Answer:
Step-by-step explanation: Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
p*(x)-((2*x^2-9*x+7)*(x-2))=0
STEP
1
:
Equation at the end of step 1
px - (((2x2 - 9x) + 7) • (x - 2)) = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 2x2-9x+7
The first term is, 2x2 its coefficient is 2 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 2 • 7 = 14
Step-2 : Find two factors of 14 whose sum equals the coefficient of the middle term, which is -9 .
-14 + -1 = -15
-7 + -2 = -9 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -2
2x2 - 7x - 2x - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-7)
Add up the last 2 terms, pulling out common factors :
1 • (2x-7)
Step-5 : Add up the four terms of step 4 :
(x-1) • (2x-7)
Which is the desired factorization
Equation at the end of step
2
:
px - (2x - 7) • (x - 1) • (x - 2) = 0
STEP
3
:
Equation at the end of step 3
px - 2x3 + 13x2 - 25x + 14 = 0
STEP
4
:
Solving a Single Variable Equation:
4.1 Solve px-2x3+13x2-25x+14 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
Supplement : Solving Quadratic Equation Directly
Solving 2x2-9x+7 = 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:
5.1 Find the Vertex of y = 2x2-9x+7
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 2 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.2500
Plugging into the parabola formula 2.2500 for x we can calculate the y -coordinate :
y = 2.0 * 2.25 * 2.25 - 9.0 * 2.25 + 7.0
or y = -3.125
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 2x2-9x+7
Axis of Symmetry (dashed) {x}={ 2.25}
Vertex at {x,y} = { 2.25,-3.12}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 3.50, 0.00}
3 Solving 2x2-9x+7 = 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 = 2
B = -9
C = 7
Accordingly, B2 - 4AC =
81 - 56 =
25
Applying the quadratic formula :
9 ± √ 25
x = —————
4
Can √ 25 be simplified ?
Yes! The prime factorization of 25 is
5•5
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).
√ 25 = √ 5•5 =
± 5 • √ 1 =
± 5
So now we are looking at:
x = ( 9 ± 5) / 4
Two real solutions:
x =(9+√25)/4=(9+5)/4= 3.500
or:
x =(9-√25)/4=(9-5)/4= 1.000
Read Question On PNG Picture
Answer:
10 1/2
Step-by-step explanation:
You’ve learned to identify whether a function is even or odd both graphically and algebraically. How does the notation for reflections over the x-axis and over the y-axis relate to the notation for even and odd functions? Remember that if f(-x) = f(x), a function is even, and if f(-x) = -f(x), then the function is odd.
Answer:
Because even and odd are 2 different ways to determine whether or not you get the right answer for the chosen function.
Step-by-step explanation:
Hope this helps!!!
Answer:
For even functions, we take f(-x) to be the starting function. The y-axis reflection of this function is f(-(-x)), which is equal tof(x). So the relationship f(-x) = f(x) means that the function is the same as its y-axis reflection.
For odd functions, there are two reflections that must occur. First, we start with f(-x). The y-axis reflection of this function is f(-(-x)) = f(x). When we apply an x-axis reflection to this result, we get -f(-(-x)) = -f(x). So the fact that f(-x) = -f(x) means that odd functions are the same as sequential reflections across both the x-axis and the y-axis. (The same sequence of reflections also represents a rotation 180 degrees about the origin).
Step-by-step explanation:
Please help!!!! I will mark brainliest!!
Answer:
1 4 6 8 Have a good night ✨ ☺
By what percent is 16 greater than 12.
Answer:
28 i assume.
Answer:
The answer is 28% :))
Suppose a country's population at any time t grows in accordance with the rule dP dt = kP + I where P denotes the population at any time t, k is a positive constant reflecting the natural growth rate of the population, and I is a constant giving the (constant) rate of immigration into the country. If the total population of the country at time t = 0 is P0, find an expression for the population at any time t.
Answer:
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
Step-by-step explanation:
Given that:
A country population at any given time (t) is:
[tex]\dfrac{dP}{dt}= kP+I[/tex]
where;
P = population at any time t
k = positive constant
I = constant rate of immigration into the country.
Using the method of separation of the variable;
[tex]\dfrac{dP}{kP+1}= dt[/tex]
Taking integration on both sides:
[tex]\int \dfrac{dP}{kP+I}= \int \ dt[/tex]
[tex]\dfrac{1}{k} log (kP + I) = t+c_1 \ \ \ here: c_1 = constant \ of \ integration[/tex]
[tex]log (kP + I) =k t+kc_1[/tex]
By applying the exponential on both sides;
[tex]e^{log (kP + I) }=e^{k t+kc_1 }[/tex]
[tex]KP+I = e^{kt} *e^{kc_1}[/tex]
Assume [tex]e^{kc_1 }= C[/tex]
Then:
[tex]kP + I = Ce^{kt}[/tex]
[tex]kP = Ce^{kt}-I[/tex]
[tex]P =\dfrac{ Ce^{kt}-I}{k} \ \ \---- Let \ that \ be \ equation \ (1)[/tex]
When time t = 0, The Total population of the country is also [tex]P_o[/tex]
[tex]P_o = \dfrac{Ce^{0(t)} -I}{k}[/tex]
[tex]P_o = \dfrac{Ce^{0} -I}{k}[/tex]
[tex]P_o = \dfrac{C-I}{k}[/tex]
C - I = kP₀
C = kP₀ + I
Substituting the value of C back into equation(1), we have:
[tex]P =\dfrac{ (kP_o+1)e^{kt}-I}{k}[/tex]
[tex]P =\dfrac{ (kP_o+1)e^{kt}}{k} - \dfrac{I}{k}[/tex]
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
Please help!!! I will make brainliest
Answer:
I believe that all should be checked except for f(x) = x^6 which u already didn't check
Step-by-step explanation:
The equation is y = ab^x and all the equations, except that one, follow this formula
When the price of Xis RM4 and the price of Y is RM10, which of the following combinations would be the intercept of axes
(X,Y) if you have an income of RM 100?
Select one:
A. (25X, 10Y)
B. (20X, 5Y)
C. (10X, 25Y)
D. (5X, 20Y)
Use the commutative property of multiplication to rewrite 10.5.12. Which expression is equivalent? O A. 10.5.(5+5) OB. 10. 12.5 O C. (10.5) + 12 OD. 10 + 5 + 12
Answer:
b
Step-by-step explanation:
i did the math for over an hour and got the same answer 25 times
A certain radioactive isotope has a half-life of 50 years. A scientist determines that there are 200 grams of the radioactive material present today. How
Much of the isotope was present 200 years ago?
im guessing 800 50X4 = 200 and 200X4 = 800
i never learned this but i hope its correct.
6/15 of a ton of wood is to be split between 8 decks evenly. How much wood will be used for each deck?
Answer:
1/16 tons of wood per deck
Step-by-step explanation:
6/15 ÷ 8
6/15 × 1/8 (Keep Change Flip)
6/96 = 1/16
Harold cut 18 and a half
inches off a rope that was 60 inches long. How is the length of the remaining rope in inches written in decimal form?
The length of the remaining rope is 41.5 inches.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Harold cut 18 and a half inches off a rope that was 60 inches long.
Let the remaining length of the rope be x.
This can be written as,
⇒ [tex]x=60-18.5[/tex]
⇒ [tex]x=41.5[/tex]
Hence we can conclude that the length of the remaining rope is 41.5 inches.
Learn more about word problems here
brainly.com/question/20594903
#SPJ2
In 1992, Jason bought a gallon of gas for $1.15. Yesterday, he bought a gallon of gas for $2.12. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
A.
84.3%
B.
45.8%
C.
54.2%
D.
15.7%
Once again Plssssssss Help Meh
Help ASAP!!!!!A side of the triangle below has been extended to form and exterior angle of 159 degrees.Find the value of s
Answer:
x=21
Step-by-step explanation:
45+x+the last angle=180
x+159=180
180-159=21
21+45= 66
180-66=114
so i think x would be 21 degrees but im not entirely sure do not quote me on this sorry
Help out pleaseeeeeeeeeeeeeeeee
Explain how to solve the equation.
B - 7 = 12
Answer:
So if you take the 12 and add it to the 7 you get 19 then do 19 mines 7 and you get 12 so always add the sum to the number given to get the missing number
Step-by-step explanation:
Have a great day
can someone please answer as soon as possible
Answer:
A) {-1,2,8}
Step-by-step explanation:
fill in all domain values in f(x) and you get:
f(-1) = -1
f(0) = 2
f(2) = 8
The set of results is the range.
What is the answer answer and plz give me step by step explaining
Answer:
x = 5
Step-by-step explanation:
6 + 8(x - 1) = 2(3x + 4)
We evaluate the numbers in the brackets first.
(8 × x = 8x, 8 × 1 = 8, 2 × 3x = 6x, 2 × 4 = 8)
6 + 8x - 8 = 6x + 8
The left hand side of the equation is not exactly simplified, so we will evaluate it further first.
(6 - 8 = -2)
8x - 2 = 6x + 8
Now we can start shifting the x and the numbers separately.
Note that when pushing 6x from the right side to the left side, it needs to change to a negative 6x and vice versa for -2 turning into +2.
8x - 6x = 8 + 2
Further evaluation
2x = 10
Now we can simply find x.
Note that for this, ×2 becomes ÷2 when it shifts from the left side to the right side of the equation.
x = 10 ÷ 2
Evaluate.
x = 5
I need help please I am having hard time doing this
Answer:you are corect its negetive
Step-by-step explanation:
Someone help me out please
Caroline is correct because the equation y = (x-1)(x-5) is in factored form. If you solve the terms (x-1) and (x-5), you get the zeros (aka x-intercepts) of the graph.
Solve (set the terms equal to 0):
x-1 = 0 x = 1
x-5 = 0 x = 5
∴ the x-intercepts are (1,0) and (5,0).
The purple graph corresponds to the zeros in the equation, not the green graph. The green graph has negative x-intercepts, whereas the purple graph has positive x-intercepts like in the equation.
The slope of a line perpendicular to y = 2x + 1 is -2.
False
True
Answer:
incorrect.
Step-by-step explanation:
the slope of the line perpendicular is the negative reciprocal, which in this case is -1/2
Answer:
False
Step-by-step explanation:
To find the slope of a perpendicular, flip the slope and change the sign.
The slope pf the given line is 2.
The slope of a line perpendicular to y = 2x + 1 is -1/2.
Answer: False
Divide. Write in simplest form.
3/4 divided by 1/8
Answer:
when you divide 3/4 by 1/8 you get 6
Compré 18 cuadernos, 24 carpetas y 17 lapiceras. El precio de las carpetas excede al de los cuadernos en un 40%, mientras que el precio de las lapiceras es el 20% del precio de los cuadernos. Si el importe de la compra fue de $11.825, calcular el precio unitario de cada artículo
Answer:talk some English dude
Step-by-step explanation:
The quotient of 5 plus a number w and negative 5 is 36
155 i think this is correct if not its 205
Find 56(−4⋅27). Write your answer in simplest form.
Answer:
[tex]-6048[/tex]
Step-by-step explanation:
[tex]---------------------------------[/tex]
[tex]56\left(-4\cdot27\right)[/tex] = [tex]-6048[/tex] [tex]because[/tex]
[tex]---------------------------------[/tex]
[tex]56\left(-4\cdot27\right)[/tex] = [tex]?[/tex]
[tex]\left(-4\cdot27\right)[/tex] = [tex]-108[/tex]
[tex]56\left(-108\right)[/tex] = [tex]?[/tex]
[tex]56\left(-108\right)[/tex] = [tex]-6048[/tex]
[tex]---------------------------------[/tex]
Hope this helps! <3
[tex]---------------------------------[/tex]
Noah painted 3/20 of a fence in 1/2 a day how many days will it take him to paint the entire fence
Answer:
approximately 7 days
Step-by-step explanation:
20 ÷ 3 = 6.6 repeating, round up to 7 days
Answer:
3days and 8hours
Step-by-step explanation:
he painted 3/20 in 1/2day then
3/20 painted for 1/2 day =12 hours so
1/20 was painted in 12/3=4 hours
since 20 /20 will be how long will be needed to paint the entire fence
20*4hour = 80hours which is (24*3)+8 that will make
3days and 8hours or
3and 1/3 days
Why was the ancient Egyptian teenager confused?
Answer: her daddy was a mummy
Step-by-step explanation:
Let f(x) = 9x and g(x) = x + 7. What's
the smallest number that is in the domain of
fºg?
Enter the correct answer.
OOOO
DONE
Clear all
Answer:
Let `f` be a function defined on [0,2]. Then find the domain of function `g(x)=f(9x^2-1)
Step-by-step explanation:
I'm not sure if that's right
how do you Graph y = 1/5x+3.
Answer: If you can see with this Image I created, the Y Intercept (3) is dotted on the line. You move one up, and move five units to the right. You keep on doing this until you can make a line (Which I did).
I hope this helps, and Happy Holidays! :)
Answer:
rise
----
run
Something like these
Step-by-step explanation:
find 3 on the vertical line if the graph
then from that point rise 1 time to should get you to 2 on the horizontal axis, run 5 times to get to 7, and keep doing that. opposing that rise over run but with negatives when going from the other side of the graph
Write the equation of the line in fully simplified slope-intercept form.
Step-by-step explanation:
For every 3 squares across, the line drops by 1 square.
Therefore the slope of the lina is -1/3.
The y-intercept of the line is -8 (when x = 0)
The equation of the line is y = -1/3 x - 8.