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
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.
How do you do this question?
Answer:
Diverges
Step-by-step explanation:
3/(4ⁿ) = 3 (¼)ⁿ is a geometric series with r = ¼, which converges.
7/n is a harmonic series, which diverges.
The sum of a convergent series and a divergent series is divergent.
(45 points!)
Line n contains points (3, 4) and (-6, -2). What is the slope of a line perpendicular to the given line?
Answer: -3/2
Step-by-step explanation:
Answer:
y=nx−2+6n
Step-by-step explanation:
I have used the slope-intercept form to find the answer.
Hope this helps :)
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
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
the sum and twice the number and 18 is greater than 25
Answer:
Step-by-step explanation:
45
can someone find the inverse and explain it step to step please!!!!!!! (FOR QUESTION 3)
Answer:
f^-1(x) = 4(x+5)/3
Step-by-step explanation:
Let f(x) = y
So, y = (3/4)x - 5
y + 5 = (3/4)x
4(y+5)/3 = x
The steps are first to make a variable that holds the same value as the function, then from there you simplify and eventually make x the subject of the equation.
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 :)
Find the polynomial function of degree 3 such that f(2)=24 and x-1, x and x+2 are factors of the polynomial
Answer:
f(x) = 3x^3 + 3x^2 - 6x.
Step-by-step explanation:
Let:
f(x) = x(x - 1)(x + 2)
= x(x^2 + x - 2)
= x^3 + x^2 - 2x - this might be the answer or it might be some multiple of this.
Now f(2) = 24 so
24 = a(2^3 + 2^2 - 2(2)) where a is a constant.
24 = 8a
a = 3
So the function is
3( x^3 + x^2 - 2x)
= 3x^3 + 3x^2 - 6x.
2d + 7 = 9
Hellllllpppppp
Answer:
Doesn't 2+7 = 9 itself?
Step-by-step explanation:
Solve the following inequality. Graph the solution.
4b + 3 < 19
Answer:
b<4 , I am not 100% sure on the graphing part and I have done this in 7th grade but I think it is A, not 100% sure.
You are assigned 32 math questions for homework. You complete 87.5% of these before dinner. How many questions do you have left to do after dinner?
Answer:
4 questions
Step-by-step explanation:
To find a percentage of a number, you move the decimal mark all the way to the left.
87.5% becomes 0.875
Next you multiply 32 by 0.875 to find the percentage of questions that are completed
32 x 0.875 = 28
28 out of 32 questions have been solved, so now you subtract 28 from 32
32 - 28= 4
There are 4 questions to complete
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
Translate the sentence into an equation.
Twice the difference of a number and 2 equals 6.
Use the variable b for the unknown number.
Answer:
2(b-2)=6
Step-by-step explanation:
Twice the difference means multiply the difference by two
It explains the difference being between the unknown number(b) and 2
The answer is said to be six
So you put the difference (b-2)
Multiply it 2(b-2)
and finally, add the answer: 2(b-2)=6
The equation for the given sentence is 2(b-2)=6 and the unknown number is 5.
Given that, twice the difference of a number and 2 equals 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Use the variable b for the unknown number.
2(b-2)=6
⇒ b-2=3
⇒ b=5
Therefore, the equation for the given sentence is 2(b-2)=6 and the unknown number is 5.
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What are the coefficients of this expression 7a+23b +2c + 16
Answer:
Step-by-step explanation:
A coefficient is basically the number infront of a variable or term.
E.g. the coefficient in 7x is 7
The coefficient in 23y is 23
The coefficient in 43a is 43.
So for your question: 7a + 23b + 2c + 16,
The coefficients are 7, 23 and 2
what value for x makes this equation true? 0.6x-5=0.1x+7
Find the unknown value in the proportion.
4/7=?/14. please help
Answer:
8
Step-by-step explanation:
4/7 = ?/14
Multiply the numerator and denominator of the left fraction by 2.
8/14 = ?/14
That means that ? = 8
Answer: 8
Answer:
8
Step-by-step explanation:
Step 1:
4/7 = x/14 Proportion
Step 2:
7x = 56 Multiply
Step 3:
x = 56 ÷ 7 Divide
Answer:
x = 8
Hope This Helps :)
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?
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
d+fg=h (solve for the variable “g”)
Answer:
g = h/f - d/f
Step-by-step explanation:
A food scientist determine the new type of orange is 15.38 mg of vitamin c/oz how much vitamin C is in orange that weighs 6 3/5 oz in your answer as a decimal to the nearest 10th in the box
Answer:
(Sorry this is a late response) This fraction 6 3/5 would equal 6.6 so 6 3/5=6.6 Then you will do 6.6 times 15.38=101.508 or 101.5
Step-by-step explanation:
You would divide 3 and 5 or 5 and 3 because 3 and 5 equals the fraction 3/5. The dividend is 3 and the 5 is the divisor. The quotient of this is 0.6. So the next step would be to add the 6 from 6 3/5 so this is the whole number so add it in front of 0.6 so it would turn into 6.6. The last step is to multiply the weight of the orange by the mg of vitamin C/oz that is 15.38 so multiply 6.6 by 15.38 this would equal 101.508 so you would just round this to a better answer and that would make it 101.5. I hope this helps :0
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
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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A triangle has vertices on the coordinate grid at points A(2, 4), B(2, 9) and C(5, 6) . What is the length, in units, of AB ?
Answer:
5 units long
Step-by-step explanation:
If you graph it, it is a simple straight line 5 units long between A and B.
You could also use the distance formula if you had to do more advanced distance calculations.
The distance formula is d=√((x2-x1)²+(y2-y1)²)
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!
What is an equation of the line that passes through the points (0, -2) and (6,6)
Answer:
y= 4/3x -2 or y=1[tex]\frac{1}{3}[/tex] -2
Step-by-step explanation:
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.
Round 1,439 to the nearest ten
Answer:
1,440.
Step-by-step explanation:
39 is closer to 40.
1,400 is unchanged.
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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