Suppose that the functions f and g are defined as follows F(x)=5/x+7g(x)=2/xFind f/g then give its domain using an interval or union of intervals Simplify your answer as much as possible (f/g)(x)=Domain of f/g:
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Given the functions:
[tex]\begin{gathered} f(x)=\frac{5}{x+7} \\ \text{AND} \\ g(x)=\frac{2}{x} \end{gathered}[/tex]Let's solve for the following:
• (a) f/g
To solve for f/g let's divide f(x) by g(x).
We have:
[tex]\frac{f}{g}=\frac{f(x)}{g(x)}=(\frac{f}{g})(x)=\frac{\frac{5}{x+7}}{\frac{2}{x}}[/tex]Solving further, we have:
[tex]\begin{gathered} (\frac{f}{g})(x)=\frac{5}{x+7}\ast\frac{x}{2} \\ \\ (\frac{f}{g})(x)=\frac{5x}{2(x+7)} \end{gathered}[/tex]Therefore, the function f/g is:
[tex](\frac{f}{g})(x)=\frac{5x}{2(x+7)}[/tex]• (b) Domain of f/g.
The domain is the set of all possible x-values where the function is defined.
To find the domain, set the denominator to zero and solve for x.
We have:
[tex]2(x+7)=0[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2(x+7)}{2}=\frac{0}{2} \\ \\ (x+7)=0 \end{gathered}[/tex]Subtract 7 from both sides:
[tex]\begin{gathered} x+7-7=0-7 \\ \\ x=-7 \end{gathered}[/tex]Therefore, the domian is:
[tex]\mleft(-\infty,-7\mright)\cup(-7,\infty)[/tex]ANSWER:
[tex](a)\text{ ( }\frac{f}{g})(x)=\frac{5x}{2(x+7)}[/tex][tex](b)\text{ Domain: }(-\infty,-7)\cup(-7,\infty)[/tex]Related Questions
how would I solve the system of equations using elimination?8x - 5y = 114x - 3y =5
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Using elimination. In elimination process the two system of equations are multiplied by a apropiate factor , in order to eliminate one of the variables
then
multiplicate first equation by 4
and multiplicate second equation by 8
once obtained both results, then substract them
So then
4• (8x-5y) = 4•11= 44
8• (4x-3y) = 8•5= 40
32x -20y= 44
32x - 24y= 40
4y= 4 then y=1
now replace y=1 in any of both equations
8x -5= 11. Then x= (11+5)/8= 2
x=2
b.InOut133171066co38Rule:
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Suppose that the rule is of the form
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept
The slope can be found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can take any two consecutive x and y values from the given table.
[tex]\frac{17-3}{3-1}=\frac{14}{2}=7[/tex]Similarly,
[tex]\frac{66-17}{10-3}=\frac{49}{7}=7[/tex]As you can see, you will end up with the same slope.
Now let us find the intercept b.
Take any x, y coordinates from the table
[tex](x,y)=(1,3)[/tex]Now substitute them in the slope-intercept equation.
[tex]\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}[/tex]So the rule is
[tex]y=7x-4[/tex]Verification:
Let us verify whether we got the correct rule or not
Substitute the input x coordinates into the rule and check the outputs y coordinates.
[tex]\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}[/tex]As you can see, we have got the same results therefore, the rule is correct.
What is the residual of a performance with a revenue of $700 and 70 seats occupied?
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Jackson types 120 words in 2 minutes. Enter the number of words Jackson types in 4 minutes at this ratewords
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if in 2 minutes Jackson Typed 120 words, in 4 minutes will type twice the amount. SO
[tex]w=120\cdot2=240[/tex]he will type 240 words in 4 minutes
Multiply the following [tex] \sqrt{ - 15} \times \sqrt{ - 15} [/tex]
Answers
Answer: -15
Given:
[tex]\sqrt[]{-15}\times\sqrt[]{-15}[/tex]Since the radical rule states that:
[tex]\begin{gathered} \sqrt[]{a}\sqrt[]{a}=a \\ \Rightarrow\sqrt[]{-15}\times\sqrt[]{-15}=-15 \end{gathered}[/tex]Therefore, the answer is -15.
Part 2: Write limits given outputs.Use the graph of the function to write limit equations given limit values.Use the graph to write a limit equation for f(x) that satisfies each given condition. (2 points for each)a. b. c. d. e. Are there other values than what you chose for x where the limit of the function approaches 4? Is the graph continuous at these points? Explain your reasoning. (4 points)
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a) From the graph, we see that the function takes the value y = 4 when x = 4, so we have:
[tex]\lim _{x\rightarrow4}f(x)=4.[/tex]b) We see that the curve tends to -∞ when x approaches zero from the left, so we have:
[tex]\lim _{x\rightarrow0^-}f(x)=-\infty.[/tex]c) We see that curve increases without limit when x tends to infinity, so we have:
[tex]\lim _{x\rightarrow\infty}f(x)=\infty.[/tex]d) From the graph, we see that the function tends to y = 0 when x approaches zero from the right, so we have:
[tex]\lim _{x\rightarrow0^+}f(x)=0.[/tex]e) Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
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a, b, c, d
[tex]\begin{gathered} \lim _{x\rightarrow4}f(x)=4 \\ \lim _{x\rightarrow0^-}f(x)=-\infty \\ \lim _{x\rightarrow\infty}f(x)=\infty \\ \lim _{x\rightarrow0^+}f(x)=0 \end{gathered}[/tex]e. Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
i’m taking an algebra pretest & i’m very confused. i haven’t learned this material. please help!!
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ANSWER
7 (Option D)
EXPLANATION
Given:
Number of times the traffic light Green = 6
Number of times the traffic light Yellow = 2
Number of times the traffic light Red = ?
Desired Outcome:
Number of times the traffic light Red
Total number of times for the traffic lights
[tex]\begin{gathered} \text{ Total times = Times for traffic light Red + Times for traffic light Green + Times for traffic light Yellow} \\ 15=Red+6+2 \\ 15=Red+8 \\ substract\text{ 8 from both sides} \\ 15-8=Red+8-8 \\ \text{ Times for traffic light Red = 7} \end{gathered}[/tex]Hence, the number of times the traffic light Red was 7.
Find the area of each rectangle using the given information.(A=W x H)Question 9:6 and a height of 36 inches.
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The rule of the area of a rectangle is
[tex]A=W\times H[/tex]W is the width
H is the height
Since the ratio between width and height is 9: 6 and the height is 36 inches, then we will use the ratio method
[tex]\begin{gathered} W\rightarrow H \\ 9\rightarrow6 \\ W\rightarrow36 \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} W\times6=9\times36 \\ 6W=324 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6W}{6}=\frac{324}{6} \\ W=54 \end{gathered}[/tex]Then the width of the rectangle is 54 inches
Substitute W by 54 and H by 36 in the rule of the area to find it
[tex]\begin{gathered} A=54\times36 \\ A=1944inches^2 \end{gathered}[/tex]The area of the rectangle is 1944 square inches
hey ms or mr can you please help me out?
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B'C' = 3BC
Explanations:Note:
When a figure is dilated by a scale factor, a similar figure of the same shape but of different size is formed.
When a triangle ABC is dilated by a scale factor of 3, the vertices of the image of ΔA'B'C' formed will have a distance from the center of dilation that is three times that of the vertices of ΔABC
Therfore:
A'B' = 3AB
B'C' = 3BC
A'C' = 3AC
The correct choice is option B
That is, B'C' = 3BC
write an equation of a line passing through the point (-6,-3) and perpendicular to JK with J (-2, -7) and K (6,5)
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EXPLANATION
Given the point: (-6,-3) and the vector JK with J=(-2,-7) K=(6,5)
First we need to the slope of the vector applying the slope formula:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing the ordered pairs J=(-2,-7) and K=(6,5) give us the slope:
[tex]\text{Slope}=\frac{(5-(-7))}{(6-(-2))}=\frac{12}{8}=\frac{3}{2}[/tex]Now, we have the slope and we can use this to find the line that contains the point (-6, -3) applying the generic form:
y= -2x/3 + b where -2/3 is the negative and reciprocal slope perpendicular to the vector JK.
Finally, replacing the point (-6,-3) give us the y-intercept, b,
-3 = -2(-6)/3 + b
Multiplying terms:
-3 = 12/3 + b ---> -3 = 4 + b
Subtracting 4 to both sides:
-3 - 4 = b
Switching sides:
b= -7
The linear equation is y = (-2/3)x - 7 OPTION B
Please just put the answer for this question On D
Answers
Answer
The liters of air takes in during 150 seconds is 25 liters
Step-by-step explanation:
A man takes in 5 liters of air in 30 seconds
Firstly, we need to find the rate
Given:
Volume = 5 liters
time = 30 seconds
Rate =?
Volume = rate x time
5 = rate * 30
rate = 5/30 liters / second
Find the volume of air takes in during 150 seconds at the same rate
Volume = rate * time
Volume = 5/30 * 150
Volume = 5 * 150 / 30
Volume = 25 liters
Hence, the liters of air takes in during 150 seconds is 25 liters
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
Answers
The amount of money that Hudson will need to save each week is $106.25.
How to calculate the value?From the information, they determine that the trip will cost $3,200. Mr. and Mrs. Hudson have already set aside $1,500 for the trip.
Let the amount saved each week be represented as w.
Based on the information given, this will be illustrated as:
1500 + 16w = 3200
Collect like terms
16w = 3200 - 1500
16w = 1700
Divide
w = 1700 / 16
w = 106.25
The amount is $106.25.
Learn more about money on:
brainly.com/question/24373500
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write a recursive rule for the sequence -10,-3,4,11
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Let the given sequence is -10,-3,4,11
The objective is to write recursive rule for the sequence.
In the given sequence each number has an equal difference between them
[tex]\begin{gathered} -3-(-10)=7 \\ 4-(-3)=7 \\ 11-4=7 \end{gathered}[/tex]So, consider the terms as,
[tex]\begin{gathered} a_1=-10 \\ a_2=-3 \\ a_2=a_1+7 \\ a_3=a_2+7 \\ a_4=a_3+7 \end{gathered}[/tex]Hence the recursive series is
[tex]a_n=a_{n-1}+d[/tex]Marcia sells lemonade for $2 per cup and candy for $1.50 per candy bar. She earns $425 selling lemonade and candy bars. If marcia sold 90 bars of candy, which equation could be used to figure out how many cups of lemonade she sold?
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Answer: 145 cups of lemonade
Step-by-step explanation:
hope it helped :)
Question 7b: Let g(x) be a polynomial function. Name all horizontal andvertical intercepts of the graphsg(x) = (x - 1)2 (x + 2)Horizontal intercepts: 1, -2; vertical intercepts: 2Horizontal intercepts: 2, vertical intercepts: 1,-2Horizontal intercepts: -1, 2, vertical intercepts: 4Horizontal intercepts: 4, vertical intercepts: -1,2
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The given function is expressed as
g(x) = (x - 1)^2(x + 1)
It can be written as
y = (x - 1)^2(x + 1)
The horizontal intercept is also known as the x intercept. The x intercept is the value of x when y = 0
If we substitute y = 0 into the function, it becomes
0 = (x - 1)^2(x + 2)
This means that
(x - 1)^2 = 0 and x + 2 = 0
For (x - 1)^2 = 0, if we take the square root of both sides, it becomes
x - 1 = 0
x = 1
For x + 2 = 0,
x = - 2
Thus, the horizontal intercepts are 1 and - 2
The vertical intercept is also known as the y intercept. The y intercept is the value of y when x = 0
If we substitute x = 0 into the function, it becomes
y = (0 - 1)^2(0 + 2)
y = (- 1)^2(2)
y = 1 * 2 = 2
Thus, the vertical intercept is 2
Thus, the correct option is
Horizontal intercepts: 1, -2; vertical intercepts: 2
i need help with this
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graphing the points
answer: (- 8, 6)
what is the difference in a probability that the student will spin a factor of 83 times in a row in the probability that a student will spin a number greater than 63 times in a row
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The number 8 has factors 1, 2, 4 and 8.
The only numbers in the spin greater than 6 are 7 and 8,
The probability that the student will spin a factor of 8 three times in a row is given by: (4/8)*(4/8)*(4/8) = (1/2)*(1/2)*(1/2) = 1/8
The probability that the student will spin a number greater than 6 three times in a row is given by (2/8)*(2/8)*(2/8) = (1/4)*(1/4)*(1/4) = 1/64
Then, the difference between these two probabilities is given by 1/8 - 1/64 = 7/64
1v=9. Which equation represents the equation of theparabola with focus (-3,3) and directrix y = 7?A),= (x+3)2 – 5B) y = 5(? – 3)2 +5C) y=-( + 3)2 +5D) y=-2 (2-3)2 +5
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SOLUTION
From the focus (-3, 3) and the directrix y = 7 given, note that the vertex is usually between the focus and the directrix.
So, the vertex will have the same x-coordinate as the focus, which is -3, and the y-coordinate of the vertex becomes
[tex]\begin{gathered} \frac{3+7}{2} \\ that\text{ is 3 from the y-coordinate of the focus and 7 from the directrix} \\ y=7 \\ \frac{3+7}{2}=\frac{10}{2}=5 \end{gathered}[/tex]Hence coordinate of the vertex is (-3, 5)
Now, equation of a parabola is given as
[tex]\begin{gathered} (x-h)^2=4p(y-k) \\ where\text{ \lparen h, k\rparen is the coordinate of the vertex and p is the focal length} \\ y=k-p,\text{ so we have } \\ 7=5-p \\ p=5-7=-2 \end{gathered}[/tex]So putting in the values of h, k and p into the equation, we have
[tex]\begin{gathered} (x-h)^{2}=4p(y-k) \\ (x-(-3)^2=4(-2)(y-5) \\ (x+3)^2=-8(y-5) \\ -\frac{1}{8}(x+3)^2=y-5\text{ that is dividing through by -8} \\ making\text{ y the subject, we have } \\ y=-\frac{1}{8}(x+3)^2+5 \end{gathered}[/tex]Hence the answer is
[tex]y=-\frac{1}{8}(x+3)^{2}+5[/tex]this graphic organizer is being used to classify triangles based on their angle measures or sideways which list shows all of the ways that strangle could be classified
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D
1) Examining the sides of that triangle, we can state that this is an equilateral triangle (at least 2 sides have the same measure). But Since isosceles is a triangle that has 2 sides with the same measure.
Then we can state that about their sides this is an equilateral and isosceles triangle.
2) Examining their angles. An equilateral triangle has 3 angles with 60º measure. A 60º angle is lesser than 90º, then we can classify this triangle as an acute triangle
3) Hence, the answer is D
Find the probability of X successes, using Table B in Appendix A of the textbook or some other method.n = 10, p = 0.3, X = 7
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SOLUTION
The probability is a binomial probability
The probability is given as
[tex]\text{nCxp}^xq^{n-x}[/tex]Where p= proability of succes=0.3
q=probability of failure=1-p=1-0.3=0.7
n=10, x=7
Then, substitute the parameters into the formula
[tex]10C_7(0.3)^7(0.7)^3[/tex][tex]\begin{gathered} 10C_7=120 \\ 120\times2.187\times10^{-4}\times0.343 \end{gathered}[/tex]Then we have
[tex]\begin{gathered} 9.0017\times10^{-3} \\ 0.0090017 \end{gathered}[/tex]The probability of x-success is 0.009
Need help with number five. The question is solve each system
Answers
5)
The given equations are
- 4x - 2y + 3z = 7
- 3x + 5y - 3z = 13
- 5x + y - z = 11
From equation 3, we have
y = 11 + 5x + z
We would substitute y = 11 + 5x + z into equations 1 and 2. For equation 1, we have
- 4x - 2(11 + 5x + z) + 3z = 7
- 4x - 22 - 10x - 2z + 3z = 7
- 4x - 10x - 2z + 3z = 7 + 22
- 14x + z = 29
For equation 2, we have
- 3x + 5(11 + 5x + z) - 3z = 13
- 3x + 55 + 25x + 5z - 3z = 13
- 3x + 25x + 5z - 3z = 13 - 55
22x + 2z = - 42
Dividing both sides of the equation by 2, we have
11x + z = - 21
z = - 21 - 11x
Substituting z = - 21 - 11x into - 14x + z = 29, we have
- 14x - 21 - 11x = 29
- 14x - 11x = 29 + 21
- 25x = 50
x = 50/- 25
x = - 2
z = - 21 - 11(- 2) = - 21 + 22
z = 1
Substituting x = - 2 and z = 1 into y = 11 + 5x + z, we have
y = 11 + 5(-2) + 1
y = 11 - 10 + 1
y = 2
The solutions are
x = - 2, y = 2, z = 1
hi help I've been trying to solve this for an hour and this is due in 10 minutes I just really need the correct answer please help
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We have the following:
We can confirm the intercepts with the y-axis, since it is when x = 0, in the case of the first equation it is 2 and in the second equation it is 1
Therefore, we limit ourselves to the answers C and D, now we can calculate the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point are (0, 2) and (-6, -1)
[tex]m=\frac{-1-2}{-6-0}=\frac{-3}{-6}=\frac{1}{2}[/tex]The slope is 1/2, therefore, the equations are
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]The answer is the option C
A survey of 85 persons was conducted at TCC, and it was found that 54 persons carried a cell phone, 19 persons carried a tablet computer, and 16 carried both a cell phone and a tablet.How many people carried a cell phone or a tablet?How many people carried neither a cell phone nor a tablet?How many people carried a cell phone only?How many people carried a tablet but not a cell phone?
Answers
Answer:
The universal set is given below as
[tex]\xi=85[/tex]The number of people with cell phone is
[tex]n(C)=54[/tex]The number of persons with tablet is
[tex]n(T)=19[/tex]The number of people who carry both cellphone and tablet
[tex]n(C\cap T)=16[/tex]Step 1:
To figure our the number of students that carry cellphone or tablets will be
[tex]\begin{gathered} =38+16+3 \\ =57\text{ }people \end{gathered}[/tex]Hence,
The number of people that carried cell phone or tablet
[tex]\Rightarrow57people[/tex]Step 2:
How many people carried neither a cell phone nor a tablet?
[tex]\begin{gathered} =85-(38+16+3) \\ =85-57 \\ =28 \end{gathered}[/tex]Hence,
The number of people that carried neither cell phone nor a tablet is
[tex]\Rightarrow28people[/tex]Step 3:
How many people carried a cell phone only?
Hence,
The number of people who carried cell-phone only is
[tex]\Rightarrow38people[/tex]Step 4:
How many people carried a tablet but not a cell phone?
Hence,
The number of people that carried a tablet but not a cell phone is
[tex]\Rightarrow3people[/tex]What transformations were applied to the toolkit function to create the new function?
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The parent functions is f(x) = 1/x
We have 1/(x+2) -1
The 1/(x+2) is f(x+2) which is a horizontal translation left 2 units
Then we have -1 which is f(x+2) -1 which is a vertical translation down 1 unit
The total transformation is a horizontal translation left 2 units and a vertical translation down 1 unit
Answer: left 2 units down 1 unit
which function will have the greatest value of x equals 80
Answers
In order to solve this, we can replace 80 for x into each one of the three given functions, then we identify what value of y is the greatest, like this:
For the first function:
y = 4x
y = 4×80
y = 320
For the second function:
y = x² - 15x + 88
y = 80² - 15×80 + 88
y= 6400 - 1200 + 88
y = 5288
For the third function:
[tex]\begin{gathered} y=1.1135^{80} \\ y=5435.23 \end{gathered}[/tex]As you can see, at x = 80 the function that has the greatest value is the third one.
Chris tries to copy
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The Chris's error is that he does not consider he can not draw the upper oblique line crosses trough the end the of the arc.
To coorect that, Chris must to draw the upper line crosses trough the center of the arc. In this way he is going to obtain a exact copy of angle ∠T.
By taking into account the previous specifications you obtain the following draw of the angle:
As you can notice, it is necessary that the upper line crosses trough the center of the arc.
State weather the triangles are similar. If so write a similarity statement and that postulate or theorem you used. The diagram is not drawn to scale.
Answers
Given:
To prove the similarity.
Two triangles similarity condition:
If two triangles are similar then the corresponding sides are proportional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex][tex]\begin{gathered} \frac{OK}{ON}=\frac{OJ}{OM}=\frac{KJ}{NM} \\ \frac{3}{3+1}=\frac{30}{30+10} \\ \frac{3}{4}=\frac{30}{40} \\ \frac{3}{4}=\frac{3}{4} \end{gathered}[/tex]From the given values the corresponding sides are proves as propotional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex]A sales person is given a choice of two salary plans. Plan 1 is a weekly salary of 700 plus 4% commission of sales. Plan 2 is a straight commission of 12%Of sales. How much in sales must he make in a week for both plans to result in the same salary?
Answers
Let 's' represent the amount of sales.
Plan 1:
[tex]\text{ \$700 + (4\% of s)}[/tex][tex]\begin{gathered} \text{ \$700+(}\frac{\text{4}}{100}\times s) \\ \text{ \$700+(0.04}\times s)=\text{ \$700}+0.04s \end{gathered}[/tex]Plan 2:
[tex]12\text{ \% of s}[/tex][tex]\begin{gathered} \frac{12}{100}\times s \\ 0.12\times s=0.12s \end{gathered}[/tex]Equating the two plans together and solving for the amount of sales,
[tex]\begin{gathered} \text{Plan 2=Plan 1} \\ 0.12s=\text{ \$700+0.04s} \\ \end{gathered}[/tex]Collecting like terms,
[tex]\begin{gathered} 0.12s-0.04s=\text{ \$700} \\ 0.08s=\text{\$700} \end{gathered}[/tex]Divide both sides by 0.08,
[tex]\begin{gathered} \frac{0.08s}{0.08}=\frac{\text{ \$700}}{0.08} \\ s=\text{ \$8750} \end{gathered}[/tex]Hence, the amount of sales is $8,750.
For almost all mortgage lenders, a home buyer must put down a certain percentage ofthe selling price towards the sale and financing of a home. Different banks and differentkinds of loans have set standards. Based on the given information, solve the problems.A buyer decides to put a contract on a house he/she would like to purchase. For eachscenario given, find the amount of down payment, the loan amount, the realestate commission, and tax assessment.#1 Selling price is $250,000.00 10% down payment would be $______ the real estate commissionthe seller would pay (at 6% commission) would be $______ and the amount for the mortgage(selling price - down payment) would be $______ House assesses for $245,000.00 and the taxrate is $1.15 per $100.00 of assessed value so taxes on the house would be $_____ for theyear#2 Selling price is $195,000.00 10% down payment would be $______ the real estate commissionwould be (at 6%) $______ and the mortgage amount would be for $_______ House assesses for$189,000.00 and the tax rate is $1.09 per $100.00 so the real estate taxes for the yearwould be $______
Answers
Answer:
(1)
• 10% down payment would be $25,000.
• The real estate commission would be $15,000.
• The amount for the mortgage would be $225,000.
• Taxes on the house would be $2817.50 for the year.
(2)
• 10% down payment would be $19,500.
• The real estate commission would be $11,700
• The amount for the mortgage would be $175,000.
• Taxes on the house would be $2060.10 for the year.
Explanation:
Part 1
The selling price is $250,000.00.
[tex]\begin{gathered} \text{ Down Payment}=10\%\text{ of }250,000 \\ =0.1\times250,000 \\ =25,000 \end{gathered}[/tex]• 10% down payment would be $25,000.
[tex]\begin{gathered} \text{ Real Estates Commission}=6\%\text{ of }250,000 \\ =0.06\times250,000 \\ =15,000 \end{gathered}[/tex]• The real estate commission the seller would pay (at 6% commission) would be $15,000.
[tex]\begin{gathered} \text{ Mortgage Amount}=\text{ Selling Price}-\text{ Down Payment} \\ =250,000-25,000 \\ =225,000 \end{gathered}[/tex]• The amount for the mortgage would be $225,000.
[tex]Tax=\frac{1.15}{100}\times245,000=2817.50[/tex]• Taxes on the house would be $2817.50 for the year.
Part 2
The selling price is $195,000.00.
[tex]\begin{gathered} \text{ Down Payment}=10\%\text{ of }195,000 \\ =0.1\times195,000 \\ =19,500 \end{gathered}[/tex]• 10% down payment would be $19,500.
[tex]\begin{gathered} \text{ Real Estates Commission}=6\%\text{ of }195,000 \\ =0.06\times195,000 \\ =11,700 \end{gathered}[/tex]• The real estate commission the seller would pay (at 6% commission) would be $11,700.
[tex]\begin{gathered} \text{ Mortgage Amount}=\text{ Selling Price}-\text{ Down Payment} \\ =195,000-19,500 \\ =175,500 \end{gathered}[/tex]• The amount for the mortgage would be $175,000.
[tex]Tax=\frac{1.09}{100}\times189,000=2060.10[/tex]• Taxes on the house would be $2060.10 for the year.
- 3/4 m - 1/2 = 2 + 1/4 m2345