Answer:
The correct answer option is dependent.
Step-by-step explanation:
We are given the following two equations and we are to determine whether these are independent, dependent or inconsistent:
[tex]y = 3x + 6[/tex] --- (1)
[tex]6x - 2y = -12[/tex] --- (2)
To compare these equations with each other, it is a good idea to write them in the same format with y being the subject. So rearranging equation (2) to get:
6x - 2y = -12
6x + 12 = 2y
2y = 6x + 12
y = 3x + 6
A system of equations is said to be dependent when the same line is written in two different forms so that there are infinite solutions.
Hence, this system of equations is dependent having infinite solutions.
The system of equations are classified as independent
How to determine the termTo classify the system of equations as independent, dependent, or inconsistent, we can analyze their coefficients.
The given system of equations is:
y = 3x + 6
6x - 2y = -12
Comparing the coefficients, we can see that the slopes of the equations are equal (-2/-6 )
Reduce the fraction to smaller forms, we get;
1/3
Now, since the slopes are different, the system is consistent and has a unique solution, indicating an independent system.
Thus, the equations are independent.
Learn more about linear equations at: https://brainly.com/question/2030026
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how to solve the algebraic expression 25=5/3(d+5/8)
Answer:
Alright well solve for d by cross multiplying
Exact form: d = 115/8
Decimal form: d = 14.375 Hope this helps have a nice day : )
Step-by-step explanation:
Each year, thousands of people visit Yellowstone national park. Audiotapes for visitors include interviews with early settlers and information about geology, wildlife, and activities of the park. The revenue r(x) from the sale of x tapes is r(x)=9.5x. Suppose that the function for the cost of manufacturing x tapes is c(x)=0.8x+1940.
What function could be used to find the profit on x tapes?
a. Write the profit function.
b.find the profit on 500, 1000, and 5000 tapes.
c. Check by finding the revenue and the cost for each number of tapes and subtracting to find profit
Answer: p(x) = 8.7x - 1940
p(500) = $2410
p(1000) = $6760
p(5000) = $41,560
Step-by-step explanation:
p(x) = r(x) - c(x)
= 9.5x - (0.8x + 1940)
= 9.5x - 0.8x - 1940
= 8.7x - 1940
**********************************************************************
p(500) = 8.7(500) - 1940
= 4350 - 1940
= 2410
p(1000) = 8.7(1000) - 1940
= 8700 - 1940
= 6760
p(5000) = 8.7(5000) - 1940
= 43,500 - 1940
= 41,560
***************************************************************************
p(500) = r(500) - c(500)
= 9.5(500) - [0.8(500) + 1940]
= 4750 - (400 + 1940)
= 4750 - 2340
= 2410
p(1000) = r(1000) - c(1000)
= 9.5(1000) - [0.8(1000) + 1940]
= 9500 - (800 + 1940)
= 9500 - 2740
= 6760
p(5000) = r(5000) - c(5000)
= 9.5(5000) - [0.8(5000) + 1940]
= 47500 - (4000 + 1940)
= 47500 - 5940
= 41,560
$64 jacket; 20% discount [plzzzzz help me ]
Answer:
$51.20
Step-by-step explanation:
A 20% discount makes it 80% of the original price.
80% is 0.8 of something so multiply $64 by 0.8 to get your answer of $51.20
Literal Equations
c-b/a=1
Equation for a
a= b/c - 1
Equation for b
b= ca - a
Equation for c
c= b/a + 1
What is the value of y ?enter your answer in the box
Answer:
I believe the answer is 20.
Step-by-step explanation:
So I don't if I'm right help would be much appreciated
Answer:
A is the correct equation
Step-by-step explanation:
Which function is the best inverse of f(x)=x2-9
Answer:
The inverse is sqrt(x+9)
Step-by-step explanation:
f(x)=x^2-9
To find the inverse of the function, we interchange x and y and solve for y
y = x^2 -9
x = y^2 -9
Add 9 to each side
x+9 = y^2 -9+9
x+9 = y^2
Take the square root of each side
sqrt(x+9) = sqrt(y^2)
sqrt(x+9) = y
f^-1 (x) = sqrt(x+9)
Rita has 3/4 gallon of lemonade she pours 1/24 gallon of lemonade into each glassk Rita has 3/4 gallons of lemonade she pours one 24 gallon of lemonade into each glass how many glasses of lemonade can she pour
Answer:
18 number of glasses of lemonade can she pour
Step-by-step explanation:
Unit rate defined as rates are expressed as a quantity of 1, such as 3 feet per second or 8 miles per hour, they are called unit rates.
As per the statement: Rita has 3/4 gallon of lemonade she pours 1/24 gallon of lemonade into each glass.
Number of lemonade Rita has = 3/4 gallon
[tex]\text{Unit rate per glass} = \frac{1}{24} \text{gallons}[/tex]
By definition of unit rate;
[tex]\text{Number of glasses} = \frac{\text{Number of lemonade}}{\text{Unit rate per glass}}[/tex]
Substitute the given values we get;
[tex]\text{Number of glasses} = \frac{\frac{3}{4}}{\frac{1}{24}}[/tex]
[tex]\text{Number of glasses} = \frac{3}{4} \times 24 = 3 \times 6 = 18[/tex]
Therefore, number of glasses of lemonade can she pour is, 18
Select the three ratios that are equivalent to 3 boys/5 girls.
8 boys/10 girls
15 boys/25 girls
9 boys/15 girls
30 boys/50 girls
99 points!!
[tex]\dfrac{3\ boys}{5\ girls}\to\dfrac{3}{5}\\\\\dfrac{8}{10}=\dfrac{8:2}{10:2}=\dfrac{4}{5}\\\\\dfrac{15}{25}=\dfrac{15:5}{20:5}=\dfrac{3}{5}\\\\\dfrac{9}{15}=\dfrac{9:3}{15:3}=\dfrac{3}{5}\\\\\dfrac{30}{50}=\dfrac{30:10}{50:10}=\dfrac{3}{5}\\\\Answer:\\\\\boxed{\dfrac{3\ boys}{5\ girls}=\dfrac{15\ boys}{25\ girls}=\dfrac{9\ boys}{15\ girls}=\dfrac{30\ boys}{50\ girls}}[/tex]
sheral got theses socres on her spelling test
95,89,99,85,82
what is the mean of absolute devitationof her test scores
The beginning balance on the money bank staremaent for Dorsey checking account was 452.76 and the ending balance was 197.59 what can be said about Dorsey transactions for the month ?
Answer: D He has 255.17 more in debts than in credits
Step-by-step explanation:
Finished A P E X
solving multi step equations x+x+2=3(x+1)+12
Will mark brainliest! :D
Answer: 137 + 4(n-1)
Step-by-step explanation:
137 + 4(n-1)
Okay, let's test this starting with week 1:
137 + 4(1-1)
137 + 4*0
137, which is correct because she starts with 137.
Week 2:
137 + 4 (2-1)
137 + 4 * 1
137 + 4
141
Alright, let's see if it is correct if we do week 5:
137 + 4 (5-1)
137 + 4(4)
137 + 16
153
To know that 153 is right we could do 137 + 4 + 4 + 4 + 4, which equals 153.
Heidi's mom made flower arrangements for a party.She made 4 times as many rose arrangements as tulips arrangements.Heidi's mom made a total of 40 arrangements. How may arrangements of each type did Heidi's mom make?
Answer: 32 Rose Arrangements & 8 Tulip Arrangements
Step-by-step explanation: The number of arrangements for each flower is unknown (n) but the total is known, 40 arrangements. There are 4 times as many rose arrangements than tulip meaning 4n rose + n tulip = 40, 4n + n = 40, 5n = 40, 40 ÷ 5 = n, n = 8. Roses = 4n = 4x8= 32. Tulips = n = 8.
solve the inequality algebraically. express your answer using interval or set notation. graph the solution set. -5 less than or equal to 4 - 3x less than or equal to 2
Step-by-step explanation:
This ≤ inequality sign means:
Less than/Equal toNo more thanAt mostMaximum of-5 ≤ 4
And then:
-3x ≤ 2
OR:
-5 ≤ 4 -3x ≤ 2
Hi!!! Sorry, I didn't know if they were suppose to be together or separate, so I just did it both ways!!! :) Really sorry if I am wrong...
−4/1a−4= 4/7a−3 solve for a
Answer:
a = (-7)/32 or a= 0.21875
Step-by-step explanation:
Solve for a:
-4 a - 4 = (4 a)/7 - 3
Put each term in (4 a)/7 - 3 over the common denominator 7: (4 a)/7 - 3 = (4 a)/7 - 21/7:
-4 a - 4 = (4 a)/7 - 21/7
(4 a)/7 - 21/7 = (4 a - 21)/7:
-4 a - 4 = (4 a - 21)/7
Multiply both sides by 7:
7 (-4 a - 4) = (7 (4 a - 21))/7
(7 (4 a - 21))/7 = 7/7×(4 a - 21) = 4 a - 21:
7 (-4 a - 4) = 4 a - 21
Expand out terms of the left hand side:
-28 a - 28 = 4 a - 21
Subtract 4 a from both sides:
(-28 a - 4 a) - 28 = (4 a - 4 a) - 21
-28 a - 4 a = -32 a:
-32 a - 28 = (4 a - 4 a) - 21
4 a - 4 a = 0:
-32 a - 28 = -21
Add 28 to both sides:
(28 - 28) - 32 a = 28 - 21
28 - 28 = 0:
-32 a = 28 - 21
28 - 21 = 7:
-32 a = 7
Divide both sides of -32 a = 7 by -32:
(-32 a)/(-32) = 7/(-32)
(-32)/(-32) = 1:
a = 7/(-32)
Multiply numerator and denominator of 7/(-32) by -1:
Answer: a = (-7)/32
The solution to the equation is [tex]\(a = -\frac{25}{32}\)[/tex].
To solve the equation [tex]\(\frac{-4}{1}a - 4 = \frac{4}{7}a - 3\) for \(a\)[/tex], follow these steps:
1. Simplify the equation by multiplying both sides by their respective denominators to eliminate the fractions:
[tex]\[ 7(-4a - 4) = 1(4a - 3) \][/tex]
2. Distribute the numbers outside the parentheses:
[tex]\[ -28a - 28 = 4a - 3 \][/tex]
3. Move all terms containing a to one side of the equation and constants to the other side:
[tex]\[ -28a - 4a = -3 + 28 \][/tex]
4. Combine like terms:
[tex]\[ -32a = 25 \][/tex]
5. Solve for a by dividing both sides by -32:
[tex]\[ a = \frac{25}{-32} \][/tex]
Therefore, the solution to the equation is [tex]\(a = -\frac{25}{32}\)[/tex].
FAST!! the hcf of 2 numbers is 98 and there LCM is 2352..the sum of their numbers may be
Answer:
Step-by-step explanation:
I hope it will help you
Attachment
express 4.08 as mixed number
Answer:
its 4 2/25 :P
Step-by-step explanation:
hi!!!
How would I put equations like these in Standard Form?
4x-y-7=0
3x+9= (7/2)y
y=-4x+12
y=(-3/4)x+(5/4)
The standard form:
[tex]Ax+By=C[/tex]
[tex]4x-y-7=0\qquad\text{add 7 to both sides}\\\\\boxed{4x-y=7}[/tex]
[tex]3x+9=\dfrac{7}{2}y\qquad\text{multiply both sides by 2}\\\\6x+18=7y\qquad\text{subtract 18 and 7y from both sides}\\\\\boxed{6x-7y=-18}[/tex]
[tex]y=-4x+12\qquad\text{add 4x to both sides}\\\\\boxed{4x+y=12}[/tex]
[tex]y=-\dfrac{3}{4}x+\dfrac{5}{4}\qquad\text{multiply both sides by 4}\\\\4y=-3x+5\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=5}[/tex]
Which statements are true? Check all that apply. (The formula for the area of a triangle is A = 1/2 bh)
A. BC = 6 cm
B. AC = 5 cm
C. BA = 4 cm
d. The perimeter of triangle ABC = 12 cm
E. The area of the triangle ABCc is 1/3 the area of triangle DEF
Answer:
C) BA=4 cm
D)the perimeter of triangle ABC= 12 cm
Step-by-step explanation:
Answer:
234
Step-by-step explanatio:acabo de
a
What is the solution to the system of equations graphed below?
Answer:
A. (3,0)
Step-by-step explanation:
When the equations are graphed, the solution is where the two graphs cross. For the red line and the blue line, the cross at (3,0)
We can check this by substituting x=3 into both equations and seeing if we get y=0
y = -x+3
y = -3+3
y =0
y = x-3
y = 3-3
y=0
In both cases, we got y=0.
Therefore (3,0) is a solution to both equations and since it solves both equations, it solves the system.
Apex please help
a.)graph d
b.) graph b
c.) graph a
d.) graph c
Answer:
GRAPH D
Step-by-step explanation:
BECASUE IT IS THE WRIGHT ANSWER
How do you solve this?
Answer:
Multiply 60 by .40
60 * .40 = 24
Answer is B
Step-by-step explanation:
Which of the following sets represents the range of the function shown?
Answer:
{0, -1, 11, 13 }
Step-by-step explanation:
the range of the function are the corresponding values of y from the set of points, in ascending order, that is
{0, -1, 11, 13 }
Answer:
Step-by-step explanation:
The range is the set of y values of the function.
{0, -1, 11, 13]
Katelyn did this work to solve an equation. Did she make an error?
4(x-2)-3=7x
4x-2-3=7x
Answer: The right answer is this:
Katelyn did make an error. She also needs to multiply 4 by −2.
4−8−3=7
Step-by-step explanation:
Answer:
Katelyn did make an error. She also needs to multiply 4 by −2.
4x−8−3=7x
Step-by-step explanation:
You are 5 feet tall. What is your height in meters (m)?
Answer:
1.524
Step-by-step explanation:
Answer:
1.52 meters
Step-by-step explanation:
Can someone please help me with this question? Thanks if you do!
A secant is a line that intersects a circle at two points.
Therefore your answer is
[tex]\boxed{D.\ \overline{AD}}[/tex]
OB - radius
DE - tangent
FC - chord
AB - some segment
what is the standard deviation of the numbers 77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86
Answer:
The standard deviation of the numbers is 16.154.
Step-by-step explanation:
The given observations are
77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86
Average or mean of the data is
[tex]\bar{X}=\frac{\text{Sum of observations}}{\text{Total number of observations}}[/tex]
[tex]\bar{X}=\frac{1432}{20}=71.6[/tex]
The Standard deviation of the data is
[tex]\sigma=\sqrt{\frac{\sum (X-\bar{X})^2}{n}}[/tex]
[tex]\sigma=\sqrt{\frac{5218.8}{20}}[/tex]
[tex]\sigma=\sqrt{260.94}[/tex]
[tex]\sigma=\sqrt{16.154}[/tex]
Therefore standard deviation of the numbers is 16.154.
jamie rolls a 6-sided die 30 times and determines that the experimental probability of rolling a 2 is 1/15. The theoretical probability of rolling a 2 is 1/6 What could Jamie do to make his experimental results more closely match the theoretical probability?
Answer:
Answer is to increase trials
Step-by-step explanation:
Theoretical Probability is what it is expected to happen whereas Experimental Probability is what actually happens.
What Jamie should take into serious consideration is that Experimental probability gets gradually closer to theoretical probability as the number of trials increases.
In other words, Jamie needs to increase the number of trials in order to match experimental and theoretical probabilities every time more and more.
Answer: letter A
to increase the number of trials
Step-by-step explanation:
How to find the measure of a triangle?
Hi there! :)
Answer:
The answer is D. 83°
Step-by-step explanation:
You should know that the interior angles of a triangle always add up to 180°.
So, what you will need to do, is add all 3 angles together and create an equation (equal to 180). Then you need to solve this equation by isolating "x":
(8x + 12) + (55 - 3x) + (10x + 23) = 180
Get rid of all the parentheses
8x + 12 + 55 - 3x + 10x + 23 = 180
Add all similar terms together
8x - 3x + 10x = 15x
12 + 55 + 23 = 90
15x + 90 = 180
Subtract "90" from each side of the equation → 180 - 90 = 90
15x = 90
Divide each side of the equation by "15" → 90 ÷ 15 = 6
x = 6
Since you now know that the value of "x" is 6, you can now find the measure of the angle at George's position by replacing the "x" by 6:
10x + 23 = Measure of the angle at George's position
10(6) + 23
Multiply 10 by 6 → 10 × 6 = 60
60 + 23
Add 60 and 23 together → 60 + 23 = 83
83 = Measure of the angle at George's position
There you go! I really hope this helped, if there's anything just let me know! :)