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
22.758 to the nearest foot
Well happy New Year everyone. I've been thinking about the upcoming year "2021" and found something interesting. Reduced to its prime factors it becomes 43*47. Yes, it resolves into 2 CONSECUTIVE 2 digit prime numbers, which does NOT happen that often. The last time this occurred was in 1927 (41 * 47). However these are NOT consecutive prime numbers. (There's another prime number between 41 and 47). If we go back to 1763 (41 * 43), it resolves into two 2-digit CONSECUTIVE primes AND they are TWIN primes (prime numbers with a difference of 2).
And now, here's the question: Can anyone find some interesting factorizations of upcoming years? For example, the year 2033 = 19*107 and the year 2041 = 13*157. In each case the factors are less than 10. Obviously, this is not THE most vital question, so don't spend too much time on it. (Although I've been told that a solution will finally bring about World Peace!!! ) LOL
Answer:
As 2021 and 1927 does not have any product of primes
HCF and LCM of 2020 and 1926 is shown below
Step-by-step explanation:
2020 = 2^2 × 5 × 101
1926 = 2 x 3^2 x 107
2 is the HCF
2 x 2 x 3 x 3 x 5 x 101 x 107 = 1945260
1945260 is the LCM
2022 and 1928 both have product of primes and their HCF and LCM is
1949208 is the LCF and 2 is the HCF
1949208 - 1945260 = 3948
3948/2 = 1974
2022-1928 = 94
2020 - 1926 = 94
1974/94 = 21
and brings us back to our year again.
Happy New Year to you.
At home, Alice noticed that she had a flat tire. With the spare, Alice drove 30 miles to the next shop at 45 mph. After getting the new tire, she drove home at 70 mph. What was Alice's average speed for her round trip?
Answer: Approximately 54.7826 mph
As a fraction, this average speed is exactly 1260/23 mph.
========================================================
Work Shown:
"Alice drove 30 miles...at 45 mph". This means
t = d/r
t = 30/45
t = 2/3
She drove for 2/3 of an hour, which is (2/3)*60 = 40 minutes.
Then "she drove home at 70 mph". She drove the same distance, meaning,
t = d/r
t = 30/70
t = 3/7
She drove for 3/7 of an hour, which is roughly (3/7)*60 = 25.714 minutes.
------------------------------
Add up the time values
(2/3 hr) + (3/7 hr)
(2/3 + 3/7) hr
(14/21 + 9/21) hr
23/21 hr
She spent 23/21 of an hour driving going to the auto shop and then back home. The total distance she traveled was 30+30 = 60 miles.
Use these values to find the speed
r = d/t
r = d divided by t
r = 60 divided by (23/21)
r = (60/1) divided by (23/21)
r = (60/1) * (21/23)
r = (60*21)/(1*23)
r = 1260/23
r = 54.7826
Her average speed for the round trip is about 54.7826 mph.
Jasmine saves $46 each month from her part-time job. She saves 2/5 of her earnings. Her earnings a can be found by using the equation 2/5a = 46.
Find her earnings.Required to answer. Single choice.
(10 points )
$ 230
$ 115
$ 92
$ 18.40
Answer:
$115 is the correct answer please mark me as brainliest
Nisha did the work below to solve an equation.
Step 1 7b+3.2b-5=18.92
Step 2 10.2b-5=18.92
Step 3 5.2b= 18.92
Step 4 b=3.64.
In which step did Nisha make her first error?
Step 1
Step 2
Step 3
Step 4
Answer:
Step 3.
Step-by-step explanation:
When 10.2b - 5 = 18.92, you cannot combine the unlike terms together on the left side to get 5.2b. Instead, add 5 to both sides:
10.2b = 18.92 + 5 = 23.92.
Answer: step 3
Step-by-step explanation:
If QRST is a kite, find the measure of QRS
Answer:
!!!!
137°
i took the test and that was the right answer.
Step-by-step explanation:
QRST is a kite therefore, the value of angle QRS in the kite is 137 degrees.
Properties of a kiteOne pair of opposite angles is equal.Diagonals are perpendicular to each other.The sum of angles in the kite is 360 degrees.
Therefore,
79 + 79 + 11x - 6 + 4x + 13 = 360
158 - 6 + 13 + 11x + 4x = 360
158 + 7 + 15x = 360
15x = 360 - 158 - 7
15x = 195
divide both sides by 15
x = 195 / 15
x = 13
Therefore,
∠QRS = 11(13) - 6 = 143 - 6 = 137 degrees.
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The HCF of two numbers is 20. The LCM of both numbers is a multiple of 14. One number is greater than the other, work out the smallest possible numbers
Answer:
20
Step-by-step explanation:
Given that the HCF of two numbers is 20 and the LCM of both numbers is a multiple of 14.
So, the LCM of both numbers = 14n where n can be any natural number.
As HCF of two numbers is always smaller than or equal to the smallest number among both the numbers.
Here, the HCF of two numbers is 20, so the smallest number is greater than of equal to 20.
Hence, the smallest possible number is 20.
What is the sum of 2x-5y+x+y
Answer:
3x - 4y
Step-by-step explanation:
2x + -5y + x + y
Group Like terms:
2x + x + -5y + y
2x + x = 3x
-5y + y = -4y
3x - 4y
a linear function contains the following points (0,-1) (3,8)
ANGLE KLM and ANGLE RST are supplementary angles. If ANGLE KLM is (7x) and ANGLE RST is (36-x) what is the value of x ? Please hurry, this is my final
19
18
30
24
Answer:
30
Step-by-step explanation:
Angle B measures 60°. What is the measure of the angle that is complementary to angle B?
30°
60°
120180°
Georgia wants to test a protein supplement
for muscle gain. It randomly selects 15
players to take the supplement and 15
players to take a placebo. Before and after
10 weeks of taking these pills, the players'
muscle mass is measured and compared.
This is an example of a(n):
A) Sample B) Observational Study
C) Census D). Experiment
Geoff earns $9.25 per hour before taxes, and he works 40 hours per week. Geoff's employer withholds (takes out) 10.65% of geoff's income for taxes. What are geoff's total weekly earnings after taxes are withheld?
A) $ 39.41
B) $59.90
C) $ 330.60
D) $ 370.00
Answer:
a
Step-by-step explanation:
A tank is being filled up with water. At t=0, we know that the tank holds 150 gallons of
water, and after one hour ( t=1) , it holds 180 gallon of water.
Answer:
What is the question?
Step-by-step explanation:
Answer: The initial value is 150 and the rate of change is 30
150+30x=y
b=9 c=4 bc+12.3=?
AAAAAAAAAAAAAAAAAAAAAAAAAASAP
Answer:
48.3
Step-by-step explanation:
since b = 9 and c = 4
9 x 4 = 36 and 36 + 12.3 = 48.3
what is the correct factorization of x^2 - 2x - 15?
Answer:
Step-by-step explanation:
x2 - 2x - 15
x2 - 5x + 3x - 15
x(x - 5) + 3(x - 5)
(x - 5) and (x + 3) are the factors
Simplify (X^5/8)^2/3
Answer: Its x5/12
Step-by-step explanation: Hope this helps!!1 <3
What are the operations of fractions by multiplications?
Marla sold 12 baseball caps for a total of $39, including tax. The equation. 12c=39 can be used to find c, the cost of one cap. What is the value of c
Answer:
$3.25
Step-by-step explanation:
12c = 39
12/12 =0
39/12 = 3.25
c = 3.25
35 points plz help
Evaluate −4(14)6x for x=13.
Enter your answer as a fraction in simplest form in the box.
Answer:
-15228
Step-by-step explanation:
Given the expression :
-4(14)6x for X = 13
To evaluate ; simply substitute 13 for X in the equation :
-14(14)6(13)
-14 * 14 * 6 * 13 = - 15228
A 2-quart carton of non-dairy creamer costs $6.32. What is the price per cup?
Answer:
you mean 2.5?????? in two quart????
Your friend's parents each have a job. Her mother's average weekly salary is $740 with a standard deviation of $43. Her father's average weekly salary is $535, with a standard deviation of $25. Find the average weekly salary of her parents combined, and the standard deviation of their combined salaries. You can assume that the amount of money her mother makes has no effect on her father's salary, and vice versa.
Answer:
M= 740 [tex] \alpha = 43[/tex]D= 535[tex] \alpha = 25[/tex]You have two samples and two standard deviations We need the average of the take home pay and their combined standard deviation.So combined both regressions to get the total combined.The average weekly salary of friends' parents is 1275$ and the standard deviation is 49.739.
What is the standard deviation?The standard deviation measures the degree of dispersion of a collection of data. Each data point is compared to the average of all the data points, and the standard deviation gives a determined number that indicates whether the data points are clustered together or dispersed. The standard deviation of a normal distribution indicates how far values deviate from the mean.
Given that, Both of my friend's parents are employed. Her mother makes $740 on average per week, with a standard variation of $43. Her father makes $535 on average each week, with a standard variation of $25.
Let X denotes the weekly salary of her mother.
X ~ Normal(740,432)
Let Y denotes the weekly salary of her father.
Y ~ Normal(535,252)
and X and Y are independent.
the average weekly salary of your parents combined = E(X+Y)
= E(X) + E(Y) = 740 + 535 = 1275
the variance of weekly salary of your parents combined = Var(X+Y) = Var(X) + Var(Y) = 432 + 252 = 2474
the standard deviation of the combined salaries = [tex]\sqrt{2474}[/tex] = 49.739
Therefore, Parents of friends make 1275 dollars on average per week, with a standard deviation of 49.739.
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30 POINTS BRAINLY FIRST REAL RESPONSE
Step 3: Applying linear functions
Grace and Claire’s parents are saving money now for their college education. Function 1 shows the growth of baby Grace’s college fund over time. Function 2 shows growth of baby Claire’s college fund over time.
a) If Grace and Claire’s parents each invested $7,600 into a college saving account when the girls were born, how much money will each girl have for college when she turns 18? Explain. (2 points)
b) Do the functions show a positive or negative correlation between time and the amount of money saved? Explain. (1 point)
Answer:
For A
For grace the x would be the number 18
y = 1000 (18) + 7600
y= 18000 = 7600
and that would mean y = 25600
Now for Claire you have to use the method rise over run
The equation for claire is y=800x + 7600
11600-10000/3=800
---------------------------------------
y= 800(18) + 7600
y= 14,400 + 7600
y= 22,000
This shows that Claire would have $22,000 when shes 18 and Grace would have $25,600 when she is 18.
Two similar cones have volume of 4 m and 108 m respectively. If the large one has surface area 54 m, find the surface area of the smaller one.
[tex]\displaystyle\bf\\Explanations:\\\\The~similarity~ratio~of~two~similar~cones=k\\\\k=is~the~ratio~between~2~corresponding~lengths\\\\k=\frac{R_1}{R_2}=\frac{h_1}{h_2}\\\\The~ratio~between~2~corresponding~areas~of~similar~cones=k^2\\\\\frac{Area~1}{Area~2}=k^2\\\\The~ratio~between~the~volumes~of~the~2~similar~cones=k^3\\\\\frac{Volume~1}{Volume~2}=k^3[/tex]
.
[tex]\displaystyle\bf\\Solving:\\\\Volume1=108~m^3\\\\Volume2=4m^3\\\\k^3=\frac{108}{4}\\\\k^3=27~~\Big|\sqrt{~}\\\\k=\sqrt[\b3]{27}\\\\k=3\\\\Area1=54~m^2\\\\\frac{Area~1}{Area~2}=k^2\\\\\frac{54}{Area~2}=3^2\\\\\frac{54}{Area~2}=9\\\\Area2=\frac{54}{9}\\\\\boxed{\bf Area2=6 m^2}[/tex]
Solve each equation for 0< theta < 2pi
3-2sin theta=5
Step-by-step explanation:
3 - 2sinθ = 5
2sinθ = -2
sinθ = -1
Therefore θ = 3π/4.
I need this done quick pls.
Answer:
58º
Step-by-step explanation:
The sum of a triangle's interior angles is 180º. We know two interior angles, and we can solve from there: 180-(65+57)=180-65-57=180-180-122=58.
what number represents 125.638 rounded to the nearest hundreth
Answer:
The answer is [tex]125.64[/tex]
Step-by-step explanation:
hope this helps :)
17 Ryan and two friends volunteered to deliver
potted flowers to one wing of the hospital.
They have 18 flowers to deliver. If they each
deliver the same number of flowers, how
many flowers will each boy deliver?
Perimeter of 316 and 67 m
Answer:
383 m
Step-by-step explanation:
Use the following scenario to answer the question below:
You are deciding between two cars with different engines and want the bigger
of the two. One engine displaces 350 cubic inches. The other displaces 5,500
cubic centimeters. How many significant figures do the values in this problem
involve?
A. 4
B. 3
C. 2
D. 1
which of the following are trinomials?
PLS, I REALLY NEED THIS ANSWER.
Answer:
Option (A) and Option (B)
Step-by-step explanation:
Trinomial is a polynomial having three terms.
Option A
[tex]\frac{5}{7}y^3+5y^2+y[/tex]
Number of terms = 3
So it's a trinomial.
Option (B)
x⁴ + x² + 1
Number of terms = 3
It's a trinomial.
Option C
6x² + 0.5y²
Number of terms = 2
It's a binomial.
Option D
x² + 3
Number of terms = 2
It's a binomial.
Option E
x¹¹
Number of terms = 1
Monomial
Option F
8x
Monomial.
Therefore, Option (A) and Option (B) are the correct options.