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
Ryan's dog weighs 50 pounds, and Mark's dog weighs p pounds. Which expression shows their combined weight? A. 50 × p B. 50 + p C. 50 ÷ p D. 50 - p
Answer:
B, 50 + p.
Step-by-step explanation:
To combine their weight, you would add them together. B is the only answer that uses addition.
Find the value of x.
Group of answer choices
25
40
65
115
Answer:
40
Step-by-step explanation
x=40 because if you time these in like this:
3(40)-10= 110
40+15=55
If you user 65 it'll be wrong because:
3(65)-10=185
And the whole thing is only 180 :]
Fewer young people are driving. In , of people under years old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to in . Suppose these results are based on a random sample of people under years old who were eligible to have a driver's license in and again in . a. At confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver's license in ?
The margin of error is 0.027 and the interval estimate at 95% confidence interval is 0.612 to 0.666
How to calculate the margin of error and the interval estimateFrom the question, we have the following parameters that can be used in our computation:
Proportion, p = 63.9%
Sample size, n = 1200
The margin of error can be calculated using:
E = z * √((p * (1 - p))/n)
Where
z = 1.96 i.e. z-score at 95% CI
Substitute the known values in the above equation, so, we have the following representation
E = 1.96 * √((0.639 * (1 - 0.639))/1200)
Evaluate
E = 0.027
The interval estimate is calculated as
I = p ± E
So, we have
I = 0.639 ± 0.027
Evaluate
I = 0.612 to 0.666
Hence, the interval estimate is 0.612 to 0.666
Read more about confidence interval at
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Question
Fewer young people are driving. In 1995, 63.9% of people under 20 years old who were eligible had a driver’s license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample of 1200 people under 20 years old who were eligible to have a driver’s license in 1995 and again in 2016.
At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver’s license in 1995?
A ps4 uses uses 8.8 watts when on stand by mode. If electricty in your area costs 0.10$ kwh, how much would this cost?
Answer0.88:
Step-by-step explanation: because for every watt 10 cents or .10 is being used so since there is 8.8 watts it would be a total of 0.88 in your area
Solve x^2 +13x+12=0 Please answer this
Answer:
x=−1 or x=−12
Step-by-step explanation:
Let's solve your equation step-by-step.
x2+13x+12=0
Step 1: Factor left side of equation.
(x+1)(x+12)=0
Step 2: Set factors equal to 0.
x+1=0 or x+12=0
x=−1 or x=−12
Answer:
Solution
=
−
1
=
−
1
2
Step-by-step explanation:
I'm not 100 % sure about my answer
Function or Non-Function
Answer:
2 is not a function.
3 is a function
Step-by-step explanation:
one x value should each have a line leading off it. there are 2 y values for one x values in question 2 so its not a function
In a class 3/4 of the boys like math, 1/2 like science, 1/4 of those who like science do not like math. How many boys like neither math nor science?
A. 1/4
B. 1/6
C. 1/2
D. 1/8
The height in feet (h) of the ball t seconds after it is released can
be modeled using the formula: – 16t^2 + 10t + 6 = h
Find the time, in seconds, passed before the ball hits the ground
(let h = 0).*
*PLEASE SHOW WORKK
Step-by-step explanation:
h = -16t² + 10t + 6
When h = 0, -16t² + 10t + 6 = 0.
=> -8t² + 5t + 3 = 0
=> (-8t - 3)(t - 1) = 0
=> t = 1 or t = -3/8 (rejected as time cannot be negative)
Hence 1 second passed before the ball hits the ground.
Geometry B Final Name Date Period Name the relationship. complementary, linear pair, vertical, adjacent, alternate interior, corresponding, or alternate exterior 1 2) 3) 4) 5) 6) 7) 8)
Answer:
but we can't write all the answers here
Answer:
Step-by-step explanation:
1. complementary
2. alt ext
3. supplementary
4. corresponding
5. b=65
6. 34
7. x=7
8.x=18
What is the area of the trapezoid.
Answer:
60
Step-by-step explanation:
base times height
Write the mixed number as a percent.
4 7/500
Answer:
4 7/500 as a percent is 401.4%
The mixed fraction [tex]4\frac{7}{500}[/tex] can be represent as 401%.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Fraction : 4 7/500
Now, writing the fraction in normal fraction form
= 4 7/500
= 2007/500
Now, to convert into percent
= 2007/ 500 x 100
= 2007/ 5
= 401%
Learn more about fraction here:
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what’s the answer to this ?
Answer:
the answer should be [tex]-20.2m - 11.8[/tex]
Step-by-step explanation:
I need help pleas I need it please please please free 50 points
Answer:
answer is 0
Step-by-step explanation:
Answer:
its zero
Step-by-step explanation:
28 divided by 4 is 7
7 to the power of 2 is 49
49 divided by 7 is 7
7-7 is 0
Helpppppppppppp!!!!!!!!!
Answer: The answer is D. 1/16
Step-by-step explanation: If you think about it, 2 to the 4th power is 16. But in this situation, you have a negative exponent. To solve an exponent situation with a negative situation, put a 1 as the numerator and put the answer of the expression but with the exponent's positive value as the denominator. Hope this helps :D
Investors buy a studio apartment for $140,000. Of this amount, they have a down payment of
$42,000. Their down payment is what percent of the purchase price? What percent of the purchase
price would a $49,000 down payment be?
Their down payment is % of the purchase price.
Answer:
their down payment is 30%
Step-by-step explanation:
Answer:
Step-by-step explanation:
if the price of the apartment is 140,000 dollars
lets find out how much is 1%
140,000/100=1400
42,000/1400=30
42,000 is 30% of the apt price
49,000/1400=35
49,000 is 35% of the apt price
HELP!
during a back to school sale, a store sold jeans at a 25% discount. if one pair of jeans originally cost $35, what was its price during the sale?
Answer:
15$
Step-by-step explanation:
hope this helped
Answer:
35*0.25= 8.75 (multiply by the discount converted into a decimal)
35- 8.75= 26.25 (subtract that from the original to find the discount price)
or
35* 0.75= 26.25 (multiply by the percentage of the original price that you bought the jeans at)
Step-by-step explanation:
either way the answer is $26.25 is the discounted price
Evaluate 32 divided by 1.6
show work
Answer:
20
Step-by-step explanation:
32/1.6= 20
How do you want me to show the work? Long division?
Answer:
20
Step-by-step explanation:
Idk how you want me to show the work, sorry. The formatting will be weird unless I attach a pic or something
My head is hurting can you help me
It’s 16 points
Answer:
-6, -4
Step-by-step explanation:
If you flip the shape over the Y axis you can see
ILL GIVE YOU BRAINLIEST IF YOU HELP ME
Answer:
y = (1/2) x - 2
Step-by-step explanation:
Let us consider the points (- 2, - 3) & (0, - 2)
Equation of line in two point form is given as:
[y-(-3)]/[-3-(-2)] = [x - (-2)]/[-2 - 0]
(y + 3)/(-3 +2) = (x + 2)/ (-2)
(y + 3)/(-1) = (x + 2)/(-2)
(y + 3)/(1) = (x + 2)/(2)
2(y + 3) = (x + 2)
2y + 6 = x + 2
2y = x + 2 - 6
2y = x - 4
y = (1/2) x - 2
PROCEED IN THE SAME WAY TO FIND OUT THE REMAINING FUNCTIONS.
help asaap dont use me for points please
Answer:
-1.5
Step-by-step explanation:
You were on the free points page
solve for X enter your answer in the Box
Answer:
x = 10
Step-by-step explanation:
Since the angles are equal I believe you can just set the ratios equal, cross multiply and solve
Please help soon! Thanks! Solve for x
Answer:
[tex]x=30^{\circ}[/tex]
Step-by-step explanation:
Looking at [tex]\triangle LMN[/tex]:
[tex]\angle NML = 180 - (90+45)[/tex] (angle sum of triangle is [tex]180^{\circ}[/tex])
[tex]=45^{\circ}[/tex]
Looking at [tex]\triangle KNM[/tex]:
[tex]\angle KNM = 180-105[/tex] (angle of straight is [tex]180^{\circ}[/tex])
[tex]=75^{\circ}[/tex]
[tex]\angle KNM + \angle NKM + \angle KMN = 180[/tex] (angle sum of triangle is [tex]180^{\circ[/tex])
[tex]75+2x+45 = 180[/tex]
[tex]2x+120 = 180[/tex]
[tex]2x=60[/tex]
[tex]x=30^{\circ}[/tex]
Hope this helps :)
Which two integers are 7 units away from the number 0 an a number line ?
1. -2 and 12
2. -2and 2
3. -2and 7
4. -7 and 7
Answers ASAP!!!!!
Question:
Which two integers are 7 units away from the number 0 an a number line ?
Answer:
-7 and 7
The heights of dogs, in inches, in a city are normally distributed with a population standard deviation of 7 inches and an unknown population mean. If a random sample of 20 dogs is taken and results in a sample mean of 21 inches, find a 95% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.
Answer:
The 95% confidence interval is [tex] 17.932 < \mu < 20 + 22.068[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma =7 \ inches[/tex]
The sample size is n = 20
The sample mean is [tex]\= x = 20[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{7 }{\sqrt{20} }[/tex]
=> [tex]E = 2.068[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 20 - 2.068 < \mu < 20 + 2.068[/tex]
=> [tex] 17.932 < \mu < 20 + 22.068[/tex]
can somebody help me with that
Given: GI¯¯¯¯¯¯¯ bisects ∠HGJ and ∠H≅∠J
Prove: △GIJ≅△GIH
Answer:
tbh how we suppose to help
1. An iPhone is on sale for $780. It originally cost $1000.00. What is the percent of change?
Answer:
your answer is going to be 220.
a.
[tex] \cot^{2} - \cos ^2a = \cot ^{2} a \times \cos ^{2} a[/tex]
Step-by-step explanation:
We need to prove that,
[tex]\cot^2 a-\cos^2 a=\cot^2 a\times \cos^2 a[/tex]
Taking LHS,
[tex]\cot^2 a-\cos^2 a[/tex]
We know that,
[tex]\cot a=\dfrac{\cos a}{\sin a}[/tex]
[tex]=(\dfrac{\cos a}{\sin a})^2 -\cos^2 a\\\\=\cos^2 a(\dfrac{1}{\sin^2 a}-1)\\\\=\cos^2 a(\dfrac{1-\sin^2a}{\sin^2 a})\\\\=\cos^2 a\times \dfrac{\cos^2 a}{\sin^2 a}\\\\=\dfrac{\cos ^2 a}{\sin^2 a}\times \cos^2a\\\\\because \ \dfrac{\cos ^2 a}{\sin^2 a}=\cot^2 a\\\\=\cot^2 a \times \cos^2a\\\\=RHS[/tex]
So, LHS = RHS
Hence, proved.
The sum of two numbers is 14 one number is two less than three times the other. find the numbers
Answer:
The two numbers are 4 and 10
Step-by-step explanation:
give me a thanks bro
A new window costs $600 plus VAT 20%. How much is the total bill?
Answer:
720
Step-by-step explanation:
600*.2=120
120+600
720
Answer:
720 dollars
Step-by-step explanation:
find 20% of 600 dollars
[tex]\frac{20}{100} * 600[/tex]
= 120 dollars
600 + 120
= 720
I hope this helped!
please mark me as brainliest
if the nth term of a sequence is n^2 -3, find the first 3 terms and the 10th term.
Answer: -2, 1, 6,...97
Step-by-step explanation:
1st term: 1^2 - 3 = -2
1^2 = 1
1-3=-2
2nd term: 2^2-3 = 1
2^2 = 4
4-3=1
3rd term: 3^2-3 = 6
3^2 = 9
9 -3 = 6
10th term: 10^2-3 = 97
10^2 = 100
100-3=97