Prove the polynomial identity. (2x−1)2+2(2x−1)=(2x+1)(2x−1) Drag and drop the expressions to correctly complete the proof of the polynomial identity. (2x−1)2+2(2x−1)=(2x+1)(2x−1) Response area+4x−2=(2x+1)(2x−1) Response area=(2x+1)(2x−1) Response area=(2x+1)(2x−1)
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Answer:
Step-by-step explanation:
Given expression is,
(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)
To prove this identity we will take the left hand side of the equation and will prove equal to the right side.
(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)
4x² - 4x + 1 + 4x - 2 = (2x - 1)(2x + 1)
4x² - 1 = (2x - 1)(2x + 1)
(2x - 1)(2x + 1) = (2x - 1)(2x + 1) [Since a² - b² = (a - b)(a + b)]
Related Questions
If a • b = 0, and a ≠ 0, then b=
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Answer: 5573
Step-by-step explanation:
I need help fast
please help
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-2x=8
x=-4
(I’m not sure if this is right but this is how I’d go about it)
I don’t understand this question.
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Explanation: x=7 in this case. When its says, TQS, it means that particular angle.
7 more than 3 times a number is 49.What is the number?
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Answer:
14
Step-by-step explanation:
Let x be the missing number
3x + 7 = 49 [Given equation]
3x = 42 [Subtract 7 from both sides of the equal sign]
x = 14 [Simplify]
Hope this helps! I apologize if I get this incorrect.
Answer:14
Step-by-step explanation: I hope this helps plz tell me if its wrong so i can fix it :)
6x^2-18x-18=6
CAN SOMEONE EXPLAIN PLS
Answers
6x2 + -18x + -18 = 6
Reorder the terms:
-18 + -18x + 6x2 = 6
Solving
-18 + -18x + 6x2 = 6
Solving for variable 'x'.
Reorder the terms:
-18 + -6 + -18x + 6x2 = 6 + -6
Combine like terms: -18 + -6 = -24
-24 + -18x + 6x2 = 6 + -6
Combine like terms: 6 + -6 = 0
-24 + -18x + 6x2 = 0
Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -3x + x2) = 0
Factor a trinomial.
6((-1 + -1x)(4 + -1x)) = 0
X^2-3x-3=1
X^2-3x-4=0
(X-4)(x+1)=0
X=4 x=-1
how do you find the solution to this inequality? please explain to me step by step how to do this
x - 8 > -3
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Answer:
x > 5
Interval form: (5, infinity)
Step-by-step explanation:
Just add 8 to both sides of the inequality:
x > 5
Therefore, x must be greater than 5.
Write the equation of the line passing through the points (6,16) and (9,25).
First find the slope!
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Answer:
y = 3x - 2
Step-by-step explanation:
Find the slope using rise over run (y2 - y1) / (x2 - x1), where (x1, y1 ) and (x2, y2) are points on the line.
Plug in the 2 points:
(y2 - y1) / (x2 - x1)
(25 - 16) / (9 - 6)
9 / 3
= 3
So, the slope is 3. Plug this and a point into y = mx + b to find b:
y = mx + b
16 = 3(6) + b
16 = 18 + b
-2 = b
Then, plug in b and the slope into the equation:
y = mx + b
y = 3x - 2 is the equation of the line
Given a normal distribution with u = 75 and o = 40, if you select a sample of n = 16, a) what is the probability that the sample mean is above 95? (4 d.p.) b) What is the value, of which there is 97.5% chance that a sample mean is less than that value? (1 d.p.)
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Answer:
a) 0.0228
b) 94.6
Step-by-step explanation:
The formula for calculating a z-score when you are given a random.number of samples is z = (x-μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation
n = random number of samples
Given a normal distribution with u = 75 and o = 40, if you select a sample of n = 16,
a) what is the probability that the sample mean is above 95? (4 d.p.) b)
= x = 95
Hence:
z = 95 - 75/40/√16
= 20/40/4
= 20/10
= 2
Probability value from Z-Table:
P(x<95) = 0.97725
P(x>95) = 1 - P(x<95) = 0.02275
The probability that the sample mean is above 95 to 4 decimal places = 0.0228
b) What is the value, of which there is 97.5% chance that a sample mean is less than that value?
97.5% chance = z score for the confidence interval = 1.96
Hence:
z = (x-μ)/σ/√n
1.96 = x - 75/40/√16
1.96 = x - 75/ 40/4
1.96 = x - 75/10
Cross Multiply
1.96 × 10 = x - 75
19.6 = x - 75
x = 19.6 + 75
x = 94.6
The value, of which there is 97.5% chance that a sample mean is less than that value is 94.6
What numbers rounded to 200,000 when rounded to the nearest hundred thousand
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Answer:
The answer would be 150,000 to 249,999
Carolyn is using the table to find 360% of 15. What values do X and Y represent in her table? Percent Total 100% 100% 100% 20% 20% 20% 360% X X X Y Y Y X = 2.5; Y = 2.5 X = 5; Y = 0.75 X = 15; Y = 3 X = 15; Y = 5
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Answer: c
Step-by-step explanation:
Based on the percent breakdown of 360%.
100% 100% 100% 20%20%20%
15. 15. 15. 3. 3. 3.
100% is all of it, so 15. This is x.
20% of it would be calculated as 0.2 x 15 or 3. This is y.
Answer:
c
Step-by-step explanation:
-18 - 6n= 6 (1 + 3n)
Answers
Answer:-1
Step-by-step explanation:-18-6n = 6 + 18n
-6n=6
divide
n=-1
Answer:
-1
Step-by-step explanation:
First, divide by 6
-18/6- 6n/6=6/6(1+3n)
-3-n= 1+3n
Then move the variable to one side
-3-n+n= 1+3n+n
-3=1+4n
Then isolate the variable
-3-1=1-1+4n
-4=4n
Isolate more
-4/4=4n
-1=n
20 POINTS PLEASE HELP!!!!! Charlie bought hamburgers and drinks for his coworkers. Each hamburger cost $3.75
and each drink cost 50 cents. In total, Charlie paid $25.50 for his order.
Write an equation that represents the relationship between the number of
hamburgers he bought, h, and the number of drinks he bought, d.
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Answer:
3.75h + 0.5d = 25.50
Step-by-step explanation:
3.75h is $3.75 multiplied by h, the amount of hamburgers they buy. same goes for 0.5d it’s 50¢ multiplied by d, the amount of drinks they buy. then both those variables added has to equal $25.50 because that’s how much they spent total.
x y
-1 3
0 5
1 7
2 9
1. What is the slope? m=
2. What is the y-intercept? b=
3. Write the equation in slope-intercept form:
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Answer:
m=2(0,5)2x+5Step-by-step explanation:
The slope is achieved through (5-3)/((0-(-1)) which is 2. The y-intercept is just where x=0 on the equation so (0,5). 3. Put it all together in y=mx+b to get 2x+5. Hope that helps!
Suppose there is a 27.4% probability that a randomly selected person aged 40 years or older is a jogger. In addition, there is a 29.3% probability that a randomly selected person age 40 years or older is male, given that he or she jogs.
Required:
a. What is the probability that a randomly selected person age 40 years or older is male and jogs?
b. Would it be unusual to randomly select a person aged 40 years or older who is male and jogs?
Answers
Answer:
a
[tex]P(M \ n \ J ) = 0.0802 [/tex]
b
Yes
Step-by-step explanation:
From the question we are told that
The probability that a random selected person of age 40 years or older is a jogger is [tex]P(J) = 0.274[/tex]
The probability that a random selected person of age 40 years or older is a male given that he/she jogs is [tex]P(M |J) = 0.293[/tex]
Generally the probability that a randomly selected person age 40 years or older is male and jogs
[tex]P(M \ n \ J ) = P(M|J) * P(J)[/tex]
[tex]P(M \ n \ J ) = 0.293 * 0.274 [/tex]
[tex]P(M \ n \ J ) = 0.0802 [/tex]
Generally it would be unusual because the probability that a randomly selected person age 40 years or older is male and jogs is greater than 0.05[border line for statistical significance]
Round 0.051866 to 2 significant figure
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Answer:
your answer would be 0.052
The figures below are scaled copies. Identify the corresponding parts.
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Answer:
a. ∠U
b. ∠D
c. WX
d. ST
Step-by-step explanation:
A resident of Bayport claims to the City Council that the proportion of Westside residents
(1) with income below the poverty level is lower than the proportion of Eastside residents
(2) The City Council decides to test this claim by collecting a random sample of resident incomes from the Westside of town and a random sample of resident incomes from the Eastside of town. Seventy-six out of 578 Westside residents had an income below the poverty level. Hundred-and-twelve out of 688 Eastside residents had an income below the poverty Specify the hypotheses.
Calculate the value of the test statistic (round to 4 decimal places).
Calculate the p-value (round to 4 decimal places).
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Answer:
The test statistics is [tex]z = -1.56 [/tex]
The p-value is [tex]p-value = 0.05938 [/tex]
Step-by-step explanation:
From the question we are told
The West side sample size is [tex]n_1 = 578[/tex]
The number of residents on the West side with income below poverty level is [tex]k = 76[/tex]
The East side sample size [tex]n_2=688[/tex]
The number of residents on the East side with income below poverty level is [tex]u = 112[/tex]
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 < p_2[/tex]
Generally the sample proportion of West side is
[tex]\^{p} _1 = \frac{k}{n_1}[/tex]
=> [tex]\^{p} _1 = \frac{76}{578}[/tex]
=> [tex]\^{p} _1 = 0.1315 [/tex]
Generally the sample proportion of West side is
[tex]\^{p} _2 = \frac{u}{n_2}[/tex]
=> [tex]\^{p} _2 = \frac{112}{688}[/tex]
=> [tex]\^{p} _2 = 0.1628 [/tex]
Generally the pooled sample proportion is mathematically represented as
[tex]p = \frac{k + u}{ n_1 + n_2 }[/tex]
=> [tex]p = \frac{76 + 112}{ 578 + 688 }[/tex]
=> [tex]p =0.1485[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^ {p}_1 - \^{p}_2}{\sqrt{p(1- p) [\frac{1}{n_1 } + \frac{1}{n_2} ]} }[/tex]
=> [tex]z = \frac{ 0.1315 - 0.1628 }{\sqrt{0.1485(1-0.1485) [\frac{1}{578} + \frac{1}{688} ]} }[/tex]
=> [tex]z = -1.56 [/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(z < -1.56 )[/tex]
From z-table
[tex]P(z < -1.56 ) = 0.05938[/tex]
So
[tex]p-value = 0.05938 [/tex]
Can someone explain both of these ratios and answers to me?
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Answer:
15 ( for Herimone) And 8 ( For Stranger Things)
Step-by-step explanation:
When Herimone uses 5 grams of Pearl Sheen she creates 30 fluid ounces of love potion. Last week she created 90 ounces which is 3 times larger than 30 ounces so you have to multiply 5 by 3 to figure out the amount of Pearl Sheen she used which is 15
For stranger things they Multiplied 3 by 2 so you have to multiply 1 by 2 to get 2. Then you have to add 6 and 2 to get 8 kids.
Hope This Helps!
Which equation could be used to generate the following table?
x y
-2 7
-1 6
0 5
1 4
2 3
a
y = -x + 5
b
y = x + 5
c
y = 5x - 1
d
y = -x - 5
Answers
Answer:
ur welcome
Step-by-step explanation:
x is first so -2 and -1 and 0 and 1 and 2 all cancel each other out so no worries there then on to the other side you add it all and boom you done
Today it rained 2 inches and continues to rain at a rate of one fourth inch per hour what is the liner model in y=X+
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Answer:
y=[tex]\frac{1}{4}[/tex]h+2
Step-by-step explanation:
Luke ate a snack with 91 total calories. If the chips he ate were 41.2
calories, how many calories were in the rest of his snack? *
50.8
132.2
049.8
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Answer:
132.2
Step-by-step explanation:
you just add the percentage of its calories
Luke and Leia are selling hot dogs and hamburgers at a minor league baseball game. At the end of the day they determine they have sold a total of 45 items and earned $195. If hot dogs cost $4 and hamburgers cost $5, how many did they sell of each?
What would be a system of equations for the scenario above?
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Answer:
15 hamburgers were sold and 30 hotdogs were sold.
The systems of equations are x + y = 45 and 4x + 5y = 195.
Step-by-step explanation:
Let's make two equations.
x + y = 45
This represents the total of hotdogs and hamburgers sold
4x + 5y = 195
This represents the amount of money made for each food.
These are systems of equations, when you use 2 equations to solve a problem. I will use the strategy, Elimination for the following systems of equations. Anyways the goal is to multiply a number to x + y = 45 to cancel out one of the variables in 4x + 5y = 195. In other words, when we add these equations, the sum of the xs or ys will equal 0.
Let's multiply -5 to both x and y.
Now we have -5x -5y = -225 + 4x + 5y= 195
We will end up with -x = -30. This means that x = 30.
Now that we know x = 30, we can plug in 30 as x in one of the equations. I will plug in 30 into x + y = 45. 30 + y = 45.
Solve for y in 30 + y = 45, so y=15.
This means 15 hamburgers were sold and 30 hotdogs were sold.
Item 10
A 5-ounce can of tuna costs $0.90. A 12-ounce can of tuna costs $2.40. Which is the better buy?
5-ounce can
12-ounce can which is the right answer 5-ounce can or 12-ounce can help fast pls
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Answer:
The 5-ounce can if divided by five to how to cost for 1-ounce would be $0.18. Then you divide the 12-ounce by 12 for 1-ounce which is $0.2. So the 5-ounce is better.
Step-by-step explanation:
Hope this helped!
9.The Bridgeport water department has a monthly service charge of $12.60 and a volume charge of
$1.38 for every 100 cubic feet of water. Write an equation that can be used to determine the Morgan
family's monthly water bill.
Answers
[tex]y = 1.38x + 12.60[/tex]
Step-by-step explanation:
the 12.60 is going to be charged every months no matter what it's fixed so that's why it's added! the 1.38 is a rate, so how many cubic inches she uses in increments of 100 she will be charged so that depends on how much she uses in addition to that 12.60for example she uses 700 cubic feet of water once month well (x) will be 7 because u divide it by 100 and it'll give u ur "x". put it into the formula and it'll give the price she'll have to pay. 1.38(7) + 12.60 and this will equal $21.70 !The function y=30x represents the distance in miles, y, a car travels after x hours.
Answers
Answer:
first option
Step-by-step explanation:
Answer:
A. The total distance the car travels in miles between hours 3 and 7.
Step-by-step explanation:
I took the test!
If sea turtles can travel 2.8 at top speed in two hours how far did it travel in one hour
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Answer
1.4 miles
Step-by-step explanation:
2.8÷2=1.4
what is 7 - 4 = 5x - 13
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Answer:
x=16/5
Step-by-step explanation:
7-4=5x-13
3=5x-13
+13. +13
16=5x
16/5 = x
If 6 bags of chocolate chips are needed to make 86 cookies, how many cookies can 8 bags chocolate chips make?
Answers
Answer:
114.666666667
Step-by-step explanation:
Step 1:
6/86 = 8/x Equation
Step 2:
6x = 688 Multiply
Step 3:
x = 688 ÷ 6 Divide
Answer:
x = 114.666666667
Hope This Helps :)
I NEED HELP
(-8, 6); slope = 1/4
Answers
6 = 1/4(-8) +b
6 = -2 +b
8 = b
y = 1/4x +8The equation of this line having slope 1/4 and points (-8,6) is y = (1/4)x + 8.
What is slope ?Slope is the rate of change.It can also be thought of as rise over run.
According to the given question slope(m) is 1/4 and point is (-8,6).
We know equation of a line in slope intercept form is y = mx + b, where b is the y intercept.
∴ 6 = (-8)1/4 + b.
6 = - 2 + b.
b = 8.
Now the equation of this line in slope intercept from can be written as
y = (1/4)x + 8.
learn more about equation of a line here :
https://brainly.com/question/2564656
#SPJ2
2. Given the linear equation 2x + 3y = 9.
a.
Write the equation in the form y = mx + b.
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Answer:
y = -2/3x + 3
Step-by-step explanation:
3y = -2x + 9
y = (-2x + 9)/3
y = -2/3x + 3