Jane has a pre-paid cell phone with A Fee and Fee. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 430 minutes and the cost was $227.50. In July she used 780 minutes and the cost was $385.00.
Answers
Given:
the plan of the pre-paid cell phone
The plan has a monthly fee and a charge for each minute
Let the monthly cost = C
and the number of minutes = x
the general equation will be:
C = ax + b
Where (b) is the monthly fee, and (a) is the charge per minute
We will find the values of (a) and (b) using the following:
1) 430 minutes cost $227.50
2) 780 minutes cost $385.00.
So, we have the following equations:
[tex]\begin{gathered} 430a+b=227.5\rightarrow(1) \\ 780a+b=385\rightarrow(2) \end{gathered}[/tex]Solve the equations, subtract equation (1) from (2) to eliminate (b), and solve for (a):
[tex]\begin{gathered} 780a-430a=385-227.5 \\ 350a=157.5 \\ a=\frac{157.5}{350}=0.45 \end{gathered}[/tex]Substitute with (a) into equation (1) to find the value of (b)
[tex]\begin{gathered} 430\cdot0.45+b=227.5 \\ 193.5+b=227.5 \\ b=227.5-193.5=34 \end{gathered}[/tex]So, the equation of the monthly cost will be:
[tex]C=0.45x+34[/tex]Part (b): When x = 484 minutes, we will find C
so, substitute with (x) into the equation of C
[tex]\begin{gathered} C=0.45\times484+34 \\ C=217.8+34 \\ C=251.8 \end{gathered}[/tex]So, the answer will be:
A) C = 0.45x + 34
B) $251.8
Related Questions
Kennedy goes to a store an buys an item that costs xx dollars. She has a coupon for 35% off, and then a 7% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Kennedy paid at the register.
Answers
We are given that an item has a cost xx.
First, we will calculate the 35% discount on the total price. To do that we will subtract 35% of the initial cost from the initial cost
To calculate the 35% we multiply the price by 35/100, like this:
[tex]xx\times\frac{35}{100}[/tex]Now we subtract this from the initial price, which was "xx". Subtracting we get:
[tex]P_d=xx-xx\times\frac{35}{100}[/tex]This is the cost with the discount. Now, we will add to this the tax of 7%. First, we calculate the 7% of the price with the discount by multiplying it by 7/100, like this:
[tex](xx-xx\times\frac{35}{100})\times\frac{7}{100}[/tex]Now, we add this to the price with the discount, like this:
[tex]T=(xx-xx\times\frac{35}{100})+(xx-xx\times\frac{35}{100})\times\frac{7}{100}[/tex]Now, we can simplify. We start by using the distributive property on the second parenthesis:
[tex]T=xx-xx\times\frac{35}{100}+xx\times\frac{7}{100}-xx\times\frac{35}{100}\times\frac{7}{100}[/tex]Now we solve the product of 35/100 by 7/100, we get:
[tex]T=T=xx-xx\times\frac{35}{100}+xx\times\frac{7}{100}-xx\times\frac{49}{2000}[/tex]Now we take xx as a co
Write the inequality shown by the Shaded region in the graph with the boundary line 4x + 3y = -3
Answers
ANSWER
[tex]y\text{ }\leq\text{ -}\frac{4}{3}x\text{ - 1}[/tex]EXPLANATION
We want to write the inequality represented by the shaded region of the graph.
The boundary line of the graph is given as:
4x + 3y = -3
Let us put this in slope-intercept form:
=> 3y = -4x - 3
=> y = -(4/3)x - 1
Now that we have the equation in that form, we have to consider a few things:
=> The line used to represent the boundary line is a solid line. This means that the inequality we need has either a less than/equal to or a greater than/equal to sign.
=> The shaded region is on the left hand side of the boundary line. This means that the inequality represented is less than or equal to.
Therefore, the inequality represented by the shaded region is:
[tex]y\text{ }\leq\text{ -}\frac{4}{3}x\text{ - 1}[/tex]You have a rectangular backyard that is 90 feet wide. It has an area of 10,800 square feet. You are putting a fence along one length of the yard.Use the formula for the area of a rectangle A = l * w, where I is the length, and w is the width. Find the length of your backyard.
Answers
ANSWER:
120 feet
STEP-BY-STEP EXPLANATION:
We hve the following:
A = 10800 ft²
w = 90 ft
The area of a rectangle is the product between the length and the width, we do not know the length but we do know the area, therefore, we calculate the length as follows:
[tex]\begin{gathered} A=w\cdot l \\ \\ \text{ We replacing} \\ \\ 10800=90\cdot l \\ \\ l=\frac{10800}{90} \\ \\ l=120\text{ ft} \end{gathered}[/tex]The length of your backyard is equal to 120 feet
is f(-2) negative?which values of x is >0which values of x if f(x) =0
Answers
We know that a function is greater than 0 when the graph of the function is above the x-axis.
Meaning that if the function is below the x-axis the function is taking negative values.
For that reason we can say that:
A) f(-2) is positive because the graph at that point is above the x-axis
B) the function is greater than 0 o values greater than -3 until 5, in interval notation it will be (-3,5]
c) We can say that the function is equal to 0 when x=-3 because at that point the graph is exactly crossing the x-axis
A triangle has two sides of length 3 and 3. What value could the length of thethird side be? Check all that apply.A. 6B. 12C. 5D. 8E4F. 2
Answers
To find out the length of the third segments of the triangle, we can use this formula.
[tex]\begin{gathered} a^2=b^2+c^2 \\ a^2=3^2+3^2 \\ a^2=9+9 \\ a^2=18 \\ a=4.25 \end{gathered}[/tex]The, third length is very close to the 4. thus, the option (E) is correct.
Hello can you please tell me if this is right please Simplify expressions by distributing
Answers
distribute the fraction into all the terms inside the parentheses
[tex]8\cdot\frac{1}{2}-4g\cdot\frac{1}{2}[/tex]solve the product
[tex]\frac{8}{2}-\frac{4g}{2}[/tex]simplify the fractions
[tex]4-2g[/tex]I got x > 12 for my answer, but when I checked it, it didn't work. Please help me solve and check!
Answers
Given the graph given I need help with questions A - D
Answers
Using the graph and the table we can infer that the value of the premium for the insurance amount of $50,000 is $28.29 .
From the given table we can see that the function f(x) represents the insurance amount and the premium for the male population.
therefore we can simply substitute the values from the table.
a)f(50000) = $ 28.29
f(25,000) = $ 14.15
b)From the given table we can see that the function g(x) represents the insurance amount for the female population.
g(75000) = $ 19.25
g(25000) = $ 6.42
c) at f(x) = 14.15 the value of x is $25000
d) From the graph let us compare each values for f(x) and g(x).
f(20000)>f(20000)
f(25000)>g(25000)
f(50000)>g(50000)
f(75000)>g(75000)
f(100000)>g(100000)
One party will promise another party reimbursement in the event with a specific loss, damage, or injury in exchange for a fee in order to protect oneself from financial loss. It is a risk management technique used primarily to guard against the risk of a potential loss.
Hence we can infer that for all values of x , f(x)>g(x).
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I will show the answer options later because I can’t add two pictures
Answers
We will have the following:
* If Kristin does not decrease the price of her cakes, her projected weekly revenue from cake sales will be $2500.
*If Kristin decreases the price of her cakes, her projected weekly revalue will be $2520.
*Kristin will obtain the same revenue if she sells the cakes for $24 or $21.
Twelve students in mrs.taylors class want to start band. Seven students each made a drum.The rest of the students made 2 shakers each. How many shakers were made? Use the bar model. Need help have to show work on this whole page.
Answers
Solution
What do I need to find?
Number of shakers
what information do I need to use?
12 students
7 made a drum each
The remain students made 2 shakers each
how I will use the information?
We need to find the number of students who made shakers and then multiply by 2
Solve the problem
12-7 = 5 students
5* 2= 10 shakers
Then the final answer would be:
10 shakers in total
Savings ($)
200
160
120
80
40
O
5 10 15 20 25
Time (weeks)
Find the constant of proportionality and write an equation for the relationship
The constant of proportionality is
The equation for the relationship is
Answers
For the given graph related to savings on y-axis and time on x-axis, the constant of proportionality is equal to 4, and the equation representing the relationship between the savings and the time is given by y = 4x.
As given in the question,
From the graph,
y-axis represents the savings in dollars
x-axis represents the time in seconds
Let us consider savings represents by y and time represents by x.
Form the graph we can see that,
When x = 10 ⇒ y = 40
when x = 15 ⇒ y = 60
Graph represents the straight line so it is linear function.
y = 40
⇒ y= 4(10)
⇒ y= 4x
⇒y ∝ x
⇒Constant of proportionality 'k' = 4
Now, for the equation consider two coordinates on the graph,
(x₁ , y₁) = (10, 40)
(x₂ , y₂) = (15, 60)
( y-y₁)/ (x-x₁) = (y₂ -y₁) / (x₂ - x₁)
⇒( y- 40)/(x-10) = (60 -40)/ (15-10)
⇒ y-40 = 4(x-10)
⇒y = 4x
Therefore, for the given graph related to savings on y-axis and time on x-axis, the constant of proportionality is equal to 4, and the equation representing the relationship between the savings and the time is given by y = 4x.
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Write the sum of the first three terms in the binomial expansion, expressing the result in simplified form.(x – 4y)^7
Answers
ANSWER:
[tex](x-4y)^7=x^7-28x^6y+336x^5y^2\ldots[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\mleft(x-4y\mright)^7[/tex]In this case we can apply the binomial theorem, which is the following:
[tex](a+b)^n=\sum ^n_{i\mathop=0}(\frac{n!}{i!(n-i)!}a^{n-i}\cdot b^i[/tex]we replace and calculate for the first three terms:
[tex]\begin{gathered} 1st=\sum ^7_{i\mathop{=}0}(\frac{7!}{0!(7-0)!}x^{7-0}\cdot(-4y)^0=1\cdot x^7\cdot1=x^7 \\ 2nd=\sum ^7_{i\mathop{=}1}(\frac{7!}{1!(7-1)!}x^{7-1}\cdot(-4y)^1=7\cdot x^6\cdot-4y^1=-28x^6y \\ 3rd=\sum ^7_{i\mathop{=}2}(\frac{7!}{2!(7-2)!}x^{7-2}\cdot(-4y)^2=21\cdot x^5\cdot16y^2=336x^5y^2 \end{gathered}[/tex]solve for x:
7x=6+5 (3x+3)-x
Answers
Answer: x= -3
Step-by-step explanation:
7x = 6+ 15x + 15 - x
7x = 21 + 14x
-7x = 21
x= -3
у20f15(4,12)10g(4,6)(-2,0)(0,25) 2,4,(3,5)(2,0)0,47Use the graph off and g.Find (gof)(2).ما
Answers
The first step is to find the fuctions, f(x) and g(x)
Since function f(x) is represented by the curve, it's a quadratic function. The curve cuts the x axis at x = 2 and x = - 2. Thus, the factors are (x + 2) and (x - 2). The quadratic function would be
(x + 2)(x - 2)
= x^2 - 2x + 2x - 4
f(x) = x^2 - 4
Since the function g(x) is represented by a straight line, it is a linear function. We would represent the function in the slope intercept form which is expressed as
y = mx + c
where
m = slope
c = y intercept
To find slope, the formula is
m = (y2 - y1)/(x2 - x1)
From the given points,
when x1 = - 2, y1 = 0
when x2 = 2, y2 = 4
m = (4 - 0)/(2 - - 2) = 4/(2 + 2) = 4/4
m = 1
the y intercept is the value of y when x = 0. Thus, c = 2
The function is
g(x) = x + 2
To find (g o f)(x), we would substitute function f into function g. Thus,
gof(x) = x^2 - 4 + 2
gof(x) = x^2 - 2
To find gof(2), we would substitute x = 2 into gof(x). It becomes
gof(2) = 2^2 - 2 = 4 - 2
gof(2) = 2
Is the ordered pair (2, 7) a solution of the function f(x) = x + 5? *
Answers
The ordered pair (2, 7) is NOT a solution of the function
f(x) = x + 5
Explanation:If (2, 7) is a solution of the function f(x) = x + 5, then
f(2) = 7
f(2) = 2 + 2 = 4
Since this is not 7, we conclude that the ordered pair is NOT a solution of the function
how can I find which statements can be deducted from the picture
Answers
The following statements can be deduced by knowing some previous knowledge from Parallelism.
2) Examining and commenting
∠1 ≅ ∠2 FALSE This is a linear pair. So they are supplementary angles, not congruent ones.
∠5≅ ∠7 TRUE Vertical Angle Theorem states that they are congruent ones.
m∠7≅ m∠4 True Linear pair a+ b are supplementary as well.
∠1 ≅ ∠7 True Corresponding Angles are always congruent.
≅
Find the surface area and volume of the sphere. Round your answers to the nearest whole number.C = 4 in.The surface area is aboutsquare inchesThe volume is aboutcubic inches
Answers
The circumference of a sphere with radius r is given by the following formula:
[tex]C=2\pi r[/tex]Isolate r from the equation and substitute the value of C to find the raius of the sphere:
[tex]\begin{gathered} \Rightarrow r=\frac{C}{2\pi} \\ \Rightarrow r=\frac{4\pi\text{ in}}{2\pi} \\ \Rightarrow r=2\text{ in} \end{gathered}[/tex]The surface area of a sphere with radius r is given by:
[tex]S=4\pi r^2[/tex]The volume of a sphere with radius r is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Substitute r=2 in on each formula to find the volume and surface area of the sphere:
[tex]\begin{gathered} S=4\pi(2in)^2 \\ =4\pi\cdot4in^2 \\ =16\pi in^2 \\ =50.26\ldots in^2 \\ \approx50in^2 \end{gathered}[/tex][tex]undefined[/tex]May I please get help with this. I don’t know the definitions of each, therefore I cannot state weather each of them are true or false
Answers
Quadrilateral: Plane figure that has four sides. All squares are quadrilaterals but not every quadrilateral is a square.
1- False
A square is considered as a rhombus because all the sides are equal in length, the diagonals are perpendicular to each other and bisecs opposite angles. Then, a square is a rhombus but as not all the rhombus has right angles not every rhombus is a square
2- False
A square is a parallelogram (quadrilateral with two pairs of parallel sides) with four sides of equal length. Then, every square is a parallelogram
3- True
A square is considered as a rhombus with right angles. Then, every rhombus with foru right angles is a square.
4-True
Factorise the following quadratic:
e² - 17e + 70
Answers
Answer:
Step-by-step explanation:
I think you're supposed to use the quadratic formula Samanth
Know it?
-b ± [tex]\sqrt{b^{2}-4ac }[/tex] / (2a)
so for starters, let me mention, that if 4ac happens to be greater than [tex]b^{2}[/tex] contrary to what all math teacher say, about not being able to taking the square of a negative number, you can, but you just end up with a complex number in the form of A + Bi , where 'i' represents [tex]\sqrt{-1}[/tex] anyway,
for the given equation
A = 1
B = -17
C = 70
{ -(-17) ± [tex]\sqrt{(-17)^{2}-4*1*70 }[/tex] } / (2*1)
{ 17 ± [tex]\sqrt{289-280}[/tex] } / 2
wow, now i'm glad I mentioned about the 4ac being greater :P
it was close, huh
{ 17 ± [tex]\sqrt{9}[/tex] } / 2
{ 17 ± 3 } /2
let's take each case now, the plus and then the minus
{ 17+3 } /2
20 /2
10
now the minus
{17 - 3 } / 2
14 /2
7
now that i've done all that work, I think we could have just done this by inspection :P
(e-7)(e-10)
anyway, hope that helps, ask if you have any questions :)
The Pentagon building in Washington, D.C., is named because it is in the shape ofa regular pentagon. What is the measure of each interior angle?
Answers
The formula to find the sum of the interior angles of a polygon is given below,
[tex]\text{Sum of angles of polygon = (n-2)180}^0[/tex]Number, n, of sides of a regular pentagon is 5 i.e n = 5,
To find the sum of angles in a regular pentagon, substitute for n into the formula above,
[tex]\text{Sum of angles of a pentagon=(5-2)180}^0=3\times180^0=540^0[/tex]To find the measure of each angle of the pentagon, the formula is given below
[tex]\begin{gathered} for\text{ each interior angle=}\frac{Sum\text{ of angles}}{n} \\ \text{Where n = 5} \\ \text{For each interior angle=}\frac{540^0}{5}=108^0 \end{gathered}[/tex]Hence, each interior angle is 108°
A large vat has a faucet to allow liquid to enter the vat and a drain to allow liquid to leave the vat.
Each minute, the faucet allows 40 1/5 gallons of liquid to enter the vat, and the drain allows 44 3/4 gallons to leave the vat.
What is the change in the amount liquid in the vat after 12 minute?
Answers
After some mathematical operations, the rate of change is -273/5.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, the rate of change will be:
12(40⅕) - 12(44¾)Evaluate as follows:
12(40⅕) - 12(44¾)12(201/5) - 12(179/4)12 × 201/5 - 12 × 179/42,412/5 - 5372,412 - 5(537)/52412 - 2,685/5-273/5Therefore, after some mathematical operations, the rate of change is -273/5.
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A teacher asks his students to use the Addition Property of Equalityto write an equation equivalent to x - 9 = 11 Antonio writes* - 9 + 9 + 11 + 9. Stefan writes x - 9+2 -11 + 2 Have bothstudents followed the teacher's instructions? Explain your reasoning
Answers
Both students followed the teacher's instruction. The addition property of equality states that if 2 numbers x and y are equal x=y, then, x+a=y+a.
In this case both students applied the property correctly. One of them added 9 to both sides of the equation and the other one added 2 to both sides.
The answer is yes, both followed the teacher's instruction.
Write an explicit formula for An, the n' term of the sequence 14, 10, 6,..
Answers
An explicit formula for the arithmetic sequence is aₙ = 14 - 4(n - 1).
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 14
Second term, a₂ = 10
Third term, a₃ = 6
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = 10 - 14
Common difference, d = -4
Substituting the parameters into the mathematical expression, we have;
aₙ = 14 + (n - 1)(-4)
aₙ = 14 - 4(n - 1).
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Are there any extraneous solutions? If yes, write the solution in the box, if no write "none"). x=
Answers
Given:
[tex]\sqrt[]{x+1}+2=4[/tex]x=3 is the only solution for the given equation.
There is no other solutions for the given equation.
So none is the final answer.
George is making an elaborate meal. he can only cook one thing at a time in his microwave oven. his turkey takes 65 minutes; the pie takes 15 minutes; rolls take 60 seconds; and his coffee takes 45 seconds to heat. how much time does he need to cook the meal? when does he need to start in order to complete the cooking at 4:00pm?
Answers
operator nameEXPLANATION
STEP 1: Find the time taken to cook the meal.
The amount of time does George needs to cook the meal is the sum of all the time it would take to cook each of the individual meal
Therefore,
[tex]\begin{gathered} \text{Total time=65mins+15mins+60secs+45secs} \\ =80\min utes\text{ 105 secs} \\ This\text{ can be rewritten as:} \\ =60\text{ mins+ 20mins +60secs +45secs} \\ \sin ce\text{ 60 mins=1hr and 60 secs = 1min} \\ \text{This gives;} \\ =1\text{hour 21mins 45secs} \end{gathered}[/tex]STEP 2: Find the time he needs to start to cook the meal.
The right time to start cooking the meal is simply subtracting 1hour 21 mins 45 secs from 4.00 pm
1) Remove 1hour from 4.00 pm =3.00pm
2) Remove 21 mins from 3.00pm=2.39 pm
3)Remove 21 secs from 2.39pm= 2.38pm 15secs
Therefore the right time for George to start cooking is 15secs after 2.38pm
Can you please help me figure out how to do this?
Answers
Given
[tex]f(x)=2x^2-4x-3[/tex]
Procedure
[tex]\begin{gathered} f(-1)=2\cdot(-1)^2-4\cdot(-1)-3 \\ f(-1)=2+4-3 \\ f(-1)=3 \end{gathered}[/tex]
The answer would be f(-1) = 3
please help! so confused and every tutor keeps dropping my question
Answers
First of all, we see that this curve is indeed a function of x.
A function, by definition, assigns exactly one value (generally called y) for each x in the domain.
For a continuous domain like this, if we pass a vertical line through the graph, and this line touches exactly one point at a time, then this graph represents a function of x. And this happens for the given graph.
For the second part, we need to determine the domain and range of this function.
The domain consists of all the values of x for which the function is defined. When it has a filled ball at an ending point of the graph, this means the domain is closed in that point, that is, the x-coordinate of this ending point belongs in the domain.
In this case, for interval notation, we use square brackets to represent the domain - "[" or "[".
When we have a point with an empty ball, on the other hand, the x-coordinate of that point doesn't belong in the domain, and we use parentheses - "(" or ")".
Now, concerning the graph in this question, we see that both endings have filled balls. So, both -3 and 2 (the x-coordinates of these points) belong in the domain.
Therefore, in interval notation, the domain of this function is:
[-3, 2]
Finally, the range is formed by all values of y that are reached by the graph, from the smallest to the larger (global minimum and maximum of the function).
Therefore, the range of this function is:
[-3, 3]
Notice that we also use square brackets to represent the range, since both points with y-coordinates -3 and 3 belong in the graph.
Consider the line . 7x-8y=-1Find the equation of the line that is parallel to this line and passes through the point . (-3,-6)Find the equation of the line that is perpendicular to this line and passes through the point . (-3.-6)
Answers
we have the line
7x-8y=-1
Find out the slope of the given line
isolate the variable y
8y=7x+1
y=(7/8)x+1/8
the slope is m=7/8
Part a
Find the equation of the line that is parallel to this line and passes through the point . (-3,-6)
Remember that
If two lines are parallel, then their slopes are equal
so
The slope of the parallel line is m=7/8 too
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=7/8
point (-3,-6)
substitute and solve for b
-6=(7/8)(-3)+b
b=-6+(21/8)
b=-27/8
therefore
The equation is
y=(7/8)x-27/8Part b
Find the equation of the line that is perpendicular to this line and passes through the point . (-3.-6)
Remember that
If two lines are perpendicular, then their slopes are negative reciprocal
so
The slope of the perpendicular line is m=-8/7
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=-8/7
point (-3,-6)
substitute and solve for b
-6=-(8/7)(-3)+b
b=-6-(24/7)
b=-66/7
therefore
the equation is
y=-(8/7)x-66/7What is the domain of the following function?A) {-6, -2, 1, 5, 7, 8}B) {-2, 7}C) {-6, 1, 5, 8}D) all Real numbers
Answers
In this problem, we have that
The domain or input values are the data set {-6, 1, 5, 8}
The range or output values are the data set [-2,7]
therefore
The answer is the option CI don't understand. I get an answer that doesn't exist. The question is to multiply in a+bi form. (5/2 + 2i)(1/4 - 6i)
Answers
Given the below
[tex](\frac{5}{2}+2i)(\frac{1}{4}-6i)[/tex]Multiplication of the vectors in the a+bi form gives
Applying the complex arithmetic rule below
[tex](a+bi)(c+di)=(ac-bd)(ad+bc)i[/tex]The expansion of the vectors gives
[tex](\frac{5}{2}+2i)(\frac{1}{4}-6i)=\frac{5}{2}(\frac{1}{4}-6i)+2i(\frac{1}{4}-6i)[/tex]Opening the brackets
[tex]\begin{gathered} (\frac{5}{2}+2i)(\frac{1}{4}-6i)=\frac{5}{2}(\frac{1}{4}-6i)+2i(\frac{1}{4}-6i) \\ =\frac{5}{8}-\frac{30}{2}i+\frac{2}{4}i-12i^2 \\ \text{Where i}^2=-1 \\ =\frac{5}{8}-\frac{30}{2}i+\frac{2}{4}i-12(-1) \\ ==\frac{5}{8}+12-\frac{30}{2}i+\frac{2}{4}i \end{gathered}[/tex]Simplifying the above expression
[tex]\begin{gathered} =\frac{5+96}{8}+\frac{-60i+2i}{4}=\frac{101}{8}+\frac{-58}{4}i \\ =\frac{101}{8}+\frac{-29}{2}i=\frac{101}{8}-\frac{29i}{2} \\ (\frac{5}{2}+2i)(\frac{1}{4}-6i)=\frac{101}{8}-\frac{29i}{2} \end{gathered}[/tex]Hence, the answer is
[tex]=\frac{101}{8}-\frac{29i}{2}[/tex]