Tavon has a gift card for $130 that loses $3 for each 30-day period it is not used. He has another gift card for $110 that loses $2.50 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal. b. What will the value of each card be when they have equal value? a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-day periods until the values of the gift cards will be equal.
(Type an equation. Use integers or decimals for any numbers in the equation.)​

Answer:

a) [tex]a = 2[/tex] and [tex]b = -4[/tex], b) [tex]c = -10[/tex], c) [tex]f(-2) = -\frac{5}{3}[/tex], d) [tex]y = -\frac{5}{2}[/tex].

Step-by-step explanation:

a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:

1) A root of the polynomial at numerator is -2. (Removable discontinuity)

2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.

We analyze each polynomial by factorization and direct comparison to determine the values of [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex].

Denominator

i) [tex](x+2)\cdot (x-1) = 0[/tex] Given

ii) [tex]x^{2} + x-2 = 0[/tex] Factorization

iii) [tex]2\cdot x^{2}+2\cdot x -4 = 0[/tex] Compatibility with multiplication/Cancellative Property/Result

After a quick comparison, we conclude that [tex]a = 2[/tex] and [tex]b = -4[/tex]

b) The numerator is analyzed by applying the same approached of the previous item:

Numerator

i) [tex]c\cdot x - 5\cdot x^{2} = 0[/tex] Given

ii) [tex]x \cdot (c-5\cdot x) = 0[/tex] Distributive Property

iii) [tex](-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0[/tex] Distributive and Associative Properties/[tex](-a)\cdot b = -a\cdot b[/tex]/Result

As we know, this polynomial has [tex]x = -2[/tex] as one of its roots and therefore, the following identity must be met:

i) [tex]\left(x -\frac{c}{5}\right) = (x+2)[/tex] Given

ii) [tex]\frac{c}{5} = -2[/tex] Compatibility with addition/Modulative property/Existence of additive inverse.

iii) [tex]c = -10[/tex] Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result

The value of [tex]c[/tex] is -10.

c) We can rewrite the rational function as:

[tex]f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}[/tex]

After eliminating the removable discontinuity, the function becomes:

[tex]f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)[/tex]

At [tex]x = -2[/tex], we find that [tex]f(-2)[/tex] is:

[tex]f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right][/tex]

[tex]f(-2) = -\frac{5}{3}[/tex]

d) The value of the horizontal asympote is equal to the limit of the rational function tending toward [tex]\pm \infty[/tex]. That is:

[tex]y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}[/tex] Given

[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right][/tex] Modulative Property

[tex]y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right][/tex] Existence of Multiplicative Inverse/Definition of Division

[tex]y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)[/tex]   [tex]\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}[/tex]

[tex]y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)[/tex]   [tex]\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}[/tex]/[tex]x^{m}\cdot x^{n} = x^{m+n}[/tex]

[tex]y = -\frac{5}{2}[/tex] Limit properties/[tex]\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0[/tex], for [tex]n \geq 1[/tex]

The horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex].

Using asymptote concepts, it is found that:

a) Building a quadratic equation with leading coefficient 2 and roots 1 and -2, it is found that a = 2, b = -4.

b) c = -10, since the discontinuity at x = -2 is removable, the numerator is 0 when x = -2.

c) Simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex].

d) The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]

-------------------------

Item a:

[tex]2(x - 1)(x - (-2)) = 2(x - 1)(x + 2) = 2(x^2 + x - 2) = 2x^2 + 2x - 4[/tex]

[tex]2x^2 + ax + b = 2x^2 - 2x - 4[/tex]

Thus a = 2, b = -4.

-------------------------

Item b:

[tex]-2c - 5(-2)^2 = 0[/tex]

[tex]-2c - 20 = 0[/tex]

[tex]2c = -20[/tex]

[tex]c = -\frac{20}{2}[/tex]

[tex]c = -10[/tex]

-------------------------

Item c:

With the coefficients, the function is:

[tex]f(x) = \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \frac{-5x(x + 2)}{2(x - 1)(x + 2)} = -\frac{5x}{2(x - 1)}[/tex]

At x = -2:

[tex]-\frac{5(-2)}{2(-2 - 1)} = -\frac{-10}{-6} = -(\frac{5}{3}) = -\frac{5}{3}[/tex]

Thus, simplifying the function, it is found that at [tex]x = -2, f(x) = -\frac{5}{3}[/tex]

-------------------------

Item d:

The horizontal asymptote of a function is:

[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]

Thus:

[tex]y = \lim_{x \rightarrow \infty} \frac{-10x - 5x^2}{2x^2 + 2x - 4} = \lim_{x \rightarrow \infty} \frac{-5x^2}{2x^2} = \lim_{x \rightarrow \infty} -\frac{5}{2} = -\frac{5}{2}[/tex]

The equation for the horizontal asymptote to the graph of f is [tex]y = -\frac{5}{2}[/tex]

A similar problem is given at https://brainly.com/question/23535769

Answer:did you check and see if anybody asked this question before??

Step-by-step explanation:

The total distance did Aaron walk today is 4.70 miles.

It is required to find the total distance.

What is distance?

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given :

Aaron walks 2 1/8 miles to his friends.

He walk 5/6 miles to the park.

Again he walks 1 3/4 miles to get back home.

Total distance=

2 1/8 miles+5/6 miles+ 1 3/4 miles

=17/8+5/6+7/4

=4.70 miles

Therefore, the total distance did Aaron walk today is 4.70 miles.

Learn more about distance here:

brainly.com/question/17342454

#SPJ2

Answer:

Se obtendrá 9 trozos de cuerda.

Step-by-step explanation:

Para que sea cada trozo de igual extensión, pero lo más posible, se tiene que encontrar el máximo común divisor de 96 y 120 para determinar la longitud máxima del trozo. Se realiza el siguiente procedimiento para determinar el máximo común divisor:

1) Se determina cada número como producto de números primos:

[tex]96 = 2^{5}\times 3[/tex]

[tex]120 = 2^{3}\times 3 \times 5[/tex]

2) Se determina los números primos comunes de cada número y se multiplican entre sí:

[tex]x = 2^{3}\times 3[/tex]

[tex]x = 8\times 3[/tex]

[tex]x = 24\,m[/tex]

Cada trozo debe ser de 24 metros de longitud.

Ahora se determina el número de trozos al dividir la longitud total por el resultado anterior:

[tex]n = \frac{120\,m+96\,m}{24\,m}[/tex]

[tex]n = 9[/tex]

Se obtendrá 9 trozos de cuerda.

Answer:Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

range is The zero doesn't matter. You still subtract the lowest number from the highest. If zero is the lowest number, then the highest number is the range. If the set consists of negative numbers, and zero is the highest number, then the lowest number (without its negative sign) is the range.

0

Answer:

24

Step-by-step explanation:

We are given segment XZ and point Y. First, draw a number line. Draw X and Z on either side of the number line. We know that Y is between X and Z since there are the distances of XY and YZ. To find XZ, add the distance of XY and YZ, which are respectively 7 and 17. Adding 7 and 17, we get 24 as the answer.

The value of XZ is 24.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

+ Addition operation: Adds values on either side of the operator.

For example 12 + 2 = 14

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment XZ, where the length of line segment XZ refers to the distance between its endpoints, X and Z.

Given that a line segment XZ and point Y that lies on XZ

XY = 7 and YZ = 17

Here XZ = XY + YZ

X_____________Y_______________Z

⇒ XZ = XY + YZ

Substitute the values of  XY = 7 and YZ = 17, we get

⇒ XZ = 7 +  17

Apply the addition operation in the above equation,  

⇒ XZ = 24

Therefore, the value of XZ is 24.

Learn more about the line segment here:

brainly.com/question/25727583

#SPJ2

Answer:

C.$150

Step-by-step explanation:

The sales man told her that he would sell it to he for ⅓ of the marked price.

Given:

Marked Price= $450

⅓

Required:

⅓ of the marked price or $450

Formula:

⅓*$450

Solution:

⅓ of $450

⅓*$450

$450/3

$150

Hope this help ;) ❤❤❤

Answer:

A.180

Step-by-step explanation:

Answer:

83 degress

Step-by-step explanation:

We know that every hour it dropped 8 degress. If it dropped from 4pm to 8pm, that means it dropped 4 times. 3x4=12 so we do 95-12 which equals 83.

Answer:

18

Step-by-step explanation:

2a+3b

2•3+3•4

6+12

18

Answer:

2124+272cd

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]2 . 4x =\\2 \times 4x\\\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8\\\\= 8x[/tex]

Answer:

Step-by-step explanation:

step one :

first and foremost we are going to list the sample space related to a die

the same space is  S= {1,2,3,4,5,6}= 6

step two:

now the even numbers in the sample space are ={2,4,6}= 3

hence we can solve for the probability of obtaining an even number to be

Pr(even number)= 3/6= 1/2.

step three:

since we are to provide the answer in percentage format, we can easily do this by multiplying the answer by 100 to get the percentage

(1/2)*100= 0.5*100= 50%

Answer:

5 quarters and 3 nickels

Step-by-step explanation:

x = nickels

y = quarters

x + y = 8

x(0.05) + y(0.25) = 1.40

3 + 5 = 8

3(0.05) + 5(0.25) = 1.40

0.15 + 1.25 = 1.40

1.25 + 0.15 = 1.40

Answer:

It makes the calculation easy and quick.

Step-by-step explanation:

When you multiply as it is given:

Using the commutative property makes it much easier:

Answer:

see below.

Step-by-step explanation:

its a commutative property of multiplication.

it doesn't matter in order or not... the result will always be the same.

form your example 5×87×2, if you use a calculator it doesn't matter which number you start.

say 2 x 87 x 5 = 870

or 87 x 5 x 2 = 870

or 5 x 2 x 87 = 870

see the results are all the same no matter which way you go.

Answer:

yes

Step-by-step explanation:

[tex](3x-1)(3x+1)=9x^{2}-1[/tex] [tex]=\frac{9x^{2} }{9}-\frac{1}{9}=[/tex] [tex]x^{2} -\frac{1}{9}[/tex]

[tex](x-1/3)(x+1/3)=x^{2} -\frac{1}{9}[/tex]

Answer:

5x+3x+6>14

8x>14-6

8x>8

divide both sides by 8

x>1

Answer:

14

Step-by-step explanation:

Since gaining fourteen pounds means going in a positive direction, we can say the gain of fourteen pounds numerically as 14.

Apples and people don't make much sense as an answer here, so we can rule out B and D. Choice A can be ruled out as it seems redundant to say "money compares money over time". It makes more sense to say "Money compares value (over time)".

Answer:

Step-by-step explanation:

2a + 3 - 4a + 8 = 7

-2a + 11 = 7

-2a = -4

a = 2

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(2a + 3) - (4a - 8) = 7}[/tex]

When there is a ( - ) in front of an expression in parentheses , change the sign of sign of each term in the expression

[tex] \longrightarrow{ \sf{2a + 3 - 4a + 8 = 7}}[/tex]

Collect like terms

[tex] \longrightarrow{ \sf{ - 2a + 3 + 8 = 7}}[/tex]

Add the numbers: 3 and 8

[tex] \longrightarrow{ \sf{ - 2a + 11 = 7}}[/tex]

Move 11 to right hand side and change it's sign

[tex] \longrightarrow{ \sf{ - 2a = 7 - 11}}[/tex]

Subtract 11 from 7

[tex] \longrightarrow{ \sf{ - 2a = - 4}}[/tex]

Divide both sides by -2

[tex] \longrightarrow{ \sf{ \frac{ - 2a}{ - 2} = \frac{ - 4}{ - 2} }}[/tex]

Calculate

[tex] \longrightarrow{ \sf{a = 2}}[/tex]

Hope I helped!

Best regards! :D

Answer:

450 x 15 = 6750 ft 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is given by the formula=4× 90/ n

where n = number of sides

exterior angle= 4 x 90/13

=360/13=[tex]27.7[/tex]°

Answer:

-4.

Step-by-step explanation:

5(m - 1) = -25

m - 1 = -5

m = -4.

Answer:

m = -4

Step-by-step explanation:

Divide both sides by the numeric factor on the left side, then solve.

m = -4

Answer:

I think your suppose to multiply the lengths together then you multiply the width together and the add those two

Step-by-step explanation:

srry if i am wrong lol

Answer:

23

Step-by-step explanation:

(4 x 23) -20 = 72

Answer: 8 students per team and 4 pencils each student

Step-by-step explanation:

Answer:

Both C and D

Step-by-step explanation:

Answer:

z = -6

Step-by-step explanation:

[tex]-4z=24\\\\\frac{-4z=24}{-4}\\\\ \boxed{z=-6}[/tex]

Hope this helps.

Answer: The answer is (-∞, ∞)

Step-by-step explanation:I hope this helps!

Answer: Answer is in the steps

Step-by-step explanation:

If the system of equations have the same slope and same y-intercepts then it means that they have infinitely many solutions.

if the system of equations have the same slope but different y-intercepts it means that they have no solution because they will never intersect but will always form parallel lines.

If the system of equations have different slopes and different y-intercepts or have same y-intercepts and different slopes it means that they have exactly on solution.

Answer:

1/2

Step-by-step explanation:

Step 1:

4/6x + 3/6 + 5/6

Step 2:

4/6x = 2/6

Step 3:

2/6 times 6/4

Answer:

1/2

Hope This Helps :)