Answer: The function is EVEN.
Step-by-step explanation:
For this exercise it is important to remember that:
1. A function f(x) is even if and only if:
[tex]f(-x) = f(x)[/tex] for all "x"
2. A function f(x) is odd if and only if:
[tex]f(-x) = -f(x)[/tex] for all "x"
So knowing that, and given the following function k(x):
[tex]k(x)=x^6 - x^2 + 7[/tex]
You can plug [tex]-x[/tex] in for "x", order to know if this is even. Then, you get:
[tex]k(-x)=(-x)^6 - (-x)^2 + 7\\\\k(-x)=x^6-x^2+7[/tex]
Therefore, since:
[tex]f(-x) = f(x)[/tex]
You can determine that that the given function [tex]k(x)=x^6 - x^2 + 7[/tex] is Even.
How do u solve
1×-2y=4
-1×+10y=8
Answer: x = -8 ; y = -6
Step-by-step explanation:
1*x-2*y=4
1*x = 4 + 2*y
x = 4 + 2*y
Now you replace the value of x on the following equation:
-1*x+10*y=8
-1*(4 + 2*y) = 8
-4 - 2*y = 8
-2*y = 8+4
-2*y = 12
y = -12/2
y = -6
You replace the value of y in the previous equation:
x = 4 + 2*y
x = 4 + 2*(-6)
x = 4 - 12
x = -8
x-3=5 what does x equal
Answer:
8
Step-by-step explanation:
x-3=5
add the 3 to both sides of the equal sign
x-(3+3)=(5+3)
x=8
Answer: X = 8
Step-by-step explanation: To solve for x in this equation, we want to get x by itself on the left side of the equation. Since 3 is being subtracted from x, to get x by itself, we need to add 3 to the left side of the equation. If we add 3 to the left side, we must also add 3 to the right side.
Notice that on the left side -3 and +3 cancel each other out so we're simply left with x. On the right side, 5 + 3 gives us 8 so we have x = 8.
We can check our answer by substituting 8 back into the original equation. So we have (8) - 3 = 5 or 5 = 5 which is a true statement so our answer is correct.
A point is reflected across the x-axis the new point is (-7.5, 6) what is the difference between the two points
Answer:
The y-coordinate of the original point is negative and the y-coordiinate of the new point is positive.
The transformation is:
[tex](-7.5, 6)[/tex] → [tex](-7.5, -6)[/tex]
Step-by-step explanation:
For this exercise it is important to remember the definition of "Reflection".
A Reflection is a transformation that consists in folding an figure over a line called "Line of reflection",
In tranformations, the original figure is called "Pre-image" and the figure obtained after the transdformation is called "Image".
Given a point [tex](x,y)[/tex], if this is reflected across the x-axis, the x-coordinate of the point does not change, but the sign of the y-coordinate is transformed into its opposite. Then:
[tex](x,y)[/tex] → [tex](x,-y)[/tex]
So, given the new point:
[tex](-7.5, 6)[/tex]
You can determine that the original point is:
[tex](-7.5, -6)[/tex]
Simpify pls help
(x^7)^2
Answer:
x^14
Step-by-step explanation:
(x^7)^2=x^7×2
=x^14
Write the expression that represents the phrase,
"two times the difference of a number and 17."
Use x as the variable.
Answer:
2x + 17
Step-by-step explanation:
Answer:
2(x-17).
Step-by-step explanation:
The given phrase is "two times the difference of a number and 17."
We need to find the expression for given phrase.
Let x be the unknown variable.
Difference is denoted by "-" symbol.
Time is denoted by "×" symbol.
Difference of a number and 17 = x-17
Two times the difference of a number and 17 = 2×(x-17) = 2(x-17)
Therefore, the required expression is 2(x-17).
Kendra works 20 hours each week. So far this week, she has worked 5.5 hours on Tuesday and 5.25 hours on Thursday. Which sentence
could be used to find h, the number of hours remaining for Kendra to work this week?
A. 5.5 +5.25 = h + 20
B. 5.5 +5.25 = h x 20
c. h= 20 - (5.5 +5.25)
D. h-5.5+5.25 = 20. E. h= 20 - 5.5 +5.25
Answer:
Step-by-step explanation:
she works 20 hrs each week....so far, she has worked 5.25 hrs and 5.5 hrs
h = hours remaining
so we are basically taking the total hrs and subtracting the combined hrs she has worked
h = 20 - (5.5 + 5.25) <== ur equation
The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).
What is the expression?
An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Kendra works 20 hours each week. So far this week, she has worked 5.5 hours on Tuesday and 5.25 hours on Thursday.
Let h be the number of hours remaining for Kendra to work this week.
The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is;
A number of hours remaining for Kendra to work this week = Total number of hours - working on Tuesday - working on Thursday.
h = 20 - 5.5 - 5.25
h = 20 - (5.5 + 5.25)
Hence, the sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).
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Please answer if you know the solution. Thx
Answer:
the first blank is 10
and the second blank is 5
Step-by-step explanation:
Find an equation of the line satisfying the given conditions. Write the equation in standard form. Horizontal; through ( 3,6)
Answer:
Step-by-step explanation:
A horizontal line has the equation "y = " something, while a vertical line has the equation "x = " something. If our line is horizontal through (3, 6), it will be horizontal through the y coordinate (and vertical through the x coordinate). Our equation is y = 6
(The vertical equation through this point would be x = 3, just so you understand what I meant above.)
write two division equations for each multiplication equation.
a. 15 x 2/5=6
b. 6 x 4/3=8
c. 16 x 7/8=14
Two division equations were found for each given multiplication equation. The division equations are the inverse of the multiplication equations, essentially reversing the operation.
Explanation:The goal is to find two division equations that correspond to each given multiplication equation. Basically, we are undoing or reversing the multiplication operation.
a. 15 x 2/5 = 6
First Division Equation: 6 ÷ 15 = 2/5Second Division Equation: 6 ÷ 2/5 = 15b. 6 x 4/3 = 8
First Division Equation: 8 ÷ 6 = 4/3Second Division Equation: 8 ÷ 4/3 = 6c. 16 x 7/8 = 14
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besides spectators the capacity limit of victory stadium includes players, news reporters and stadium workers.how many nonspectators could be at a sold-out game
Answer:
Victoria Stadium
Step-by-step explanation:
Answer:
whats the answer
Step-by-step explanation:
If 32x+1 - 3x+5, what is the value of x?
оооо
Answer:
x = [tex]\frac{4}{35}[/tex]
Step-by-step explanation:
Given
32x + 1 = - 3x + 5 ( add 3x to both sides )
35x + 1 = 5 ( subtract 1 from both sides )
35x = 4 ( divide both sides by 35 )
x = [tex]\frac{4}{35}[/tex]
Answer:
[tex]x = \frac{ - 6}{29} [/tex]
Step-by-step explanation:
[tex]32x + 1 - 3x + 5[/tex]
Collect like terms
[tex]32x - 3x + 1 + 5[/tex]
[tex] 29x + 6[/tex]
For simplifying, equate the expression to zero. Thus,
[tex]29x + 6 = 0[/tex]
Add -6 to both sides of the equation
[tex]29x + 6 - 6 = 0 - 6[/tex]
[tex]29x = - 6[/tex]
Divide through by 29
[tex] \frac{29x}{29} = \frac{ - 6}{29} [/tex]
[tex]x = \frac{ - 6}{29} [/tex]
what is
7/4 times 10
Answer: 17.5 hope this helps
the answer is 17.5
:D
Can someone help me with these problems? I'm in k12 and this assignment was in classkick, so if anyone already completed this and can help, please do. I also am going to be asking some more questions, if you can help with those too. Thanks! (Will give brainliest.)
PLEASE HELP ME!
SOLVING QUESTIONS FROM 1ST PAGE
Given the point B(-5, 0)y = -3x - 5
Putting x = -5, and y = 0 in y = -3x - 5
0 = -3(-5) - 5
0 = 15 - 5
0 = 10 ∵Putting B(-5, 0) in y = -3x - 5 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
Given the point C(-2, 1)y = -3x - 5
Putting x = -2, and y = 1 in y = -3x - 5
1 = -3(-2) - 5
1 = 6 - 5
1 = 1 ∵Putting C(-2, 1) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
Given the point D(-1, -2)y = -3x - 5
Putting x = -1, and y = -2 in y = -3x - 5
-2 = -3(-1) - 5
-2 = 3 - 5
-2 = -2 ∵Putting D(-1, -2) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
SOLVING QUESTIONS FROM 2ND PAGE
Given the point B(6, 18)y = -2x + 18
Putting x = 6, and y = 18 in y = -2x + 18
18 = -2(6) + 18
18 = -12 + 18
18 = 6 ∵Putting B(6, 18) in y = -2x + 18 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
Given the point C(9, 24)y = 2x + 6
Putting x = 9, and y = 24 in y = 2x + 6
24 = 2(9) + 6
24 = 18 + 6
24 = 24 ∵Putting C(9, 24) in y = 2x + 6 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
SOLVING QUESTIONS FROM 3RD PAGE
Given the point D(2, 7)y = 3x + 4
Putting x = 2, and y = 7 in y = 3x + 4
7 = 3(2) + 4
7 = 6 + 4
7 = 10 ∵Putting D(2, 7) in y = 3x + 4 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
SOLVING QUESTIONS FROM 4th PAGE
b. Which function could have produced the values in the table.
A. y = 3x + 4
B. y = -2x + 18
C. y = 2x + 6
D. y = x + 9
The Table:
x y
3 12
6 18
9 24
Checking A) y = 3x + 4
Putting (3, 12), (6, 18) and (9, 24) in y = 3x + 4
For (3, 12)
y = 3x + 4
12 = 3(3) + 4
12 = 13 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (6, 18)
18 = 3(6) + 4
18 = 18 + 4
18 = 22 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (9, 24)
24 = 3(9) + 4
24 = 27 + 4
24 = 31 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
So, the equation y = 3x + 4 could have not produced the all values in the table as the the ordered pairs in table do not satisfy(equate) the equation.
Checking B) y = -2x + 18
Putting (3, 12), (6, 18) and (9, 24) in y = -2x + 18
For (3, 12) ⇒ y = -2x + 18 ⇒ 12 = -2(3) + 18 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = -2x + 18 ⇒ 18 = -2(6) + 18 ⇒ 18 = 6 ⇒ L.H.S ≠ R.HSFor (9, 24) ⇒ y = -2x + 18 ⇒ 24 = -2(9) + 18 ⇒ 18 = 0 ⇒ L.H.S ≠ R.HSSo, y = -2x + 18 could have not produced all the values in the table, as (6, 18) does not equate the equation.
Checking C) y = 2x + 6
Putting (3, 12), (6, 18) and (9, 24) in y = 2x + 6
For (3, 12) ⇒ y = 2x + 6 ⇒ 12 = 2(3) + 6 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = 2x + 6 ⇒ 18 = 2(6) + 6 ⇒ 18 = 18 ⇒ L.H.S = R.HSFor (9, 24) ⇒ y = 2x + 6 ⇒ 24 = 2(9) + 6 ⇒ 24 = 24 ⇒ L.H.S = R.HSSo, y = 2x + 6 could have produced the values of in the table as all the orders pairs in the table satisfy/equate the equation.
Checking D) y = x + 9
Putting (3, 12), (6, 18) and (9, 24) in y = x + 9
For (3, 12) ⇒ y = x + 9 ⇒ 12 = 3 + 9 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = x + 9 ⇒ 18 = 6 + 9 ⇒ 18 = 15 ⇒ L.H.S ≠ R.HSFor (9, 24) ⇒ y = x + 9 ⇒ 24 = 9 + 9 ⇒ 24 = 18 ⇒ L.H.S ≠ R.HSSo, y = x + 9 could have also not produced all the values in the table, as (6, 18) and (9, 24) do not satisfy/equate the equation.
So, from all the verification we conclude that:
HENCE, ONLY y = 2x + 6 COULD HAVE PRODUCED THE VALUES IN THE TABLE AS ALL THE ORDERED PAIRS OF THE TABLE SATISFY/EQUATE THE EQUATION.
SOLVING QUESTIONS FROM 5th PAGE
What is the domain and range of the relation?
{(-3, 7), (6, 2), (5, 1), (-9, -6)}
Domain: Domain is the set of all the x-coordinates of the ordered pairs of the relation, meaning the all first elements of the ordered pairs in a relation include in the domain of the relation. Range: Range is the set of all the y-coordinate of the ordered pairs of the relation, meaning the all second elements of the ordered pairs in a relation include in the range of the relation.As the given relation is {(-3, 7), (6, 2), (5, 1), (-9, -6)}
The domain is: {-3, 6, 5, -9}
Note: generally, we write the numbers in ascending order for both the domain and range.
The domain could also be written in order as: {-9, -3, 5, 6}
The range is: {7, 2, 1, -6}
The range could also be written in order as: {-6, 1, 2, 7}
Keywords: equation, point, ordered pair, domain, range
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7/8÷2/8 equal gfffghgddth
Answer:
3.5
Step-by-step explanation:
If James borrows $4,200 to pay his college tuition. He signs a 5 year simple interest loan. If monthly payments are $78.40, what is the interest rate on the loan?
0.024 /yr
Step-by-step explanation:
Without interest, the monthly repayment would be;
5 yrs = 12 months * 5 = 60 months
$4200 / 60
= $70
James, however, pays $78.40 monthly. The interest therefore is;
Jmaes pays a total of $78 * 60 = $4704 at the end of the 5 years. The formula for finding simple interest is;
A = P(1 + rt)
Where:
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
4704 = 4200 (1 + 5r )
4704 = 4200 + 21000r
504 = 21000r
r = 504/21000
r = 0.024
Interest rate = 0.024 /yr
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A circle with a radius of 9cm sits inside of a circle with a radius of 11cm. What is the area of the shaded region? Round your answer to the nearest hundredth. PLEASE HELP DUE TOMORROW
Answer:
[tex]A=125.66\ cm^2[/tex]
Step-by-step explanation:
The complete question is
The area of the shaded region is the area inside the larger circle and outside the smaller circle
so
To find out the area of the shaded region subtract the area of the smaller circle from the area of the larger circle
Remember that
The area of the circle is
[tex]A=\pi r^{2}[/tex]
therefore
The area of the shaded region is
[tex]A=\pi [r_1^2-r_2^2][/tex]
where
[tex]r_1=11\ cm[/tex] ---> radius of the larger circle
[tex]r_2=9\ cm[/tex] ---> radius of the smaller circle
assume
[tex]\pi =3.1416[/tex]
substitute
[tex]A=3.1416 [11^2-9^2][/tex]
[tex]A=3.1416 [40][/tex]
[tex]A=125.66\ cm^2[/tex]
The ages of three siblings combined is 27. The oldest is twice the age of the youngest. The middle child is 3 years older than the youngest. Write and solve an equation to find the ages of each sibling
Answer:
Youngest Age = 6
Middle Age = 9
Oldest Age = 12
Step-by-step explanation:
Let youngest age be x
Middle one age be y
Oldest age be z
So,
x < y < z
Now lets come up with the equations using the statements.
Three age combined is 27, so we can write:
x + y + z = 27
Oldest is TWICE youngest, so we can write:
z = 2x
Middle is 3 YEARS OLDER than youngest, so we can write:
y = x + 3
Now we replace first equation with 2nd and 3rd, to get:
x + y + z = 27
x + x + 3 + 2x = 27
We can solve this for x:
x + x + 3 + 2x = 27
4x + 3 = 27
4x = 24
x = 24/4
x = 6
Now finding y:
y = x + 3
y = 6 + 3
y = 9
Now finding z:
z = 2x
z = 2(6)
z = 12
Thus,
Youngest Age = 6
Middle Age = 9
Oldest Age = 12
A dress costs p dollars. An 8% sales tax must be added to the cost of the dress. Martha wants to multiply the cost of the dress by 0.08 to find the tax and then add it to the cost of the dress. Esther thinks that the cost of the dress should be multiplied by 1.08. The expressions for the two methods are shown below.
Martha: p+0.08p
Esther: 1.08p
Are the two expressions equivalent? Explain.
What does this mean in terms of the methods outlined by Martha and Esther?
Answer:
Yes, both expressions for the two method are equivalent.
Step-by-step explanation:
Let the cost of the dress be p as given.
Marta want to evaluate the tax which is proportional to the cost.
8% sales tax will correspond to (8/100)*p=0.08p
Then she will add 0.08 p to p to obtain 0.08p+p= p(0.08+1)= 1.08p
On the other hand, Esther thinks that the cost of the dress, p, should be multiplied by 1.08 to obtain 1.08p at once!
Thus both expressions are equivalent. Only that Martha is wanting to pay much attention to the details , while Esther is a quick one :-)!
I WILL GIVE YOU A BRILLIANT
Jessica's hamster cage is shaped like a rectangular prism. The cage has a height of 24 inches and a volume of 6,480 cubic inches. Jessica puts a piece of paper on the bottom of the cage. The paper fits the bottom of the cage perfectly.
What is the area of the paper on the bottom of the cage?
Enter your answer in the box.
in²
Answer:
270
Step-by-step explanation:
I am not sure if i am correct but i think you should divide 6,480 by 24 which is 270
Answer:
270 in2
Step-by-step explanation:
Divide 6480 . by 24
Servey says!?: 270 is the awnser!
The equation a company uses to
calculate pay checks is p = 12h +0.25s
where h is the number of hours worked
and s is total sales. What is the equation
solved for s?
The equation solved for s is s = 4p - 48h
Solution:
Given that equation a company uses to calculate pay checks is p = 12h +0.25s
Therefore the given equation is:
p = 12h + 0.25s
Where "h" is the number of hours worked
"s" is the total sales
To find: equation for "s"
Let us solve the given equation for "s"
p = 12h + 0.25s
Now move 12h from R.H.S to L.H.S
p - 12h = 0.25s
Now move from 0.25 from R.H.S to L.H.S
[tex]s = \frac{p-12h}{0.25}\\\\s = \frac{p}{0.25} -\frac{12h}{0.25}[/tex]
We know that, [tex]0.25 = \frac{1}{4}[/tex]
[tex]s = \frac{p}{\frac{1}{4}} -\frac{12h}{\frac{1}{4}}\\\\s = p \times \frac{4}{1} - 12h \times \frac{4}{1}\\\\s = 4p - 48h[/tex]
Thus the equation for s is s = 4p - 48h
The circumference of a circle is 8.97cm.
Find the length of the diameter.
Give your answer rounded to 2 DP
The length of the diameter is 2.86 cm rounded to 2 DP
Step-by-step explanation:
The formula of the circumference of a circle is
C = 2πr, where r is the radius of the circleC = πd, where d is the diameter of the circle∵ The circumference of a circle is 8.97 cm
- We need to find the diameter of the circle, then we will use
the 2nd formula of circumference above
∵ The circumference = πd
- Substitute the value of the circumference in the formula
∴ 8.97 = πd
- Subtract both sides by π
∴ 2.855 = d
- Round it to 2 decimal places (to the nearest hundredth)
∴ d = 2.86 cm
The length of the diameter is 2.86 cm rounded to 2 DP
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The frequency table shows the number of times some people visited a movie theater last year . which set could the frequency table represent?
Answer:
The frequency table shows the number of times some people visited a movie theater last year . which set could the frequency table represent?
Step-by-step explanation:
Solve for a.
a-15=4a-3
Answer:-4
Step-by-step explanation:
a-15=4a-3
a-4a=-3+15
-3a=12
a=-4
What is the value of x in the equation 3/4x+2=5/4x-6
Solving for x...
3/4x+2=5/4x-6
8=2/4x
8=1/2x
x=16
To find the value of x in the given equation, we can eliminate the fractions, combine like terms, and solve for x. The value of x is 16.
Explanation:To find the value of x in the equation 3/4x+2=5/4x-6, we need to isolate x on one side of the equation. We can do this by first getting rid of the fractions. Multiplying each term in the equation by the LCD (Least Common Denominator) of 4 will help us eliminate the fractions. Then, we can combine like terms and solve for x.
Multiplying both sides of the equation by 4, we get: 4(3/4x+2) = 4(5/4x-6), which simplifies to: 3x + 8 = 5x - 24.Next, we can subtract 3x from both sides to isolate the x terms: 3x + 8 - 3x = 5x - 24 - 3x, giving us: 8 = 2x - 24.Then, we can add 24 to both sides of the equation to further isolate x: 8 + 24 = 2x - 24 + 24, which simplifies to: 32 = 2x.
Finally, we can divide both sides by 2 to solve for x: (32/2) = 2x/2, resulting in x = 16.
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Find the value of x that makes ABCD a parallelogram.
Answer:
x=70
Step-by-step explanation:
I'm pretty sure the sum of all angles has to be 360°
and 70+70+40+40=220
so 220+x=360
we figure this out by taking 360-220 which equals 140
and then we divide 140 by 2 which is 70.
To double check, if you add 70+70+40+40+70+70, it equals 360.
The value of x from the given parallelogram is 70°. Therefore, option B is the correct answer.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
Given that, ABCD is a parallelogram.
Here, ∠A+∠B+∠C+∠D=360°
70°+x+40°+70°+x+40°=360°
220°+2x=360°
2x=360°-220°
2x=140°
x=70°
Therefore, option B is the correct answer.
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How would I graph these equations in a system? : 2r + b = $8.40, and 3r + b = $9.35. If you need specifics, I can tell you the whole story problem. I will mark the best answer as Brainliest.
Answer:
The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown
Step-by-step explanation:
Given as :
The two line equation are
2 r + b = $8.40 .........A and
3 r + b = $9.35 .........B
Now, Solving equations A and B
i.e (3 r + b) - (2 r + b) = $9.35 - $8.40
Or, (3 r - 2 r) + (b - b) = 0.95
or, r + 0 = 0.95
∴ r = $0.95
Now, put the value og r into eq A
∵ 2 r + b = $8.40
So, 2× $0.95 + b = $8.40
Or, $1.9 + b = $8.40
Or, b = $8.40 - $1.9
∴ b = $6.5
So, The value of r = $0.95 and b = $6.5
Now, for plotting the equation on graph
let put r on x axis
and put b on y-axis
Hence, The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown . Answer
Which graph shows the system of equations 4x+y=3 and 2x-3y=3?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]4x+y=3[/tex] ----> Red line
[tex]2x-3y=3[/tex] ---> blue line
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (0.857,-0.429)
The graph in the attached figure
any 10th grader solve it
for 50 points
Answer:
[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex] is proved for the sum of pth, qth and rth terms of an arithmetic progression are a, b,and c respectively.
Step-by-step explanation:
Given that the sum of pth, qth and rth terms of an arithmetic progression are a, b and c respectively.
First term of given arithmetic progression is A
and common difference is D
ie., [tex]a_{1}=A[/tex] and common difference=D
The nth term can be written as
[tex]a_{n}=A+(n-1)D[/tex]
pth term of given arithmetic progression is a
[tex]a_{p}=A+(p-1)D=a[/tex]
qth term of given arithmetic progression is b
[tex]a_{q}=A+(q-1)D=b[/tex] and
rth term of given arithmetic progression is c
[tex]a_{r}=A+(r-1)D=c[/tex]
We have to prove that
[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)=0[/tex]
Now to prove LHS=RHS
Now take LHS
[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)[/tex]
[tex]=\frac{A+(p-1)D}{p}\times (q-r)+\frac{A+(q-1)D}{q}\times (r-p)+\frac{A+(r-1)D}{r}\times (p-q)[/tex]
[tex]=\frac{A+pD-D}{p}\times (q-r)+\frac{A+qD-D}{q}\times (r-p)+\frac{A+rD-D}{r}\times (p-q)[/tex]
[tex]=\frac{Aq+pqD-Dq-Ar-prD+rD}{p}+\frac{Ar+rqD-Dr-Ap-pqD+pD}{q}+\frac{Ap+prD-Dp-Aq-qrD+qD}{r}[/tex]
[tex]=\frac{[Aq+pqD-Dq-Ar-prD+rD]\times qr+[Ar+rqD-Dr-Ap-pqD+pD]\times pr+[Ap+prD-Dp-Aq-qrD+qD]\times pq}{pqr}[/tex]
[tex]=\frac{Arq^{2}+pq^{2} rD-Dq^{2} r-Aqr^{2}-pqr^{2} D+qr^{2} D+Apr^{2}+pr^{2} qD-pDr^{2} -Ap^{2}r-p^{2} rqD+p^{2} rD+Ap^{2} q+p^{2} qrD-Dp^{2} q-Aq^{2} p-q^{2} prD+q^{2}pD}{pqr}[/tex]
[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2}-pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]
[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2} -pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]
[tex]\neq 0[/tex]
ie., [tex]RHS\neq 0[/tex]
Therefore [tex]LHS\neq RHS[/tex]
ie.,[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex]
Hence proved
Solve equation by completing the square round to the nearest hundredth if necessary
X2-4x-=5
Answer:
x=-1 and x=5
Step-by-step explanation:
we have
[tex]x^{2} -4x=5[/tex]
Solve it by completing the square method
We take the coefficient of x that is -4, divide it by 2 and then square it
so
[tex]-\frac{4}{2}=-2[/tex]
square it
[tex](-2)^2 = 4[/tex]
Adds 4 both sides
[tex]x^{2} -4x+4=5+4[/tex]
Combine like terms right side
[tex]x^{2} -4x+4=9[/tex]
Rewrite as perfect squares
[tex](x-2)^{2}=9[/tex]
take square root both sides
[tex]x-2=\pm3[/tex]
[tex]x=2\pm3[/tex]
therefore
[tex]x=2+3=5[/tex]
[tex]x=2-3=-1[/tex]
Complete the recursive formula of the arithmetic sequence
a(1) =
a(n)= a(n-1)+
Answer:
The recursive formula of the arithmetic sequence
[tex]a_{1}=First term of the arithmetic sequence[/tex]
[tex]a_{n}= a_{n-1}+common difference(d)[/tex].
Step-by-step explanation:
A recursive formula is used to find any term of an arithmetic sequence using a function of the preceding term. Each term is the sum of the previous term and the common difference.
To find the recursive formula of the arithmetic sequence
[tex]a_{1}=First term of the arithmetic sequence[/tex]
[tex]a_{n}= a_{n-1}+common difference(d)[/tex]