What is the complete factorization of 8x2 − 8x + 2?
A. 2(4x − 1)2
B. 8(x − 1)(x + 1)
C. 2(2x − 1)2
D. 2(x − 2)(x + 2)
Answers
Answer:
Step-by-step explanation:
8x^2 - 8x + 2
2(4x^2 - 4x + 1)
2(2x - 1)(2x - 1) or 2(2x - 1)^2
answer is C
The complete factorization of \(8x^2 - 8x + 2\) will be \(2(2x-1)^2\) .
What is factorization ?Factorization is a process consists of writing a number or another mathematical object as a product of several factors solving it into other factors.
We have,
\(8x^2 - 8x + 2\)
Using the mid term splitting method;
\(=8x^2-4x-4x+2\)
\(=4x(2x-1)-2(2x-1)\)
\(=(4x-2)(2x-1)\)
\(=2(2x-1)(2x-1)\)
\(=2(2x-1)^2\)
So, the factorization of the given expression is given in option \((c)\) i.e. \(2(2x-1)^2\) .
Hence, we can say that the complete factorization of \(8x^2 - 8x + 2\) will be \(2(2x-1)^2\) .
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Related Questions
write the equation of the graph below
Answers
Answer:
Step-by-step explanation:
This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:
\(y=a(x-h)^2+k\) and this will allow us to solve for the value of a:
\(6=a(6-4)^2+5\) and
\(6=a(2)^2+5\) and
6 = 4a + 5 and
1 = 4a so
\(a=\frac{1}{4}\) and the equation is
\(y=\frac{1}{4}(x-4)^2+5\)
what is .75 into a percent
Answers
Answer:
75 percent trust me bro okay
a major disadvantage of correlations is that they cannot make a(n) blank statement. multiple choice question.
Answers
A major disadvantage of correlations is that they cannot make a cause-and-effect statement.
What are correlations?Correlations are statistical measures that describe the size and direction of a relationship between variables.
Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.
The disadvantages of correlations include:
There are no causes and effects.Results can find no inference.The strength of the relationship is not explained.There is the possibility of a confounding factor.Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.
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* You have a dog that can run 5 km/hr. How fast can she run in mi/hr? (i.e. convert the rate to miles per hour) (1.6 km=1mi) DO NOT JUST TYPE THIS INTO A CONVERTER ONLINE. YOU WILL NOT GET THE ANSWER RIGHT. Express your answer as decimal, rounded to the nearest thousandth (three decimal places) in mi/hr - no spaces EXAMPLE: 78.345mi/hr
Answers
The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.
To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.
However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.
Therefore, the dog can run at approximately 3.125 mi/hr.
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Answer choices:
30 degrees
124 degrees
94 degrees
35 degrees
Answers
Answer:
A. 94 degrees
Step-by-step explanation:
Both the angles are similar and can be called parallel angles.
They are equal to each other so:
m∠2 = m∠3
4x - 26 = 3x + 4
4x - 3x = 4 + 26
x = 30°
m∠2 = 4x - 26
= 4(30) - 26
= 94°
Answer:
∠ 2 = 94°
Step-by-step explanation:
∠ 2 and ∠ 3 are vertically opposite angles and are congruent, so
4x - 26 = 3x + 4 ( subtract 3x from both sides )
x - 26 = 4 ( add 26 to both sides )
x = 30
Then
∠ 2 = 4x - 26 = 4(30) - 26 = 120 - 26 = 94°
Which graph represents the function f {x} = -log (x-1) + 1?
Graph A
Graph B
Graph C
Graph D
Answers
Solve the following equation: 3.3+4x=-6.9x+6.6
Round your answer to the nearest tenth.
Answers
The solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.
To solve the equation 3.3 + 4x = -6.9x + 6.6, we need to isolate the variable x on one side of the equation.
First, let's simplify the equation by combining like terms:
3.3 + 4x = -6.9x + 6.6
Next, let's move the variable terms (4x and -6.9x) to one side and the constant terms (3.3 and 6.6) to the other side:
4x + 6.9x = 6.6 - 3.3
Combine the x terms on the left side:
10.9x = 3.3
Now, divide both sides of the equation by 10.9 to solve for x:
x = 3.3 / 10.9
Using a calculator, we can find the decimal approximation of x:
x ≈ 0.3028
Rounding to the nearest tenth, the solution to the equation is x ≈ 0.3.
In summary, the solution to the equation 3.3 + 4x = -6.9x + 6.6, rounded to the nearest tenth, is x ≈ 0.3.
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Two rectangles are joined together to form a single large area. The rectangles do not overlap. The first rectangle has side lengths of 333 meters and 555 meters. The second rectangle has side lengths of 777 meters and 444 meters. What is the combined area?
Answers
Answer:
Step-by-step explanation:
333 times 555=184815
777 times 444=344988
now add 184815+344988=529803
a vertical vector of 3 units combined with a horizontal vector of 4 units has a resultant of
Answers
The resultant of the vertical vector of 3 units combined with the horizontal vector of 4 units has a magnitude of 5 units.
To find the resultant of a vertical vector of 3 units combined with a horizontal vector of 4 units, we can use the Pythagorean theorem.
The magnitude of the resultant vector can be calculated as the square root of the sum of the squares of the individual vector components.
Using the given values, the vertical vector has a magnitude of 3 units and the horizontal vector has a magnitude of 4 units.
Using the Pythagorean theorem, we can find the magnitude of the resultant vector:
Resultant magnitude = √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5
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Can someone help me with this pleaseee…….
Answers
The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.
We have,
To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:
Distance Formula:
If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:
AB = √((4 - (-5))² + (5 - 5)²) = 9
BC = √((2 - 4)² + (0 - 5)²) = √(29)
CD = √((-5 - 2)² + (-2 - 0)²) = √(74)
DA = √((-5 - (-5))² + (5 - (-2))²) = 7
Therefore,
The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.
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Which expression does NOT represent the product of 3 and 7?
A. 3⋅7
B. 3(7)
C. 37
D. 3×7
Answers
Answer:
C: 37
Step-by-step explanation:
37 isn't divisible by 3 or 7. 37/3=12 1/3, 37/7=5 2/7
All the others are different ways to write multiplication.
(-5, 2) ,(4, 2)
Find the slope of the line
Answers
Answer: 0
Step-by-step explanation:
Slope (m) is defined by the formula change in y divided by the change in x. You could denote "change in" using Δ (delta).
The change in y is your final postion along the y-axis, subtracted by your initial position on the y axis.
The change in x is your final position among the x-axis, subtracted by your initial position.
Think of these two sets of coords like two positions. Your final y was 2, and your initial was also 2. Do 2 - 2 to get 0. We dont even need to solve for delta x because 0 divided by anything is zero. Therefore your slope will be 0. That basically means you have a critical point of the function. The tangent line will be completely horizontal along that interval of coords.
To find the slope of the line, I will be showing you the table method.
To find the slope of the line using the table method,
we start by making a table for our ordered pairs.
We will put the x values in the left column
and the y values in the right column.
Our first ordered pair is (-5, 2), so we put a
-5 in the x column and a 2 in the y column.
Our second ordered pair is (4, 2), so we put a
4 in the x column and a 2 in the y column.
Next, remember that the slope or m, is always equal to
the rate of change or the change in y over the change in x.
Using our table, we can see that the y values
go from 2 to 2 so the change in y is 0.
The x values go from -5 to 4 so the change in x is 9.
Therefore, the rate of change, or the change in y
over the change in x is 0/9 which simplifies 0.
This means that the slope is also equal to 0.
Pleaseee help asap 20 points!!! : Which of the following is the expanded form of a number? Select all correct answers.
(A) 7·1000+8·100+3· 1/100
(B) 4·100+9·100+3· 1/10 +4· 1/10
(C) 71·10+4·1+6· 1/100 +5· 1/1000
(D) 5·1000+5·100+5·1+5·1/100
(E) 3·1000+8·1000+9·1/1000
(F) 9·1000+3·101+5· 1/10
Answers
(A) 7·1000+8·100+3· 1/100 is in expanded form.
(B) 4·100+9·100+3· 1/10 +4· 1/10 is in expanded form.
(C) 71·10+4·1+6· 1/100 +5· 1/1000 is in expanded form.
(D) 5·1000+5·100+5·1+5·1/100 is in expanded form.
(E) 3·1000+8·1000+9·1/1000 is in expanded form.
(F) 9·1000+3·101+5· 1/10 is not in expanded form because 3·101 is not a specific place value.
Therefore, the expanded form of a number is given by options A, B, C, D, and E.
4400 dollars is placed in an account with an annual interest rate of 7%. To the nearest year, how long will it take for the account value to reach 10100 dollars?
Answers
Answer:
19 years approx
Step-by-step explanation:
Given data
Principal P= $4400
Rate r=7%
Final amount A=$10100
Time t= ???
Let us apply the simple interest expression
A=P(1+rt)
substitute
10100=4400(1+0.07*t)
open bracket
10100=4400+308t
10100-4400=308t
5700=308t
t= 5700/308
t= 18.50
Hence the time is 19 years approx
A cargo plane flew to Las Vegas and back. On the trip there it flew 325 mph and on the return trip it went 195 mph. How long did the trip there take if the return trip took ten hours?
Answers
The time it will take for the trip is 6 hours.
How to find how long the trip took?The cargo plane flew to Las Vegas and back.
On the trip there it flew 325 mph and on the return trip it went 195 mph.
The time the trip took can be found as follows;
speed = distance / time
Therefore, the return trip took 10 hours.
195 = d / 10
cross multiply
d = 1950 miles
Therefore, the time it will take on the trip is as follows:
time = 1950 / 325
time = 6 hours
Therefore, the time it will take for the trip is 6 hours.
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when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5
Answers
When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13 degrees
The distance between point a to point b = 5.3 feet
The length of the top side = 3 feet
Therefore, it will form a right triangle
Here we have to use trigonometric function
Here adjacent side and the hypotenuse of the triangle is given
The trigonometric function that suitable for the given conditions is
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos θ = 3 / 5
θ = cos^-1(3 / 5)
θ = cos^-1(0.6)
θ = 53.13 degrees
Therefore, the value of θ is 53.13 degrees
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how many solutions does 10x - 10= -10x + 10
Answers
If im wrong im so sorry!! ):
A new iPhone cost $700. There is 8% sales tax in Philadelphia. What is the total cost of the iPhone including tax
Answers
Answer:
56
Step-by-step explanation:
im noy one hundred percent sure
hello i really need ur help
Answers
Answer: Im sorry if i'm wrong but i think the intercept is 2
Step-by-step explanation:
Find a value of c so that P(Z ? c) = 0.71. a) -1.11 b) 0.75 c) -0.55 d) 0.55 e) 1.55
Answers
Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.
The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.
Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.
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What is the length of the leg of a right triangle if one leg is 4 and the hypotenuse is 5?
a.25
b.3
c.16
d.9
Answers
Answer: B. 3
Step-by-step explanation:
4^2 + b^2 =5^2
16 + b^2= 25
-16 -16
b^2 = 9
\(\sqrt{9} =3\)
Mike deli just sold 328 ham sandwiches this week around how many ham sandwiches did mike sell every eat this week (round to the nearest number)
Answers
Answer:
To the nearest number = 47 ham sandwiches
Step-by-step explanation:
Mike deli just sold 328 ham sandwiches this week around how many ham sandwiches did mike sell every day this week (round to the nearest number )
Total ham sandwiches Mike sold this week = 328
Total number of days in a week = 7
how many ham sandwiches did mike sell every day this week
Number of ham sandwiches mike sell every day this week = Total ham sandwiches Mike sold this week / Total number of days in a week
= 328 / 7
= 46.9
To the nearest number = 47 ham sandwiches
Find the reciprocal of 20.95 to 4 decimal places using the tables of reciprocals
Answers
0.0477 is the equivalent reciprocal of 20.95
Finding the reciprocal of decimalsReciprocals, also known as multiplicative inverses, are numbers that, when multiplied together, result in the product of 1.
For instance, the reciprocal of 'a' is 1/a
Given the decimal value 20.95, this can also be written as:
20.95 = 2095/100
The reciprocal will be expressed as;
2095/100 = 1/(2095/100)
2095/100 = 100/2095
100/2095 = 0.0477
Hence the reciprocal of 20.95 to 4 decimal places is 0.0477
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To find the x-intercept, we let y = 0 and solve for x and to find y-intercept, we let x=0 and solve for y. Figure out the x-intercept and y-intercept in given equation of the line.
6x + 2y = 12
Answers
Answer:
x-intercept = 2
y-intercept = 6
Step-by-step explanation:
x-intercept: 6x = 12; x = 2
y-intercept: 2y = 12; y = 6
What is the nth term rule of the quadratic sequence below?
6, 20, 40, 66, 98, 136,...
Answers
~Hope this helps.
Help that’s it just help I’ll give brainiest
Answers
Answer:
1725 ft^2
Step-by-step explanation:
\(\frac{b_{1} + b_{2}}{2} (h) = \frac{65 + 50}{2} (30) = \frac{115}{2} (30) = 57.5(30) = 1725\)
Brainliest would be appreciated!
help with both please :)
Answers
Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:
Method of Elimination1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i) multiplied by 2
10x + 2y = 18 - - - - (i)
10x - 7y = - 18 - - - - (ii) {subtraction of eq. (ii) from eq. (i)}
0 + 9y = 36
y = 36/9
y = 4
From eq. (i),
5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
-> x = 5/5
-> x = 1
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (ii) multiplied by 3
- 4x + 9y = 9 - - - - (i)
3x - 9y = - 18 - - (ii) {addition of eq. (ii) and eq. (i)}
- x + 0 = - 9
x = 9
From eq. (ii),
x - 3y = - 6
-> 9 - 3y = - 6
-> - 3y = -6-9
-> y = -15/-3
-> y = 5
So, x = 9 and y = 5
Method of Substitution1) 5x + y = 9 - - - - (i)
10x - 7y = - 18 - - - - (ii)
eq. (i)
5x + y = 9
-> y = 9 - 5x
Value of eq. (i) in eq. (ii)
10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x = 1
From eq. (i),
5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4
So, x = 1 and y = 4
2) - 4x + 9y = 9 - - - - (i)
x - 3y = - 6 - - - - (ii)
eq. (i)
- 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4
Value of eq. (i) in eq. (ii)
x - 3y = - 6
-> (9 - 9y) / -4 -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y = 5
From eq. (ii)
x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9
So, x = 9 and y = 5
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hope it helped
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What would be the most appropriate first step if you wanted to solve this system of equations using elimination? 3x+2y=7 x+4y=−8 A. Multiply the first equation by −1 B. Multiply the second equation by −2 C. Multiply the first equation by −2 D. Multiply the second equation by -1−1
Answers
Answer:
A. Multiply the first equation by −1
Step-by-step explanation:
From the above question, our system of equations is
3x+2y=7... Equation 1
x+4y=−8..... Equation 2
Hence, solving by Elimination, the first step would be if we are eliminating x first, we are to Multiply Equation 1 by -1
Option A is the correct option
5x-4 ≥12 or 12x+5 ≤-4
Answers
Answer:the answer is in fact 3/4
Step-by-step explanation:
-24x(x-27). multiply
Answers
Answer:
I think it 648.
Step-by-step explanation: