The equation so that y is a function of x is y = [15 - 3x]/5 and the value of y is 18/5.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given the equation 3x + 5y = 15
to convert it in form of y,
5y = 15 - 3x
and divide both sides by 5
y = [15 - 3x]/5
substitute x = -1
y = [15 - 3x]/5
y = [15 - 3(-1)]/5
y = 18/5
Hence equation is y = [15 - 3x]/5 and y = 18/5.
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6. Sally would like to lease a car worth $48,000 for a three-year period. The leasing company told Sally that after three years, the car would have a
will Sally have to pay off during her three-year lease?
a.
b.
C.
d.
$1,133
$7,200
$11,210
$36,790
The will Sally have to pay off during her three-year lease is d. $36,790.
How much Sally have to pay off during her three-year lease?To determine the amount Sally will have to pay off during her three-year lease, we need to understand the concept of depreciation.Depreciation is the decrease in value of an asset over time due to factors such as age, wear and tear, and market changes.For example, if a car is worth $48,000 and depreciates by 10% per year, its value after one year would be $48,000 * (1 - 0.1) = $43,200.After two years, its value would be $43,200 * (1 - 0.1) = $38,880. After three years, its value would be $38,880 * (1 - 0.1) = $34,992.So, the amount Sally would have to pay off during her three-year lease is $48,000 - $34,992 = $13,008.In conclusion, the answer is d. $36,790.
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During an election for city council, you hear a candidate say that 68% of children in the city live in poverty. A
typical school in this city has about 1,200 students.
Based on the candidate statement about how many children in a typical school live in poverty
It can be estimated that about 816 children in the typical school are living in poverty.
Percentage calculationBased on the candidate's statement, approximately 816 children in a typical school in this city live in poverty.This is calculated from the 68% of children in the city that live in poverty, multiplied by the 1,200 students in a typical school. This rate of poverty among children is a concerning statistic, and one that needs to be addressed. It highlights the need for effective solutions to help children in this city out of poverty.These solutions could include initiatives such as providing better access to education and employment opportunities, increasing access to healthcare, or providing more social services and supports. Given that poverty has a long-term, negative effect on the health, wellbeing and life chances of children, this is a pressing issue that needs to be addressed.It is important that city council candidates have a plan in place to tackle this issue and help improve the lives of children in this city.To learn more about percentage calculation refer to:
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can someone help me out?
Answer: I'm pretty sure it's z<-6, so on the number line it would be an open circle at -6 and an arrow pointing left
Need help with these questions:
1. If you have $330 in the bank but your bank balance shows $331, what is the percentage error? Do not put a minus sign.
2. A rectangle has width 4.1 and height 3.9. What is the percentage error if an approximate value of 4×4=16 is used for the area of this rectangle?
Answer: they are stilling your money
Step-by-step explanation:
if f(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and "f '(6) = 6", find f '(1).
If function F(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6, the value of an F'(1) is 114.
We know that the chain rule of differentiation (derivative)
The derivative of composite function f(g(x)) is: f'(g(x))⋅g'(x)
Consider function F(x) = f(xf(xf(x)))
We need to differentiate above function with respect to x.
F'(x) = f'(xf(xf(x))) × d/dx[x f(xf(x))]
We use product rule of derivative to find d/dx[x f(xf(x))]
d/dx[x f(xf(x))] = f(xf(x)) d/dx(x) + x d/dx(f(xf(x)))
After simplifying these expressions we get.
F'(x) = f'(xf(xf(x))) [f(xf(x)) + xf'(xf(x)) + x(f(x) + xf'(x))]
For x = 1 above expression would be,
F'(1) = f'(1 f(1 f(1))) [f(1 f(1)) + 1 f'(1 f(1)) + 1 (f(1) + 1 f'(1))]
F'(1) = f'(f(4)) [f(4) + f'(4) + (4 + 4)]
F'(1) = f'(6) [6 + 5 + 8]
F'(1) = 6 × 19
F'(1) = 114
Therefore, the value of F'(1) = 114.
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The complete question is:
If F(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6, find F '(1).
What is 1 1/2 x 1/2.
Answer:
3/4 or 0.75
Step-by-step explanation:
1 1/2 is 3/2
so 3/2*1/2
then you multiply the numerators and then the denominators so you get 3/4 and that's you answer
Please help me with this
Extra points
Answer:
2x + 9
Step-by-step explanation:
Nathan made a mistake while solving an equation. His work is shown.
Where did Nathan make a mistake?
In Step 1, Nathan did not multiply
both terms in parentheses by 3.
In Step 2, Nathan did not simplify
52-3x correctly.
In Step 3, Nathan did not divide
by the correct number.
In Step 4, Nathan did not simplify
-24
correctly.
8
Step t
Step 2:
Step 3.
Step 4.
3(x - 8) = 5x
3x - 24
5x
- 3x
-24 = 8x
8x
-24
8
8
- 3x
"
-3 = x
The solution to the equation is x = -12 and Nathan made a mistake while simplifying in Step 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
3 ( x - 8 ) = 5x
On simplifying the equation , we get
3x - 24 = 5x
Adding 24 on both sides , we get
3x = 5x + 24
Subtracting 3x on both sides , we get
3x - 5x = 24
-2x = 24
Divide by 2 on both sides , we get
-x = 12
So , x = -12
Hence , the solution is x = -12
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11
3
Question 8
Upon purchasing a new car for $15,000, you discover that its value will decrease
linearly for the next 10 years until it is worth $0. Complete the mathematical model
below that describes the value of the car as a function of the number of years you
have owned the car.
This is a linear function that describes the value of the car as a function of the time (t) in years.
What is linear function?A linear function is a type of mathematical function that shows a linear relationship between two variables. It is represented as a straight line when plotted on a graph. Linear functions are used to describe a wide variety of phenomena, including position, velocity, acceleration, and much more. Linear functions are also used in various fields of mathematics, such as algebra, calculus, and optimization. Linear functions can be written in the form of an equation, with the equation representing the line.
V(t) = 15000 - 1500t
This is a linear function that describes the value of the car as a function of the time (t) in years. V(t) is equal to the initial value of the car (15000) minus 1500 multiplied by the amount of years (t) since the car was purchased. As t increases, V(t) decreases, linearly, until it is worth $0.
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A Harris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries?” The survey found that 23% of the respondents stick with their tour group. In a sample of six international travelers, what is the probability that two will stick with their tour group? In a sample of six international travelers, what is the probability that at least two will stick with their tour group? In a sample of 10 international travelers, what is the probability that none will stick with the tour group? in statistics
What is the value of the expression 30-(-6)?
Answer:
-5
30x6=5
5 and convert to negative -5
pls HELP ME ASAP DUE TODAY NOW HURRY PLEASE
Answer: so yea its the first one. im not that sure im just like saying what I know
Step-by-step explanation:
y intercept of f(x) = -2/9 x + 1/3
Answer:
Y-intercept: 1/3
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
In this case, the y-intercept is 1/3
player A had 653 less than twice the number of home runs player b had, r
You can represent the problem with an equation. Let x be the number of home runs player B had.
According to the statement, player A had 653 less than twice the number of home runs player B had.
so you can write the equation:
Player A = 2x - 653
This equation shows the relationship between the number of home runs player B had (x) and the number of home runs player A had (2x - 653). To find the number of home runs player B had, you can solve for x by adding 653 to both sides of the equation:
x = (Player A + 653) / 2
So if you know the number of home runs player A had, you can use this equation to find the number of home runs player B had.
Find the quotient of these complex numbers.
Answer: The answer is B
Step-by-step explanation:
( 2 + 2 ) divided by ( 5 + 4) is the same as 4/9 which is also the same as 2/9 + 2/9 which equals 4/9.
(Slope-Intercept Form MC)
Which equation represents the graph?
a graph of a line that passes through the points 0 comma negative 2 and negative 2 comma 2
y equals negative 2 times x plus one half
y equals negative one-half times x plus one half
y = −2x − 2
y equals negative one-half times x minus 2
Question 2(Multiple Choice Worth 5 points)
(Slope MC)
What is the slope of the linear relationship shown on the graph?
a graph of a line that passes through the points 0 comma negative 2 and negative 2 comma 1
negative two thirds
two thirds
negative three halves
three halves
Question 3(Multiple Choice Worth 5 points)
(Systems of Linear Equations MC)
Which graph shows the solution to the system of linear equations?
y equals one third times x
x + 3y = 6
coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1
coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1
coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1
coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3
Question 4(Multiple Choice Worth 5 points)
(Systems of Linear Equations LC)
Determine the number of solutions to the system of linear equations shown on the graph.
coordinate plane with one line that passes through the points negative 1 comma 4 and 0 comma 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 3
One solution at (1, −2)
One solution at (−2, 1)
Infinitely many solutions
No solution
Question 5(Multiple Choice Worth 5 points)
(Systems of Linear Equations MC)
Which point is a solution to the system of linear equations?
y = −x + 3
x − 3y = 15?
(−1, 5)
(0, 3)
(3, 0)
(6, −3)
Question 6(Multiple Choice Worth 5 points)
(Slope MC)
Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $60, plus $28 per hour. What is the slope of this situation?
28
32
60
88
Question 7(Multiple Choice Worth 5 points)
(Slope-Intercept Form MC)
A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 14 inches long and is melting at a rate of 0.9 inches per hour. Find and interpret the slope for this relationship.
−0.9; for every additional hour, the length of the icicle decreases by 0.9 inches
0.9; for every additional hour, the length of the icicle increases by 0.9 inches
−14; the length of the icicle when the student first measures it
14; the length of the icicle when the student first measures it
Question 8(Multiple Choice Worth 5 points)
(Graphing Linear Equations MC)
A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $8.50
4 $11.50
5 $13.00
8 $17.50
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
Question 9(Multiple Choice Worth 5 points)
(Systems of Linear Equations MC)
The system of linear equations 3x + 2y = −4 and y equals one half times x plus 1 is graphed on a coordinate plane. Approximate the solution to the system.
coordinate plane with one line that passes through the points 0 comma negative 2 and negative 2 comma 1 and another line that passes through the points 0 comma 1 and 2 comma 2
(−1.5, 0.25)
(−0.5, 0.75)
(1.5, 0.25)
(−2.5, 1.5)
On solving the provided question we can say that we have the slope -5/7 and the equation will be 5x +7y -c = 0
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
here,
we have the slope -5/7
y = /5x/7 +c
7y = -5x +c
5x +7y -c = 0
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solve for x.
NM=X-6, ML=9, LK=2X-19, NK=23
The value of the variable x is 11
How to determine the value of the variableFrom the information given, the segment is from N - K
We have the midpoints as; NM, ML, LK
This is represented as;
NM + ML + LK = NK
Substitute the values, we get
x - 6 + 9 + 2x - 19 = 23
collect like terms, we get;
x + 2x = 23 +6 - 9 + 19
add or subtract the like terms
3x = 42 - 9
3x = 33
Now, make 'x' the subject of formula by dividing both sides by the coefficient of x, we get;
3x/3 = 33/3
Divide the values
x = 11
Hence, the value is 11
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EASY POINTS!
Let's say you are ordering books online and the online store is having a 12% off sale. If the subtotal of the books, before the discount, is $25, what is the total cost of the books if there is also a state sales tax of 7.5%?
$23.65
$26.13
$22.00
$23.13
A car consumes fuel at a rate of 8litres/100 km.
(1) How many litres is needed to travel 400 km? (2)How far you can travel with 50 /?
For one litre the cars travels
=400/400
=10
therefore it can travel 10 km in 1 lit
so, the distance travelled by car in 50 litres is
=50×10
For the function f(A,B,C,D) = A'B+BD what would be the canonical sum of products expansion?A) f(A,B,C,D)= A'BC'D'+A'BC'D+A'BCD'+A'BC'D+ABCDB) f(A,B,C,D)= A'BCD'+A'BC'D'+A'BC'D+A'BCD+ABC'D'C) f(A,B,C,D) = A'B'C'D+A'B'CD+A'BC'D'+A'BCD'+AB'C'D+AB'CD+ABC'D'+ABCD'D) the function is already expressed in canonical form
The function f(A,B,C,D) = A'B + BD is already in canonical sum of products (SOP) form,
So the answer is D the function is already expressed in canonical form.
A canonical form is a member of a collection of representations of form equivalence classes such that there is a function or method that projects every element of each equivalence class onto that single element, the canonical form of that equivalence class.
In general, a canonical form for a class of objects on which an equivalence relation is specified consists in selecting a single item from each class. As an example: Jordan normal form is a canonical matrix similarity form.
p′+q+r. This is the standard PoS output form, f. This function can alternatively be represented using the two notations below. We expressed the function as a product of respective Max terms in one equation.
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What is the arc length of the sector shown?
The required length of the sector shown is given as 22π feet.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
A circle is shown, where radius = 36 feet and the measure of the length of the arc for a sector with an angle of 110° is to be determined.
We know that,
arc = angle × radius
arc= 110 × π/180 π 36
arc = 22π
Thus, the required length of the sector shown is given as 22π feet.
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56 parts were lost 3% of the total parts were lost. how many total parts were there
The total parts that were lost is 1867
How to determine the total parts that were lostLet's call the number of total parts "x".
From the question, we have the following parameters that can be used in our computation:
56 parts were lost, which is 3% of the total, so we can write:
56 = (3/100) * x
To isolate x, we can divide both sides by (3/100):
56 / (3/100) = x
Rewrite the equation as
x = 56/(3/100)
Express as product
So, we have
x = 56 * 100/3
Evaluate the product
x = approximately 1867
So there were approximately 1867 total parts.
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Identify the solid formed by a given net.
A: Cylinder
B: Triangular prism
C: Square pyramid
D: Rectangular prymid
[60 points]
The solid formed by a given net is option D. Rectangular pryramid
What is a Rectangular Pyramid?A rectangular pyramid is a three-dimensional shape that has a square base and four triangular sides that meet at a single point at the top. It is a type of polyhedron
Also rectangular pyramid is a polyhedron with a rectangular base and four triangular faces that meet at a common point called the apex.
Therefore, the correct answer is as given above. It can be concluded that the solider formed is option D. rectangular pyramid
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Accounting systems are important because they are a primary source of information for managers.
Thw given statement " Accounting systems are important because they are a primary source of information for managers" is true.
What kinds of accounting systems exist?Two categories of accounting systems exist: In the first, a small business uses a single entry system to log each transaction as a line item in a ledger. The alternative is a double entry system, in which each transaction is entered in two different accounts as both a debit and a credit.
Accounting systems are crucial since they serve as managers' main informational resource. The accounting system is likely to provide the information that is needed for many, if not most, decisions. Whether the accounting system is giving managers access to the "best" information is our main concern.
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complete question:
TRUE OR FALSE Accounting systems are important because they are a primary source of information for managers.
for the data given below, we construct a 90% confidence interval for the population mean n. 42.3 59.2 45.4 55.8 49.0 39.7 56.2 54.6 45.8 60.6 55.7 46.1 58.3 44.4 find the lower bound (round off to first decimal place).
The lower bound of the 90% confidence interval for the population mean is 44.3.
To calculate the lower bound of the 90% confidence interval for the population mean, we will use the formula:
Lower bound = sample mean - (1.645 * (standard deviation / square root of sample size))
Calculate the sample mean:
Sample mean = (42.3 + 59.2 + 45.4 + 55.8 + 49.0 + 39.7 + 56.2 + 54.6 + 45.8 + 60.6 + 55.7 + 46.1 + 58.3 + 44.4) / 14 = 51.09
Calculate the sample standard deviation:
Sample standard deviation = √(((42.3 - 51.09)2 + (59.2 - 51.09)2 + (45.4 - 51.09)2 + (55.8 - 51.09)2 + (49.0 - 51.09)2 + (39.7 - 51.09)2 + (56.2 - 51.09)2 + (54.6 - 51.09)2 + (45.8 - 51.09)2 + (60.6 - 51.09)2 + (55.7 - 51.09)2 + (46.1 - 51.09)2 + (58.3 - 51.09)2 + (44.4 - 51.09)2) / 13) = 8.37
Calculate the lower bound:
Lower bound = 51.09 - (1.645 * (8.37 / √14)) = 44.3
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additional Vocabulary Support 3-1 help please I need this rn
Answer:
Step-by-step explanation:
this set of ordered pairs is a relation but it is not a function
each value in the right oval of the arrow diagram is an output
each value in the left oval of the arrow diagram is an input
this set of ordered pairs is a relation and a function
a rectangular residential lot with the area 7475 is 50m longer then it is wide find the dimensions of the lot
The Area of path is 400cm of a rectangular residential lot with the area 7475 is 50m longer then it is wide.
What is area of the path?The difference between the areas of the two rectangles represents the path's area. To calculate the two areas, we shall utilize the rectangle's area formula. To get the necessary size of the path, first calculate the area of the larger rectangle by subtracting the area of the smaller rectangle.
In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle. In contrast, when we talk about a rectangle's perimeter, we mean the total of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.
Area of park = l × b = 40 × 35 = 1350
Area of park with path is = 45 + 2.5 + 2.5 x 30 + 2.5 + 2.5 = 1750 cm
Therefore,
Area of path = Area of park with path - Area of rectangular park
= 1750 - 1350 = 400cm
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complete question:
A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.
A particle is moving on the perimeter of a circle with radius r=5 with angular speed of π/8 radians per second. After completing 4 full rotations, the particle traveled for 7 more seconds and stopped. What is the length of the total distance the particle traveled?
The length of the total distance the particle traveled is, 327π/8.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
A particle is moving on the perimeter of a circle with radius r=5 with angular speed of π/8 radians per second.
Now, First of all, let's calculate the the circumference. This is found by this equation:
⇒ P = 2πr
Here, r = 5
⇒ P = 2π × 5
⇒ P = 10π
And, The distance of completing 4 full rotations is,
⇒ D = 4P
⇒ D = 4 × 10π
⇒ D = 40π
Since, In one second the particle traveled π/8 radians.
Here, the particle traveled for 7 more seconds and stopped, this distance is,
⇒ 7 (π/8)
⇒ 7π/8
Thus, the length of the total distance the particle traveled is;
⇒ 40π + 7π/8
⇒ 327π/8
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Complete the expression so that it is equivalent to 2 (x+6)
The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.
What is an expression?
A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Given expression is
2 (x+6)
Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.
The mathematical representation is a(b+c) = ab + ac.
Apply the Distributive property in the given expression:
(2×x) + (2×6)
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a car wash uses 50 gallons of water every 40 sec. how much water does it use per sec?
Answer:
1.25 gallons per second
Step-by-step explanation:
To find out the amount of water per second, we must divide the gallons by the time.
50/40 = 1.25
Answer: 1.25
Step-by-step explanation: If they use 50 gallons of water every 40 seconds you just divide 50 and 40 which equals 1.25
