in 2000 to 1640 ppt in 2014.23 The reduction has been approximately linear. Let C(t) be the concentration of CFCs in ppt in year t.
(a) Find C(2000) and C(2014).
(b) Estimate C′(2000) and C′(2014).
(c) Assuming C(t) is linear, find a formula for C(t).
(d) When is C(t) expected to reach 1500 ppt, the level before CFCs were introduced?
(e) If you were told that in the future, C(t) would not be exactly linear, and that C″(t) > 0, would your answer to part (d) be too early or too late?
Answer:
a) C(2000)=1915
C(2014)=1915
b) [tex]C'(2000)=-\frac{275}{14}[/tex]
[tex]C'(2014)=-\frac{275}{14}[/tex]
c) [tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]
d) t=2021
e) too early
Step-by-step explanation:
a)
Since C(t) is the concentration of CFCs in ppt in year t, all we need to do to solve this part is determine what the concentration of CFCs is in years 2000 and 2014. Luckily for us, the problem already gives us those values, so:
C(2000)=1915 concentration in year 2000
C(2014)=1915 concentration in year 2014
b)
By definition, the derivative of a function at a given point is interpreted as the slope of the tangent line to the point of interest, so in order to find this answer, we need to find the slope of the line. Since the problem specifies that the behavior is linear, this means that the slope will always be the same no matter the year, so we get:
[tex]m=C'(t)=\frac{C'(t_{2})-C'(t_{1})}{t_2-t_1}[/tex]
so:
[tex]C'(t)=\frac{1640-1915}{2014-2000}=-\frac{275}{14}\approx -19.64[/tex]
therefore:
[tex]C'(2000)=-\frac{275}{14}[/tex]
[tex]C'(2014)=-\frac{275}{14}[/tex]
c)
Since the behavior is linear, we can calculate it with the point-slope form of the line which is:
[tex]y-y_{1}=m(x-x_{1})[/tex]
in this case:
[tex]C(t)-C(t_1)=C'(t)(t-t_{1})[/tex]
so we get:
[tex]C(t)-1915=-\frac{275}{14}(t-2000)[/tex]
and we can now solve for C(t) so we get:
[tex]C(t)=-\frac{275}{14}t+\frac{275000}{t}+1915[/tex]
for a final answer of:
[tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]
d)
So next we solve the equation for C(t)=1500 so we get:
[tex]1500=-\frac{275}{14}t+\frac{288405}{7}[/tex]
[tex]1500-\frac{288405}{7}=-\frac{275}{14}t[/tex]
[tex]-\frac{277905}{7}=-\frac{275}{14}t[/tex]
[tex]t=2021 \frac{7}{55}[/tex]
so we will reach that concentration level at the year 2021 approximately.
e)
Since the second derivative of the concentration function is greater than zero, this means that the original function might be a function in the form: .
This means that the decrease of the concentration levels is slower than that of a linear equation. So the projected date will be too early than the real date.
Cheryl read for 30 minutes twice yesterday.Today she read for twice as long as she did yesterday.choose the expression that is a correct translation of the problem.
Answer:
(30x2)x2
Step-by-step explanation:
Answer:
Step-by-step explanation:
O
The ratio of boys to girls in a classroom is 7 to 11. If there are a total of 49 boys in the classroom, then how many boys and girls are there all together?
Answer: 65
Step 1: Multiply and add until you get 49.
11 x 4 = 44.
44 + 5 = 49.
Step 2: Multiply and add until you get 26, because 7:11 to 49 boys is 26, 26 : 49.
7 x 3 = 21.
21 + 5 = 26.
Step 3: Add 26 and 49.
26 + 49 = 65
Answer:
126 students
Step-by-step explanation:
Boys : Girls
7 : 11
How do you get from 7 to 49?
49 ÷ 7 = 7
Therefore, you should multiply the number of boys by 7.
Multiply:
7 : 11
7 × 7 = 49
49 : 11
Remember that whatever we do to the left, do to the right.
Multiply:
49 : 11
11 × 7 = 77
49 : 77
Now, let's add the number of boys and girls in the class to find the total number of students.
Add:
49 + 77 = 126
Therefore, there are 126 students in all.
Your paycheck is 500. If you want to save 2,000 dollars in one year, how much should you set aside from your paycheck each week
Answer:
how many weeks are in a year? 52 so 2000 / 52 = ?
Step-by-step explanation:
the question asks how many WEEKS to save 2000.... so just divide the weeks of one year into 2000 that you want to save for that year
my calculator says 2000/52=38.46
so save $ 38.46 each week
hello please help will give brainliest!
Answer:
The Answer is D
Step-by-step explanation:
Do what answer D tells you to do. Obviously.
Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.
Answer:
0.32472
Step-by-step explanation:
Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.
The formula for calculating a z-score is z = (x-μ)/σ
where x is the raw score
μ is the population mean
σ is the population standard deviation
z = (9 - 10)/2.2
z = -1/2.2
= -0.45455
Probability value from Z-Table:
P(x ≤ 9) = P(x < 9)
= 0.32472
Therefore, the proportion of trees having a diameter less than 9 inches is
0.32472
The proportion of trees having a diameter less than 9 inches is 32.64%
z score is used to determine by how many standard deviations the raw score is above or below the mean.
It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ raw\ score.\mu\ is\ mean,\sigma\ is \ standard \ deviation[/tex]
Given that μ = 10, σ = 2.2, hence:
[tex]For\ x<9:\\\\z=\frac{9-10}{2.2} =-0.45[/tex]
From the normal distribution table, P(x < 9) = P(z < -0.45) = 0.3264 = 32.64%
The proportion of trees having a diameter less than 9 inches is 32.64%
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A tractor trailer has maximum capacity of 8,000 pounds. The equipment needed to load
and unload the tractor trailer must travel with the trailer and weighs a combined 1,500
pounds. The trailer will be loaded with x containers, each of which weighs 300 pounds.
What is the largest value of x such that the trailer's capacity is not exceeded?
Answer:
subtract from the maximum load the 1500 of the loading equipment and you have 6500 pounds of capacity for the containers you divide this by 300 which is what each of the containers weighs gives you 21,666 which tells us that the maximum of containers is 21
8000-1500 = 6500
6500/300 = 21.66
Step-by-step explanation:
An investment of $9,875 earns 4.8% interest
Answer:
474$
Step-by-step explanation:
Find each product mentally using the distributive property show the steps that you used.
1.8x71
2.6x83
Answer:
1.8 x 71 = 127.8, just 18 x 71 = 1278, then count the the decimal place from the right, i.e 127.8
same for 2.6 x 83 = 215.8
.......ok try 5.52 x 5
Answer:
27,579.24 OR 343.6
Step-by-step explanation:
I don't know if this is what you mean but 1.8x71x2.6x83=27,579.24
Also, (if that was not what you meant), 1.8x71=127.8, 2.6x83=215.8, 127.8+215.8=343.6
how do you factor 450 a2 +242c2 + 660ac
Name the relationship: complementary, linear pair, vertical, adjacent, alternative interior, corresponding, or alternate exterior.
Answer:
Step-by-step explanation:
9. Alternative exterior
10. Alternate interior
11. Complementary
12. Corresponding
13. Corresponding
14. Alternate exterior
15. Vertical
16. Linear Pair
A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is, a fish that really weighed 26 g was reported to weigh 24 g. What is the mean and standard deviation after correcting for the error in the scale
Answer:
Correct mean = 32 grams
Correct Standard deviation = observed S.D = 2 grams
Step-by-step explanation:
We are told in the question above :
A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is
The mean after correcting the error in the scale is :
= observed mean + 2g
= 30g + 2g = 32g
The standard deviation after correcting the error in the scale remains the same as the difference of 2g has no significant effect on the Standard deviation.
This standard deviation = 2g
Of the following statements, which are equivalent?
I. 0
II. x(x−3)<0
III. −5
(A) I and II
(B) I and III
(C) II and III
(D) I, II, and III
(E) none of the above
Answer:
i think its C
Step-by-step explanation:
sorry if i get it wrong
Use the figure at the right. If JK = 2x + 12 and NO = 14, what is the value of x?
Answer:
X=8
Step-by-step explanation:
JK would equal 28, since it basically is double the side of that triangle. So now we have the equation, 2x+12=28. Now we solve using inverse operation. 28-12=16 and then 16 divided by 2 is 8, so x=8.
The required simplified value of x is 8, for the given triangle.
What is the midpoint?A midpoint is a point on the line whose distance from both ends of the line is equal.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The property of a triangle states that the line joining the midpoints of the two adjacent sides is equal to half of the third side.
So,
JK = 2NO
2x + 12 = 24
x = 16 / 2
x = 8
Thus, the required simplified value of x is 8, for the given triangle.
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Which fraction is equivalent to 20
Answer:
4/16
Step-by-step explanation:
Find a pair of numbers with
1. a sum of 40 and a product of 400
2. a sum of 15 and a product of 54
15 ounces
2.5 servings
Answer:
6 ounces per serving
Step-by-step explanation:
If you divide 15 ounces by 2.5 servings, you get 6 ounces per serving. I guess this is what you are trying to find, and hopefully it helps!
The sum of two numbers is 43, the difference is 7. Find the numbers
Answer:
25 and 18
Step-by-step explanation:
d+fg=h (solve for the variable “g”)
Answer:
g = h/f - d/f
Step-by-step explanation:
F is between E and G, EF= 7, and FG= 6 . Find EG
Answer:
13
Step-by-step explanation:
Step 1:
EF + FG = EG Equation
Step 2:
7 + 6 = EG input values
AnsweR:
13 = EG Add
Hope This Helps :)
Add.
0.125 + 0.25 + 0.33
Answer:
0.705
Step-by-step explanation:
Answer: the answer is .705
Step-by-step explanation:
the numbers 0.25 and 0.33 are technically 0.250 and 0.330
so just line them up and add. 0.250+0.125+0.330=0.705
Martha is standing on a street corner in a big city, facing south.
She walks 5 blocks to the south. Then, she turns right and walks 2
blocks. Then, she turns right and walks 3 blocks. Then, she turns
right again and walks 1 block. Finally, she turns left and walks 4
blocks. What direction is she facing when she is done?
A. East
B. North
C. South
D. West
(Answer is north)
Answer:
If the answer is north why did you post it?
A data obtained by conducting a survey is called?
Answer:
Survey data
Step-by-step explanation:
Survey data is defined as the resultant data that is collected from a sample of respondets that took a survey
The data obtained by conducting a survey is called as "survey data".
It is given that we are conducting a survey.
what will we call the data which is obtained through the survey.
What is a survey ?
Survey is a research method of gathering information or collecting the data.
Survey data is defined as the resultant data that is collected from a sample of respondents that took a survey.
The survey data is generally precise and enclosed within the topic of survey.
Thus, the data obtained by conducting the survey is called "survey data".
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