ax + by = 12
2x + 8y = 60
In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a/b
?
Answers
Answer:
1/4
Step-by-step explanation:
If the system has infinitely many solutions, then
[tex]\sf \boxed{\bf \dfrac{a_1}{b_1}= \dfrac{a_2}{b_2}= \dfrac{c_1}{c_2}}[/tex]
ax + by = 12 ⇒ a₁ = a ; b₁ = b ; c₁ = 12
2x + 8y =60 ⇒ a₂ = 2 ; b₂ = 8 ; c₂ = 60
[tex]\sf \dfrac{a}{2}= \dfrac{b}{8}= \dfrac{12}{60}\\\\\\ \dfrac{a}{2}= \dfrac{12}{60}\\\\a = \dfrac{12}{60}*2\\\\a = \dfrac{2}{5}[/tex]
[tex]\sf \dfrac{b}{8}= \dfrac{12}{60}\\\\ b = \dfrac{12}{60}*8\\\\b = \dfrac{8}{5}\\[/tex]
[tex]\sf \dfrac{a}{b}= \dfrac{ \dfrac{2}{5}}{ \dfrac{8}{5}}\\\\[/tex]
[tex]\sf = \dfrac{2}{5}* \dfrac{5}{8}\\\\ = \dfrac{1}{4}[/tex]
Related Questions
Find the surface area of the cylinder.
Answers
18.84 in² is surface area of cylinder .
What does surface area mean?
The quantity of space enclosing a three-dimensional shape's exterior is its surface area.Latitudinally, curvedly, and overall, there are three different forms of surface area.A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².Surface area is the amount of space covering the outside of a three-dimensional shape.sa = 2πr² + 2πrh
= 2 × 3.14 × 1 × 1 + 2 × 3.14 × 1 × 2
= 6.28 + 12.56
= 18.84
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for a sequence(chapter3) of numbers, suppose that you attach 1, then 2, then 3, and so on up to n. what is the big-o time analysis for the combined time of attaching all n numbers?
Answers
The big-o time analysis for the combined time of attaching all n numbers i O(n).
The big-O running time gives the relationship between the steps taken for the algorithm and its running time. it is denoted by O(.), where . refers to the some f(n). f(n) is determined by the way of the algorithm in each step.
Here, we attach 1, then 2,then 3 and so on up to n to make a sequence of numbers. So at a time, only 1 number is attached and therefore one step of the algorithm is working. So we can say that the big-O time analysis for the combined time of attaching all n numbers is O(n).
This means that at n = 1, only 1 step is taken by the algorithm .At n=2, two steps and continued like this up to n steps.
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What is the range of the function f(x)=6x^2+x-1/2x^2+x-6
Answers
Answer:
Range: [tex]\:f\left(x\right)\ge \:-\frac{68}{11}[/tex]
Interval notation [tex][-\frac{68}{11},\:\infty \:)[/tex]
Step-by-step explanation:
I got a little confused with the x - 1/2x^2 term and I am taking to to be:
[tex]x\:-\frac{1}{2}x^2[/tex] . If this is incorrect please mention the correct term in your comment and I will edit this post. Or you can re-post the question
We have
[tex]f\left(x\right)=6x^2+x\:-\frac{1}{2}x^2+\:x\:-\:6[/tex]
Simplify by grouping like terms:
[tex]=-\frac{1}{2}x^2+6x^2+x+x-6[/tex]
[tex]= \frac{1}{2}x^2+6x^2+2x-6[/tex]
Add similar elements
[tex]-\frac{1}{2}x^2+6x^2[/tex][tex]= -\frac{1x^2}{2}+\frac{12x^2}{2} = \frac{11x^2}{2}[/tex]
So the original function expression becomes
[tex]y=\frac{11}{2}x^2+2x-6[/tex]
This is the equation of a parabola which in standard form is [tex]ax^2 + bx + c[/tex]
Here
[tex]a=\dfrac{11}{2},\:b=2,\:c=-6[/tex]
We can compute the vertex of this parabola using the fact that the x, y coordinates of the vertex are given by
[tex]x_v =-\dfrac{b}{2a}[/tex]
Plugging in values for b and a give us
[tex]x_v =-\dfrac{b}{2a} = -\dfrac{2}{2\left(\dfrac{11}{2}\right)} =-\dfrac{2}{11}[/tex]
Plugging in this value of [tex]x_v[/tex] into the parabola equation will give the value for [tex]y_v[/tex] which is the function value at the vertex
Plug in [tex]x_v = -\frac{2}{11}[/tex] t find the [tex]y_v[/tex] value:
[tex]y_v=\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2}+2\left(-\dfrac{2}{11}\right)-6[/tex]
Simplify
[tex]\dfrac{11\left(-\dfrac{2}{11}\right)^2}{2} =\dfrac{2}{11}[/tex]
[tex]2\left(-\dfrac{2}{11}\right) = -\dfrac{4}{11}[/tex]
Combining the terms we get
[tex]y_v =[/tex] [tex]\dfrac{2}{11}-\dfrac{4}{11}-6[/tex] [tex]= -\dfrac{68}{11}[/tex]
[tex]\textsf{Therefore the parabola vertex is at }[/tex] [tex]\left(-\dfrac{2}{11},\:-\dfrac{68}{11}\right)[/tex]
For a parabola of the form [tex]ax^2 + bx + c[/tex] with vertex [tex]\left(x_v,\:y_v\right)[/tex]
[tex]\circ \;\mathrm{If}\:a < 0\:\mathrm{the\:range\:is}\:f\left(x\right)\le \:y_v[/tex]
[tex]\circ \;\mathrm{If}\:a > 0\:\mathrm{the\:range\:is}\:f\left(x\right)\ge \:y_v[/tex]
Here [tex]a=\frac{11}{2}[/tex] so the range is [tex]f\left(x\right)\ge \:-\dfrac{68}{11}[/tex]
Answer range of f(x) is
[tex]f\left(x\right)\ge \:-\dfrac{68}{11}[/tex]
In interval notation it is [tex][-\frac{68}{11},\:\infty \:)[/tex]
It is much easier if you visualize it in a graph
Hope that helps
What is the multiplive rate change for the expenstial function f(x)2 5/2-x
Answers
0.4 is the multiplive rate change for the Expenstial function .
What exactly makes a function exponential?
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.We have to find the multiplicative rate of change for:
f ( x ) = 2 * ( 5/2 ) ^(-x)
F (X ) = [tex]f(x) = 2 * ( \frac{5}{2} )^{-x}[/tex]
2/5 = 0.4
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Question 8
1 pts
You have $50 in your bank account. You spend $35, deposit $15, and spend $40. How much do you have in our account ? Use negative if the account is over drawn
Answers
Answer: $-10
Step-by-step explanation:
The starting value is $50 and you use $35 of it meaning you only have $15 left.
You then deposite $15 meaning you now have $30 in your bank account.
After that, you spend $40 meaning you have $-10 in your bank account.
Rewrite 8x + 64 using a common factor.
8x(x + 64)
8x(x + 8)
8(x + 64)
8(x + 8)
Answers
The expression (8x+64) can be rewritten as a common factor as 8(x+8).
According to the question,
We have the following expression:
(8x+64)
It is to be noted that a common factor is such a number including a variable that it can completely divide a term. For example, in this expression, 8 is such a number that it can divide both 8x as well as 64.
(This can be better understood using more examples. For example, 4 is a common factor in 4x+24 and 5 is a common factor in 5x+30.)
Now, taking 8 as a common factor:
8 (x+8)
Hence, the correct expression is D (the fourth one).
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I have no clue how to do this.
Answers
So the equation will be:
7t +1 = 8t -8 combine like terms
-8t. -8t
-t +1 = -8. Combine like terms
-1. -1
-t = -9 therefore t=9 now plug in 9 for t in the equation
7(9) + 1 = 8(9) - 8 and so on. Both angles should equal the same degree.
I hope this helps
Represent the sample space using set notation.
4) A bag contains one red marble and two
green marbles. You randomly pick a
marble and keep it to play with. Then
your friend picks a marble from the bag.
Answers
Answer:
{(Red , Green) ; (Green , Red) ; ((Green , Green)}
Step-by-step explanation:
Here ,we notice that we draw two marbles without replacement.
Then
The possible outcomes are :
• Red then Green
• Green then Red
• Green then Green
NOTE : we can’t have the outcome Red then Red ,because if you pick a red marble and keep it to play with. Then your friend has only the choice of picking a Green marble from the bag.
Therefore,
The sample space is {(Red , Green) ; (Green , Red) ; ((Green , Green)}.
Becca made 2 trays of rolls and biscuits. Each tray had 12 rolls and 6 biscuits. How many total rolls and biscuits did Becca make?(1 )point
Answers
Answer:
24 roles and 12 biscuits
Step-by-step explanation:
She had 2 trays which each had 12 ROLES and 6 BISCUTS.
Roles: 12x2 = 24
Biscuits: 6x2 = 12
So the total is 24 roles and 12 biscuits.
a local nonfrofit organization is selling popcorn to raise money for hurrican relief. the organization paid $4 per bag for the popcorn and sold $5 per bag. what was the percent makeup on each bag of popcorn?
Answers
The percent makeup on each bag of popcorn is 25%.
When a fraction of a whole is expressed as a number between 0 and 100, it is called a percentage. The percentages 100%, 50%, 0% indicate all of some quantity, half of the quantity, and none of the quantity respectively.
Popcorn is being sold by a neighborhood nonprofit to support hurricane relief.
The organization paid $4 for each bag of popcorn.
The organization sold each bag of popcorn for $5.
The markup or gain from selling the popcorn is:
$5 - $4 = $1
Therefore, the percent makeup on each bag of popcorn will be:
= ( the gain / the amount organization paid for each bag ) × 100
= ( 1 / 4) × 100
= 0.25 × 100
= 25 %
Hence, the percent makeup on every bag of popcorn is 25%.
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Under his cell phone plan, Carson pays a flat cost of $37.50 per month and $3 per gigabyte. He wants to keep his bill under $40 per month. Which inequality can be used to determine g, the maximum number of gigabytes Carson can use while staying within his budget?
Answers
Based on the flat cost paid by Carson for his cell phone plan, and the amount of he wants to keep his bill under, the inequality that can be used to determine g is 37.50 + 40g ≤ 40
How to find the inequality?The inequality that can be used to find the maximum number of gigabytes that Carson can use while staying in his budget can be found as:
Flat cost for the cell phone plan + Cost per gigabyte x Number of gigabytes ≤ Maximum preferred bill by Carson
When we put in the figures from Carson's cell phone plan, we get:
37.50 + 3 x g ≤ 40
37.50 + 3g ≤ 40
In conclusion, the inequality that represents g is 37.50 + 3g ≤ 40.
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A tablet data provider offers different plans for data usage. The plan Raul chose has a monthly fee of $29.99 per month for 5 GB if data with an additional cost of $10 for each gigabyte over 5.
a. Write an expression for Raul’s monthly data costs.
b. Raul learns that his data provider is iffy unlimited data plan for $59.99 per month. Find the minimum number if gigabytes Raul could use per month to make the unlimited plan cheaper than his current plan. Explain your solution process.
Answers
(a) The expression for Raul's monthly data costs is 29.99 + 10 (n - 5).
(b) The minimum number is 9 GB to make the unlimited plan cheaper.
The plan Raul chose has a monthly fee of $29.99 per month for 5 GB of data, with an additional cost of $10 for each gigabyte over 5.Assume that he will use "n" gigabyte per month.The monthly fee is $29.99 for 5 GB.The cost per GB after the first 5 GB is $10.The number of GB whose cost is $10 is (n - 5).His monthly fees = 29.99 + 10 (n - 5) ⇒ current planThe fees for the unlimited plan is $59.99 per month.We need an unlimited cheaper plan than the current one.Let the current plan be expensive than the unlimited plan.29.99 + 10 (n - 5) > 59.99Subtract 29.99 from both sides.10 (n - 5) > 30Divide both sides by 10.n - 5 > 3Add 5 to both sides.n > 8The minimum number is 9 GB to make the unlimited cheaper.To learn more about numbers, visit :
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Identify the reason for each step in the solution.
3x+6=2x+3
3x+6-2x=2x+3-2x
x+6+3
x+6-6+3-6
x+-3
Answers
The reason are as follows:
subtraction of equality i.e., 2xSubtractionsubtraction of equality i.e., 2xSubtractionWhat is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given:
3x+6=2x+3
3x+6-2x=2x+3-2x (subtraction of equality i.e., 2x)
x+6=3 (Subtraction)
x+6-6=3-6 (subtraction of equality i.e., 6)
x=(-3) (Subtraction)
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The city park has a circular pond with a diameter of 4 yards. What is the pond's circumference?
Use 3.14 for .
Answers
If the city park has a circular pond with a diameter of 4 yards. The pond's circumference is: 12.56 yrd.
Circumference of the pond
Using this formula to determine or to calculate the pond's circumference
C = π × d
where:
C = Circumference
d = diameter = 4 yards
π = 3.14
Let plug in the formula
C = 3.14×4
C= 12.56 yards
Based on the above calculation the circumference of the pond will be 12.56 yards.
Therefore If the city park has a circular pond with a diameter of 4 yards. The pond's circumference is: 12.56 yrd.
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if martha can rake the yard in 4 hours and her brother can rake the yard in 8 hours, how long does it take them to do it together?
Answers
Answer: 12
Step-by-step explanation:
add
solve for y 9=y/4-2
pleas help need to submit soon
Answers
Answer:
Y = 44
Step-by-step explanation:
44/4 - 2 = 9
11 - 2 = 9
Y = 44
<3
Answer quickly please
Answers
Answer:
No
Step-by-step explanation:
Does not pass the vertical line test.
an article in forbes noted that the intercounty connector toll road that connects two counties in maryland was not generating as much toll revenue as predicted. at that time, the toll rate was $8 for a passenger car making a round trip from end to end on the tollway during rush hour. what additional information would you need to know in order to determine if the toll should be increased or decreased?
Answers
The additional information would you need to know in order to determine if the toll should be increased or decreased is The price elasticity of demand
The additional information required is
In this situation, it is necessary to consider the price elasticity of demand since it demonstrates how changes in price may either increase or decrease a product's consumption.Since the toll road wasn't generating as much toll money as was anticipated in this scenario, it's possible that the toll road's price has increased.The price elasticity of demand will be required in this scenario as extra data.Therefore,The additional information would you need to know in order to determine if the toll should be increased or decreased is The price elasticity of demand
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PRACTICING SKILLS & CONCEPTS
1. Solve the shape equation puzzle.
+
+
=
= 10
6=
8 =
Answers
The value of box/ square is 5, value of circle is 3 and the value of star is 6.
Let box/ square be denoted by x
let the circles be denoted by y
let the stars be denoted by z
now, let us make three linear equation based on the diagram provided
1. x + x = 10
2. y + z= 9
3. y+ x = 8
solving equation 1
x + x = 10
2x = 10
x = 5
Putting the value of x in equation 3
y + x=8
y + 5 = 8
y = 3
Putting the value of y in equation 2
y + z = 9
3 + z= 9
z = 6
Hence , The value of box/ square is 5, value of circle is 3 and the value of star is 6.
A linear equation is one in which the variable's maximum power is always 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. In this equation, x is a variable, A is a coefficient, and B is constant. A linear equation in two variables has the conventional form Ax + By = C.
A linear equation is an equation with the maximum degree of one. This means that in a linear equation, no variable has an exponent greater than 1. A linear equation's graph is always a straight line.
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What is the value of |90|?
Answers
Answer:
90
Step-by-step explanation:
|90| = 90
polygon b is a scaled copy of polygon a using a scale factor of 5 . polygon a area is what fraction of polygon b area
Answers
The area of polygon A would be a fraction 1/25 of the size of polygon B.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object
The formula of the scale factor is shown as;
Area of Polygon B = (scale factor)²×(Area of Polygon A).
Using a scale factor of 5, we get
(Area of Polygon B) = (5)²× (Area of Polygon A)
(Area of Polygon B) = (25) × (Area of Polygon A)
Area of Polygon A = (1/25) × Area of Polygon B
Therefore, the area of polygon A would be a fraction 1/25 of the size of polygon B.
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A garden table and a bench cost $987 combined. The garden table costs $87 more than the bench. What is the cost of the bench?
Answers
Answer:
$450
Step-by-step explanation:
let the price of the bench = x
Then, the price of the table is x + 87.
x + x + 87 = 987
2x + 87 = 987
2x = 900
x = 450
Answer: $450
Need help with Q6. Kdkdndndnfndndndndndncjndjfjc
Answers
Answer:
Because:
30.5^2+73.2^2=79.3^2
=> Right triangle
=> Cos0 = 73.2/79.3 => A
Step-by-step explanation:
Each year a certain amount of money is deposited in an account which pays an annual interest rate of r so that at the end of each
year the balance in the account is multiplied by a growth factor of z=1+r.$500 is deposited at the start of the first year, an
additional $200 is deposited at the start of the next year, and $600 at the start of the following year.
a. Write an expression for the value of the account at the end of three years in terms of the growth factor z
Answers
The value of the account at the end of three years of the growth factor z will be $1350.684.
According to the growth factor z, the value of the account after three years is,
Given r, is the yearly interest rate that is compounded by a growth factor z= 1 +r. $500 at the end of each year.
The initial year's deposit is in the amount of $500.
Both the next year and the third-year deposits are made correspondingly, $200 and $600.
As a result, the account will be worth at the end of the three years is:
$(500 x3 + 200 x2 + 600 x) ---(1)
If r= 2%, then x=(1 + 2/100), , substituting the value of x in (1)
The sum will then be:
$(500(1 + 2/100)3 + 200 (1 + 2/100)2 + 600(1+2/100))
Solving the above equation, the amount will be equal to $1350.684.
Hence, The value of the account at the end of three years of the growth factor z will be $1350.684.
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What does the point (1,2) represent?
Answers
Answer:
In points (1,2), 1 is the value of X which represents Time in Hours and 2 is the value of Y which means Cost or $ per hour for the duration of the parking in the lot. I hope this helps.
Step-by-step explanation:
Select all the correct answers.
Which three expenses could money invested in a 529 plan be used for without penalty?
оооо
clothes
gas
gym membership
room and board
textbooks
tuition
Answers
Gym Membership and gas and clothes is my option
Find the equation of the line that passes through the points (1, 3) and (2, 4)
Answers
Answer:
y = x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 4 )
m = [tex]\frac{4-3}{2-1}[/tex] = [tex]\frac{1}{1}[/tex] = 1 , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 3 )
3 = 1 + c ⇒ c = 3 - 1 = 2
y = x + 2 ← equation of line
A client asked Nathan to design a rectangular garden with an area of 22 square feet. The client also requested that the length of the garden be eight feet less than seven times the width
Answers
The length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.
Let the width of the garden be x units.
According to the given question.
The area of the rectangular garden is 22 square feet.
Also, the length of the garden be eight feet less than seven times the width.
⇒ length of the garden = 7x - 8
Thereofore, the area of the rectangular garden is given by
22 = x(7x - 8)
⇒ 22 = 7x^2 - 8x
⇒ 7x^2 - 8x - 22 = 0
⇒ x = [tex]\frac{8 \pm \sqrt{64 + 616} }{14}[/tex]
⇒ x = [tex]\frac{8 \pm \sqrt{680} }{14}[/tex]
⇒ x = [tex]\frac{8\pm 26}{14}[/tex]
⇒ x = 8 + 26/14
⇒ x = 34/14
⇒ x = 2.43 feet
So,
the length of the rectangular garden = 7(2.43) - 8 = 9.01 feet
Hence, the length of the rectangular garden is 9.01 feet and width of the garden is 2.43 feet, if its area is 22 square feet.
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MARKING BRAINLEIST If CORRECT BE QUICK!
Answers
Answer:
Answer on attached figure
Step-by-step explanation:
please help me solve the problem i took a screen shot to show the problem.