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 is the completely factored form of 18x4 – 42x3 + 24x2?
3x(3x - 4)(2x - 2)
3x2(3x - 4)(2x - 2)
6x(3x – 4)(x - 1)
6x²(3x - 4)(x - 1)
Answer:
D
Step-by-step explanation:
The completely factored form is 6x² (3x - 4) (x - 1).
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
18[tex]x^4[/tex]– 42x³ + 24x²
Now,
The common factor of 18, 42, and 24 is 6.
And x² is common to all the terms.
So,
6x² (3x²– 7x + 4) _____(1)
Now,
(3x²– 7x + 4)
3x² - (4 + 3)x + 4
3x² - 4x - 3x + 4
x(3x - 4) - 1(3x - 4)
(3x - 4) (x - 1) ______(2)
Now,
From (1) and (2) we get,
6x² (3x - 4) (x - 1)
Thus,
6x² (3x - 4) (x - 1) is the completely factored form.
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can you help please/
?
Answer:
B.
Step-by-step explanation:
Hope this helps!!
What is the value of x in the equation below? 1/3(12x-24)=16
2
6
8
10
What is the domain and range of the function Y=2x-4
Answer:
Domain: all real numbers
Range: all real numbers
Solve for
-1/7x = -2
Answer: I hope this is correct -9
Step-by-step explanation: This is right
The price of a train ticket is 155.00 What would it be if you had a 75% discount
Answer:116.25
Step-by-step explanation:
Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)
Complete Question
The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 9-year period. Assume each year is independent.
Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)
Answer:
The probability is [tex]P(X > 2) = 0.0007 [/tex]
Step-by-step explanation:
From the question we are told that
The probability of an IRS audit for a tax return with over $25,000 in income is p= 0.02
The sample size n = 9
Generally the distribution of IRS audit for a tax return follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that a person is not audited at all is mathematically
[tex]P(X = 0) = ^{9}C_0 * (0.02)^0 * (1- 0.02 )^{9-0}[/tex]
[tex]P(X = 0) = ^{9}C_0 * (0.02)^0 * (0.98 )^{9-0}[/tex]
[tex]P(X = 0) = 0.8337[/tex]
Generally the probability that a person is audited once is mathematically
[tex]P(X = 1) = ^{9}C_1 * (0.02)^1 * (1- 0.02 )^{9-1}[/tex]
[tex]P(X = 1) = 9* (0.02)^1 * (0.98 )^{8}[/tex]
[tex]P(X = 1) = 0.1531[/tex]
Generally the probability that a person is audited twice is mathematically represented
[tex]P(X = 2) = ^{9}C_2 * (0.02)^2 * (1- 0.02 )^{9-2}[/tex]
[tex]P(X = 2) = 36 * (0.02)^2 * (0.98 )^{7}[/tex]
[tex]P(X = 2) = 0.0125 [/tex]
Generally the probability that a person is audited more than twice is mathematically represented
[tex]P(X > 2) = 1 - [P(X = 0 ) + P(X = 1 )+ P(X =2)] [/tex]
=> [tex]P(X > 2) = 1 - [0.8337 + 0.1531+0.0125 ] [/tex]
=> [tex]P(X > 2) = 0.0007 [/tex]
Round 17.68694 to the nearest tenth
Answer:
17.7
Step-by-step explanation:
The tenths place is the very first value after the decimal. The number 17.68694 rounds up to 17.7, because .68 is closer to .7 than it is to .6.
solving equations 1/2(x+3)=2/5(x+2)
Answer:
x=-7
Step-by-step explanation:
convert to decimals 0.5(x+3)=0.4(x+2)
simplify the brackets 0.5x+1.5=0.4x+0.8
isolate x to one side 0.1x=-1/7
divide both sides by 0.1 x=-7
The total cost of a cab ride can be represented by the function f(x) = 3x + 2.5, where x is the number of miles driven
Estimate how much the cab will cost if the cab ride is 8 miles and 25 miles.
Answer:
8 miles: $26.50
25miles: $77.50
Step-by-step explanation:
Substitute (x) for the number of miles
8 miles: f(x)=3(8)+2.50
=24+2.50
=26.50
25miles: f(x)=3(25)+2.50
=75+2.50
=77.50
Solve the following inequality 4(3-3x)+4x>20
Answer:
x<-1
Step-by-step explanation:
Researchers at Mississippi State University were studying the impact of different environmental sounds on ecosystems. For their study, they created 333 similar ecosystems in their lab containing a variety of insects and plants. They randomly assigned each ecosystem to be exposed to rock music, country music, or a conventional city soundscape for two consecutive weeks. At the end of the study, they measured how successful the species were in each ecosystem. What type of experiment design is this?
Answer:
The experiment design used in this case is the between-subjected design.
Step-by-step explanation:
Between-subject design is a sort of experimental design where the individuals of an experiment are allocated to varied situations, with each individual being treated with only one of the experimental conditions.
In this case three similar ecosystems are designed containing a variety of insects and plants. Then each ecosystem to be exposed to rock music, country music, or a conventional city soundscape for two consecutive weeks.
Then after two weeks period they measured how successful the species were in each ecosystem.
The experiment design used in this case is the between-subjected design.
Answer:
A completely randomized design
Step-by-step explanation:
The 3 ecosystems were each randomly assigned a treatment. They were not grouped in any way with random assignment happening within each group, so this is a completely randomized design. (From Kahn)
the equation y = 1/5x represents a proportional relationship. explain how you can tell the relationship is proportional from the graph of the equation, and you can find the constan of proportionality.
Answer:
Yes, y = [tex]\frac{1}{5}[/tex] x represents a proportional relationship and the constant of proportionality is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
The Proportional is a relationship between two quantity one of them equals the product of the other and a constant, where this constant called the constant of proportionality
If x and y are proportion, then y = k x, where k is the constant of proportionalityThe proportional relationship represented graphically by a line passing through the origin point (0, 0)Let us solve the question
∵ y = [tex]\frac{1}{5}[/tex] x
→ It the same as the form of the proportional equation above
∵ [tex]\frac{1}{5}[/tex] is a constant
∴ y is the product of x and constant
∴ y = [tex]\frac{1}{5}[/tex] x represents a proportional relationship
Substitute x by 0 to find y and show it represented by a line passing through the origin
∵ x = 0
∴ y = [tex]\frac{1}{5}[/tex] (0) = 0
→ That means point (0, 0) lies on the line which represents the equation
∴ The line which represents this relation is passing through the origin
∴ y = [tex]\frac{1}{5}[/tex] x represents a proportional relationship
∵ y = kx, k is the constant of proportionality
∵ y = [tex]\frac{1}{5}[/tex] x
∴ k = [tex]\frac{1}{5}[/tex]
∴ The constant of proportionality is [tex]\frac{1}{5}[/tex]
Expression for divide the difference between 1200 and 700 by 5
Step-by-step explanation:
(1200-700)/5
=500/5
=
The expression results to 100.
What is Expression?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Given:
divide the difference between 1200 and 700 by 5
so, mathematically
(1200- 700)/5
= 500 /5
= 100
Hence, the expression results to 100.
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what is the increase of y=26(0.904)x
The rectangle below is enlarged using a scale factor of 1.5. What will be the new length and width of the rectangle?
Answer: length = 4.5 m, width = 3 m
Step-by-step explanation:
When a shape is enlarged using a scale factor, you simply multiply each of the sides by the scale factor.
length = 3 * 1.5 = 4.5 m
width = 2 * 1.5 = 3 m
Can u please help I will do Brainleyist
Answer:
the answer is B this other guy messed up his math trust me i know it's right
Step-by-step explanation:
if you add up all the numbers it equals 27 squar units
The
perimeter of
rectangle is 36 cm
If its width is 7cm Exaluate to its length
Answer:
11
Step-by-step explanation:
Who got the answer for 3,7 and 9
Answer:
i did
Step-by-step explanation:
3. Jean purchased 6 yards of felt to make banners. Each banner requires 1 1/2 yards. How many
banners can she make?
A. 2
B. 4
C. 6
D. 9
B.
Explanation:
1.5+1.5=3+1.5= 4.5+1.5= 6
(How much 1.5 is there?) (1.5=1 1/2 btw)
help me please I will mark brainlyest
Answer:
B
Step-by-step explanation:
The equation is y=mx+b
Where m is the slope
And B is the y point of the y-intercept
Answer:
The answer is b to this question
I’m confused how to do ratios
Answer:
i will explain it to you
Step-by-step explanation:
What is 12 plus 364 divided by 2/7?
Answer:1316
Step-by-step explanation:
Answer:
thanks
Step-by-step explanation:
I want explaintationWhat is the common ratio between successive terms in a sequence?
1.5, 1.2,0.96, 0.768, ...
9514 1404 393
Answer:
0.8
Step-by-step explanation:
The ratio of the first two terms is ...
1.2/1.5 = 4/5 = 0.8
That is also the ratio of successive adjacent terms.
0.96/1.2 = 0.768/0.96 = 0.8
The common ratio is 0.8.
Katie has 50 chickens she eats 90% how many chickens are left?
Answer:
First off dang Katie you can eat. And the answer is 5
Step-by-step explanation:
She just gobbling them up like no tommrow
ANSWER FAST PLZ FOR BRAINILIST
Answer:The 1st one
Step-by-step explanation:
Suppose you take a simple random sample of size n=175 from the population of Reese's Pieces, still assuming that 45% of this population is orange (LaTeX: \piπ=.45).
What is the probability that a sample proportion of orange candies will be between .35 and .55?
Answer:
The probability is [tex]P(0.35 <X < 0.55) = 0.9921772[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 175
The population proportion is p = 0.45
Generally the mean of the sampling distribution is [tex]\mu_{x} = 0.45[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma_{x} = \sqrt{\frac{p (1-p)}{n} }[/tex]
=> [tex]\sigma_{x} = \sqrt{\frac{0.45 (1-0.45)}{175} }[/tex]
=> [tex]\sigma_{x} = 0.0376[/tex]
Generally the probability of that the sample proportion of orange candies will be between 0.35 and 0.55 is
[tex]P(0.35 < X < 0.55) = P( \frac{0.35 - 0.45}{0.0376} < \frac{X -\mu_{x}}{\sigma_{x}} < \frac{0.55 - 0.45}{0.0376} )[/tex]
=> [tex]P(0.35 <X < 0.55) = P( -2.696 < \frac{X -\mu_{x}}{\sigma_{x}} < 2.6595 )[/tex]
Generally [tex]\frac{X - \mu_{x}}{\sigma_{x}} = Z (The \ standardized \ value \ of X)[/tex]
So
[tex]P(0.35 <X < 0.55) = P( -2.6596 < Z< 2.6595 )[/tex]
=> [tex]P(0.35 <X < 0.55) =P( Z< 2.6595 ) - P( Z < -2.6596 )[/tex]
From the z-table
[tex]P( Z< 2.6595 ) = 0.99609[/tex]
and
[tex]P( Z< - 2.6595 ) = 0.0039128[/tex]
So
[tex]P(0.35 <X < 0.55) =0.99609 - 0.0039128[/tex]
=> [tex]P(0.35 <X < 0.55) = 0.9921772[/tex]
Use the word SCHOOL to answer this question.
If the letters of this word were written on paper and then cut into squares with one letter
per square, what is the probability of this event?
P(consonant)
1
3
1
2
1
6
2
3
Answer:
2/3
Step-by-step explanation:
4/6 * 100% = 66.66% = 2/3
PLEASE HELP!!!
Please help me answer the questions that are circled, I really need help!
Answer:
Here:
Step-by-step explanation:
23. f(x) = [tex]\sqrt{x}[/tex] and g(x) = [tex]x^2-5x[/tex]
24. f(x) = [tex]x^2[/tex] and g(x) = [tex]x^3+1[/tex]
28. f(x) = [tex]e^x[/tex] and g(x) = [tex]sinx[/tex]
29. f(x) = [tex]cosx[/tex] and g(x) = [tex]\sqrt{x}[/tex]
Basically, you try to find a function contained inside a function if that makes sense. For example in question 23, g(x) itself is a function = [tex]x^2-5x[/tex]. Same with f(x) = [tex]\sqrt{x}[/tex] . In this case, when we try to fo f(g(x)), we are basically replacing x in the f(x) function by the equation in g(x). Hope this makes sense.
HELP ASAP!! WILL MARK BRAINLIEST!
Question 8 Multiple Choice Worth 5 points)
(03.04 MC)
Solve for x:
(-4/3) x -6 = 26
Answer:
X = -24
Step-by-step explanation:
Using the inverse:
26 + 6 = 32
x = 32 / (-4/3) = -24