Answers
The center of dilation is (1, -4).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From the given graph,
Vertices of RSTV are R(1, -4), S(2, 0), T(1, 2) and V(-2, 1).
Vertices of R'S'T'V' are R'(1, -4), S'(4.5, 2), T'(2, 5) and V'(-2.5, 3.5).
Here, the center of dilation is (1, -4).
The transformation is enlargement by scale factor 1.5
Therefore, the center of dilation is (1, -4).
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Related Questions
For all x≠±y , x/(x+y)+y/(x−y)= ?
Answers
The value of the equation is A = ( x² + y² ) / ( x² - y² )
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
A = x / ( x + y ) + y / ( x - y )
On simplifying the equation , we get
Multiply by the LCM , we get
x / ( x + y ) + y / ( x - y ) = [ x ( x - y ) + y ( x + y ) ] / ( x + y ) ( x - y )
where the denominator ( x + y ) ( x - y ) = ( x² - y² )
Substituting the values in the equation , we get
x / ( x + y ) + y / ( x - y ) = [ x² - xy + xy + y² ] / ( x² - y² )
On further simplification , we get
A = ( x² + y² ) / ( x² - y² )
Hence , the equation is A = ( x² + y² ) / ( x² - y² )
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Let f(x) = -3x + 2, g(x) = g(x)=x/5 h(x)= -2x^2+9 j(x)= 5-x
Find each value or expression.
I need help on # 5, which is #12, # 7, which is# 13, and # 9, which is 14. See attached photo below
Answers
Let f(x)=-3x+2, g(x)=5 h(x) = -2x+9, and j(x) = 5-x. Find each value or expression.
1. (f +j)(3) = -5
3. (h + g)(-5) = 10
5. (f + g)(2) = 1
7. (g f)(-5) = 22
9. f((5)) = -11
How did we get the values?1. (f + j)(3) = f(3) + j(3) = (-3(3)+2) + (5-3) = -7 + 2 = -5
3. To find the value of (h + g)(-5), we need to first add the functions h(x) and g(x), then evaluate the result at x = -5.
h(x) = -2x + 9
g(x) = 5
h(x) + g(x) = -2x + 9 + 5 = -2x + 14
So, (h + g)(-5) = -2(-5) + 14 = 10.
The answer is 10.
5. To find the value of (f + g)(2), we need to first add the functions f(x) and g(x), then evaluate the result at x = 2.
f(x) = -3x + 2
g(x) = 5
f(x) + g(x) = -3x + 2 + 5 = -3x + 7
So, (f + g)(2) = -3(2) + 7 = 1.
The answer is 1
7. (To find the value of (g + f)(-5), we need to first add the functions g(x) and f(x), then evaluate the result at x = -5.
f(x) = -3x + 2
g(x) = 5
f(x) + g(x) = -3x + 2 + 5 = -3x + 7
So, (g + f)(-5) = -3(-5) + 7 = 22.
The answer is 22
9. f(5) = -3(5) + 2 = -13 + 2 = -11
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Change from base 4 to base 10. Show your thinking and solve each problem in 2 ways.
13 v4
303 v4
132 v4
Answers
Answer: PLS CROWN ME / brainly :)
13^4 in base 4:
Method 1: Convert 13^4 to base 10 using powers of 4.
13 in base 4 = 1 * 4^1 + 3 * 4^0 = 1 * 4 + 3 * 1 = 7
So, 13^4 in base 4 = (1 * 4^4 + 3 * 4^3) = (1 * 256 + 3 * 64) = 256 + 192 = 448.
Method 2: Convert 13 to base 10 and then find (13 in base 10)^4
13 in base 4 = 1 * 4^1 + 3 * 4^0 = 1 * 4 + 3 * 1 = 7
So, (13 in base 10)^4 = 7^4 = 2401
So, 13^4 in base 10 = 2401.
303^4 in base 4:
Method 1: Convert 303^4 to base 10 using powers of 4.
303 in base 4 = 3 * 4^2 + 0 * 4^1 + 3 * 4^0 = 3 * 16 + 0 * 4 + 3 * 1 = 51
So, 303^4 in base 4 = (3 * 4^6 + 0 * 4^5 + 3 * 4^4) = (3 * 4096 + 0 * 1024 + 3 * 256) = 12288 + 768 = 13056.
Method 2: Convert 303 to base 10 and then find (303 in base 10)^4
303 in base 4 = 3 * 4^2 + 0 * 4^1 + 3 * 4^0 = 3 * 16 + 0 * 4 + 3 * 1 = 51
So, (303 in base 10)^4 = 51^4 = 132651.
So, 303^4 in base 10 = 132651.
132^4 in base 4:
Method 1: Convert 132^4 to base 10 using powers of 4.
132 in base 4 = 1 * 4^2 + 3 * 4^1 + 2 * 4^0 = 1 * 16 + 3 * 4 + 2 * 1 = 22
So, 132^4 in base 4 = (1 * 4^8 + 3 * 4^7 + 2 * 4^6) = (1 * 65536 + 3 * 16384 + 2 * 4096) = 65536 + 49152 + 8192 = 19880.
Method 2: Convert 132 to base 10 and then find (132 in base 10)^4
132 in base 4 = 1 * 4^2 + 3 * 4^1 + 2 * 4^0 = 1 * 16 + 3 * 4 + 2 * 1 = 22
So, (132 in base 10)^4 = 22^4 = 10648.
So, 132^4 in base 10 = 10648.
Step-by-step explanation:
Answer:10101
Step-by-step explanation:
Suppose that you have at your disposal a software package that solves a square nonsingular system of equations Cx=d. Assume that the package either finds the unique solution of Cx=d or terminates with an error message if C is singular. Given an m×n matrix A of rank n and an m -vector b, briefly describe in words how you would use the package to find whether or not the equations Ax=b are compatible, and if they are, compute a solution x. Comment briefly on the uniqueness of a solution if one exists.
Answers
The equations Ax = b are not compatible.
What do you mean by equation?It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.
An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.
To determine whether the equations Ax = b are compatible and to compute a solution x, you would first form the augmented matrix [A|b]. Then, you would perform row operations on [A|b] to reduce it to an upper triangular matrix [C|d]. Finally, you would use the software package to solve the square system of equations Cx = d.
If the software terminates with an error message, it means that C is singular, and the equations Ax = b are not compatible. If the software finds the unique solution of Cx = d, it means that the equations Ax = b are compatible and that the solution x is unique. However, it is important to note that the uniqueness of the solution depends on the rank of A being equal to n. If the rank of A is less than n, the equations are not compatible, and if the rank of A is greater than n, the equations have infinitely many solutions.
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help me please!!!!!!!
Answers
Answer:
see explanation
Step-by-step explanation:
W(2) = 5 , means
a puppy of 2 months has a weight of 5 pounds.
W(6) > W(4) , means
a puppy at 6 months has a greater weight than a puppy of 4 months
W(12) = W(15) , means
a puppy at 12 months is the same weight as a puppy of 15 months
HELP WHICH ONE IS IT
Answers
Step-by-step explanation:
try the suggested solution; the lines and their inequalities are shown with the same colours. Points A[0;-1] and B[0;-3] are interception points, according to them to define equations of the lines.
Marip has a piece of string. He cuts off six -eights of its length. How much is left?
Answers
Answer:
if marip has a piece of string. He cuts off six-eights of it's length. how much is left it's 2
The polygon in the diagram is a square with center P. The length from the center to the vertex is 6sqrt(2) in. Find the area of the square to the nearest tenth of an inch.
A) 24.0 in^2
B) 72.0 in^2
C) 36.0 in^2
D) 144.0 in^2
Answers
Area = (3sqrt(2))^2
Area = 9 * 2
Area = 18
So the answer is 18 in^2, and rounded to the nearest tenth, the area of the square is 18.0 in^2, which corresponds to option C: 36.0 in^2.
What is the rise-over-run value for the relationship represented in the graph?
1/35
2/17
35
40
Answers
Answer:
Below
Step-by-step explanation:
Pick any two points on the graph say 2,70 and 3 , 105
rise is 70 to 105 = 35 run is 2 to3 = 1
rise/run = 35/1 = 35
Answer:
35
Step-by-step explanation:
gradient= rise/run
= 70-35/2-1
= 35
help asap PLEASE SOMEBODY TELL ME THE CODE TO THIS ASSIGNMENT.
Answers
Answer:
Is there meant to be a picture? I can still try to help if you explain in the comment under this, but I think the picture didn't submit fully!! :)
I'll edit the answer when you edit the question to add the full image
Step-by-step explanation:
There is a harvest festival each year on the planet Bozone. During that time, most of the Bozone residents sit down to rejoice and eat roast snig. Past history shows that a reasonable price-demand equation is: p= 300 – 20x where x is the number of kilograms of snig sold, and p is the price per kilogram of snig in the local currency, the Bozat. a. To sell an additional kilogram of snig, how much does the price need to decrease? Price needs to decrease by ______Bozats. b. Solve the price-demand equation for æ in terms of p. x =
Answers
x = (300 - p) / 20
According to the equation, the quantity of kilos (x) of snig that will be sold is equal to the difference between 300 and p, divided by 20.
The price-demand connection for roast snig at the harvest festival on the planet Bozone can be represented by the equation p=300 - 20x. The formula specifies that 300 minus 20 times the number of kilogrammes (x) of snig sold is the price per kilogramme of snig (p) in the local currency (Bozats).
Using this equation, one can determine how much of the price must be reduced in order to sell 1 extra kilogramme of snig. The equation can be rewritten to solve for x in terms of p in order to accomplish this. This can be done by taking 300 off of both sides of the equation, multiplying both sides by 20, and then solving for x = (300 - p) / 20. This rearrangement has the effect of dividing the number of kilogrammes of snig that will be sold in terms of price per kilogramme by the difference between 300 and p. This equation can be used to calculate the price reduction required to sell an extra kilogramme of snig.
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Consider the exponential function E(t)=6⋅1.02^t where t is measured in seconds. Find the amount of time it takes for E to increase by 10%.
it takes ____ seconds (give answer in exact form)
Answers
The amount of time it takes for E to increase by 10%. it takes 4.81 seconds.
What is exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Given that,
Let the amount of time it takes for E to increase by 10% be x.
Thus, after (t + x) seconds, E is increased by 10%.
E(t + x) = E(t) + 10% of E(t)
= E(t) + 10/100 E(t)
= E(t) + 0.1 E(t)
E(t + x) / E(t) = 1.1
As,
[tex]E(t) = 6(1.02)^t\\\\E(t + x) = 6(1.02)^{t + x}\\\\\frac{E(t + x)}{E(t)} = \frac{6(1.02)^{t + x}}{6(1.02)^{t}}\\\\\frac{E(t + x)}{E(t)} = (1.02)^{t + x - t}\\\\(1.02)^x = 1.1[/tex]
Taking log on both sides:
x = log (1.1) / log (1.02)
x = 4.81 seconds.
Hence, the amount of time it takes for E to increase by 10%.
it takes 4.81 seconds.
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A square plastic tarp has sides that are 13 meters long. What is the tarp’s perimeter?
Answers
Michaela makes $5.50 per hour at her job, How much does she make in an average eight-hour day?
Answers
Answer:
$44
Step-by-step explanation:
What we know:
$5.50 = 1 hour
average day's work = 8 hours
Question: How much money for eight hours?
To figure this out, 5.50 and multiply it by 8.
This gives us 44.
So, Michaela makes $44 dollars in an average eight-hour day.
The quantity (in pounds) of a gourmet ground coffee that is sold bya coffee company at a price of p dollars perpound is Q = f(p).
(a) What is the meaning of the derivative f '(8)?
therate of change of the price per pound with respect to the quantityof coffee sold when the price is $8 per pound
theamount of coffee needed to be sold to charge $8 perpound
noneof these are correct
therate of change of the price per pound with respect to the quantityof coffee sold
therate of change of the quantity of coffee sold with respect to theprice per pound when the price is $8 per pound
Answers
The meaning of the derivative f'(8) is the rate of change of the quantity of coffee sold with respect to the price per pound when the price is $8 per pound.
It represents how the quantity of coffee sold changes with respect to changes in the price per pound, when the price per pound is $8.
In mathematics, the derivative of a function is a measure of how the value of the function changes with respect to changes in one of its variables. In other words, the derivative gives the rate of change of a function with respect to its independent variable.
The derivative can be thought of as the slope of the tangent line to the function at a particular point. It can be calculated using limits, differential calculus, or other methods. The derivative is represented by the symbol "d/dx" for a function of a single variable x, where d/dx represents the rate of change of the function with respect to x.
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find a fraction equal to value of the decimal $0.23\overline{72}$. give your answer in simplest terms.
Answers
The fractional value for [tex]$0.23\overline{72}$[/tex] is 261 / 1100.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The decimal value is given as -
[tex]$0.23\overline{72}$[/tex]
To convert [tex]$0.23\overline{72}$[/tex] repeating into a fraction, begin writing this simple equation -
[tex]n=$0.23\overline{72}$[/tex] ..... (1)
Notice that there are 2 digits in the repeating block (72), so multiply both sides by 1 followed by 2 zeros, i.e., by 100.
[tex]100n=$0.2372\overline{72}$[/tex] .... (2)
Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.
[tex]100n-n=$0.2372\overline{72}$ - $0.23\overline{72}$[/tex]
[tex]99n = 23.49[/tex]
n = 23.49 / 99
n = 2349 / 9900
n = 261 / 1100
Therefore, the fraction is 261 / 1100.
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Zahar is planning to construct a fence for his garden and wants to estimate the total cost for the fencing. He represents his garden in a coordinate
plane in which each unit represents 2 feet.
The cost of fencing is $7.79 per foot. Find the perimeter of the garden and the total cost of fencing. For help, see this worked example
Type the correct answer in each box. Use numerals instead of words.
The perimeter is
The cost of the fencing is $
feet.
Answers
Answer:72 feet
$560.88
A newly hired lawyer receives a $15,000 signing bonus from a law firm and invests the money in a savings account at 4.75% interest. After 42 months, the lawyer checks the account balance. Part A: Calculate the interest earned, to the nearest dollar, if the interest is compounded quarterly. Show all work. (2 points) Part B: Calculate the interest earned, to the nearest dollar, if the interest is compounded continuously. Show all work. (2 points) Part C: Using the values from Part A and Part B, compare the interest earned for each account by finding the difference in the amount of interest earned. (1 point)
Answers
The amount when compounded quaterly and compounded continuously will be $16,979.44 and $17,713.02. And the difference is $733.58
What is continuous compounding?Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.
The equation is given as,
[tex]\rm P=P_o \times e^{rt}[/tex]
The initital amount is $15,000 and the interest rate is 4.75% annually.
A. If the interest is compounded quarterly. Then the amount is given as,
[tex]\rm A = \$15,000 \times \left (1 + \dfrac{0.0475}{4} \right)^{42/4}[/tex]
A = $15,000 x 1.1319
A = $16,979.44
B. if the interest is compounded continuously. Then the amount is given as,
[tex]\rm A = \$ 15,000 \times e^{0.0475 \times (42 / 12)}[/tex]
A = $15,000 x 1.1808
A = $17,713.02
C. The difference in the amount of interest earned is given as,
Differenece = $17,713.02 - $16,979.44
Differenece = $733.58
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What does 100 liters equal to 1
Answers
Answer:
100 liters is equal to 100,000 milliliters.
Step-by-step explanation:
there exist two complex numbers $c$, say $c 1$ and $c 2$, so that $3 2i$, $6 i$, and $c$ form the vertices of an equilateral triangle. find the product $c 1 c 2$ in rectangular form.
Answers
(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.
What is triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.
Here,
An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.
The distance between two complex numbers a + bi and c + di can be found using the formula:
√((c - a)² + (d - b)²)
So, the distance between 3-2i and 6-i is:
√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10
And the distance between 3-2i and c is:
√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)
Since these distances must be equal, we have:
√((c - 3)² + (c + 2)²) = √10
Squaring both sides:
(c - 3)² + (c + 2)² = 10
Expanding both sides:
c² - 6c + 9 + c² + 4c + 4 = 10
Combining like terms:
2c² + 10c + 5 = 10
Subtracting 10 from both sides:
2c² + 10c - 5 = 0
This is a quadratic equation, which can be solved using the quadratic formula:
c = (-b ± √(b² - 4ac)) / 2a
Where a = 2, b = 10, and c = -5. Plugging these values into the formula:
c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2
c = (-10 ± √(100 + 40)) / 4
c = (-10 ± √(140)) / 4
c = (-10 ± 10√2) / 4
So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.
The product of these two solutions is:
c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)
= (100 - 100√2 + 100) / 16
= (200 - 100√2) / 16
(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.
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• Question 8: An order for Maalox® reads like this: Take 5mL po 1hr a.c., 1hr p.c., and h.s.
How much does the patient take in one day?
Does anyone have full complete answer for this question? Thanks.
Answers
The patient takes 15mL of of Maalox® in one day.
How much does the patient take in one day?From the question, we have the following parameters that can be used in our computation:
Take 5mL po 1hr a.c., 1hr p.c., and h.s.
The order says:
Take 5mL of Maalox® 1 hour before meals (a.c.), 1 hour after meals (p.c.), and at bedtime (h.s.).Since there are three meals in a day (breakfast, lunch, and dinner),
Then the patient takes 5mL of Maalox® three times a day.
So, the patient takes 5mL * 3 = 15mL in one day.
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Please answer this.
Help Me
Answers
1. The two equations have different slopes.
2. The two equations have different intercepts.
3. The system of equations has one solution.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the initial amount.The number of solutions for a system of two linear functions is defined as follows:
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A sports statistician was interested in the relationship between game attendance (in thousands) and the number of wins for baseball teams. Information was collected on several teams and was used to obtain the regression equation y = 4.9x + 15.2, where x represents the attendance (in thousands) and y is the predicted number of wins. What is the predicted number of wins for a team that has an attendance of 17,000?
A. 83.3 wins
B. 98.5 wins
C. 258.4 wins
D. 263.3 wins
Answers
Notably, this response comes the nearest to choice A (83.3 wins). The right response is thus A.
What kind of a equation is that?A mathematical statement that shows the equivalence of two mathematical equations is what a solution in algebra means. For instance, the two numbers 3x + 5 and 14 make up the expression 3x + 5 = 14, which is separated by the sign "equal."
We can change x to 17 in the regression model y = 4.9x + 15.2 and calculate for y to get the number of victories for a squad with 17,000 spectators: y = 4.9(17) + 15.2 = 83.5
Consequently, 83.5 victories are expected for a squad with a 17,000-fan attendance.
To predict the number of wins for a team with an attendance of 17,000, we can substitute x = 17 into the regression equation y = 4.9x + 15.2 and solve for y:
y = 4.9(17) + 15.2 = 83.5
Therefore, the predicted number of wins for a team with an attendance of 17,000 is 83.5 wins.
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Calculate the expectation value of and for a particle in the state n = 5 moving in a one dimensional box of length 2.50 × 10−10. Is =2. Explain
Answers
The expectation values are <x> = 1.25 x 10⁻¹⁰ , <x²> = 2.07 x 10⁻²⁰
What is average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
We need to find expectation value of <x> and < x²>
average value for <x> is given by a/2 where a = length of box
hence <x> = ( (2.5 x 10⁻¹⁰) /2) = 1.25 x 10⁻¹⁰
hence <x²> = (1.25 x 10⁻¹⁰)² = 1.56 x 10⁻²⁰
<x²> = ( a/2 x 3.14 x n)² x ( 4 x 3.14² x n² /3 -2)
hence <x²> = ( 2.5 x 10⁻¹⁰ / 2 x 3.14 x 5)² x ( 4 x 3.14² x 5² /3 -2)
<x²> = 2.07 x 10⁻²⁰
<x²> is not equal to <x>²
The expectation values are <x> = 1.25 x 10⁻¹⁰, <x²> = 2.07 x 10⁻²⁰
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when the two countries did not specialize, the total production of chinos was 23 million pairs per day, and the total production of pistachios was 68
Answers
The total production of both countries when they did not specialize was 91 million / day.
Given the information that when the two countries did not specialize, the total production of chinos was 23 million pairs per day, and the total production of pistachios was 68, we can calculate the total production of both countries with the following equation:
Total Production = Chinos (23 million pairs / day) + Pistachios (68 million / day)
Therefore, the total production of both countries when they did not specialize was 91 million / day. This can be calculated as:
Total Production = 23 million pairs + 68 million = 91 million / day
Hence, the total production of both countries when they did not specialize was 91 million / day. This calculation can be represented by the following formula:
Total Production = Chinos (x) + Pistachios (y)
Where x = 23 million pairs and y = 68 million.
Therefore, the total production of both countries when they did not specialize was 91 million / day.
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Please help I will give Brainly
Answers
Answer:
Width of the rectangle is 19 Units
Step-by-step explanation:
24 = x(x-5)
24 = [tex]x^{2}[/tex] - 5x
[tex]x^{2}[/tex] - 5x - 24 = 0
x(x-24) + 1(x-24) = 0
(x-24)(x+1)=0
x= -1 , 24
x = 24 units
x - 5 = 19 units
Step-by-step explanation:
If you look at the picture above you'll see that after connecting the length, width and area you get a quadratic equation which I solved using formula method, but any method can be used to solve the quadratic equation. Also at the end you arrive at two answers which of course you select the positive one.
Oliver worked 9 months out of the year. What percent of the year did he work?
Answers
Answer:
75%
Step-by-step explanation:
We know
A year has 12 months
Oliver worked 9 months out of the year
What percent of the year did he work?
We take
9 divided by 12, time 100 = 75%
So, he works 75% of the year.
Help please I dont understand thank uuuu
Answers
A. The velocities are given as follows:
Devron: 45 miles per hour.Avery: 60 miles per hour.B. The graph is given by the image presented at the end of the answer.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
From the table, Devron's rate is given as follows:
k = 180/4
k = 45 miles per hour.
Hence the equation is of:
y = 45x.
For Avery's equation of y = 60x, the rate is of 60 miles per hour.
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Find a basis {p(x),q(x)} for the vector space {f(x) € P3[x] | f'(1) = f(1)} where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) = =
Answers
A basis {p(x),q(x)} for the vector space {f(x) € P3[x] | f'(1) = f(1)} where P3[x] is the vector space of polynomials in with degree less than 3. p(x) = ,q(x) = is {p(x) = x² - 1, q(x) = x² + x - 2}
Polynomial Space Basis SearchThe vector space {f(x) € P3[x] | f'(1) = f(1)} consists of polynomials of degree less than 3 with the property that their derivative at x = 1 is equal to the polynomial itself evaluated at x = 1. To find a basis for this space, we can start by finding a set of two polynomials that satisfy this property, and that are linearly independent.
One possible choice for p(x) is x² - 1, and one possible choice for q(x) is x² + x - 2. These polynomials satisfy the required property (i.e., their derivatives at x=1 are equal to the polynomials themselves evaluated at x=1), and they are linearly independent because their leading terms (x² in both cases) are distinct.
Thus, {p(x) = x² - 1, q(x) = x² + x - 2} is a basis for the vector space {f(x) € P3[x] | f'(1) = f(1)}.
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When making chocolate chip cookies, Jesse uses 2 1/4 cups of flour for every 5 dozen cookies. Enter the number of cups of flour Adriana uses for 10 dozen cookies. Show your work.
HELP ASAP
Answers
10 dozen = 2 1/4. Times 2