The student used the gift card to spend the same amount of money at the coffee shop every day until the remaining value of the card was $0. This function represents f(n), the value, in dollars, of the gift card after n days.f(n) = −2.5n + 75A. Based on the function, what was the original value, in dollars, of the giftcard? Show or explain how you got your answer.B. Based on the function, how much money, in dollars, did the student spend each day at the coffee shop? Show or explain how you got your answer.C. What was the remaining value, in dollars, of the gift card after 20 days? Show or explain how you got your answer.D. How many days in total did it take until the remaining value of the gift

the slope of the line means in this situation "a. The cost is $4 per T-shirt".

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Seth owns a printing shop that makes customized T-shirts.

Since The cost to make T-shirts is proportional to the number of T-shirts he makes.

Thus,

The y-intercept of the line will be 0 cause the line is passing through the origin point.

The general formula of the equation of a line:

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

b = 0

m = (8 - 4)(2-1)

m = 4

And m represents The cost is $4 per T-shirt.

therefore,  the slope of the line means in this situation "a. The cost is $4 per T-shirt".

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The properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation

What are the properties of equality?

The "division property of equality" states that if you divide both sides of an equation by the same non-zero number, the two sides will remain equal.

The "simplification" step is used to simplify an expression by combining like terms, reducing fractions, or performing other operations to simplify the expression.

The "multiplication property of equality" states that if you multiply both sides of an equation by the same non-zero number, the two sides will remain equal.

The "addition property of equality" states that if you add the same number to both sides of an equation, the two sides will remain equal.

The "subtraction property of equality" states that if you subtract the same number from both sides of an equation, the two sides will remain equal.

These properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation.

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1) The number of laps that Reuben completes is; 2 laps

2) The number of laps that Maria completes is; 3 laps

3. It will take 18 minutes for Reuben and Maria to meet again at the starting line.

The parameters to solve the problem are;

Time for each lap by Reuben = 9 minutes

Time for each lap by Maria = 6 minutes

Let us find the L.C.M(Lowest common multiple) of 6 and 9;

Factors of 6 = 2 * 3

Factor of 9 = 3 * 3

Thus, L.C.M = 2 * 3 * 3 = 18 Minutes

This represents the time it will take for them to meet again at the starting line.

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a) The measure of <ABC is 131 degree.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.

Given:

a) As <ACD= 90

and Triangle BCD is an equilateral triangle then each of its angle measure 60 degree.

So, <ACD= 90

<ACB + <BCD = 90

<ACB = 90 - 60

<ACB = 30

and, <BAC = 19

Using Angle sum property in Triangle ACB

19 + <ABC + 30 = 180

<ABC = 180 - 49

<ABC = 131 degree.

b) Bow, In Triangle HEF using Angle sum property

<E + <F + <EHF = 180

<EHF = 180 - (69+ 40)

<EHF = 71 degree.

Then, <GHE + <EHF + <FHI

= 72 + 71 + 37

= 180, which forms on straight line.

Thus, GHI is a straight line.

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Answer:

14q/25

Step-by-step explanation:

14q/25

The function rule for this situation is f(n) = 1/36n

From the question, we have the following parameters that can be used in our computation:

The length of a string in yards is a function ƒ(n) of the length n in inches.

The conversion of yards to inches is

Yard = 1/36 * Inches

When represeted as a function, we have

f(n) = 1/36n

Hence, the function is f(n) = 1/36n

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For the first function, the domain and the range are given as follows:

For the second function, the domain and the range are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function, hence it is given by the set that contains all the values of x in the graph of the function.

The range of a function is the set that contains all the output values that can be assumed by the function, hence it is given by the set that contains all the values of y in the graph of the function.

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The linear function to model how much further he'll have to go over time is h(t) = 330 - 55t

Total distance between home and college= 330 miles

Distance remaining to cover= 275 miles

Distance covered= Total distance between home and college - Distance remaining to cover

= 330 miles - 275 miles

= 55 miles

Time taken to cover 55 miles= 1 hour

h(t) = 330 - 55t

Where,

h = distance remaining to cover

t = time

Ultimately, h(t) = 330 - 55t is the linear function which represents how much further he'll have to go over time.

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[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=8 \end{cases}\implies S=180(8-2)\implies S=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{just one angle is}}{\cfrac{1080}{8}\implies 135^o}\hspace{5em}\stackrel{\textit{for six angles}}{(6)(135)\implies \boxed{810^o}}[/tex]

Answer:

bbbbbbbbbbbbbb

see attched image for sol

Probability that the shopper selected at random was satisfied with the service they received is 845 / 1522.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total number of customers = 1522

Out of these,

Number of customers made a purchase = 624

Number of customers not made a purchase = 898

Number of customers who purchased satisfied with the service = 130

Number of customers who does not purchase satisfied with the service = 715

Total number of customers who are satisfied with the service = 130 + 715 = 845

Probability that the randomly selected shopper satisfied with the service = 845 / 1522

Hence the probability is 845 / 1522.

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the number of sides of the polygon​ 12 sides

An interior angle is a shape's internal angle. The closed shape with sides and vertices is a polygon. All of the inner angles of a regular polygon are equal to one another. For instance, a square has interior angles that are all exactly right angles, or 90 degrees.

In a regular polygon, all internal angles are equal. Interior angle of a polygon = sum of interior angles number of sides is the formula for determining the amount of an interior angle.

The n-sided polygon's inner angle total equals (n-2).

180°, thus as follows:

140°+160°+ (n-2)150 = (n-2)180°

or, 300° = (n-2)(180° - 150°).

or, 300° = (n-2) 30°

or, 10= n - 2.

alternately, n = 10 + 2 = 12 sides.

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The values of D, Dx, Dy , x and  y are

D=28

Dx= -56

Dy= -56

x=-2

y=-2

What are matrices ?

The word "matrix" can be used to refer to a rectangular array or table with numbers or other components arranged in rows and columns. Any number of columns and rows are allowed. Matrix operations include addition, multiplication, transposition, scalar multiplication, and many others.

Write the matrices by taking coefficients of x and y in different columns as:

[tex]\begin{bmatrix} -8 & 4 \\ 3 & -5 \end{bmatrix} =\begin{bmatrix} 8 \\ 4&\end{bmatrix}[/tex]

Determinant of LHS = D

[tex]D=\begin{vmatrix} -8 & 4 \\ 3 & -5 \end{vmatrix}[/tex]  

D=28

Substitute the  x-column with the RHS to find Dx

Substitute the  y-column with the RHS to find Dy

[tex]Dx=\begin{vmatrix} 8 & 4 \\ 4 & -5 \end{vmatrix}[/tex]  

Dx= -56

[tex]Dy=\begin{vmatrix} -8 & 8 \\ 3 & 4 \end{vmatrix}[/tex]

Dy= -56

x=Dx / D = -56/28 = -2

y=Dy / D = -56/28 = -2

The values of D, Dx, Dy , x and  y  are

D=28

Dx= -56

Dy= -56

x=-2

y=-2

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Answer:x=1

Step-by-step explanation:

For this, you will need to use substitution.

we know that a²+b²=c²

plug it in

[tex]x^2+3^2=y^2[/tex]

simplify to find

[tex]x^2+9=y^2[/tex]

[tex]y=\sqrt{x^2+9}[/tex]

repeat with the other side

[tex](x+8)^2+3^2=z^2[/tex]

[tex]x^2+16x+73=z^2[/tex]

[tex]z=\sqrt{x^2+16x+73}[/tex]

plug these in for the larger triangle

[tex]y^2+z^2=(2x+8)^2[/tex]

[tex]x^2+9+x^2+16x+73=4x^2+32x+64[/tex]

[tex]2x^2+16x+82=4x^2+32x+64[/tex]

set equal to 0 and simplify

[tex]-2x^2-16x+18=0[/tex]

pull out a -2

[tex]x^2+8x-9=0[/tex]

factor

[tex](x-1)(x+9)=0[/tex]

x=-9,1

x cannot be negative since it a measurement so x=1

The horizontal distance is 150 meters

From the question, we have the following parameters that can be used in our computation:

Gradient = 2/15

Vertical distance = 60 meters

The gradient is calculaed as

Gradient = Vertical distance/Horizontal distance

So, we have

Horizontal distance = Vertical distance/Gradient

This gives

Horizontal distance = (60)/(2/5)

Evaluate

Horizontal distance = 150

Hence, the distance is 150 meters

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On solving the provided question, we can say that by solving the interest  the amount after his 21st birthday =  $ 10,806

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.

P = $6000

Rate=  4 %

Time, t= 12 years  

Formula of Compound Interest

[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{12}\\A = 9606.19332[/tex]

On his 19 th birthday

[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{13}\\A = 9990. 44106[/tex]

After 21st year S. I is

S. I =  10390.058700 × 4/100

S. I = 415.602348

A= 415.602348 + 10390.058700

A = $ 10,805.661.

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The value of function for f(5) is 3125.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given that, f(1) = 5 and f(n) = 5f(n − 1)

Now, for finding the the 5th term we have to find the remaining four term before the 5th term.

So, n=2

f(2) = 5f(1)

f(2)=  5(5)

f(2)=  25

Now, n=3

f(3) = 5f(2)

f(3)=  5(25)

f(3)=  125

Now, n=4

f(4) = 5f(3)

f(4)=  5(125)

f(4)=  625

Now, n=5

f(5) = 5f(4)

f(5)=  5(625)

f(5)=  3125

Hence, the value of function for f(5) is 3125.

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Answer:

17

degree

jjaokaohshdh

Step-by-step explanation:

Joppa

also

aijsiwso

akoakwbd

The discounted price of the set of dishes would be = $63.89

The original cost of the dishes = $57.68

The percentage increase of the cost of the dishes = 125%

That is,

= 125/100 × 57.68

= 7210/100 = $72.10+57.68 = $129.78

After one month, the store marked it down by 50%, therefore the discounted price;

= 50/100 × 129.78/1

= 6489/100

= $65.89

= 129.78-65.89 = $63.89

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The discounted price is $64.89

From the question, we have the following parameters that can be used in our computation:

Cost =  $57.68

Mark up = 125%

Mark down = 50%

The discounted price is then calculated as

price = cost * (1 + mark up) * (1 - mark down)

So, we have

price = 57.68 * (1 + 125%) * (1 - 50%)

Evaluate

price = 64.89

Hence, the price is 64.89

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The given function  f(x) = x² + 2x when x <0 and f(x) = x³ - 2x when x > 0  is continuous at x=0

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  = x² + 2x       {x ≤ 0}

        = x³ - 2x      { x > 0}  

To check whether it is continuous at x = 0

First taking LHL,

F(0)  = 0² + 2x0

        =  0

Now, taking RHL

F(0)  =  0³ - 2x0

At x = 0

F(0)  = 0² + 2x0

        =  0

RHL = LHL = F(0)

Hence, the given function is continuous at x =0

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The solution of the system of equations is (0, 1).

Here we want to solve the system of equations:

12x - 3y  = -3

6x + y = 1

To use the elimination method, we can take the difference between the first equation and two times the second one, then we will get:

12x - 3y - 2*(6x + y) = -3 - 2*1

12x - 3y - 12x - 2y = -5

-5y = -5

y = -5/-5 = 1

Now we know the value of y, we can replace it in one of the equations ot find the value of x.

6x + y = 1

6x + 1 = 1

6x =  1 - 1 = 0

x = 0

The solution is (0, 1)

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Answer:

At an x-intercept

Step-by-step explanation:

y = sin x

y = sin 0

y = 0

(0,0) is an x-intercept but not it's maximum or minimum.

The volume of the sculpture is 92.316 feet³.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

Cone-shaped sculpture:

Height = 5 feet

Base circumference = 26.376

This means,

2πr = 26.376

r = 26.376/(2 x 3.14)

r = 4.2 feet

Now,

The volume of the sculpture.

= 1/3 x 3.14 x 4.2 x 4.2 x 5

= 92.316 feet³.

Thus,

92.316 feet³ is the volume of the sculpture.

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The piecewise function for the Tax due on an income of x dollars are:

From the case, we know that there are 3 scenariois for filling tax due based on an individual's income, where:

To construct the piecewise function for the Tax due, we need to translate the given conditions into mathematical formulation.

We assume that:

T(x) = tax due

x = $ amount of taxable income

For taxable income between $0 until $15,000, the tax is 3.5% of taxable income; then:

T(x) = 3.5% x

T(x) = 0.035x

For taxable income between $15,000 until $30,000, the tax is $525 plus 6.25% of excess over $15,000. Then:

T(x) = 525 + 6.25% (x - 15,000)

T(x) = 525 + 0.0625 (x- 15,000)

Please note that the additional 6.25% only will be counted based on the remaining of the taxable income deducted by $15,000.

For taxable income over than $30,000, the tax is $1462.50 plus 6.8% of excess over $30,000. Then:

T(x) = 1462.50 + 6.8% (x - 30,000)

T(x) = 1462.50 + 0.068 (x - 30,000)

Please note that the additional 6.8% only will be counted based on the remaining of the taxable income deducted by $30,000.

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Answer: Cody gave the cashier $2.87.

Step-by-step explanation:

To determine the amount of money Cody gave to the cashier, you can subtract the amount of change he received from the cost of the carrots.

$4.41 (change) - $1.54 (cost of carrots) = $2.87

So, Cody gave the cashier $2.87.

The congruence postulate used to prove the congruence of triangles KLM and KLN is given as follows:

E. ASA.

The Angle-Side-Angle (ASA) congruence theorem states that if any of the two angles on a triangle are the same, along with the side between them, then the two triangles are congruent.

For this problem, we have that the two angles between segment LK are equal for each triangle, as LK is a bisection of these two angles, along with segment LK, hence the ASA congruence postulate was used and the correct option is given by option E.

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The solution is Option C.

The value of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 3 ( x - 3 ) ( x - 7 )   be equation (1)

On simplifying the equation , we get

y = 3 ( x - 3 ) ( x - 7 )

And , the point ( 8 , 15 ) lies on the graph

Substituting the values in the equation , we get

when x = 8

y = 3 ( 8 - 3 ) ( 8 - 7 )

y = 3 ( 5 )

y = 15

Therefore , the point P ( 8 , 15 ) lies on the graph of the function

And , the graph has two zeros at (3,0) and (7,0)

Hence , the graph of the function is f ( x ) = 3 ( x - 3 ) ( x - 7 )

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Answer:

c

Step-by-step explanation:

c

The reason 0.667 is equal to 2/3 is because when you divide:

2 ÷ 3 = 0.6666666667.

You can shorten 0.6666666667 to 0.667.

That is how 2/3 is equal to 0.667.

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