Answer: 8x^2 + xy - 15y^2
Step-by-step explanation:
first do the FOIL method than add 3xy to the equation after
Answer:
[tex]8x^2+xy-15y^2[/tex]
Step-by-step explanation:
[tex](4x+5y)(2x-3y)+3xy\\\\=(4x)(2x)+(4x)(-3y)+(5y)(2x)+(5y)(-3y)+3xy\\\\=8x^2-12xy+10xy-15y^2+3xy\\\\=8x^2+xy-15y^2[/tex]
5x+2y=-7 and 10x+4y= -14 no solution, solution, or infinite solution?
The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).
In general, a system of linear equations can have one of three possible outcomes:
One unique solution (as in this case)
No solution (if the equations are inconsistent)
Infinitely many solutions (if the equations are dependent)
To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.
First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:
-10x - 4y = 14
5x + 2y = -7
-5x = 7
Now we can solve for x:
-5x = 7
x = -7/5
We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:
5x + 2y = -7
5(-7/5) + 2y = -7
-7 + 2y = -7
2y = 0
y = 0
Therefore, the solution to the system of equations is (x,y) = (-7/5,0).
This is called a unique solution, meaning there is only one possible solution for the system of equations.
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Complete Question:
Solve
5x + 2y = -7
10x + 4y = -14
And find the number of solutions for the equation
in forecasting, there is more than one use for linear regression. what are they? check all that apply.
Casual relationship forecasting and Time series forecasting uses linear regression in forecasting.
Linear regression is a statistical tool used in forecasting to model the relationship between a dependent variable and one or more independent variables. Some of the common uses of linear regression in forecasting are:
Predictive modeling: Linear regression can be used to build a predictive model that estimates the value of the dependent variable based on the values of the independent variables..Trend analysis: Linear regression can be used to analyze the trend of the dependent variable over time.Forecast accuracy evaluation: Linear regression can be used to evaluate the accuracy of a forecasting model by comparing the predicted values to the actual values of the dependent variable. Causal analysis: Linear regression can be used to identify the causal relationship between the independent variables and the dependent variable. .Therefore, linear regression is a versatile tool in forecasting, with many useful applications for predicting future values, analyzing trends, evaluating accuracy, and identifying causal relationships.
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The complete question is :
In forecasting, there is more than one use for linear regression. What are the? Check all that apply.
1. Causal relationship forecasting
2. Time series forecasting
A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 62. 7 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.
The density and mass are related to each other with the formula -
Density = mass/volume
So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.
Volume of hemisphere = 2/3πr³, where r represents radius.
Volume = 2/3×π×5³
Performing multiplication, division and taking cube
Volume = 261.8 feet³
Now, mass = density × volume
Mass = 62.7 × 261.8
Performing multiplication
Mass = 16,414.86 pounds
Rounding off
Mass = 16,415 pounds
Thus, the mass of liquid will be 16,415 pounds.
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1. Which equation has a quotient of 1 1/5?
A 5÷6=
B 6÷5=
C 4÷5=
D 5÷4=
Answer:
none of them do
Step-by-step explanation:
5/6=0.83
6/5=1.2
4/5=0.8
5/4=1.25
11/5=2.2
Aldo debe escoger una camisa y un par de pantalones para su atuendo de hoy. Puede escoger entre 2 camisas y 3 pares
de pantalones. ¿Cuántos diferentes atuendos puede crear?
The number of different outfits that Aldo can create from the shirts and the pairs of pants are 6 outfits.
How to find the number of outfits ?In this case, Aldo has 2 options for his shirt and 3 options for his pants. To find the total number of outfits, we can multiply these numbers together:
= Number of shirts x Number of pairs of pants
= 2 x 3
= 6 outfits
Therefore, Aldo can create 6 different outfits by choosing a shirt and a pair of pants from the available options.
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each of two persons tosses three gair coincs. what is the probability that they obtain the same numbre of heads
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
1/8
The probability of getting a head or a tail when flipping a coin is 1/2.
Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.
The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.
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the satellite is in the shape of a rectangular prism. which polynomial represents the volume of the satellite? a rectangular prism with length 4 x minus 3 feet, a width of x plus 1 feet, and a height of x plus 2 feet.
The volume of the rectangular prism will be (4x - 3)(x + 1)( x+2) cubic feet.
What is the volume?The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.
Given that the length, width, and height of the rectangular prism are,
The volume of the rectangular prism will be calculated as,
Volume = Length x width x Height
Volume = (4x - 3)(x + 1)( x+2) cubic feet
Therefore, the polynomial for the volume will be (4x - 3)(x + 1)( x+2) cubic feet.
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How many positive whole numbers less than 2016 have digit sum of 8?
The total number of numbers less than 2016 with a digit sum of 8 is 116 numbers.
How many positive whole numbers less than 2016 are there that have a digit sum of 8?The sum of the digits in the positive whole numbers is to be 8.
So the possibilities are obtained by means of permutation as follows:
Three 0's and an 8; ⁴P₁ = 4
One 1 and one 7, ⁴P₂ = 12
One 2 and one 6; ⁴P₂ = 12
One 3 and one 5; ⁴P₂ = 12
Two 1's and a 6; (⁴P₃/2!) = 12
One 1, one 2, and one 5; ⁴P₃ = 24
Two 2's and a 4; (⁴P₃/2!) = 12
Two 3's and a 2; (⁴P₃/2!) = 12
Two 4's and a 0; (⁴P₃/2!) = 12
Three 1's and a 5; (⁴P₃/3!) = 4
Total = 116 numbers
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Which graph shows the solution to the system of linear equations?
y = 2x − 2
4x − 2y = 4
- Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0.
- Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
- Coordinate plane with one line that passes through the points 0 comma 1 and 1 comma 2.
- Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0 and another line that passes through the points 0 comma 1 and 1 comma 2.
Answer:
A
Step-by-step explanation:
Answer: the answer is A
Step-by-step explanation:
Jamal mows lawns and wants to save money. Jamal currently
has $25 and plans to save an additional $25 per month. Which
graph represents the number of months it will take Jamal to
save at least $250?
Answer: eat grass whor
Step-by-step explanation:
HELLLPPPP PLEASEEEEEEEEEEEEE
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Answer: the home of it is 78 degrees
Step-by-step explanation:
as the angular bisector is shown then we can say that its right
Melitha would like to purchase a music system worth of R12 000.And she is offered an interest rate of 7.5 p.a on a hire purchase agreement.The terms or the agreement on the loan are that 10% deposit is paid initially and the loan will be paid back monthly over a period of 3 years.
a.Calculate the cash deposit Melitha paid.
b.Calculate how much Melitha will have to pay over 3 years.
c.Calculate the monthly installment which Melitha will have to make.
d.What is the total amount that Melitha paid for the music system?
a) The cash deposit (down payment) that Melitha paid is R1,200.
b) The total amount (sum of periodic payments) that Melitha paid over 3 years is R12,094.20.
c) The monthly installment Melitha made is R335.95.
d) The total amount that Melitha paid for the music system is R13,294.20, including the total installments and initial deposit.
What is the down payment?The down payment is the initial cash deposit made for the purchase of an item on credit.
The down payment provides financial evidence of the transaction and testifies about the borrower's ability to undertake the credit arrangement.
a) Cash deposit = R1,200 (R12,000 x 10%)
N (# of periods) = 36 months
I/Y (Interest per year) = 7.5%
PV (Present Value) = R10,800 (R12,000 - R1,200)
FV (Future Value) = R0
Results:
Monthly Payment (PMT) = R335.95
Sum of all periodic payments = R12,094.20
Total Interest = R1,294.20
Total amount paid for the music system = R13,294.20 (R1,200 + R12,094.20)
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Latanya plans to repaint some classroom bookcases. She has 5 3/5 gallons of paint. All of the bookcases are the same size and each requires 1/2 gallon of paint. What is the maximum number of complete bookcases she can paint?
With her 5 3/5 gallons of paint, Latanya can paint up to 11 full bookcases.
What does the equation's solution consist of?Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is a solution to the problem. Solving an equation is locating its solution or solutions.
Let's first translate 5 3/5 gallons of paint into an incorrect fraction:
5 3/5 = (5 x 5 + 3)/5 = 28/5
Next, we can find the number of bookcases she can paint by dividing the total amount of paint by the amount needed for each bookcase:
28/5 ÷ 1/2
= 28/5 x 2/1
= 56/5
=11 1/5.
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if \cos \theta =(4)/(9), tan\theta <0, sin\theta =?
Answer: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
Step-by-step explanation:
cosθ = 4/9
tan < 0
This means our reference angle is either in Quadrants II or IV, (where tangent is negative). Since cosine is positive, it must be Quadrant IV.
Therefore we know that sinθ will be negative.
we also know that [tex]cos^2(\theta) + sin^2(\theta) = 1[/tex], from the Pythagorean identities
.: 16/81 + sin^2(θ) = 1,
.: sinθ = [tex]\sqrt{\frac{65}{81} }[/tex]= [tex]\frac{\sqrt{65}}{9}[/tex]
But since this angle is in Quadrant IV, sinθ will be negative.
.: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
f(-3) if f(x) =-4x -8
Answer:
f(-3)=4
Step-by-step explanation:
The answer is 4. To get f(-3), you must plug in -3 into the x.
Therefore, -4(-3)-8=f(-3).
Then you multiply -4 and -3. 12-8=f(-3)
Finally, you subtract 8 and get the answer:
f(-3)=4
???????????????????????????????????
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
y=x^2 6 units to the left 2 units up
The translation of the graph is represented by y = -6(x+2)² - 7.
What is translation ?A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
Given that the graph of y= x² translated left 2 units and up 8 units. The translated equation is:-
Start with y = x².
Shift 2 units left to get y = (x+2)².
Vertically stretch to get y = 6(x+2)².
Reflect across x-axis to get y = -6(x+2)².
Shift 7 units down to get y = -6(x+2)² - 7.
Hence, the translation of the graph is represented by y = -6(x+2)² - 7.
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The question is incomplete so solved for,
Suppose the graph of y= x^2 translated left 2 units, and up 8 units
Given: ABCD is a parallelogram and AD is perpendicular to BD
Prove: AB congurent to BC
Answer:
...here is the answer...
pg 558selling online according to a recent pew research center report, many american adults have made money by selling something online. in a random sample of 4579 american adults, 914 reported that they earned money by selling something online in the previous year.15 assume the conditions for inference are met. determine the critical value z* for a 98% confidence interval for a proportion. construct a 98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year. interpret the interval from part (b).
The true proportion of all American adults who would report having earned money by selling something online in the previous year lies between 0.178 and 0.221.
A confidence interval is computed from the sample data and provides a range of values within which the true population parameter is expected to lie. The confidence level is the probability that the confidence interval contains the population parameter.
Using this critical value, we can construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year. To do this, we use the formula:
confidence interval = sample proportion ± z* (standard error)
The sample proportion is the number of adults who reported earning money by selling something online (914) divided by the total sample size (4579), which gives us a proportion of 0.1997.
The standard error is calculated as:
standard error = √ [(sample proportion)(1 - sample proportion) / sample size]
Substituting the values, we get:
standard error = √ [(0.1997)(1 - 0.1997) / 4579] = 0.009
Plugging in the values, we get:
confidence interval = 0.1997 ± 2.33(0.009)
This gives us a confidence interval of 0.178 to 0.221.
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ratio of pirates to sailors was 18 to 19. If there were 198 sailors, how many pirates were there?
There were 198 sailors and the ratio of18 pirates, so 198 divided by 19 equals 10.4, meaning there were approximately 176 pirates.
Find the ratio of pirates to sailors
Ratio of pirates to sailors
= 18 : 19
Convert the ratio to a fraction
Ratio of pirates to sailors
= 18/19
Find the number of pirates
Number of pirates
= (18/19) × 198
Number of pirates = 176
The ratio of pirates to sailors is 18 to 19. This means that for every 19 sailors, there are 18 pirates. To figure out how many pirates there are when there are 198 sailors, we can use a proportion. First, set up the proportion with the ratio given. The ratio is 18:19, so the proportion is 18/19 = x/198. Then, cross multiply, 18 x 198 = 19x. Now, divide both sides by 19, and we get 18 x 198/19 = x. Then, solve for x by multiplying both sides by 19, and we get 18 x 198 = 19x. Finally, divide both sides by 198 to get x, and x =176. So, there were approximately 176 pirates.
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The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool
Answer:
Step-by-step explanation:
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The actual distance between the basketball court and the pool is 37.5 feet
Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.
The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.
We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:
3 inches / 5 feet = 22.5 inches / x
We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:
3 inches x x = 5 feet x 22.5 inches
3x = 112.5
x = 37.5 feet
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Complete Question:
The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?
With the given budget, what’s the farthest distance a truck can travel from the warehouse to the retail outlet?
Help me with thiss Pllllllllll
Step-by-step explanation:
the answer for -1/4(-8x+12y)
2x-3y
Answer:
2x-3y
Step-by-step explanation:
For this equation we are using distributive property
-1/4(-8x) -1/4(12y)
↓ ↓
2x -3y
So, 2x-3y is the answer.
y=-1/2x-1
y=1/4x-4
graphing method
Suppose the following sequence of matrix operations was used to translate AABC.
The horizontal and vertical translations applied to ΔABC:
A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
What is matrix ?It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.
Given that,
[tex]\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right][/tex] = ?
After using matrix operation it can be further solved as,
[tex]\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right][/tex]
Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
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I need help is due today!!!
The length of a living room is 12 feet and it’s width is 10 1/2 feet. The length of the room is being expanded by x feet. Select all the expressions that represent the area of the living room in square feet.
A. 10.5 (12x) square feet
B. (10.5 + 12 + x) square feet
C.10.5( 12 + x) square feet
D.126x square feet
E.(126 + 10.5) square feet
F.( 22.5 + x) square feet
Answer:
answer is A
Step-by-step explanation:
because area of a rectangle is L × B
or length × width
since the length is expanded by x
10.5 (12x)
Answer:
Option C
Step-by-step explanation:
The original length of the room = 12 feet
After expansion, the new length = [tex](12 + x)[/tex] feet
Width of the room = 10[tex]\frac{1}{2}[/tex] feet = 10.5 feet
Area of a rectangle = Length × Width
The shape of the living room is a rectangle.
∴Area of living room = [tex](12 + x)[/tex] feet × [tex](10.5)[/tex] feet
[tex]= 10.5(12 + x)[/tex] square feet
Expand the brackets or parenthesis by applying the Distributive Law:
[tex]= (12)(10.5) + (10.5)(x)[/tex] square feet
= [tex](125 + 10x)[/tex] square feet
∴Option C
The bank would exchange 1.6 Canadian dollars for one US dollar. How many Canadian dollars would the bank exchange for $160 US dollars?
The number of Canadian dollars the bank exchange for $160 US dollars is 100.
What is money?Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.
A current medium of exchange in the form of coins and banknotes.
Given that, the bank would exchange 1.6 Canadian dollars for one US dollar.
Here, there are $160 US dollars.
So, number of Canadian dollars
= 160/1.6
= 100
Therefore, the number of Canadian dollars the bank exchange for $160 US dollars is 100.
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The temperature at noon was $-4\degree$ C. By midnight, the temperature dropped $8\degree$ C. Which expression represents the temperature at midnight?
The temperature at midnight would be -4°C - 8°C since the temperature at noon was -4°C and at midnight it dropped 8°C.
The temperature at midnight would be -4°C minus 8°C, which can be expressed as:
-4°C - 8°C = -12°C
Therefore, the temperature at midnight would be -12°C.
Temperature is a measure of the degree of hotness or coldness of a body or an environment. It is a physical quantity that expresses the amount of thermal energy in a substance or a system, typically measured using a thermometer in units such as Celsius (°C) or Fahrenheit (°F). In general, the higher the temperature, the more thermal energy is present in the system, and the lower the temperature, the less thermal energy is present.
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A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
Does the region form a right triangle? Justify your answer.
Answer: no it does not
Step-by-step explanation: Because 1,007 squared is 1,014,049 and the sum of 911 squared is 829,921 and then 829 squared is 687,241 then add 829,921+687,241=1,517,162 when it should equal 1,014,049 which is the amount of 1,007 squared to make it a right triangle.
The solution is : no, it does not form a right triangle.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
given that,
A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
now, we get,
Because 1,007 squared is 1,014,049
and the sum of 911 squared is 829,921
and then 829 squared is 687,241
then add 829,921+687,241=1,517,162
when it should equal 1,014,049
which is the amount of 1,007 squared to make it a right triangle.
as we know that,
in right triangle,
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.
so, we get,
The solution is : no, it does not form a right triangle.
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Which scatter plot most likely has a line of best fit represented by y = 3x + 1?
The graph showing the line of best fit for the function y = 3x + 1 is attached below
What is line of best fitThe line of best fit is a line that is used to represent the relationship between two variables in a scatterplot. It is a line that passes through the center of the data points in the scatterplot in such a way that the total distance between the line and the data points is minimized. The line of best fit can be used to make predictions about the value of one variable based on the value of another variable. There are several methods to obtain the line of best fit, including the method of least squares, which finds the line that minimizes the sum of the squares of the differences between the observed values and the values predicted by the line.
In the problem given, the line of best fit the line of best fit can be plotted on a graph using a graphing calculator.
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