Under her cell phone plan, Caroline pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $74 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Caroline can use while staying within her budget.

[tex]\displaystyle\\Answer:\ y=\sqrt{\frac{x-1}{2} } \ \ \ \ (x\geq 1,\ \ \ \ y\geq 0)[/tex]

Step-by-step explanation:

[tex]y=2x^2+1\\[/tex]

We change the argument and the value:

[tex]\displaystyle\\x=2y^2+1\\\\x-1=2y^2+1-1\\\\x-1=2y^2\\[/tex]

Divide both parts of the equation by 2:

[tex]\displaystyle\\\frac{x-1}{2}=y^2\\\\ \sqrt{\frac{x-1}{2} }=y \ -\ the\ desired\ inverse\ function\\\\[/tex]

The restrictions are imposed on the inverse function by on x:

[tex]x-1\geq 0\\x\geq 1[/tex]

The restrictions are imposed on the inverse function by on y:

[tex]y\geq 0[/tex]

Then the original function is defined on the sets:

[tex]x\geq 1,\ \ \ \ y\geq 0[/tex]

The initial function, a parabola, is constrained because of the inverse function; only in this case the functions are reciprocal.

The equation which represents the relationship between 'h' the number of hours, and c, the total cost is y = 250x+850.

A straight line equation is a mathematical equation that describes the relationship between the coordinate points on that straight line. It can be written in several ways and indicates the slope, x-intercept, & y-intercept of a line.

Now, as per the given question;

The attorney charges price for an initial meeting = $850.

And, the charges for each hour is = $250.

Thus, the equation which shows the given situation is-

y = 250x + 850.

In which, 250 is the value of the slope 'm'.

The y- intercept is shown by 850.

Thus, the total cost will be found out by equation  y = 250x+850.

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The solution of the expression ( 9y² - 4x )( 9y ² + 4x) will be 81y⁴ - 16x².

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression ( 9y² - 4x )( 9y ² + 4x) will be solved as below:-

Use the formula:- ( a + b ) ( a - b ) = a² - b²

a = 9y²

b = 4x

( 9y² - 4x )( 9y ² + 4x ) = ( 9y² )² - ( 4x )²

Therefore, solution of the expression ( 9y² - 4x )( 9y ² + 4x) will be 81y⁴ - 16x².

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The obtained two numbers by substitution method are 5 and 12.

The algebraic method for solving simultaneous linear equations is the substitution method.

Let the first number be 'x'.

Let the second number be 'y'

From the given condition that second number is 3 times 1 less than the first number.

That is;

y = 3(x - 1)

Now the sum of both number are given as 17.

x + y = 17.

Use substitution method, and put the value of y in the total sum.

x + y = 17.

x + 3(x - 1) = 17

Simplify the given equation;

x + 3x - 3 = 17

4x = 17 + 3

4x = 20

x = 5 (first number)

Put the value of x in y to find the value.

y = 3(x - 1)

y = 3(5 - 1)

y = 12 (second number)

Therefore, the values of two numbers are 5 and 12.

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Answer:

6m sqared to 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

(2m6)3

- if you mean (2m^6)^3

it is 8m^18.

After spending the money on oranges and apple, Sarah is left with 20p.

As per the given question;

Sarah spend the amount to buy the 3 oranges is 30p each.

Total spending on oranges = 3 x 30p = 90p.

For buying 1/2 kg of apple; Sarah spend the amount of  £1.20 per kg.

Cost for half kg of apples = 60p.

Total cost =  apple + oranges

Total cost = 60p + 30p = 90p.

Total cost = £1.50

Now, the only money Sarah has is one 50p coin and six 20p coins.

Sarah' money = 50p + (6 x 20)p

Sarah' money = 50p + £1.20

Sarah' money = £1.70

Money left = £1.70 - £1.50

Money left = £0.20 = 20p

Thus, the money left to Sarah is 20p.

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The correct question is -

Sarah wants to buy some fruit. She wants to buy and 3 oranges at 30p each 1/2kg apples at £1.20 per kg.

The only money Sarah has is one 50p coin and six 20p coins.

She pays for the fruit.

Work out how much money Sarah has left.

The left over fabric area is; 0.03 m²

Now, if the radius of a circle is r, then the diameter is;

d = 2r

Now, there are 16 identical circles to be cut from a square sheet of fabric whose sides are 0.4 m long.

Thus, the height of the square will be the diameter of four circles.

Height of square = 4(2r) = 8r

Thus;

8r = 0.4

r = 0.4/8

r = 1/20 m

Left over fabric area = (0.4 * 0.4) - (π × (1/20)²)

Left over fabric area = 0.03 m²

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Answer:

a good estimation is 190

Step-by-step explanation:

(2x25)+(3x12)+(7x8)+(9x5)=187

187 rounds to 190

Answer: (a) 0-2 (b) 3.2

Step-by-step explanation:

modal = the number that appears the most

mean = average

(a) modal class interval: 0 - 2

(b) first, find the mean of each class interval (number of letters delivered):

1, 3.5, 6 and 9

1 x 25 = 25

3.5 x 12 = 42

6 x 8 = 48

9 x 5 =45

25 + 42 + 48 + 45 = 160

number of houses:

25 + 12 + 8 + 5 =50

mean:

160 / 50 = 3.2

Answer:

10xto the power of 7

Step-by-step explanation:

Multiply x2x2 by x5x5 by adding the exponents.Tap for fewer steps...Move x5x5.5⋅2(x5x2)5⋅2(x5x2)Use the power rule aman=am+naman=am+n to combine exponents.5⋅2x5+25⋅2x5+2Add 55 and 22.5⋅2x75⋅2x7Multiply 55 by 22.10x710x7

For the entire independent-measures experiment 24 individuals are participated.

Different participants are utilized in each condition of the independent variable in an experimental design known as an independent measures design, or between-groups. This indicates that a different group of participants is present for each condition of the experiment. A research strategy known as an independent measures design uses numerous experimental groups with subjects only being assigned to one group. Throughout the experiment, each participant is solely exposed to one independent variable condition. A drug trial for a novel medicine would serve as an example. This has the benefit of preventing order effects, which occur when participants behave differently as a result of the order in which conditions are done, often as a result of factors like boredom or exhaustion.

We are given the value  t(22) = 5.30, p < .01

So here degree of freedom (df) is 22 and it is independent so there is two samples,

so df= n₁+n₂-2

⇒ 22 =  n₁+n₂-2

⇒ n₁+n₂ = 24.

Thus for the entire experiment 24 individuals are participated.

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Answer:

1/20

Step-by-step explanation:

hope this helps

Answer:

49/20

Step-by-step explanation:

Bye! ~ SunnyBunny <3

Adrianna's distance from her house increases from 60 yards to 180 yards, her distance from the bus stop varies from 340 yards to 220 yards.

What is the straightforward meaning of distance?

Adrianna walks from her house to a bus stop that is 400 yards away.

as Adrianna walks to the bus stop the distance between Adrianna and bus stop will b decreasing .  

Further As Adrianna's distance from her house is  60 yards then she is 400 -60 = 340 yards away from bus stop

Also As Adrianna's distance from her house is  180 yards then she is 400 -180 = 220 yards away from bus stop .

As Adrianna's distance from her house increases from 60 yards to 180 yards, her distance from the bus stop varies from 340 yards to 220 yards.

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The dimensions of the fence that will maximize the area are-

Multiply the width by the height of a rectangle to find its area. If we know the lengths of two sides of a rectangle, we can calculate the height and width.

Now, as per the question;

Let 'L'  be the length and,

'W' width of the rectangular

Also, let the river is running along L.

Perimeter to be covered by fence:

P = L + 2W

2700 = L + 2W

Thus, L= 2700 - 2W

Substitute the value of L in the area

Area, A= LW

A = (2700 - 2W)W

A = 2700W - 2W²

This is a quadratic equation;

Now, the vertex of the rectangular with the greatest area will have the greatest width.

(W,A), where W= -b/2a where b = 2700 and a = -2

Solve for W,

W = -2700/2×(-2)

   = -2700/-4

W = 675 ft.

Substitute the value of W in L to find it.

L= 2700 - 2W

 = 2700 - 2×675

L = 1350 ft

Thus, the maximum area will become;

Maximum area A = 1350 × 675

Maximum area A = 911250 sq. ft

Therefore, the maximum area is found to be 911250 sq. ft

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The complete question is-

A farmer has 2700 feet of fencing available to enclose a rectangular area bordering a river. if no fencing is required along the​ river, find the dimensions of the fence that will maximize the area. what is the maximum​ area

The value modulus functions of x are found as 12 and -3.

A modulus function returns the magnitude of a number regardless of its sign.

The modulus function's value is always non-negative. Whenever f(x) is a modulus function, we get:

for the given function;

m(x) = |2x - 9|, where m(x) = 15.

then,

15 = |2x - 9|

Open the modulus function in its corresponding positive and negative values;

15 = 2x -9 and also 15 = -(2x - 9).

Solving both;

15 = 2x -9

2x = 15 + 9

2x = 24

x = 12

and, the second functions;

15 = -(2x - 9)

15 = -2x + 9

-2x = 15 - 9

x = -3

Thus, the solution for x are 12 and -3.

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The correct question is-

Given m(x) = |2x - 9|, find x when m(x) = 15.

The algebraic expression is,

⇒ 10 + c/3 = 12

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

''ten more than the quotient of c and three is 12.''

Now, We can formulate;

⇒ ten more than the quotient of c and three is 12

⇒ 10 + c/3 = 12

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Complete question is this,

Ten more than the quotient of c and three is 12.

I will use the example that they gave to describe the method

First, you need to find the difference between the new amount and the original amount. The new one is 30, while the original one is 24, so the original amount incrased by 6.

Now, you take the difference that you got, and divide it by the original amount. 6 : 24 = 1/4, or 25%. So, the percentage increase is 25%

Applying the same for the others :

32 -> 56 (increased by 24, 24:32 = 3/4 -> 75%)
15  -> 18  (increased by 3, 3:15 = 1/5 -> 20%)
30 -> 33 (increased by 3, 3:30 = 1/10 -> 10%)
150 -> 153 (increased by 3, 3:150 = 1/50 -> 2%)
120 -> 126 (increased by 6, 6:120 = 1/20 -> 5%)
200 -> 202 (increased by 2, 2:200 = 1/100 -> 1%)

Answer:

nmms grbtbtbtbynybybtby

Answer:(5,-1.5)

Step-by-step explanation: So you add the x of both the points together so 3+7=10 and then divide by 2 cause there are 2 numbers. 10/2=5

Same thing with y -4+1=-3 then -3/2=-1.5

So the answer is (5,-1.5)

Answer:  Not closed under multiplication

====================================================

Explanation:

Pick any two negative numbers that you want.

I'll go for -3 and -5

They multiply to (-3)*(-5) = 15 which is a positive number. The two negatives cancel out to form a positive.

This is an example to show that multiplication is not closed for this subset of the real numbers. We consider it to be closed if the result of any two negative numbers multiplied would get us some other negative number.

In a sense, this is the complete opposite of closed since the result is never negative.

Here's an example of a set that is closed under multiplication: integers

Picking any two integers and multiplying them together gets us some other integer. Each item is found in the same set, i.e. the result never leaves or goes outside the set.

Answer:

Different solids have different melting points depending on the strength of bonding between the particles and the mass of the particles. Essentially, the heavier the particles in the solid, and the stronger the bonding, the higher the melting point.

Step-by-step explanation:

Hope this helps!

One of the solutions to the following linear inequality is the value x=-10.

What are linear inequalities?

Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. It's important to remember that if p < q, then p must be a number that is strictly less than q. If p ≤ q, then p is a number that is strictly smaller than q or exactly equal to q. The same is true for the other two inequality signs > (greater than) and ≥ (greater than or equal to).

What guidelines apply for resolving linear inequalities?

Given equation: 6x-4≤-28

Add 4 to both sides according to the addition rule:

(6x+4)+4 ≤ (−28)+4

6x-4+4≤ -24

6x≤-24

Now, divide both sides by 6 according to the division rule:

6x/6 ≤−24/6

x ≤ -4

Therefore, x ≤ -4 is the solution for the given linear inequality where, x ∈ (-∞,-4)

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The result of diving 107 by 10⁻³ is (E) 107,000.

So, we know that 10⁻³ is 0.001.

Therefore, the result of diving 107 by 10⁻³ is (E) 107,000.

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The correct question is given below:

The result of dividing 107 by 10^-3 is?

a. 10-4.

b. 102.5.

c. 1010.

d. 104.

e. 107,000

The next minimum monthly payment is expected to be $145.24

What is the balance on the credit card before interest is computed?

First and foremost, we need to determine the credit card balance after the purchases and payment for next month are considered

balance after purchases and payment=$2,064.92-$185.00+$812.61

balance after purchases and payment=$2,692.53

interest for next month=$2,692.53*32.99%/12

interest for next month=$74.02

minimum monthly payment=($2,692.53+$74.02)*5.25%

minimum monthly payment=$145.24

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Answer:

Step-by-step explanation:

12/9h - 7/10 = =1/9h - 5/4

13/9h - 7/10 = -5/4

13/9h = 14/20 - 25/20

13/9h = -11/20

h= -99/260

Answer: the pattern grows by one square being added to the figure before it. I know because when I count the squares on figure one to three I count one block being added to each side.

Step-by-step explanation:

Use 1/8*(whatever amount of days until fractions match)

it will take road x 44 days to repair (1/8*44)

road y will take 70 days to repair (1/8*70)

it will take road y 26 days longer to repair

Answer:

7 : 1.

Step-by-step explanation:

1 - 7/8 = 1/8 is syrup.

So, water to syrup

= 7/8 : 1/8

= 7 :1.

The ratio of water to syrup is 7:1

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here, 7/8 of a can of drink is water, the rest is syrup thus the fraction for syrup is 1/8 of the can. Therefore the ratio of water and syrup is

7/8:1/8=7:1

Hence, The ratio of water to syrup is 7:1

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The area of the parallelogram is [tex]\sqrt{132}[/tex].

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.

Given that,

vertices k(1, 1, 3), l(1, 3, 5), m(6, 9, 5), and n(6, 7, 3)

Area of Parallelogram = |KL × KN|

KL = (1, 1, 3) - (1, 3, 5) = (0, 2, 2)

KN = (1, 2, 3) - (3, 7, 3) = (2, 5, 0)

Area of the parallelogram = cross product of two vectors, represented by the adjacent sides.

Area of Parallelogram = |(0, 2, 2) × (2, 5, 0)|

                                    = |i(2 × 0 - 5 × 2) - j(0 × 0 - 2 × 2) + k(0 × 5 - 2 × 2)|

                                    = |i(-10) - j(-4) + k(-4)|

                                    = |-10i + 4j - 4k|

                                    = [tex]\sqrt{(-10)^{2}+(4)^{2}+(-4)^{2} }[/tex]

                                    = [tex]\sqrt{100+16+16}[/tex]

                                    = [tex]\sqrt{132}[/tex]

Hence, The area of the parallelogram is [tex]\sqrt{132}[/tex].

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The below mentioned are the factors of given equations

Factorization:

In mathematics, factorization or factoring is the method of expressing a quantity or another numerical component as a product of many factors, typically small or easier components of the same kind.

In the case of integers, ancient Greek mathematicians were the first to consider factorization. They demonstrated the fundamental theorem of arithmetic, which states that any positive integer can be taken account into a prime number product , which cannot be factored into integers greater than 1. Furthermore, this factorization is unique until the order of the factors is changed.

1)[tex]9a^{2}-18a=9a(a-2)[/tex]

2)[tex]16a^{3}b^{3} +32ab=16ab((ab)^{2} +2)[/tex]

3) inappropriate question

4)[tex]3x^{5} +4x^{4} -5x^{2} =x^{2} (3x^{3} +4x^{2} -5)[/tex]

5)[tex]2x^{3} -x=2(x-1)(x+1)[/tex]

Therefore,The above mentioned are the factors of the given questions.

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