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
?

The area of polygon A would be a fraction 1/25 of the size of polygon B.

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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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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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.

Answer:

Because:

30.5^2+73.2^2=79.3^2

=> Right triangle

=> Cos0 = 73.2/79.3 => A

Step-by-step explanation:

0.4  is the multiplive rate change for the Expenstial function .

What exactly makes a function exponential?

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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Answer:

No

Step-by-step explanation:

Does not pass the vertical line test.

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

(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.

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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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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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Answer: 12

Step-by-step explanation:

add

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:

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.

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

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

18.84 in² is surface area of cylinder .

What does surface area mean?

sa = 2πr² + 2πrh

     = 2 × 3.14 × 1 × 1 + 2 × 3.14 × 1 × 2

      = 6.28 + 12.56

      = 18.84

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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

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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Answer:

Y = 44

Step-by-step explanation:

44/4 - 2 = 9

11 - 2 = 9

Y = 44

<3

Answer:

Answer on attached figure

Step-by-step explanation:

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)}.

If the city park has a circular pond with a diameter of 4 yards. The pond's circumference is: 12.56 yrd.

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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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

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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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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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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Answer:

90

Step-by-step explanation:

|90| = 90

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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The reason are as follows:

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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