Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6y=−18.
Answers
Answer:
a. No solution, parallel lines.
b. One solution.
Step-by-step explanation:
Given the system of equations:
a. [tex]2x-4y=12[/tex]
[tex]-3x+6y=-15[/tex]
b. [tex]2x-4y=12[/tex]
[tex]-5x+3y=10[/tex]
To give a geometric description of the given system of equations.
The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.
i.e.
Number of planes = Number of variables
Number of lines = Number of equations in the system.
Here, we are given 2 variables and 2 equation in each system.
So, they can be represented in the xy-coordinates plane.
And the number of solutions to the system depends on the following condition.
Let the system of equations be:
[tex]A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0[/tex]
1. One solution:
There will be one solution to the system of equations, If we have:
[tex]\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}[/tex]
2. Infinitely Many Solutions: (Identical lines in the system)
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}[/tex]
3. No Solution:(Parallel lines)
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}[/tex]
Now, let us discuss the system of equations one by one:
a. [tex]2x-4y=12[/tex] OR [tex]2x-4y-12=0[/tex]
[tex]-3x+6y=-15[/tex] OR [tex]-3x+6y+15=0[/tex]
[tex]A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15[/tex]
Here, the ratio:
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}[/tex]
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}[/tex]
Therefore, no solution i.e. parallel lines.
b. [tex]2x-4y=12[/tex] OR [tex]2x-4y-12=0[/tex]
[tex]-5x+3y=10[/tex] OR [tex]-5x+3y-10=0[/tex]
[tex]A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10[/tex]
[tex]\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}[/tex]
[tex]\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}[/tex]
So, one solution.
Kindly refer to the images attached for the graphical representation of the given system of equations.
Related Questions
Find the mean. 217, 230, 214, 227, 196, 235, 220, 224, 208, 209, 191, 205, 184, 214, 219, 208, 227, 194, 228, 186, 201, 239
Answers
Answer:
212.54
Step-by-step explanation:
To find the mean, we take the sum of all numbers and divide by the total amount in the set
Total sum: 4676
Numbers in the set: 22
4676 divided by 22 = approx. 212.54
In each represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so that the argument in part (b) has the same logical form as the argument in part (a).
a. If all computer programs contain errors, then this program contains an error.
This program does not contain an error.
Therefore, it is not the case that all computer programs contain errors.
b. If _______________, then _____________.
2 is not odd.
Therefore, it is not the case that all prime numbers are odd.
Answers
Answer:
a
[tex]a \to b[/tex]
[tex]\neg b[/tex]
[tex]\neg a[/tex]
b
If all prime numbers are odd, then 2 is odd.
2 is not odd.
Therefore, it is not the case that all prime numbers are odd.
Step-by-step explanation:
Considering part A
The first sentence is
If all computer programs contain errors, then this program contains an error.
The second sentence is
This program does not contain an error.
The third sentence is
Therefore, it is not the case that all computer programs contain errors.
Now we will use a and b as the letter to denote the component sentences and [tex]\neg a[/tex] and [tex]\neg b[/tex] when the component sentences is not the case
So a = If all computer programs contain errors
and
b = this program contains an error.
Generally then is represented as [tex]\to[/tex]
Hence the first sentence is denoted as
[tex]a \to b[/tex]
The second sentence is represented as
[tex]\neg b[/tex]
The third sentence is represented as
[tex]\neg a[/tex]
So part a can be represented as
[tex]a \to b[/tex]
[tex]\neg b[/tex]
[tex]\neg a[/tex]
Considering part B
Here the objective is to fill in the blank spaces so that the logic of the sentence in part b is as that in part a
Now comparing the second statement a and b
"This program does not contain an error" = "2 is not odd" = [tex]\neg b[/tex]
Hence "this program contains an error." = "2 is odd" = b
Now comparing the third statement a and b
Therefore, it is not the case that all computer programs contain errors.
=
Therefore, it is not the case that all prime numbers are odd
=
[tex]\neg a[/tex]
Hence
If all computer programs contain errors, = if all prime numbers are odd.= a
While on your trip you get sick and eventually end up in the hospital. The doctor orders 120 mg of medicine to be given in the morning, and another 120 mg to be given at night. The nurse comes in to give you your morning dose and tells you that there are 30 mg in each tablet. How many tablets should you get?
Answers
Answer:
4 tablets
Step-by-step explanation:
If the morning dose is 120mg and each tablet is 30mg then all you do is divide 120 by 30 to get the answer 4
Step-by-step explanation:
4 tablets
by equatitg this term
120 = 30x ( X = number of tablets )
X = 4 tablets
A club has 16 girls and 8 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?
Answers
Answer: 8
Step-by-step explanation:
what solution is -19=b-6
Answers
Answer:
b = -13
Step-by-step explanation:
Answer:
b = - 13
Step-by-step explanation:
Step 1:
-19 = b - 6
Step 2:
- 19 + 6 = b
Answer:
b = - 13
Hope This Helps :)
A rectangle has a length of 5 root 26 i ched and a width of 2^1/5 inches find area if rectangle
Answers
Answer:
I believe the answer 2.2039 is if you meant inches by "i ched"
Step-by-step explanation:
Hope this helps
When conducting a survey, which of the following is a reason to use a random sample?1. To make cause-and-effect connections2. To avoid bias3. No answer text provided.4. To systematically favors the correct choice over every other choice on each question
Answers
Answer: 2. To avoid bias
Explanation:
The random sampling can be defined as the method of selecting the samples from the population of interest randomly. The main advantage of this method is to select the samples from the target population and eliminating the bias in sampling. The random sampling is least choice of sampling for research purpose as the researcher wants to choose only selected desired samples for the study.
Equivalent expression to 3y+4-6y-2
Answers
Answer : the answer is -3y + 2
an investment of $5000 earned $1050 for 1 year. How much will an investment of $9000 earn at the same rate for 1 year?
Answers
Answer:
Amount earned (New investment) = $1,890
Step-by-step explanation:
Given:
Amount invested = $5,000
Earned = $1,050
New investment = $9,000
Find:
Amount earned (New investment)
Computation:
Amount earned (New investment) = [Earned / Amount invested]New investment
Amount earned (New investment) = [1,050 / 5,000]9,000
Amount earned (New investment) = $1,890
Write 0.586 in simplest form
Answers
0.586 is already in simplest form but we can round if you choose to do so.
Round to the nearest hundreth.
0.586 -> 0.59
Round to the nearest tenth.
0.586 -> 0.6
Round to the nearest one.
0.586 -> 1
Best of Luck!
Elise bought 6.47 pounds of peanuts and 4.22 pounds of raisins. How many pounds of snacks did she buy in all?
Answers
Answer:
10.69 pounds
Step-by-step explanation:
4.22 + 6.47 = 10.69
Answer:
10.69 pounds of snacks
Step-by-step explanation:
Total no of raisins ;
[tex]6.47+4.22\\\\=10.69[/tex]
Yolanda will be travelling out of town for business. During her travel, she is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. Her employer will pay her
for these meals at the following rate:
$21.50 for dinner, $12.15 for lunch, and $5.73 for breakfast.
What is the total amount Yolanda will be paid for these meals?
Answers
Answer:
$163.94
Step-by-step explanation:
4 dinners at $21.50 each
5 lunches at $12.15 each
3 breakfasts at $5.73 each
4 • 21.50 = $86
5 • 12.15 = $60.75
3 • 5.73 = $17.19
86 + 60.75 + 17.19 = 163.94
Answer:
$163.94
Step-by-step explanation:
Dinners
Yolanda will have 4 dinners and each dinner costs $21.50
Multiply 4 and 21.50
⇒ 4 * 21.50
⇒ 86 = $86
Lunches
She will have 5 lunches that each cost $12.15
Multiply 5 and 12.15
⇒ 5*12.15
⇒ 60.75 = $60.75
Breakfasts
Yolanda is going to have 3 breakfasts at $5.73 for each breakfast.
Multiply 3 and 5.73
⇒ 3*5.73
⇒ 17.19 = $17.19
Find the total. Add the cost for dinners, lunches and breakfasts together.
$86 + $60.75 + $17.19
$163.94
Yolanda will be paid $163.94 for the meals.
Point A is located at (4, 7). It will be translated 5 units right and 3 units down. Write the rule and give the location of point A. Step by Step Explanation
Answers
Answer:
4,7 -> 9,4, rule: (x,y)->(x+5,y-3)
Step-by-step explanation:
Let’s write the rule first,
(x,y) -> (x+5,y-3) (right 3, down 3)
Now we add 5 to x and subtract 3 from y.
4,7 -> 9,4
Assume the heights in a male population are normally distributed with mean 70.3 inches and standard deviation 4.1 inches. If a randomly selected male’s height is at the 75th percentile, how tall is he (to the nearest tenth of an inch)?
Answers
Answer:
73.1 inches
Step-by-step explanation:
We solve for this using z score formula.
z-score is z = (x-μ)/σ,
where x is the raw score,
μ is the population mean
σ is the population standard deviation.
x = unknown = randomly selected male's height
μ = 70.3 inches
σ = 4.1 inches
z = is not given but we are given its percentile which is 75
The z score for a 75th percentile = 0.674
Hence,
0.674 = x - 70.3/4.1
Cross Multiply
0.674 × 4.1 = x - 70.3
2.7634 = x - 70.3
x = 70.3 + 2.7634
x = 73.0634 inches
The height of the randomly selected male = 73.0634
Therefore, the height of the randomly selected male to the nearest tenth of an inch is 73.1 inches
Please help I don’t understand
Answers
Answer:
2·8·78+2+712·5·33+5+12Step-by-step explanation:
The properties of addition and multiplication allow you to rearrange and/or regroup the components of a sum or a product. That is the point of this exercise.
(2·8)·7 = 2·(8·7) . . . . parentheses have moved: associative property
2 + 7 + 8 = 8 + 2 + 7 . . . . order is rearranged: commutative property
5·3·12 = 12·5·3 . . . . . order is rearranged: commutative property
(3 +5) +12 = 3 +(5 +12) . . . . parentheses have moved: associative property
_____
Additional comment
Whenever you're in doubt about the equivalence of numerical expressions, you can use your calculator to evaluate them. They will give the same result if they are equivalent. (You need a good scientific or graphing calculator that uses parentheses for this. Some seriously good calculators are available as low-cost phone apps.)
The Google search box also serves as input to the Google calculator. You can use an asterisk (*) for multiplication.
EEEE
Domain: The set of all states
Range: The set of all senators
(Remember, each state has two senators!)
This relation is
not a functions
COMPLETE
Create your own real-world example of a relation
that is a function,
Domain: The set of
Range: The set of
DONE
Answers
Answer:
Domain: The set of 0
Range: The set of 16
Step-by-step explanation:
A real-world example of a relation that is a function is
Domain: The set of voters.
Range: The set of candidates.
during an election.
What is a function?A function is a relationship from a set of inputs called domain to a set of outputs called range, such that not more than one value is assigned to an input.
How to tackle the problem?For the given example we understand that each state has two senators hence the relation is not a function.
A real-world example of a relation that is a function is
Domain: The set of voters.
Range: The set of candidates.
during an election.
This is a function because one voter can vote for only one candidate.
To learn more about functions visit- https://brainly.com/question/12431044?referrer=searchResults
#SPJ2
4) Given: f(x) = 4x – 1 g(x)= 3x - 2
Find:
f(x) + g(x)
f(x) *g(x)
f(g(x))
f(x) - g(x)
Answers
Step-by-step explanation:
f(x) = 4x - 1
g(x) = 3x - 2
1) f(x) + g(x) = (4x - 1) + (3x - 2)
= 4x - 1 + 3x - 2
= 4x + 3x -1 - 2 = 7x - 3
2) f(x) * g(x) = (4x - 1) * (3x - 2)
= 12x^2 - 8x - 3x + 2
= 12x^2 -11x + 2
3) f(g(x)) = 4(3x - 2) - 1
= 12x - 8 - 1
= 12x - 9
4) f(x) - g(x) = (4x - 1) - (3x - 2)
= 4x - 1 - 3x + 2
= 4x - 3x - 1 +2
= x + 1
ZRQS, what
of one of the
Use the diagram shown.
re collinear.
5 and LN = 17.
alue of MN?
12. If mZ1 equals (2x + 3) and m23
equals (6x - 17), what is the value
of x? What is mZ1?
13. If m 2 equals (15a + 8) and m23
equals (5a - 8), what is the value
of a?
Cso that
hat is x?
Answers
Answer:
12. x = 5, m∠1 = 13°13. a = 9°Step-by-step explanation:
12..................................Given:
m∠1 = (2x + 3) m∠3 = (6x - 17) x? m∠1?Solution:
∠1 and ∠3 are vertical angles.
We know the property that vertical angles are equal:
2x + 3 = 6x - 176x - 2x = 3 + 174x = 20x = 5m∠1 = 2*5 + 3 = 13°13 ..................................Given
m ∠ 2 = (15a + 8) m ∠ 3 = (5a - 8)a = ?Solution
∠2 and ∠3 are supplementary angles.
We know the property that supplementary angles add up to 180°:
15a + 8 + 5a - 8 = 180°20a = 180°a = 180°/20a = 9°Please answer I will make you Brainliest The answer is not Carribean Plate!
Answers
Answer:
I am implying that the correct answer would be A, The Pacific plate.
Step-by-step explanation:
The Australian, Nazca and Pacific plates move up to four times faster than the smaller African, Eurasian and Juan de Fuca plates.
The 3 fastest plates:
Australian plateNazca platePacific platewhat choice is NOT equal to the others? - 2/5. -2/5. 2/5. 2/-5
Answers
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]- 2/5= -\frac{2}{5}\\\\ -2/5= -\frac{2}{5}\\\\ 2/5 = \frac{2}{5} \\\\2/-5= -\frac{2}{5}[/tex]
Answer:
2/5
Step-by-step explanation:
It has no minus behind any of the numbers.
Milo's Ice Cream Factory sold more than 43 waffle cones yesterday. Which of the following inequalities represents the number of waffle cones Milo's Ice Cream Factory sold yesterday?
A.
x < 43
B.
x = 43
C.
x < 49
D.
x > 43
Answers
Answer:
D. X > 43
Step-by-step explanation:
You do not know the number of waffle cones sold yesterday, so let's make that the X.
The question says "sold more than 43" so we need an X and a 43.
But which sign to use?
The question says "more than 43" so that means X is bigger
The alligator > wants to eat the bigger number, so you use:
X > 43
Answer:
x > 43
Step-by-step explanation:
Please help me with this please I’ll give you a Brainly list
Answers
Answer: X-axis
Step-by-step explanation: You can use the "Desmos Graphing Calculator".
Given that QRVTSU is a regular hexagon, what are the lengths of QR and ST ?
Answers
Answer:
QR = 37
ST = 37
Step-by-step explanation:
length of all sides are equal
so QR = ST
3y + 19 = 6y + 1
combine like terms
19 -1 = 6y - 3y
18 = 3y
y = 18/3
y = 6
QR = 3(6) + 19
QR = 37
ST = 6(6) + 1
ST = 37
Answer:
QR = 37
ST = 37
Step-by-step explanation:
QR = ST
3y + 19 = 6y + 1
19 -1 = 6y - 3y
18 = 3y
y = 18/3 = 6
substitute
QR = 3(6) + 19 = 37
ST = 6(6) + 1 = 37
I didn’t study and it’s 2 am pls help
Answers
7. g(3) = 42
8. f(6) = - 124
9. g(15) = 3
10. h(-3) = 1/8
Step-by-step explanation:7. g(x) = 4x² + 6
g(3) = 4×3² + 6
= 4×9 + 6
= 36 + 6
= 42
8. f(x) = - 3x² - 4x + 8
f(6) = - 3×6² - 4×6 + 8
= - 3×36 - 24 + 8
= - 108 -16
= - 124
9. g(x) = √(x - 6)
g(15) = √(15 - 6)
= √9
= 3
10. h(x) = 2ˣ
h(-3) = 2⁻³
= 1/2³
= 1/8
Negative numbers do not have square roots that are real numbers
Answers
Answer:
Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.
find the x and y intercepts of the circle: (x-6)^2+(y+3)^2=16
Answers
Answer: x=0 y=2
Step-by-step explanation:
Answer:
-y+11
Step-by-step explanation:
(x-6)•2+(y+3)•2-(y+3)•2=16-(y+3)•2
(x-6)•2=-2y+10
(x-6)•=-2y/2+10/2
x-6=-y+5
x=-y+11
what is 5(3-12)(42-32)
Answers
Answer:
-450
Step-by-step explanation:
5(3-12)(42-32)
5(-9)(10)
-45(10)
Answer:
-450
Step-by-step explanation:
5(3-12)(42-32)
5(-9)(10)
-45(10)
= -450
A function is described by the following ordered pairs: (7, 4.5) (–4, 7.2) (–7.2, –4) (5.2, 3) Which set of ordered pairs represents the inverse of the function? (7, –4), (–7.2, –4), (3, 5.2), (4.5, –4) (7, –4), (–7.2, 5.2), (4.5, 7.2), (–4, 3) (4.5, 7), (7.2, –4), (–4, –7.2), (3, 5.2) (7, 4.5), (–4, 7.2), (–7.2, –4), (5.2, 3)
Answers
Answer: (4,5,7) ,(7.2,-4),(-4,-7.2),(3,5.2)
Step-by-step explanation:
Answer:
it's C
Step-by-step explanation:
max is thinking of a number, which he calls n. He adds 8 an then doubles the sum
Answers
decimal:
3.2
fraction:
3.2/1
Angles Q and R are supplementary. If the measure of angle Q =4x+9 and the measure of angle R is 8x+3, what is the measure of each angle?
Answers
Answer:
180°
Step-by-step explanation:
So supplementary agles are angles that add up to 180 degrees thus the measure of each angle is 180 degrees.
The 4x+ 9 and 8x+3 are meant to confuse you. But if you need help figuring out what x is i can help :)
HOPE IT HELPED.