Using linear functions, it is found that:
a) The expression to convert from Fahrenheit to Celsius is: y = 5x/9 - 160/9.
b) The inverse expression is: y = 9x/5 + 32.
What is a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
The coefficients of the function are described as follows:
m is the slope of the function, representing the rate of change of the output y in relation of the input x of the function.b is the y-intercept of the function, representing the numeric value of the function when the input x is of 0.For the conversion of Fahrenheit to Celsius, we have two points, as follows:
(32,0), (68, 20).
When the input increases by 36, the output increases by 20, hence the slope is calculated as follows:
m = 20/36 = 5/9
Hence:
y = 5/9x + b.
When x = 32, y = 0, hence the intercept b is calculated as follows:
0 = 5/9(32) + b
b = -5 x 32/9
b = -160/9
Hence the equation is:
y = 5/9x - 160/9.
To find the inverse expression, we exchange x and y and then isolate y, as follows:
x = 5/9y - 160/9.
5/9y = x + 160/9
5y = 9x + 160
y = 9x/5 + 32.
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What are the coordinates of P', the image of P(-4, 0) under the translation (x-3, y + 6)?
Answer:
I really don't understand much about math sometimes I need help
Let the graph of g be a vertical stretch by a factor of 2 followed by a translation 3 units down of the graph of f(x) = x^2 Write a rule for g.
The equation for the function after the transformation is f'(x) = 2x^2 - 3
How to write the image for the function?The initial equation is given as
f(x) = x²
The above represents the parent function
The sequence of transformations is given as
Vertically stretched by a factor of 2Shifted a distance of 3 units downThe rules of the above sequence of transformations are
Vertically stretched by a factor of 2: (x, 2y)Shifted a distance of 3 units down: (x, y - 3)When the rules are applied, we have
Stretch: f(x) = 2x^2Shifted: f'(x) = 2x^2 - 3Hence, the equation in its final position is f'(x) = 2x^2 - 3
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Write an equation of a line that passes through the point (7, 3) and is parallel to the line y = negative 2 over 3 x + 3.
We are asked to determine the equation of a line that is parallel to:
[tex]y=-\frac{2}{3}x+3[/tex]Two lines are parallel if their slopes are in the following relationship:
[tex]m_2=-\frac{1}{m_1}[/tex]Therefore, if m1 is the slope of the given line and m2 is the slope of the parallel line we may determine the value of the slope of the parallel line by replacing it in the relationship. Let's remember that when a line is written in the form:
[tex]y=mx+b[/tex]Where "m" is the slope. Therefore, m1 is -2/3. Replacing in the relationship we get:
[tex]m_2=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}[/tex]Now, we go back to the general form of a line equation and replace the value of the new slope:
[tex]y=\frac{3}{2}x+b[/tex]The value "b" is the y-intercept and can be found using the point through which the line passes:
[tex]3=\frac{3}{2}(7)+b[/tex]Now we solve the operations:
[tex]3=\frac{21}{2}+b[/tex]Subtracting 21/2 from both sides:
[tex]3-\frac{21}{2}=b[/tex]Solving the operations:
[tex]-\frac{15}{2}=b[/tex]Now we replace in the line equation:
[tex]y=\frac{3}{2}x-\frac{15}{2}[/tex]And thus we get the equation of the parallel line.
hey mr or ms could you help me out with this problem?
Point = (8,-4)
When coordinate points (x,y) are rotated by 90° the image became (y,-x)
So, for this case:
Image: (-4,-8)
Suppose the price of your dream house is $239,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30 year fixed rate mortgage at 10%. a.) Find the required down payment, b.) Find the amount of the mortgage. c.) How much must be paid for the three points at closing? d.) Find the monthly payment (excluding escrowed taxes and insurance) e.) Find the total cost of interest over 30 years.
a) The required down payment is $47,800.
b) The mortgage loan is $191,200.
c) The amount for the three points at closing is $5,736, which is 3% of the mortgage.
d) The monthly payment (excluding escrowed taxes and insurance) is $-1,677.92.
e) The total interest cost for the mortgage over its 30-year period is $412,850.06.
What is the down payment?The down payment is an upfront payment required to reduce the mortgage loan and assure the financier that the mortgagee is financially ready to engage in the mortgage transaction.
The price of a dream house = $239,000
Down payment = 20% = $47,800 ($239,000 x 20%)
Mortgage loan = $191,200 ($239,000 - $47,800)
Three points at closing = 3% of $191,200
= $5,736
Periodic Payment:N (# of periods) 360 months (30 years x 12)
I/Y (Interest per year) = 10%
PV (Present Value) = $191,200
FV (Future Value) = $0
Results:
PMT = $-1,677.92
Sum of all periodic payments = $-604,050.06
Total Interest = $412,850.06
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can you please answer my homework, its about sets.
The value of the set (A∪C)'∩B is {9 , 12} .
A subfield of mathematical logic called set theory examines sets, which are essentially collections of objects.
Set theory is a discipline of mathematics that largely addresses problems that are pertinent to mathematics as a whole, despite the fact that any kind of object can be constructed into a set.Set theory is founded on a simple binary relationship between an object o and a set A.It is written as o A if o is a part (or member) of A. Members of a set are enumerated with commas to denote separation when describing them, or a property of those parts is enclosed in braces.Sets can be associated by the membership relation since they are objects.The given sets are:
U ={1,2,3,4,5,6,7,8,9,10,11,12,13}
A = {3,7,11,13}
B = {3,6,9,12,13}
C = {2,3,5,6,7,8}
Now B' = {1,2,4,5,7,8,10,11}
b) B'∩C = {2,5,7,8,}
c) A∪C = {2,3,5,6,7,8,11,13}
(A∪C)' = {1,4,9,10,12}
(A∪C)'∩B = {9 , 12}
Hence the value of the set (A∪C)'∩B is {9 , 12} .
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Factor: x^6-5x^4-5+x
The value of the given expression x^6 -5x^4 - 5 + x simplified as; x^4(x^2 - 5) - (5 + x)
How to factor the expression?The statement is given as ;
Factor: [tex]x^6 -5x^4 - 5 + x[/tex]
From the given expression, we have
[tex]x^6 -5x^4 - 5 + x[/tex]
Group the expression in two part;
So, we have;
[tex]x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)[/tex]
Now Factorize each group of the expression;
[tex]x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)[/tex]
The given expression cannot be further simplified.
Hence, the value of [tex]x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)[/tex]
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To win a trivia game, Nevan must score 90 points. Each correct answer is worth 134 points, and each incorrect answer is worth −14 points. If Nevan gets 58 questions correct and 22 questions incorrect how many points does he score?
Answer:7464
Step-by-step explanation:
90 is the score to get
let c represent correct and w represent wrong
if they get 134 points for it being correct, we can look at it like 134c
if they get -14 points for it being incorrect, we can look at it like -14w
now to put this in the right sense we fill in those letters with how many they got right and wrong : 134(58) -14(22)
This would get 7772 -308
after subtracting these two you'd get: 7464
James wants to have earned $7,592 amount of interest in 16 years. Currently he finds that hisannual interest rate is 9.04%. Calculate how much money James needs to invest as his principal inorder to achieve this goal.Round answers to the nearest hundredth (two decimal places) of a year.
We know that
• The earnings are $7,592.
,• The time is 16 years.
,• The annual interest rate is 9.04%.
This problem is about simple interest, its formula is
[tex]A=P(1+rt)[/tex]Where A = 7,592, r = 9.04, t = 16, and P is the principal.
Let's replace each value.
[tex]7,592=P(1+0.0904(16))[/tex]Notice that 9.04% is equivalent to 0.0904.
Now, we solve it for P.
[tex]\begin{gathered} 7,592=P(1+1.4464) \\ 7,592=P(2.4464) \\ P=\frac{7,592}{2.4464} \\ P\approx3,103.34 \end{gathered}[/tex]Therefore, James needs to invest $3,103.34 as his principal in order to achieve the goal.Andrew has $9,000 in a savings account that earns 5% interest per year. How much will he have including interest in 1 year?
Andrew will have $9,450 in his savings account that earns 5% interest per year.
According to the question,
We have the following information:
Principal amount in Andrew's savings account = $9,000
Interest rate = 5% per year
Time = 1 year
We know that we use the following formula to find the simple interest on any amount:
Simple interest = (principal*rate*time)/100
Simple interest = (9000*1*5)/100
Simple interest = $450
Now, the total amount in his savings account will be the sum of the amount earned from the interest and the principal amount submitted by him.
Total amount = interest+principal
Total amount = 450+9000
Total amount = $9,450
Hence, he will have $9,450 in his savings account.
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The sum of two numbers is 6. Theirdifference is 12. Find the numbers.
Given:
Sum of two numbers-6
Difference of two numbers-12
Required:
To calculate the number
Explanation:
Consider first number-9
Consider second number--3
Sum =9+(-3)=9-3=6
Difference=9-(-3)=12
Required answer:
Option B
write the equation in standard form. identify A,B, and C
we have the following:
[tex]\begin{gathered} y=5x-8 \\ \end{gathered}[/tex]standard form
[tex]y=Ax^2+Bx+C[/tex]Therefore:
A = 0
B = 5
C = -8
PLEASE HELP!!!
Can someone help me out with this math problem.(CALCULUS 2)
picture of problem attached below.
The centre of mass of 40g, (1,3); 30g, (2,-1); 70g, (0,0) and 50g (0,-2) is located at (10/19,-1/19).
The formula to find the coordinates (X,Y) of centre of mass of a discrete particles system is,
X = (m₁x₁+m₂x₂+m₃x₃+m₄x₄)/(m₁+m₂+m₃+m₄)
Y = (m₁y₁+m₂y₂+m₃y₃+m₄y₄)/(m₁+m₂+m₃+m₄)
As we know,
m = 40
m = 30
m = 70
m = 50
Putting all the values in the formula,
for X coordinate,
X = [(40×1)+(30×2)+(70×0)+(50×0)]/(40+30+70+50)
X =(40+60+0+0)/(190)
X = 100/190
X = 10/19
For Y coordinate,
Y = [(40×3)+(30×-1)+(70×0)+(50×-2)]/(40+30+70+50)
Y= (120-30+0-100)/(190)
Y = -10/190
Y = -1/19
So, the centre of mass of the discrete particle system is at (10/19,-1/19)
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GEOMETRY ITS DUE AT 2:15 PLEASE .
1) Write an equation perpendicular to 2x + 3y = 18 that passes through the point (1, 5).
2) Write an equation parallel to y = 2x + 6 that passes through the point (0, 7).
The required equation for the line is y = x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).
The required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The equation of the line which is given as
2x + 3y = 18
3y = -2x + 18
y = -2x/3 + 6
Here the slope of the line, m = -1/3
Let the required line would be as
⇒ y₀ - y₁ = m₀ (x₀ - x₁ )
The required line passes through the point (1, 5)
Here x₁ = 1 and y₁ = 5 and m₀ = 1/3 (Since required line perpendicular)
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 5 = 1 (x - 1)
⇒ y = x - 1 + 5
⇒ y = x + 4
Therefore, the required equation for the line is y = x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).
The equation of the line which is given as
y = 2x + 6
Here the slope of the line, m = 2
The given coordinates of the line;
points on the line (0, 7)
Let the required line would be as
⇒ y - y₁ = m (x - x₁ )
Here x₁ = 0 and y₁ = 7 and m = 2
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 7 = 2 (x - 0)
⇒ y - 7 = 2x
⇒ y = 2x + 7
Therefore, the required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).
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Find the volume and surface area of a right cone with a radius of 4 inches and a height of 7 inches
Volume of a cone =
[tex]v=\frac{1}{3}\pi r^2h[/tex]From the question;
r= 4 h=7
π is a constant and it is equal to 22/7
substitute the values into the formula;
[tex]V=\frac{1}{3}\times\frac{22}{7}\times4^2\times7[/tex][tex]V=\text{ }\frac{2464}{21}[/tex][tex]V=117.33inch^3[/tex]Kelly downloaded 195 pictures from her cell phone to her computer. These pictures took up 585 megabytes of space on her computer. Each picture took up the same amount of space. How many megabytes do 39 of these pictures take?
The amount of space taken by 39 of these pictures is 117 megabytes.
What is the unitary method?The unitary approach is a problem-solving process that begins by identifying the value of a single unit and then multiplying that value by the needed value.
Given:
Number of pictures downloaded by Kelly from her cell phone to her computer = 195
Amount of space taken by the pictures = 585 megabytes
Now, an equal amount of space is taken by each picture.
To determine, the megabytes taken by 39 of these pictures.
By the unitary method,
195 pictures = 585 megabytes
39 pictures = ? megabytes
Divide 585 megabytes by the number of pictures 195 and then multiply it by 39.
= (585/195) × 39
= 117 megabytes
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The question to the second Image below
Q: Solving which system leads to a contradiction where there is no solution?
The system of equations given has infinitely number of solutions.
System of EquationA system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
system of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
In the given question, we can solve for the equation given;
[tex]y = 4x + 5\\-8x + 2y = 10\\[/tex]
Solving for both x and y;
The solution of the equation is y = 4x + 5
The system has infinitely many solutions;
In the second system of equations;
y = 0.5x + 3, x = 2y = -16
This equation is not correct.
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Help with number 1 pls make sure when you’re done to highlight the answer in bold
Answer:
Step-by-step explanation:
[tex]undefined[/tex]The sum of the angle measures of a triangle is 180 degrees angles of a triangle measure 40 and 70 degrees , so Katy concludes that the third angle measures 70inductive or Deductive ??i need help
From the fact that the sum of the angle measures of a triangle must be equal to 180º and that two angles have measures of 40º and 70º, we can deduce that the third angle must have a measure of 70º.
Therefore, this was a deductive argument.
how do you write 4.501795324E^-6 in simpler form
The number written in scientific notation is 1.12 × 10⁻² .
Scientific notation can be used to describe values that are either too large or too little to be conveniently presented in decimal form (typically would result in a long string of digits).
In the UK, it is also known as standard form, scientific form, and standard index form.Since it may make a number of mathematical operations simpler, this base ten notation is frequently employed by scientists, mathematicians, and engineers.Scientific notation for non-zero integers is written as m × 10ⁿ, or m times ten and raised to the power of n, where n is an integer and m is a non-zero real number.The given number is 4.501795324E⁻⁶
So simplifying we get :
4.501795324E⁻⁶ = 1.11588350 × 10⁻²
Therefore the number written in scientific notation is 1.12 × 10⁻² .
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Solve the system of equations.y= x2 + 3x - 4y = 2x - 4A. (-1,6) and (0,4)O B. (-1,-6) and (0, -4)C. (0,-4) and (1, -2)O D. (0,4) and (1,-6)
Answer:
(0,-4) and (-1,-6) or B
Step-by-step explanation:
Notice that equation 1 and equation 2 are both equal to y.
Substitute equation 2 into equation 1:
[tex]2x-4=x^2+3x-4[/tex]
Simplify:
[tex]x^2+x=0[/tex]
Factor:
[tex]x(x+1)=0[/tex]
Notice that the zeros for x are x = 0 and x = -1.
Now plug both values into either equation 1 or 2 to find y:
[tex]y=0^2+3(0)-4 = -4[/tex]
[tex]y=(-1)^2+3(-1)-4=-6[/tex]
Therefore, our values are (0,-4) and (-1,-6) or option B
Determine weather the sequence 6,12,24,48 could be an an arithmetic sequence.
Answer:
The sequence cannot be arithmetic.
Explanation:
Given the sequence: 6,12,24,48
We want to determine if the sequence is arithmetic.
An arithmetic sequence is a sequence made in which the next term is obtained by the addition of a constant term called the common difference.
In the given sequence:
[tex]\begin{gathered} 12-6=6 \\ 24-12=12 \\ 48-24=24 \end{gathered}[/tex]The difference between the terms is not constant.
Therefore, the sequence cannot be arithmetic.
Find the y-intercept of line on the graph.
Answer:
-3
Step-by-step explanation:
the 'y- intercept ' is ACTUALLY the 'y-axis intercept'.......this is where the graph crosses the y - axis ....for this graph this is -3
18- A clothing store sells a shirt costing $20 for $33 and a jacket costing $60 for $93.
(i) If the markup policy of the store is assumed to be linear, write an equation that expresses retail price R
in terms of cost C.
(ii) What does a store pay for a suit that retails for $240?
(i) (a) R = 1.5C + 12
(b) R = 1.5C+3
(c) R = 3C + 1.2
(d) R = 3C +1.5
(ii) (a) 158
(b) 185
(c) 155
(d) 188
I cant solve this and I need steps while solving it.
Mike is training for a race. He wants his pace to be proportional throughout the race. The table relates the number of hours he ran and the distance that he traveled. Hours 0.5 1.0 1.5 2.0 Miles 3 6 8 12 Mile then graph these points (hours, miles) to determine whether or not his pace was proportional. Mike determined his pace was proportional because the graph passes through the origin. Which statement best describes his error? Multiple choice question. cross out A) The graph passes through the point (1, 1). cross out B) The graph does not pass through the origin. cross out C) The graph both passes through the origin and is a straight line. cross out D) While the graph does pass through the origin, it is not a straight line.
The statement which best describes Mike's error is that: D) While the graph does pass through the origin, it is not a straight line.
What is a graph?A graph can be defined as a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.
In this context, we can reasonably infer and logically deduce that even though Mike's graph passes through the origin, his error is that it is not a straight line.
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A side mirror of a small pick up truck is similar to that of a larger full size pickup truck. If the smaller truck has a rectangular side mirror of width 5.0 in. and height 6.0 in., what is the height in inches of the larger mirror if the width is 10.0 in.?
If the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.
As given in the question,
Side mirror of a small pick up truck is similar to larger full size pick up truck.
Smaller truck has rectangular side mirror
Width = 5.0 in.
Height = 6.0 in.
Larger mirror
Width = 10.0 in.
Let h be the height of the larger mirror
Both the mirrors are similar and rectangular in shape.
Hence, sides are in proportion
5 /6 = 10 /h
⇒h = (6 ×10) / 5
⇒ h = 12 in.
Therefore, if the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.
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The volume of this rectangular prism is 9.044 cubic feet. What is the value of t?
The volume of a rectangular prism can be calculated with the following formula:
[tex]V=lwh[/tex]Where "l" is the length, "w" is the width and "h" is the height.
In this case, you can set up that:
[tex]undefined[/tex]which expression is a factor xsquared - 5x-6
The Factors of x² - 5x + 6 are (x-3) (x-2)
Step 1: Add the constant term to the first term's coefficient. i.e (6 x 1) = 6
Step 2:Find the two factors of 6 whose total matches the middle term's coefficient., i.e -5.
Thus, the factors are -3 and -2 as,
-3 × (-2) = 6 (Product)
-3 + (-2) = -5 (Sum)
The polynomial may be expressed as follows after dividing the middle term by the two components, -3 and -2:
x² - 3x - 2x + 6 = 0
⇒ x(x-3) -2(x-3) = 0
⇒ (x-3)(x-2) = 0
Thus, the Factors of x² - 5x + 6 are (x-3) (x-2).
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The domain is ? Type your answer in interval notation
The graph of the function is
The domain of the function is determined as the x -value of the function that satisfy the given function.
[tex](-\infty,-4)\cup(-4,1)\cup(1,\infty)[/tex]express this number in standard form:[tex]1.304 \times {10}^{7} [/tex]
To write this in standard form, we need to look at the power of 10. In this case, it's a 7. Then, we need to shift the decimal point 7 places to the right:
[tex]1.304\cdot10^7=13,040,000[/tex]We can see that behind the 1 (where was the decimal point before) now there are 7 numbers, then what we do is correct.