Answer:
181.3
Step-by-step explanation:
I hope this helps!
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I believe it is a because I had a question just like that in 8th grade
What is the end behavior of a sixth degree polynomial function whose leading coefficient is
negative?
Answer:
both ends tend toward negative infinity
Step-by-step explanation:
The ends of an even-degree polynomial go in the same direction. The sign of that direction matches the sign of the leading coefficient.
Here, the leading coefficient is negative, so ...
y → -∞ when x → ±∞
X^+17x+72=12 factoring quadratic equation
Answer:
The first term is, x2 its coefficient is 1 .
The middle term is, -17x its coefficient is -17 .
The last term, "the constant", is +60
Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .
-60 + -1 = -61
-30 + -2 = -32
-20 + -3 = -23
-15 + -4 = -19
-12 + -5 = -17 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5
x2 - 12x - 5x - 60
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
5 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x-5) • (x-12)
Which is the desired factorization
Equation at the end of step
1
:
(x - 5) • (x - 12) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x-5 = 0
Add 5 to both sides of the equation :
x = 5
Solving a Single Variable Equation:
2.3 Solve : x-12 = 0
Add 12 to both sides of the equation :
x = 12
Supplement : Solving Quadratic Equation Directly
Solving x2-17x+60 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = x2-17x+60
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000
Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :
y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0
or y = -12.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-17x+60
Axis of Symmetry (dashed) {x}={ 8.50}
Vertex at {x,y} = { 8.50,-12.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 5.00, 0.00}
Root 2 at {x,y} = {12.00, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving x2-17x+60 = 0 by Completing The Square .
Subtract 60 from both side of the equation :
x2-17x = -60
Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4
Add 289/4 to both sides of the equation :
On the right hand side we have :
-60 + 289/4 or, (-60/1)+(289/4)
The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4
So adding to both sides we finally get :
x2-17x+(289/4) = 49/4
Adding 289/4 has completed the left hand side into a perfect square :
x2-17x+(289/4) =
(x-(17/2)) • (x-(17/2)) =
(x-(17/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-17x+(289/4) = 49/4 and
x2-17x+(289/4) = (x-(17/2))2
then, according to the law of transitivity,
(x-(17/2))2 = 49/4
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(17/2))2 is
(x-(17/2))2/2 =
(x-(17/2))1 =
x-(17/2)
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-(17/2) = √ 49/4
Add 17/2 to both sides to obtain:
x = 17/2 + √ 49/4
Since a square root has two values, one positive and the other negative
x2 - 17x + 60 = 0
has two solutions:
x = 17/2 + √ 49/4
or
x = 17/2 - √ 49/4
Note that √ 49/4 can be written as
√ 49 / √ 4 which is 7 / 2
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -17
C = 60
Accordingly, B2 - 4AC =
289 - 240 =
49
Applying the quadratic formula :
17 ± √ 49
x = —————
2
Can √ 49 be simplified ?
Yes! The prime factorization of 49 is
7•7
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 49 = √ 7•7 =
± 7 • √ 1 =
± 7
So now we are looking at:
x = ( 17 ± 7) / 2
Two real solutions:
x =(17+√49)/2=(17+7)/2= 12.000
or:
x =(17-√49)/2=(17-7)/2= 5.000
Two solutions were found :
x = 12
x = 5
Step-by-step explanation:
please mark my answer in brainlist
Calculator
(4y + 10°
What is the value of y?
Enter your answer in the box.
759
(3x)
B
y =
Answer:
y = 5
Step-by-step explanation:
The base angles of this isosceles triangle are congruent, so the angle at A is ...
A = 180° -2(75°) = 30°
(4y +10)° = 30° . . . . . substitute the given expression for angle A
4y = 20 . . . . . . . . . . divide by °, subtract 10
y = 5 . . . . . . . . . divide by 4
_____
Additional comment
The value of x is 25.
x is found from 3x=75, by dividing both sides of this equation by 3.
The recursive algorithm given below can be used to compute gcd(a, b) where a and b are non-negative integer, not both zero. procedure gcd(a, b) if a > b then gcd(a, b) := gcd(b, a) else if a = 0 then gcd(a, b) := b else if a = 1 then gcd(a, b) := 1 else if a and b are even then gcd(a, b) := 2gcd(a/2, b/2) else if a is odd and b is even then gcd(a, b) := gcd(a, b/2) else gcd(a, b) := gcd(a, b − a) Use this algorithm to compute (a) gcd(124, 244) (b) gcd(4424, 2111).
Coding the given algorithm in python 3, the greatest common divisor of the values (124 and 244) and (4424 and 2111) are 4 and 1 respectively.
The program implementation goes thus :
def gcd(a, b):
#initialize a function named gcd which takes in two parameters
if a>b:
#checks if a is greater than b
return gcd (b, a)
#if true interchange the Parameters and Recall the function
elif a == 0:
return b
elif a == 1:
return 1
elif((a%2 == 0)and(b%2==0)):
#even numbers leave no remainder when divided by 2, checks if a and b are even
return 2 * gcd(a/2, b/2)
elif((a%2 !=0) and (b%2==0)):
#checks if a is odd and B is even
return gcd(a, b/2)
else :
return gcd(a, b-a)
A sample run if the program on the values given :
print(gcd(124, 244))
print()
#leaves a space after the first output
print(gcd(4424, 2111))
Learn more :brainly.com/question/25506437
What is the equation of the line in slop-intercept form?
Enter your answer in the blank spots
y= __x + __
Answer:y=2.5x+5 i thank
Step-by-step explanation:
Tell whether the fractions are equivalent. Write = or [tex]\neq[/tex]
3/4 ____ 8/12
6 dollars for 2 cans of tuna what is the rate
Answer:
3 dollars per can
Step-by-step explanation:
divide 6 by 2
i really need help on my question
Answer:
D
Step-by-step explanation:
-1.25 is less than -1.02 and 1.4.
> -1.25 + 1.02 = -0.23
1.4 is a greater amount because it is a positive number
So, if you put it this way, -1.25 is lesser, -1.02 is the 2nd least, & 1.4 is the greatest.
Which means your overall answer should be -1.25 < -1.02 < 1.4
a recipe calls for 2 1/3 cups of sugar. you wanna double your recipe how many cups of sugar do you need?
Answer:
4 2/3
Step-by-step explanation:
mega movies hotel a fil premiere on Friday night. they charged $7 for adults and $5 for children. One hundred twenty-three adults and children attended, and $829 was made in ticket sales. How many children and how many adults went to the film premiere?
Answer:
107 adults 16 children
Step-by-step explanation:
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solve pls brainliest
Answer:
circle, triangle, rectangle
Answer:
the first cross section would make a circle (option 2, the second would make a triangle (option 6), and the last one would make a rectangle (option 1). hope this helps!
If x = 5-2√6, find the value of:
(i) x + 1/x
(ii) x² + 1/x²
Please solve ASAP
Answer:
x+(1/x) = 10 and x²+ (1/x²) = 98Step-by-step explanation:
Given that :
x = 5-2√6
1/x = 1/(5-2√6)
The denominator = 5-2√6
The Rationalising factor of 5-2√6 = 5+2√6
On Rationalising the denominator then
⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]
⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]
⇛ 1/x = (5+2√6)/[5²-(2√6)²]
Since (a+b)(a-b) = a²-b²
Where ,
a = 5 and b = 2√6⇛1/x = (5+2√6)/(25-24)
⇛ 1/x = (5+2√6)/1
⇛ 1/x = 5+2√6
Now,
x +(1/x)
⇛ 5-2√6+5+2√6
⇛ 5+5
⇛ 10
Therefore, x+(1/x) = 10.
On squaring both sides then
⇛ [x+(1/x)]² = 10²
⇛ x²+2(x)(1/x)+(1/x)² =100
⇛ x²+2+(1/x)² = 100
⇛ x²+(1/x²) = 100-2
⇛ x²+(1/x²) = 98
Therefore, x²+(1/x²) = 98.
Read more:
Similar questions;
Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = 1/2 (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1.....
https://brainly.com/question/24697983?referrer
What is three times a number is increased by 11 ,the result is 32
Answer:
7
Step-by-step explanation:
let x be the number
3x + 11 = 32
3x = 21............subtract both sides by 11
x = 7................divide both sides by 3
Answer:
Expression-
3×r+11=32
r=7
Step-by-step explanation:
I have run this answer the calculator a million times so trust me on this one
You are given the first four terms of an arithmetic sequence. Under what
conditions might a recursive formula be preferred over the explicit formula?
Under what conditions might an explicit formula be preferred over the
recursive formula?
plz help meeeeeeeeeeeeeeeeeee
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Pls help I’ll brainlest ASAP
Make this sentence better the building is old and ugly
Answer:
the building is aged and unique.
Please take a look at the picture
Answer: C
Step-by-step explanation:
Anyone to help me answer this question am giving the brainliest
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
As we know,
[tex] \boxed{\sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b) }[/tex]and
[tex] \boxed{\sin(a - b) = \sin(a) \cos(b) - \cos(a \sin(b) ) }[/tex]now, let's add them as shown ~
[tex] \boxed{\sin(a + b) + \sin(a - b)} [/tex][tex] \boxed{ \sin(a) \cos(b) + \cos(a) \sin(b) + \sin(a) \cos(b) - \cos(a) \sin(b) }[/tex][tex] \boxed{2 \sin(a) \cos(b) }[/tex]This table represents the gallons of water, g, left in a hot tub after draining it for m minutes.
When graphed, all of the points in the table lie on the same line.
What is the slope and y-intercept of the line?
Drag and drop the slope and y-intercept into the corresponding boxes.
available options are -32, 15,32,480
Answer:
The answer is slope: -32 y-intercept:480
Step-by-step explanation:
I took the test
Answer: slope -32 y-intercept 480
Step-by-step explanation:
Took the k12 test
pls help me I will try to give brainleist bc i don't know how
Answer:
2195
Step-by-step explanation:
filler filler filler lol
Answer: 2,195
Step-by-step explanation:
439x5
9x5=45
3x5+4=19
4x5+1=21
2195
During a hurricane in Central Florida, the amount of rainfall R, in centimeters, is a function of time. Let R = f(t) define the amount of rain recorded by meteorologists beginning at midnight. Give an interpretation of the statements below, using the appropriate units.
A. (6) = 4.8
B. f'(6)=0.5
C. f(-1)(5) = 14
D. f(-1)'(5) = 1.5
The amount of rainfall is an illustration of inverse functions, and rates.
The function is given as: R = f(t)
(a) Interpret f(6) = 4.8
This means that:
The amount of rainfall at 6 seconds is 4.8 cm
(b) Interpret f'(6) = 0.5
f'(6) represents the rate of the function
So, this means that:
The rate at which rain falls at 6 seconds is 0.5 cm per second
(c) Interpret f^-1(5) = 14
f^-1(6) represents the inverse function
So, this means that:
The time at which 5 cm of rain falls, is 14 seconds
(d) Interpret f^-1'(5) = 1.5
f^-1'(5) represents the rate of the inverse function
So, this means that:
The rate of time when 5 cm of rain falls is 1.5 seconds per cm
Read more about functions, inverse and rates at:
https://brainly.com/question/15634149
My dinner at San Felipe cost $8.20 before tax and $9.96 after tax. What was the sales tax rate?
*Round to the nearest whole percent.
Show Your WorK
Answer:
Sale tax rate = 21.46%
Step-by-step explanation:
Sale Tax % = ( Amount after sale tax - Original cost) ÷ original × 100
Sale Tax % = ( $9.96 - $8.20) ÷ $8.20 × 100
Sale Tax % = $1.76 ÷ $8.20 × 100
Sale Tax % = .2146341463 × 100
Sale Tax % = 21.46
hii, i need help with this word problem :)
Multiply the amount per week by the number of weeks (x) and add that to the starting amount they had. Set those to equal each other and solve for x:
222 + 10x = 148 + 12x
Subtract 10x from both sides:
222 = 148 + 2x
Subtract 148 from both sides
74 = 2x
Divide both sides by 2
X = 37
Answer: 37 weeks
find the slope from the pair of points (0,-5) (2,5)
Step-by-step explanation:
given points,
(0,-5) and (2,5)
we know,
slope = y2 - y1 / x2 - x1
→ 5 - (-5) / 2 - 0
→ 5+5/2 = 10/2
→ 5
therefore, slope of the line is 5.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
what is the midrange
Answer:
Midrange Formula. Midrange in layman terms is the middle of any data set or the simply the average, mean of the data. A midrange is a statistical tool which is also known as the measure of center in statistics. Along with the existence of the midrange formula means, medium, average, mode, and range are also known as the measure of central tendency.
Step-by-step explanation:
Proxima Centauri, our nearest star except for the sun, is about 4·1013 km from Earth. Find to one decimal place its distance in parsecs.
Step-by-step explanation:
The conversion for parsecs into meters is
1 parsec (pc) = [tex]3.09×10^{16}\:\text {m}[/tex]
So if Proxima Centauri is [tex]4×10^{13}\:\text{m}[/tex] away, then in terms of parsecs, this distance is
[tex]4×10^{13}\:\text{m}×\left(\dfrac{1\:\text{parsec}}{3.09×10^{16}\:\text{m}}\right)[/tex]
[tex]\;\;\;\;\;= 1.2×10^{-3}\:\text{parsec}[/tex]
left parenthesis negative 2 minus 4 right parenthesis plus left parenthesis 5 minus 10 right parenthesis minus 6 left parenthesis 3 right parenthesis
Answer:-29
Step-by-step explanation:
(-2-4)+(5-10)-6(3)
-6+-5-18
Plsss help!, bRAInLIST!!
Megan opened a savings account with a $500 deposit. The account pays 1.25% simple interest each year. If she neither adds nor withdraws money from the account, how much interest will she earn after 3 years? help
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 1.25\%\to \frac{1.25}{100}\dotfill &0.0125\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (500)(0.0125)(3)\implies \boxed{I = 18.75}[/tex]