The standard form of the given quadratic equation in factored form is
(x+2) (x-6) = x²-4x-12
(x-4) (x+3) = x²-x-12
(x-12) (X+1) = x²-11x-12
(x-3) (x+4) = x²+x-12
what are quadratic equations?
A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero
To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.
f(x) = (x+2) (x-6)
x²+2x-6x-12
x²-4x-12
similarly, the standard form of equations 2,3 and 4 are :
(x²-x-12)
(x²-11x-12)
(x²+x-12)
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Answer:
B, D, A, C
Step-by-step explanation:
f(x) = (x + 2)(x – 6)
✔ B
f(x) = (x – 4)(x + 3)
✔ D
f(x) = (x – 12)(x + 1)
✔ A
f(x) = (x – 3)(x + 4)
✔ C
What is 3.172 rounded to the nearest tenth?
3.2
3.3
3.7
3.8
Answer: 3.2
Step-by-step explanation: 3.2 is the answer because the number 7 is higher than 5. so the number 1 goes up by one, which that equals 3.2
Select the correct answer what are the solutions of this quadratic equation x^2+8x+3=0
Answer:
x= -4 + radical 13
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each quadratic function with its respective graph. Graph Functions Graph of quadratic functions on a coordinate plane. Upward parabola vertex is at (2, 1) in quadrant 1. Left slope at (1, 2), (0, 5) enters quadrant 3. Right slope is at (3, 2), (4, 5) in quadrant 1. arrow Both Graph shows downward parabola plotted on a coordinate plane. The parabola has vertex at (minus 1, 4). The parabola has left slope at (minus 3, 0) and right slope at (1, 0). arrowBoth Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (3, minus 4). The parabola has left slope at (1, 0) and right slope at (5, 0). arrowBoth
The correctly matched quadratic functions are given as follows:
Part A) The function of the First graph is f(x) = (x-3) (x + 1) Part B) The function of the Second graph is f(x) = -2 (x - 1) ( x + 3) Part C) The function of the Third graph is f(x) = 0.5(x - 6) (x + 2) What is a Quadratic Function?Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term.
Quadratic equations are another name for it. The quadratic equation has the following general form: ax2 + bx + c = 0.
How do we correctly match the graphs?Recall that:
f(x) - a (x -c) (x - d)
where
a is the leading coefficientc and d are the roots or zeros of the function.Part A) First graph
We are given to know
The solutions or zeros of the first graph are
x=-1 and x=3
The parabola open up, so the leading coefficient a is positive, the function therefore, is equal to
f(x) = (x-3) (x + 1); Find the value of the coefficient a.The vertex is equal to the point (1, -4)
Substitute and solve for a
-4 = a(1-3)(1+1)
-4 = a(-2)(2)
a = 1
Hence, the function is equal to f(x) = (x-3) (x + 1)
Part B) Second Graph
We are also given to know that
The solutions or zeros of the first graph are
x=-3 and x=1
The parabola open down, so the leading coefficient a is negative
The function is equal to f(x) = a (x-1)(x+3)
Find the value of the coefficient a
The vertex is equal to the point (-1,8)
to solve for a, we must substitute:
8 = a(-1-1) (-1+3)
8 = a(-2)(2)
a = -2
Hence, the function is equal to: f(x) = -2 (x - 1) ( x + 3)
Part C)
We are given to know that the solutions or zeros of the first graph are
x=-2 and x=6
The parabola open up, so the leading coefficient a is positive
The function is equal to f(x) = a(x-6) (x+2).
Find the value of the coefficient a
The vertex is equal to the point (2,-8)
We substitute and solve for a:
-8 = a(2-6) (2+2)
-8 = a(-4)(4)
a = 0.5
Hence, the function is equal to f(x) = 0.5(x - 6) (x + 2)
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Which of the following correctly uses absolute value to show the distance between -80 and 15?
O-80-1511-95| = -95 units
1-80+ 15| = |-65| = 65 units
O-80-15| = |-95| = 95 units
O-80 + 15| = |-65| = -65 units
Answer:
C
Step-by-step explanation:
|-80 - 15| = 95
The distance between -80 and 15 is 95
80 to 0 plus 15.
HELP Given the set of all odd integers from 1 to 81, what is the probability
of choosing a number that is a multiple of 9?
If you enter your answer as a decimal, round to the thousandths place.
Using it's concept, the probability of choosing a number that is a multiple of 9 is of 0.111.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
From 1 to 81, there are 81 numbers, of which 81/9 = 9 are multiples of 9, hence, considering that 81 is the number of total outcomes and that 9 is the number of desired outcomes, the probability is given the following division:
p = 9/81 = 1/9 = 0.111.
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What is the behavior of the graph y=x4−2x3−11x2+12x+36 at each of its zeros?
The behavior sees the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.
What is the behavior of the graph y=x4−2x3−11x2+12x+36 at each of its zeros?The behavior of the graph of the polynomial function f(x) as the variable x approaches either positive or negative infinity represents the end behavior of the function. The final behavior of a polynomial function's graph is determined by the degree of the function as well as the leading coefficient.
Generally, the equation for is zeros mathematically given as
y=x^4−2x^3−11x^2+12x+36
Therefore
(x+2)^2(x-3)^2=0
x=-2
x=3
since the graph attached has a positive leading coefficient and a positive degree
In conclusion, If the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.
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a) The line of y = 2x + 7 meets the y-axis at A.
write down the co-ordinates of A,
b) A line parralel to y = 2x + 7 passes through B(0,3)
Find the equation of this line.
(ii) C is the point on the line y = 2x + where x = 2
Find the the co-ordinates of the midpoint of BC
a) The coordinates of point A that meet the linear equation y = 2 · x + 7 are A(x, y) = (0, 7).
b) The equation of the line parallel to the line y = 2 · x + 7 is the line y = 2 · x + 3.
c) The coordinates of the midpoint of line segment BC is M(x, y) = (1, 7).
How to analyze linear equations
Herein we find three cases related to the linear equation y = 2 · x + 7. a) We need to determine the coordinates of point A, the y-coordinate can be determined by evaluating the function:
y = 2 · 0 + 7
y = 0 + 7
y = 7
The coordinates of point A that meet the linear equation y = 2 · x + 7 are A(x, y) = (0, 7).
b) Two lines are parallel to each other whether both have the same slope but different intercept. Then, the new line is of the form:
y = 2 · x + b
Now we proceed to find the intercept of the line:
b = y - 2 · x
b = 3 - 2 · 0
b = 3
The equation of the line parallel to the line y = 2 · x + 7 is the line y = 2 · x + 3.
c) The coordinates of point C is:
y = 2 · 2 + 7
y = 11
If we know that B(x, y) = (0, 3) and C(x, y) = (2, 11), then the coordinates of the midpoint of BC is:
M(x, y) = 0.5 · B(x, y) + 0.5 · C(x, y)
M(x, y) = 0.5 · (0, 3) + 0.5 · (2, 11)
M(x, y) = (1, 7)
The coordinates of the midpoint of line segment BC is M(x, y) = (1, 7).
RemarkThe statement presents typing mistakes and omissions, complete form is shown below:
a) The line of y = 2x + 7 meets the y-axis at A, where x = 0. Write down the co-ordinates of A.
b) A line parralel to y = 2x + 7 passes through B(x, y) = (0,3) Find the equation of this line.
c) C is the point on the line y = 2x + 7 where x = 2. Find the the co-ordinates of the midpoint of BC.
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If the top ten nations were randomly selected to march, one after another, into the stadium at the closing ceremonies, in how many ways could the nations have marched in?
Step-by-step explanation:
1. Entrance of Head of State and IOC President
2. Playing of the national anthem
3. The parade of the athletes
4. The symbolic release of doves
5. Olympic Laurel Award
6. Official Speeches
7. Opening of the Games
8. Raising the Olympic flag and playing the Olympic Anthem
9. Athletes, judges and coaches’ oath
10. Lighting of the Olympic flame
11. The artistic programme
number 14 part 1 pls
Given
[tex]7 - px - x^2 = 16 - (q + x)^2[/tex]
expanding the right side gives
[tex]7 - px - x^2 = 16 - (q^2 + 2qx + x^2)[/tex]
[tex]7 - px - x^2 = 16 - q^2 - 2qx - x^2[/tex]
Two polynomials of equal degree are the same if their coefficients are identical. This means
[tex]\begin{cases}16 - q^2 = 7 \\ -2q = -p\end{cases}[/tex]
[tex]16 - q^2 = 7 \implies q^2 = 9 \implies q=\pm3[/tex]
[tex]-2q = -p \implies p = 2q = \pm6[/tex]
Both [tex]p[/tex] and [tex]q[/tex] are positive, so [tex]\boxed{p=6}[/tex] and [tex]\boxed{q=3}[/tex].
find the perimeter ( will mark u brainliest for right answer)
The perimeter of the triangle is 56.4 units.
How to find the perimeter of a triangle?The perimeter of the triangle can be found as follows:
The perimeter of a figure is the sum of the whole sides. Therefore, the perimeter of a triangle is the sum of the three sides.
perimeter of a triangle = x + y + z
where
x, y and z are the three sides of the triangle.Therefore,
perimeter of the triangle = 19.8 + (9.8 + 8.4) + (8.4 + (19.8 - 9.8))
perimeter of the triangle = 19.8 + 18.2 + 18.4
perimeter of the triangle = 56.4
perimeter of the triangle = 56.4 units
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graph the linear equation by plotting three points. 2y=-3+2
Answer:
Step-by-step explanation:
Convert 2y=-3x+2 into y=mx+b form
[tex]\frac{2y}{2} =\frac{-3x+2}{2}[/tex]
[tex]y=\frac{-3x}{2} +1[/tex]
Y intercept is 1, slope is -3/2
Graph looks like this:
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the
nearest hundredth.
The answer is 48π units³ or 150.72 units³.
To find the volume of the cone, use the formula : 1/3 × πr²h
We are given that r = 6 and h = 4.
Solving :
V = 1/3 × π × 6² × 4V = 12 × 4 × πV = 48π units³ (in terms of π)V = 150.72 units³If f(x + 1) = x + 2 then f(x - 1) is
Answer: [tex]\Large\boxed{f(x-1)=x}[/tex]
Step-by-step explanation:
Given function
f(x + 1) = x + 2
Isolate [ x + 1 ] on the right-hand side
f(x + 1) = x + 1 + 1
f(x + 1) = (x + 1) + 1
Substitute [ x + 1 ] with x
f(x) = x + 1
Substitute [ x ] with [ x - 1 ]
f(x - 1) = (x - 1) + 1
[tex]\Large\boxed{f(x-1)=x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Complete the point-slope equation of the line through (-2,6) (1,1)
Use exact numbers.
y-6=??
Answer:
y-6= -5/3(x+2)
Step-by-step explanation:
the general way to write it is y-y1 = m(x-x1), so i plugged in the values
y1 = 6, x1 = -2
m = (y2-y1)/(x2-x1) = -5/3
The periodic time, t, of a pendulum varies directly as the square root of its length, l. t = 6 when l = 9. find t when l = 25.
The periodic time, t, of a pendulum range directly as the square root of its length, l. t = 6 when l = 9. If l = 25 then the periodic time, T exists at 10.
What is periodic time?The period, or periodic time, of a periodic variation of a quantity, exists described as the time interval between two consecutive repetitions.
Given: The periodic time, t, of a pendulum goes directly as the square root of its length, l if t = 6 when l = 9.
If [tex]T \alpha\ l^2[/tex] then [tex]T^2[/tex] α [tex]\sqrt{l}[/tex]
[tex]T^2 = l[/tex]
Let, [tex]T^2 = kl,[/tex] where k exists constant
t = 6 when l = 9.
So, [tex]6^2 = k*9[/tex]
[tex]k = 6^2/9 = 4[/tex]
[tex]T^2 = 4*l[/tex]
If l = 25
[tex]T^2 = 4 * 25 = 100[/tex]
[tex]T = \sqrt{100}[/tex]
T = 10
Therefore, the periodic time, T exists 10.
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Drag the tiles to the boxes to form correct pairs. match each pair of polynomials to their sum. 12x2 3x 6 and −7x2 − 4x − 2 −2x − 2 2x2 − x and −x − 2x2 − 2 2x2 x x2 2 and x2 − 2 − x 2x2 9x − 2 x2 x and x2 8x − 2 5x2 − x 4
The sum of each of the 4 polynomials and their answers are respectively;
12x² + 3x + 6 + (-7x²) – 4x – 2 = 5x² - x + 4
(2x² - x) + (-x – 2x² – 2) = -2x - 2
(x³ + x² + 2) + (x² – 2 - x³) = 2x²
(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2
How to find the sum of Polynomials?
1) We want to find the sum of the polynomials (12x² + 3x + 6) and (-7x² – 4x – 2). Thus, we have;
12x² + 3x + 6 + (-7x²) – 4x – 2
= 5x² - x + 4
2) We want to find the sum of the polynomials (2x² - x) and (-x – 2x² – 2). Thus, we have;
(2x² - x) + (-x – 2x² – 2)
= -2x - 2
3) We want to find the sum of the polynomials (x³ + x² + 2) and (x² – 2 - x³). Thus, we have;
(x³ + x² + 2) + (x² – 2 - x³)
= 2x²
4) We want to find the sum of the polynomials (x² + x) and (x² + 8x - 2). Thus, we have;
(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2
The sum of each of the 4 polynomials and their answers are respectively;
12x² + 3x + 6 + (-7x²) – 4x – 2 = 5x² - x + 4
(2x² - x) + (-x – 2x² – 2) = -2x - 2
(x³ + x² + 2) + (x² – 2 - x³) = 2x²
(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2
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[tex]3y - 5x = 10[/tex]
Find the gradient of the linear relation
Isolate y
3y=5x+10y=5/3x+10/3Compare to slope intercept form y=mx+b
Slope=m=5/3
Answer:
[tex]\dfrac{5}{3}[/tex]
Step-by-step explanation:
To find the gradient (slope) of the given linear relation, use arithmetic operations to isolate y:
Given relation:
[tex]3y-5x=10[/tex]
Add 5x to both sides:
[tex]\implies 3y-5x+5x=10+5x[/tex]
[tex]\implies 3y=5x+10[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
[tex]\implies y=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
Slope-intercept form of a linear equation
[tex]y = mx+b[/tex]
where:
m is the slope (gradient)b is the y-interceptComparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.
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Most air travelers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less to handle than paper ticketing. However, in recent times the airlines have received complaints from passengers regarding their e-tickets, particularly when connecting flights and a change of airlines were involved. To investigate the problem, an independent watchdog agency contacted a random sample of 20 airports and collected information on the number of complaints the airport had with e-tickets for the month of March. The information is reported below.
14 14 16 12 12 14 13 16 15 14
12 15 15 14 13 13 12 13 10 13
A) What assumption is necessary before conducting a test of hypothesis?
B) What is the decision rule?
Reject H0: ? ? 15 and accept H1: ? < 15 when the test statistic is
Less than or Greater than (pick one)
C) Compute the test statistic:
D) Reject or accept the null hypothesis?
The assumption that is necessary before conducting a test of hypothesis is that there is a significant amount of complaints for use of e-tickets.
How to illustrate the information?The assumption is that there is a significant amount of complaints for use of e-tickets.
H0: there is a significant amount of complaints for use of e-tickets.
H1: Number of complaints for use of e-tickets is not significant.
H1: parameter > value
Notice the inequality points to the right
Decision Rule: Reject H0 if test statistic > critical value
Decision Rule: Reject H0 if p -value = 0.05
The hypothetical mean is 15.00 and The actual mean is 13.50
The difference between these two values is -1.50.
The sample size is 20
Mean 13.50
SD 1.50
The test statistic will be -4.459.
Lastly z it's important to reject the null hypothesis since the test statistic is greater than the critical value of 1.7291.
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The sum of 2 numbers is 73, and their difference is 11.
Find the numbers.
Answer: 42 and 31
Step-by-step explanation:
Let x be one number and y be the other.
We will write mathematical equations for these two numbers.
The sum of 2 numbers is 73.
x + y = 73
Their difference is 11.
x - y = 11
See attached for the graph.
The point of intersection is our solution.
Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x.
What is the value of x?
The value of x from the given diagram is 20
Triangular altitude theoremAccording to theorem, the right triangle altitude theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.
Using the theorem above;
RT^2 = 9 * 16
RT^2 = 144
R = 12 units
Determine the value of x using the Pythagoras theorem;
x² =12² + 16²
x² = 144 + 256
x² = 400
Take the square root of both sides
x = √400
x = 20
Hence the value of x from the given diagram is 20
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Find the error with subject-verb agreement. select the incorrect verb and type it correctly. on the ledge there is three potted geraniums that desperately need water. however the hanging ferns in the living room are thriving.
Answer:
Step-by-step explanation:
ggggggg
An observer (o) spots a plane (p) taking off from a local airport and flying at a 33° angle horizontal to her line of sight and located directly above a tower (t). the observer also notices a bird (b) circling directly above her. if the distance from the plane(p) to the tower (t) is 7,000 feet, how far is the bird (b) from the plane (p)? round to the nearest whole number. two parallel lines bp and ot with a transversal running through p and o. dotted red line from p to t and from b to o. angle pot is 33 degrees. the length of p t is 7000. the length of bp is x. 3,815 feet 5,873 feet 8,343 feet 10,779 feet
The distance between the bird (B) and plane (P) exists at 10,779 feet.
How to estimate the distance between the bird (B) and plane (P)?
Given the figure attached,
PT = OB = 7000 ft
PB = OT = x feet
and angle of elevation (∠POT) = 30°
By applying the Tan rule in the triangle POT,
tan 33° = Opposite side/Adjacent side = PT/OT
tan 33° = 7000/x
x = 7000/tan33°
x = 10779 feet
The distance between the bird (B) and plane (P) exists at 10,779 feet.
Therefore, the correct answer is option D. 10779 feet.
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Evaluate the following integral (Calculus 2) Please show step by step explanation!
Answer:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x=-\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
Using Integration by parts:
[tex]\textsf{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]
[tex]\textsf{Let }\dfrac{\text{d}v}{\text{d}x}=x^{-8} \implies v=-\dfrac{1}{7}x^{-8+1}=-\dfrac{1}{7}x^{-7}=-\dfrac{1}{7x^7}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x & = -\dfrac{1}{7x^7}\ln x- \int -\dfrac{1}{7x^7} \cdot \dfrac{1}{x}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7x^8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7}x^{-8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}-\dfrac{1}{7 \cdot 7}x^{-8+1}+\text{C}\\\\& = -\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
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Substitute [tex]y=\ln(x) \iff e^y = x[/tex] and [tex]dy=\frac{dx}x[/tex] to get
[tex]\displaystyle \int \frac{\ln(x)}{x^8} \, dx = \int ye^{-7y} \, dy[/tex]
Integrate by parts with
[tex]u = y \implies du = dy[/tex]
[tex]dv = e^{-7y} \, dy \implies v = -\dfrac17 e^{-7y}[/tex]
Then
[tex]\displaystyle \int u\,dv = uv - \int v\,du \\\\ \implies \int y e^{-7y} \, dy = -\dfrac17 ye^{-7y} + \frac17 \int e^{-7y} \, dy + C \\\\ ~~~~~~~~~~~~ = -\frac17 ye^{-7y} - \frac1{49} e^{-7y} + C \\\\ ~~~~~~~~~~~~ = \boxed{-\frac{\ln(x)}{7x^7} - \frac1{49x^7} + C}[/tex]
to make purple he must mix red and blue in ratio 5:3 if he uses 3.5 liters of red paint how much blue paint should he use
Answer:
2.1 litres
Step-by-step explanation:
the 5 part of the ratio refers to 3.5 litres of red paint
divide this amount by 5 to find the value of one part of the ratio
3.5 litres ÷ 5 = 0.7 litres ← value of 1 part of the ratio , then
3 parts = 3 × 0.7 litres = 2.1 litres ← amount of blue paint used
is (n x (n +1)) / 2 the same as (n/2)(n+1)
Answer:
nope
Step-by-step explanation:
simplify the first equation
Answer:
yes
Step-by-step explanation:
The associative and commutative properties of multiplication allow you to rearrange the product to the form shown in the question.
Division by 2 is effectively multiplication by 1/2.
[tex](n\times(n+1))/2\qquad\text{given}\\\\=\dfrac{n(n+1)}{2}=\dfrac{n}{2}(n+1)\\\\=\boxed{(n/2)(n+1)}[/tex]
__
Additional comment
Evaluation of the expressions according to the order of operations will proceed differently for the two expressions.
For the first expression, evaluation steps are ...
add 1 to nmultiply the sum by ndivide the product by 2For the second expression, evaluation steps are ...
divide n by 2add 1 to nmultiply the results of these two operationsAs we said above, the properties of multiplication ensure the results are the same either way.
As a practical matter, for integer values of n, one of n and (n+1) will be even. It is usually convenient to divide the even number by 2. This means the evaluation might be ...
((n+1)/2)n . . . . for odd n(n+1)(n/2) . . . . for even nFor certain computer representations of the numbers, results may differ depending on the specific numbers and the order of evaluation.
Use theorem 7. 4. 2 to evaluate the given laplace transform. do not evaluate the convolution integral before transforming. (write your answer as a function of s. ) ℒ t et − d 0
With convolution theorem the equation is proved.
According to the statement
we have given that the equation and we have to evaluate with the convolution theorem.
Then for this purpose, we know that the
A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.
And the given equation is solved with this given integral.
So, According to this theorem the equation becomes the
[tex]\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).[/tex]
Then after solving, it become and with theorem it says that the
[tex]\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .[/tex]
Hence by this way the given equation with convolution theorem is proved.
So, With convolution theorem the equation is proved.
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please help on this geometry question
Angles are said to be produced whenever two or more straight lines intersect. Some types of angles are right angle, obtuse angle, acute angle, etc. Thus, the required proof is stated below:
Prove: <A > <C
<B > <D
An obtuse angle is a given angle that is greater than [tex]90^{o}[/tex] but less than [tex]180^{o}[/tex]. While an acute angle is a given angle that is less than [tex]90^{o}[/tex].
Thus extend AB to F, such that BF = CD.
Draw a perpendicular from a to intersect CD at point E.
So that;
<BAD = <BAE + <DAE (addition property of an angle)
Such that;
<A is an obtuse angle, while <C is an acute angle. Thu,
<A > <C (different types of angles)
Also,
<ADC = <CDF - <ADF (subtraction property of angles)
But both angles B and D are acute angles.
So that;
<B > <C (comparison of measures of two angles)
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JDIDJRJDJF PLS HELP IM STUCK
Step-by-step explanation:
we have
B = J + 2
as the number of laps Bill ran.
to get the number of laps Jill ran we need to transform this equation, so that we get
J = ...
or
... = J
J has to be on one side, and the rest on the other (just as it is with B = ...).
so,
B = J + 2
B - 2 = J
or
J = B - 2
hey ! we are finished already !
What is the slope of a line that is perpendicular to the line whose equation is ax by=c?
Answer:
b/a
Step-by-step explanation:
Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).
In the equation
ax + by = c,
the slope of the line is
-a/b
If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.
by = -ax +c
y = -a/b x + c/b
The slope is -a/b
So a perpendicular line would be opposite sign and flipped, b/a
If six cans of soda cost nine dollars, how much would it cost for 8 cans.
Answer:
Solution:
here,
6 cans cost = 9 dollars
1 can costs = 9÷6 dollars
= 1.5 dollars
Now,
8 cans cost = 8×1.5 dollars
= 12 dollars
