The next three questions use the Fibonacci numbers. These are defined recursively by f0 = 0, f1 = 1, and fn+2 = fn+1 =fn for all n ≥ 0.3. show that for all strictly positive integers n, we have f1 + f3 + ..... + f2n-1 = f2n
Answers
The given statement, f1 + f3 + ... + f2n-1 = f2n, asserts that the sum of every other Fibonacci number up to the (2n-1)th term is equal to the (2n)th Fibonacci number. This can be proven by induction.
5We will assume that the statement holds true for some arbitrary positive integer k and show that it holds for k+1 as well. By using the recursive definition of Fibonacci numbers and substituting the induction hypothesis, we can establish the equality for k+1. Since we have shown that the statement holds true for k=1, the induction step demonstrates that the statement is valid for all positive integers n.
To prove the statement f1 + f3 + ... + f2n-1 = f2n, we will use mathematical induction. We begin by establishing the base case, which is n=1. Plugging in n=1, we get f1 = f2, which is true according to the definition of Fibonacci numbers.
Next, we assume that the statement holds true for some arbitrary positive integer k, which means that f1 + f3 + ... + f2k-1 = f2k.
Now we need to show that the statement holds for k+1 as well. We start by adding f2k+1 to both sides of the equation:
f1 + f3 + ... + f2k-1 + f2k+1 = f2k + f2k+1
By the recursive definition of Fibonacci numbers, we can rewrite the right side of the equation as f2k-1 + f2k = f2k+1:
f1 + f3 + ... + f2k-1 + f2k+1 = f2k+1
Therefore, we have shown that if the statement holds true for k, it also holds true for k+1. Since we have established the base case (n=1) and shown the induction step, we can conclude that the statement f1 + f3 + ... + f2n-1 = f2n holds for all strictly positive integers n.
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Related Questions
Pre-Algebra Question There is an image below and please do everything that it says.
Answers
Answer:
P=20
Step-by-step explanation:
S=Ph+2B
96=4(P)+2(8)
96=4P+16
96-16=4P
80=4P
P=80/4
P=20
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
20x-8 ...last option
Step-by-step explanation:
What would be a sound, simple, straightforward way to describe IQR (Interquartile range)
Answers
Answer:
IQR: is the length of the middle 50% of that interval of space
Step-by-step explanation:
In order to find IQR, subtract the third interquartile range - the first interquartile range
A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42. They will pay $4 for each box of candy and $7 for each bag of popcorn. The system of inequalities graphed below represents this information. Which combination of boxes of candy and bags of popcorn could the group buy?
Answers
Answer:
3 boxes of candy will cost $12 and 4 bags of popcorn will cost $28, adding the two gives us $40. They are only allowed to spend 42 dollars
Step-by-step explanation:
What is the total area of the figure in square feet?
Enter your answer in the box.
Answers
The total area of the figure as shown in the image below is calculated as: 59 ft².
How to Find the Total Area of the Composite Figure?The figure can be decomposed into a trapezoid and a rectangle. Therefore:
Total area of the figure = area of trapezoid + area of rectangle.
Area of trapezoid = 1/2(a + b) * h
Base (a) = 4 1/2 = 4.5 ft
Base (b) = 9 1/2 = 9.5 ft
Height (h) = 7 - 4 = 3 ft
Substitute:
Area of trapezoid = 1/2(4.5 + 9.5) * 3 = 21 ft²
Area of rectangle = Length * width
Length = 9 1/2 = 9.5 ft
Width = 4 ft
Substitute:
Area of rectangle = 9.5 * 4 = 38 ft²
Total area = 21 + 38 = 59 ft²
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Graph y=3/4 x + 2y = 43x +2
Answers
The graph of the equation is shown in the attached image
How to graph the equation of a line?An equation of a line is a mathematical representation of the relationship between the variables x and y.
To plot the graph:
Using y =3/4 x + 2
find y when x = 0:
y =3/4 x + 2
y =3/4 (0) + 2
y = 2
This implies x = 0, y = 2
Also, find x when y = 0:
y =3/4 x + 2
0 = 3/4 x + 2
3/4 x = - 2
3x = -8
x = -8/3
This implies x = -8/3, y = 0
Thus, graph x = 0, y = 2 and x = -8/3, y = 0 as shown in the image attached
Therefore, the slope, y-intercept, and x-intercept of the graph are 2, 4 and -2 respectively
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Correct Question
Graph y=3/4 x + 2
The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is . Under this null hypothesis, the number of correct answers has a binomial distribution with trials and success probability . Perform a chi-square test of this hypothesis. Can you reject at the level? Use the -value method with the TI- Plus calculator.
Answers
Answer:
hmmmm if theres choices its B
PLEASE HURRY, LIMITED TIME EARLY!!!
Question-The center of circle A with equation (x – 7)2 + (y – 1)2 = 16 is mapped to the center of circle B with equation (x + 8)2 + (y – 2)2 = 16. Determine the translation needed for this mapping.
Answers-
A. (x, y) ⟶ (x - 15, y + 1)
B. (x, y) ⟶ (x - 12, y + 9)
C. (x, y) ⟶ (x - 8, y + 2)
D. (x, y) ⟶ (x + 15, y - 1)
Answers
The solution is Option A.
The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
Let the equation for the circle A be represented as
( x - 7 )² + ( y - 1 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )
Let the equation for the circle A be represented as
( x + 8 )² + ( y - 2 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )
So , the translation of circle A to B is given by
( 7 , 1 ) to ( -8 , 2 )
So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up
Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
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Check whether 25,464 is divisible by 6 or not
Answers
Answer:
Yes it is dibisible by 6.
Step-by-step explanation:
Because it is divisible by 2 and 3 and it is the divisibility of 6.
At the football game they sold $4 pizzas and $2 sodas which made the school$260 the number of Sodas sold was five more than three times a number of pizzas sold determine the amount of pizza and sodad sold
Answers
\(\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}\)
\(\Huge \textsf{Step-by-step explanation}\)
\(\LARGE \bold{\textsf{Step 1: Assign Variables}}\)
\(\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}\)
\(\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}\)
\(\large \bold{ \textsf{From the problem, we know that:}}\)
\(\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}\)
\(\large \bold{ \textsf{We can use this information to write two equations:}}\)
\(\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}\)
\(\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}\)
\(\LARGE \bold{\textsf{Step 3: Solve the system of equations}}\)
\(\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}\)
\(\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}\)
\(\large \textsf{Simplifying this expression gives us:}\)
\(\textsf{10\textit{p} + 10 = 260}\)
\(\large \textsf{Subtracting 10 from both sides:}\)
\(\textsf{10\textit{p} = 250}\)
\(\large \textsf{Dividing both sides by 10}\)
\(\textsf{\textit{p} = 25}\)
\(\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}\)
\(\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}\)
\(\large \textsf{So, 25 pizzas and 80 sodas were sold.}\)
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Suppose
f(x,y,z)=xyz 3
+e (y−x 2
)
(a) At the point
(−1,1,2)
, find the direction in which the maximum rate of change of
f(x,y,z)
occurs. (b) What is the maximum rate of change of the function at the point
(−1,1,2)
? Enter your answer in the blank blow. Round your answer to two decimal places. Your Answer:
Answers
(a) To find the direction in which the maximum rate of change of f(x,y,z) occurs at the point (-1,1,2), we need to find the gradient vector of f(x,y,z) at that point and normalize it.
The gradient vector of f(x,y,z) is given by:
∇f(x,y,z) =
Substituting (-1,1,2) into this equation, we get:
∇f(-1,1,2) = <-8e, 9, -1>
To normalize this vector, we need to divide each component by its magnitude:
||∇f(-1,1,2)|| = √(64e^2 + 81 + 1) = √(64e^2 + 82)
So the direction in which the maximum rate of change of f(x,y,z) occurs at (-1,1,2) is:
<-(8e/√(64e^2 + 82)), (9/√(64e^2 + 82)), -(1/√(64e^2 + 82))>
(b) The maximum rate of change of f(x,y,z) at (-1,1,2) is given by the magnitude of the gradient vector:
||∇f(-1,1,2)|| = √(64e^2 + 81 + 1) = √(64e^2 + 82)
Rounding this to two decimal places, we get:
Maximum rate of change = √(64e^2 + 82) ≈ 9.08
To find the direction of maximum rate of change of f(x,y,z) at point (-1, 1, 2), we need to compute the gradient of f. The gradient is a vector of partial derivatives with respect to each variable (x, y, z).
f_x = ∂f/∂x = yz - 2xe^(y-x^2)
f_y = ∂f/∂y = xz + e^(y-x^2)
f_z = ∂f/∂z = xy
Now, evaluate the gradient at the point (-1, 1, 2):
f_x(-1,1,2) = (1)(2) - 2(-1)e^(1-(-1)^2) = 2 + 2e^0 = 4
f_y(-1,1,2) = (-1)(2) + e^(1-(-1)^2) = -2 + e^0 = -1
f_z(-1,1,2) = (-1)(1) = -1
So, the gradient at point (-1, 1, 2) is <4, -1, -1>.
(a) The direction in which the maximum rate of change occurs is given by the gradient vector: <4, -1, -1>.
(b) To find the maximum rate of change, we calculate the magnitude of the gradient vector:
Magnitude = √(4^2 + (-1)^2 + (-1)^2) = √(16 + 1 + 1) = √18 ≈ 4.24
The maximum rate of change of the function at the point (-1, 1, 2) is approximately 4.24.
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In construction, the precision used to build a structure directly influences the strength of the structure. In the Rocky Mountains, many houses’ roofs are built using trusses, which are strong enough to support the heavy load from snow, but light enough to build in a stockyard and transport to the construction site. Chris works in the stockyard. He has been told he needs to build a series of trusses for a new house using the pattern below. He has also been told the pattern may be inaccurate—so he needs to check and make sure Describe the angles you would need to know to verify that BC¯, DE¯, and FG¯ are all parallel to each other, and CD¯, EF¯, and GH¯ are also parallel.
What could be an appropriate measure for ∠CDE? Be prepared to explain your choice for that angle. Use that measure to find all other angles involved.
Answers
An appropriate measure for ∠CDE would be
∠CDE = ∠ADE - ∠ADC
How to check for the appropriate measure of CDE.we have the following angles as parallel BC¯, DE¯, and FG¯ also CD¯, EF¯, and GH¯.
The angles that we have to check in order to measure would be
∠ABC, ∠AEG, ∠ADC, ∠AHG, ∠ADE, ∠AFE, ∠AHG.
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An object moves on a trajectory given by r(t)-(10 cos 2t, 10 sin 2t) for 0 t ?. How far does it travel?
Answers
Thus, the object travels a distance of 10π units along the given trajectory.
To find out how far an object travels along a given trajectory, we need to calculate the arc length of the curve. The formula for arc length is given by:
L = ∫_a^b √[dx/dt]^2 + [dy/dt]^2 dt
where L is the arc length, a and b are the start and end points of the curve, and dx/dt and dy/dt are the derivatives of x and y with respect to time t.
In this case, we have the trajectory r(t) = (10 cos 2t, 10 sin 2t) for 0 ≤ t ≤ π/2. Therefore, we can calculate the derivatives of x and y as follows:
dx/dt = -20 sin 2t
dy/dt = 20 cos 2t
Substituting these values into the formula for arc length, we get:
L = ∫_0^(π/2) √[(-20 sin 2t)^2 + (20 cos 2t)^2] dt
= ∫_0^(π/2) √400 dt
= ∫_0^(π/2) 20 dt
= 20t |_0^(π/2)
= 10π
Therefore, the object travels a distance of 10π units along the given trajectory.
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Solve the absolute value equation [x] - 2 = 5 to find the distance Mary can walk forward, x, in
5 seconds.
x = 7 m and x = -7 m
x=-3 m and x = 7 m
x = -7 m and x = 3 m
x = 3 m and x = -3 m
Answers
Answer:
the answer is x=7 and x=-7
Step-by-step explanation:
The area of a triangled Shaped sail on a boat is 62ft squared . The height is 8ft. What is the base?
Answers
Answer:
the base of the triangle is 15.5 ft
Step-by-step explanation:
A= h x b/2
62 ft = 8 × b/2
62/8 = b/2
7.75 = b/2
7.75 x 2 = b
15.5 = b
Mae raised $80 by selling boxes of cookies. Let
b represent the number of boxes of cookies sold.
Each box cost $2.50. Which equation should be
used to determine how many boxes of cookies
Mae sold?
A. 2.50+ b = 80
C. b÷ 2.50 = 80
B. b-2.50 = 80
D. 2.50b = 80
Answers
Answer: D
Step-by-step explanation: 2.50xb=80 b= 32 boxes
to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term. group of answer choices true false
Answers
to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement
we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.
So, For his purpose, we know that the
A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.
And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.
By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.
So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
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what's the nearest tenth of 98403
Answers
The nearest tenth of 98.403 is 98.4.
First, let us understand the round to the nearest tenth:
The tenth place value is the first number that appears first after the decimal point. To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth place.
We are given;
98.403
We need to find the nearest tenth of the number.
Let us check the hundredth number.
The hundredth number is 0, that is 0 < 5.
So, the number rounded to the nearest tenth is 98.4.
Thus, the nearest tenth of 98.403 is 98.4.
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Zion sun chairs manufacturers 3,575 beach chairs each month. Determine the minimum sales price Zion sun chairs must sell each chair for to earn a monthly profit of $55,000, if the total monthly fixed costs are $17,363. 50 and the variable cost per chair is $52. 17
Answers
main answer: the minimum sales price zion sun chairs for each char must be $41.64 to earn a monthly profit of $55,000
supporting answer:
what is profit?
the amount gained from any business activity When a shopkeeper sells a product, his motivation is to profit from the buyer.
body of the answer:
the total monthly fixed costs are $7363.50 and the variable cost per chair $52.17
the cost price isC(x)=17363.50+52.17*3575
profit function is P(x)=C(x)-s
P(x)=203871.25-3575x
55000=203871.25-3575x
3575x=148871.25
x=41.64
the minimum sales price zion sun chairs for each must be $41.64 to a monthly proft of $55000
final answer: the minimum sales price zion sun chairs for each char must be $41.64 to earn a monthly profit of $55,000
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The minimum sales price zion sun chairs for each char must be $41.64 to earn a monthly profit of $55,000
What is profit?
The amount gained from any business activity When a shopkeeper sells a product, his motivation is to profit from the buyer.
The total monthly fixed costs are $7363.50 and the variable cost per chair is $52.17
The cost price is C(x)=17363.50+52.17*3575
Profit function is P(x)=C(x)-s
P(x) = 203871.25-3575x
55000 = 203871.25-3575x
3575x = 148871.25
x = 41.64
The minimum sales price of zion sun chairs for each must be $41.64 to a monthly profit of $55000
The minimum sales price of zion sun chairs for each char must be $41.64 to earn a monthly profit of $55,000
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Tell whether the angles are adjacent or vertical. Then find the value
of x. i will mark brainliest!
Answers
3x-4= 107
-4. -4
3x= 103
/3. /3
X= 34.333333
4. Use substitution to solve the following system of equations. What is the value of y?
3x + 4y = 36
2x - y = 2
Oy-6
Oy=4
Oy=-6
Oy=.4
Answers
The value of y using the substitution method is 6.
There are two given equations:
3x + 4y = 36 equation 1
2x - y = 2 equation 2
In order to use the substitution method, make y the subject of the formula in equation 24
2x - 2 = y
Substitute for y in equation 1
3x + 4(2x -2) = 36
3x + 8x - 8 = 36
Combine similar terms
11x = 36 + 8
11x = 44
Divide both sides by 11
x = 4
Substitute for x in equation 2
2(4) - y = 2
8 - y = 2
y = 6
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Answer:y-6
Step-by-step explanation:
find a parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4x2 8x 9 y2 36(z 1)2
Answers
A parametric representation using spherical-like coordinates for the upper half of the ellipsoid is given by x2 = 9 + -2.25y2 + 0.25z2.
What is ellipsoid?
A sphere can be deformed into an ellipsoid by applying directional scalings, or more generally, an affine transformation, to it.
A quadric surface, or surface that can be described as the zero set of a polynomial of degree two in three variables, is an ellipsoid. An ellipsoid among quadric surfaces has one of the two characteristics listed below. Every cross section of a flat surface is either an ellipse, empty, or reduced to a single point (this explains the name, meaning "ellipse-like"). It can be contained in a sphere that is big enough because it is bounded.
Three pairwise perpendicular axes of symmetry intersect at an ellipsoid's center of symmetry, or the
According to our question-
To each side of the equation, add "-9y2".
4x2 + 9y2 + -9y2 + -1z2 = 36 + -9y2
combining similar terms 9y2 + -9y2 = 0
4x2 + 0 + -1z2 = 36 + -9y2
4x2 + -1z2 = 36 + -9y2
To either side of the equation, add "z2".
4x2 + -1z2 + z2 = 36 + -9y2 + z2
Hence, A parametric representation using spherical-like coordinates for the upper half of the ellipsoid is given by x2 = 9 + -2.25y2 + 0.25z2.
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Manuel wants to apply a new coat of varnish to the outside of his little
brother's toy chest. The toy chest is in the shape of a rectangular prism 4 feet
long, 3 feet wide, and 2.5 feet deep. One can of varnish costs $4.50 and overs
25 square feet.
What is the surface area, not including the bottom, of the outside of his little
brother's toy chest? How many cans of varnish need to be purchased to cover
the toy chest? Show your work and clearly explain how you determined your
answer.
Answers
About 3 cans of varnish need to be purchased to cover the toy chest.
PrismA prism is a 3-dimensional shape with two identical shapes facing each other.
Given that:
length (l) = 4 ft., width (w) = 3 ft. and height (h) = 2.5 ft.
The surface area of the prism (A) is given by:
A = 2(lh + lw + hw)
Substituting:
A = 2(4 * 3 + 4 * 2.5 + 3 * 2.5) = 59 ft²
1 can covers 25 ft², for 59 ft², number of cans = 59 ft²/25 ft² = 2.36
About 3 cans of varnish need to be purchased to cover the toy chest.
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HELP ME NO LINKS :( ........................
Answers
Answer:
-1
Step-by-step explanation:
y=y
x+5=-3x+1
x+3x=1-5
4x=-4
x=-4/4
x=-1
Determine which function has the greatest rate of change as x approaches infinity.A). f(x) = 2x − 8B). g(x) = 5x^2 − x + 7C). h(x) = 4^x − 6D). There is not enough information to determine the answer.
Answers
We need to find the derivative which is the rate of change
\(\begin{gathered} f^{\prime}(x)=2 \\ g^{\prime}(x)=10x\text{ - }1\text{ + 7} \\ g^{\prime}(x)=10x+6 \\ h^{\prime}(x)=4 \end{gathered}\)So, when x is infinite, the function g(x) has the greatest rate of change
Three factories produce the same tool and supply it to the market. Factory A produces 30% of the tools for the market and the remaining 70% of the tools are produced in factories B and C. 98% of the tools produced in factory A, 95% of the tools produced in factory B and 97% of the tools produced in factory C are not defective. What percent of tools should be produced by factories B and C so that a tool picked at random in the market will have a probability of being non defective equal to 96%?
Answers
The percent of tools should be produced by factories B and C so that a tool picked at random in the market will have a probability of being non defective equal to 96% = 0.96 are 5% and 95% respectively.
We have three factories produce the same tool and supply it to the market. Let's consider three events defined as, A = event for tools produced by factory A
B = event for tools produced by factory B
C = event for tools produced by factory C and N be the count that tools produced by all factories is not defective.
The probability that the tools produced by factory A for the market, P( A) = 30%
= 0.30
The probability that the tools produced by factories B and C for the market, P( B and C) = 70% = 0.70
The Probability that tools are non- defective and that are produced in factory A, P( N/A) = 98%
= 0.98
The Probability that tools are non- defective and that are produced in factory B, P( N/B) = 95%
= 0.95
The Probability that tools are non- defective and that are produced in factory C, P( N/C) = 97% = 0.97
Now, since only three factories supply to the whole market, then by probability law, P(A) + P(B) + P( C) = 1
=> 0.3 + P(B) + P( C) = 1
=> P(B) = 0.7 - P(C) --(1)
We have to determine percent of tools should be produced by factories B and C that is P(C) and P(B) when probability of non defective, P(N) is 96% = 0.96. From the law of total probability law, P(N) is written by, P( N) = P( N/A) P(A) + P( N/B) P(B) + P( N/C) P( C)
=> 0.96 = 0.98 × 0.3 + 0.95 × ( 0.7 - P(C) ) + 0.97 × P(C)
=> 0.96 = 0.98 × 0.3 + 0.95 × 0.7 - 0.95 P(C) + 0.97 × P(C)
=> 0.96 = 0.98 × 0.3 + 0.95 × 0.7 - 0.95 P(C) + 0.97 × P(C)
=> 0.96 = 0.294 + 0.665 + 0.02 × P(C)
=> 0.96 = 0.959 + 0.02 × P(C)
=> 0.02 × P(C) = 0.96 - 0.959
=> 0.02 × P(C) = 0.001
=> P(C) = 0.05 = 5%
from equation (1), P(B) = 1 - P(C)
=> P( B) = 1 - 0.05 = 0.95
Hence, required percentage is 95%.
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Find the domain and range og tje ff. Rational function f(x) = 2/x+1
Answers
The only case where it is not is when x+1=0 because x/0 is undefined.
Therefore, x≠-1
Meaning all values except -1 is a value of x;
(-infinity, -1) U (-1, +infinity)
Is 7164 divisible by 6?
yes?
no?
Answers
Answer:
yes
7164 is divisible bt 6
Answer:
Yes
Step-by-step explanation:
Any number will be divisible by 6 if they be divisible by 2 & 3
- we know 7164 is divisible by 2
- also any number which sum of their digits are divisible by 3, the number will be divisible by 3
in this case (7164) 7+1+6+4=18 & 18 is divisible by 3 so 7164 is divisible by 3 as well.
so 7164 is divisible by 6
(08.07 mc)
the table describes the quadratic function p(x). x p(x)
−1 31
0 17
1 7
2 1
3 −1
4 1
5 7
what is the equation of p(x) in vertex form?
p(x) = 2(x − 3)2 − 1
p(x) = 2(x + 3)2 − 1
p(x) = 3(x − 3)2 − 1
p(x) = 3(x + 3)2 − 1
Answers
The equation of p(x) in vertex form is: A. p(x) = 2(x − 3)² − 1.
How to determine the vertex form of a quadratic function?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Next, we would create a system of equation by using the data points provided in the table above;
a(-1)² + b(-1) + c = 31
a - b + c = 31 .....equation 1.
a(0)² + b(0) + c = 17
c = 17 .....equation 2.
a(1)² + b(1) + c = 7
a + b + c = 7 .....equation 3.
By solving the system of equations simultaneously, the values of a, b, and c are as follows;
a = 2
b = -12
c = 17
Therefore, the required quadratic function in vertex form is given by;
ax² + bx + c = 0
2x² - 12x + 17 = 0
p(x) = 2x² - 12x + 17
p(x) = 2(x² - 6x + (-6/2)²) + 18 - 17
p(x) = 2(x² - 3x - 3x + 9) - 1
p(x) = 2(x - 3)² - 1
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Please help me solve this equation please and thank you
Answers
Answer: (x, y) = (3, 4)
This is the same as saying x = 3 and y = 4 pair up together
======================================================
Explanation:
Subtract the equations straight down.
The x terms subtract to 5x (because -5x-(-10x) = -5x+10x = 5x)The y terms subtract to 0 (because 2y-2y = 0)The right hand side values subtract to 15 (because -7-(-22) = -7+22 = 15)After all that is said and done, we have this new equation
5x = 15
Divide both sides by 5 to get x = 3
Then we use this x value to find y
-5x+2y = -7
-5(3)+2y = -7
-15+2y = -7
2y = -7+15
2y = 8
y = 8/2
y = 4
Or,
-10x+2y = -22
-10(3)+2y = -22
-30+2y = -22
2y = -22+30
2y = 8
y = 8/2
y = 4
Either way, we end up with y = 4.
Overall, the solution as an ordered pair is (x, y) = (3, 4)
If you were to graph the two equations, they intersect at the location (3,4).
Answer:
Step-by-step explanation:
-5x + 2y = -7 --------------------(I)
-10x + 2y = -22 ------------------(II)
Multiply the whole equation (I) by (-1) and then add.
(I)*(-1) 5x - 2y = 7
(II) -10x+2y= -22 {Now add. y will be cancelled}
-5x = -15
x = -15/(-5)
x = 3
Plugin x = 3 in equation (I)
-5*3 + 2y = -7
-15 + 2y = -7
2y = -7 +15
2y = 8
y = 8/2
y = 4