Answers
Answer:
2x^2 -x +1 = 0
Step-by-step explanation:
For roots α and β, the original equation can be factored as ...
f(x) = 2(x -α)(x -β)
If we add 1 to each of those roots, the factors become ...
g(x) = 2(x -(α+1))(x -(β+1))
This can be rearranged to be ...
g(x) = 2((x -1) -α)((x -1) -β)
That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.
2(x -1)² +3(x -1) +2 = 0
2x^2 -x +1 = 0
Related Questions
In a sale normal prices are reduced by 10% Angelina bought a pair of shoes in the sale for £54 what was the original pricee of the shoes?
Answers
Answer:
£60
Step-by-step explanation:
Given that
The cost after reduction = £54
So, 90% = £54
We have to find 100%
To do so, find 10% and ,multiply that by 10
90% = £54
10% = 54/9 = £6
1005 = 6x10 = £60
Hope this helps,.
Please mark brainiest
Randy is building a fence at the side of his warehouse. He has 120 m of fencing and plans to use the
side of the warehouse as one side of the rectangular fenced area. What are the dimensions of the
maximum area Randy can enclose?
Answers
Answer:
The width (side perpedicular to the wall of the werehouse): x = 30 m
The lenght (side parallel to the wall of the werehouse): y = 60 m
Step-by-step explanation:
x - the width of the fenced area
Randy has 120 m of fencing so for the lenght remain (120-2x) m of fencing:
y = 120 - 2x
Area of the fencing: A = x•y
A(x) = x•(120 - 2x)
A(x) = -2x² + 120x ← quadratic function
The maximum value of quadratic function occurs at: [tex]x=-\frac b{2a}[/tex]
a = -2 b = 120
[tex]x=-\frac b{2a}=-\frac{120}{2\cdot(-2)}=-\frac{120}{-4}=30[/tex]
y = 120 - 2•30 = 60
−6(x+7)=−4x−2 how many solutions
Answers
Answer: There is one solution, -20
Step-by-step explanation:
[tex]-6(x+7)=-4x-2\\\\Distribute\\\\-6x-42=-4x-2\\\\Add(6x)\\\\-42=2x-2\\\\Add(2)\\\\-40=2x\\\\x=-20[/tex]
There is one solution, -20
Hope it helps <3
Answer:
Only one solutionStep-by-step explanation:
Solution,
[tex] - 6(x + 7) = - 4x - 2[/tex]
Distribute -6 through the parentheses
[tex] - 6x - 42 = - 4x - 2[/tex]
Move variable to L.H.S and change its sign
[tex] - 6x + 4x - 42 = - 2[/tex]
Move constant to R.H.S and change its sign
[tex] - 6x + 4x = - 2 + 42[/tex]
Collect like terms
[tex] - 2x = - 2 + 42[/tex]
Calculate the sum
[tex] - 2 x = 40[/tex]
Divide both sides of the equation by - 2
[tex] \frac{ - 2x}{ - 2} = \frac{40}{ - 2} [/tex]
Calculate
[tex] x = - 20[/tex]
Hope this helps..
Good luck on your assignment..
If 8% of a number is 4, what is 12% of a number? Explain your reasoning.
Answers
Answer:
0.08, 4, 0.12
Step-by-step explanation:
0.08, 4, 0.12
in 2000 the median size of a new single family house was 2057 square feet in 2010 the median size was 2169 square feet.
What is the average rate of change in the median home size over this time period?
a.) 112 sq per year
b.) 89 sq per year
c.) 8.9 sq per year
d.) 11.2 sq per year
Answers
Answer:
d.) 11.2 square feet per yearStep-by-step explanation:
The difference in sizes:
2169 - 2057 = 112 square feet
It is 10 years from 2000 to 2010
112:10 = 11.2
When x= 12, y= 144. (a) Express y in terms of x. (b) Find the value of y when x= 7.
Answers
Answer:
see explanation
Step-by-step explanation:
Given x = 12, y = 144
We can see that y is 12 times the value of x, thus
(a)
y = 12x
(b)
when x = 7, then
y = 12 × 7 = 84
Mark says that the number 2 is a rational number because he can write it as the fraction >
Is Mark correct? Why or why not?
O Mark is correct because the denominator, 1, is an integer.
Mark is correct because the fraction is equal to V2.
Mark is not correct because 2 is not equal to the fraction
✓
Mark is not correct because a fraction is rational only if the numerator and the denominator are both integers.
Answers
Answer:
C and D.
Step-by-step explanation:
I am guessing that he wants to find if 2 is a rational number by comparing it to the fraction [tex]\frac{\sqrt {2}}{1}[/tex]
There are a couple of reasons why Mark is not correct:
1. A number is rational only if it can be written as a fraction made up of the numerator and denominator as integers.
2. The fraction [tex]\frac{\sqrt {2}}{1}[/tex] is not equal to 2, so, he is wrong.
So, C and D would be correct.
NOTE: In case I misinterpreted the question, use 1. to judge if it is rational or not, you should get your answer.
Answer:
Mark is not correct because a fraction is rational only if the numerator and the denominator are both integers.
Step-by-step explanation:
This is the correct answer
brainliest pls
9/20 GREATEST COMMON FACTOR
Answers
Answer:
1
Step-by-step explanation:
Factors of 9 are:
1, 3, 9
Factors of 20 are:
1, 2, 5, 10, 20
The greatest common factor is 1.
How might you describe the y values for this section of x values: -1
Answers
Answer:
Answer is below
Step-by-step explanation:
The y-values are all real numbers because they reach every possible y-value from -∞ to ∞ on the y-axis.
NEEEED HELPPP NOWWWW Use long division to find the quotient below.
(x^5+ 18x^2 - 27x) - (x+3)
Answers
Answer:
[tex] {x}^{4} - 3 {x}^{3} + 9 {x}^{2} - 9x[/tex]Option A is the correct option.
Step-by-step explanation:
[tex] \frac{ {x}^{5} + 18 {x}^{2} - 27x }{x + 3} [/tex]
Factor out X from the expression
[tex] \frac{x( {x}^{4} + 18x - 27)}{x + 3} [/tex]
Add and subtract [tex]3 {x}^{3} [/tex]
[tex] \frac{x( {x}^{4} + 3 {x}^{3} - 3 {x}^{3} + 18x - 27)}{x + 3} [/tex]
Write 18x as a difference
[tex] \frac{x( {x}^{4} + 3 {x}^{3} - 3 {x}^{3} - 9 {x}^{2} + 9 {x}^{2} + 27x - 9x - 27 }{x + 3} [/tex]
factor out [tex] {x}^{3} [/tex]from the expression
[tex] \frac{x( {x}^{3} (x + 3) - 3 {x}^{3} - 9 {x}^{2} + 9 {x}^{2} + 27x - 9x - 27) }{x + 3} [/tex]
Factor out [tex] - 3 {x}^{2} [/tex] from the expression
[tex] \frac{x( {x}^{3} (x + 3) - 3 {x}^{2}(x + 3) + 9 {x}^{2} + 27x - 9x - 27) }{x + 3} [/tex]
factor out 9x from the expression
[tex] \frac{x( {x}^{3}(x + 3) - 3 {x}^{2} (x + 3) + 9x(x + 3) - 9x - 27 }{x + 3} [/tex]
Factor out -9 from the expression
[tex] \frac{x( {x}^{3} (x + 3) - 3 {x}^{2} (x + 3) + 9x(x + 3) - 9(x + 3)}{x + 3} [/tex]
factor out x+3 from the expression
[tex] \frac{x(x + 3)( {x}^{3} - 3 {x}^{2} + 9x - 9) }{x + 3} [/tex]
Reduce the fraction with X+3
[tex]x( {x}^{3} - 3 {x}^{2} + 9x - 9)[/tex]
Distribute X through the parentheses
[tex] {x}^{4} - 3 {x}^{3} + 9 {x}^{2} - 9x[/tex]
hope this helps...
Good luck on your assignment...
n chemistry, the pH of a solution is defined by: pH space equals space minus log space left square bracket straight H plus right square bracket, where H+ is the hydrogen ion concentration of the solution in moles per liter. Distilled water has a pH of approximately 7. A solution with a pH under 7 is called an acid, and one with a pH over 7 is called a base. Tomato juice has a hydrogen ion concentration of 10 to the power of negative 4.1 end exponent mole per liter. Find the pH of tomato juice. pH space equals space 4.9 pH space equals space 2.8 pH space equals space 3.5 pH space equals space 4.1
Answers
Answer:
The correct option is;
pH = 4.1
Step-by-step explanation:
The given information are;
The hydrogen ion [H⁺] concentration in tomato juice = [tex]10 ^{-4.1}[/tex]
The pH of a solution = -㏒{H⁺] = -㏒( [tex]10 ^{-4.1}[/tex]) = -(-4.1) × ㏒(10) = 4.1
The pH of the of the tomato juice = 4.1
The pH is the term used to refer to the acidity of water with the range of pH values ranging from 0 to 14 where pH values of a solution lesser than 7 are considered acidic while pH values above 7 indicate a basic solution.
Please help me I will give BRAINLIST and a like
I rlly need help
Answers
Answer:
?=3
Step-by-step explanation:
a= 3/5 b - 7
Answer:
the number that should be in the green box is 3
Step-by-step explanation: since it is three-fifths, in numerical way, it should be written as 3/5..
7 less than three fifths of b is a gives 3/5b-7=a
Here were 87 sunflowers at the flower shop in the morning. There were 56 sunflowers left at the end of the day. How many sunflowers were sold? Explain a way to solve the problem.
Answers
Answer:
31
Step-by-step explanation:
We just have to calculate 87 - 56 which is 31 so the answer is 31 sunflowers.
Answer:
31
Step-by-step explanation:
Since we know that we started with a higher number than we ended with, it is obvious that this is a subtraction problem. Then, we simply have to find the difference by subtracting 87 by 56 (87 - 56 = x). After the calculation, we see that the answer is 31 (87 - 56 = 31).
the profit earned by a hot dog stand is a linear funsion of the number of hot dogs sold.It cost the owner $48 dollars each morning for the day's supply of hot dogs,but he earnes $2 profit for each hot dog sold which equation represent y, the profit earned bye the hot dogs sold
Answers
Answer:
Step-by-step explanation:
If he earns $2 per hot dog sold, then the algebraic expression for this is 2x, where x is the number of hot dogs sold. If he has to put out $48 to buy the supplies, that is represented as -48. The function, then, that represents the profit earned by selling the hot dogs is
y = 2x - 48
Answer:
c
Step-by-step explanation:
Help please solve this
Answers
RU is a diameter, so the two equations make half a circle which is 180 degrees.
24x+5 + 10x+5 = 180
Combine like terms:
34x + 10 = 180
Subtract 10 from both sides:
34x = 170
Divide both sides by 34
X= 5
RS= UV
RS = 10x +5
Replace x with 5
RS = 10(5) + 5 = 55
Answers:
X = 5
RS = 55
11. Three men can build a wall in 10 hours. How
many men would be needed to build the wall in
7 hours?
Answers
Answer:
Man-hours to build the wall: 3 * 10 = 30
:
let m = no. of men required to do it 7.5 hrs
7.5m = 30
m = [tex]\frac{30}{7.5}[/tex]
m = 4 men to build it in 7.5 hrs
Step-by-step explanation:
A group of 4 friends have a bag of 49 sweets. They divide the sweets equally between them. a) How many sweets does each friend get? b) How many sweets are left over
Answers
Answer:
a) Each friend gets 12 sweets
b) There is 1 sweet left
Step-by-step explanation:
When you divide 49 by 4 you will get 12 with a remainder 1.
49 ÷ 4 = 12 R1
The remainder is the left over while the total result is how much each friend gets.
Answer:
A) 12
B) 1
Step-by-step explanation:
49 cannot be divided equally among the 4 friends but 48 can be divided.
A) So,
48/4 = 12 sweets
Each friend gets 12 sweets
B) 1 sweet is left
Factor completely 4x2 − 8x + 4. A Prime B 4x(x2 − 2x + 1) C 4(x2 − 2x + 1) D 4(x2 + 4)
Answers
Answer:
4 ( x-1)^2
Step-by-step explanation:
4x^2 − 8x + 4.
Factor out the greatest common factor
4( x^2 -2x+1)
Factor inside the terms
4( x-1) (x-1)
4 ( x-1)^2
Answer:
4(x-1)(x-1)
4(x^2-2x+1) C
Step-by-step explanation:
4x^2 − 8x + 4 common factor 4
4(x^2-2x+1)
4(x-1)(x-1) or (4x-4)(x-1)
cube of -1/2 is equal to-----------. i need urgent please.I will mark brainest
Answers
Answer:
-1/8
Step-by-step explanation:
(-1/2)(-1/2)(-1/2)=-1/8
Answer:
[tex] \frac{ - 1}{8} [/tex]solution,
[tex] (\frac{ - 1}{2} ) ^{3} \\ = \frac{( { - 1)}^{3} }{( {2}^{3} )} \\ = \frac{ - 1 \times ( - 1) \times ( - 1)}{2 \times 2 \times 2} \\ = - \frac{ 1}{8} [/tex]
hope this helps...
Good luck on your assignment
What is the "k" value of the following function? Is it 3, -2, -3, or 2?
Answers
Answer:
-3
Step-by-step explanation:
we khow that the vertex form of a function is written this way :
f(x)=a(x-h)²+k
the coordinates of the vertex are (h,k) so from the graph we can deduce that k = -3
. Francisco states the following: When two or more factors are multiplied and they have the same sign, the product is positive. List two examples that support Francisco's statement. Show their products.
Your answer
6B. List an example that refutes Fracisco's statement. Show its product. Explain why it refutes his statement.
Your answer
6C. How could Francisco rewrite his statement so it is always true?
pls Help me
Answers
Answer:
6A) i) 5 and 3 product is 15
ii) (-5) and (-3) product is 15
6B. The product of 5·i and 3·i is -15
6C. When two or more real factors are multiplied and they have the same sign, the product is positive
Step-by-step explanation:
6A. To examples that support Francisco's statement are;
Given the factors that have the same sign;
i) 5 and 3 both positive
ii) (-5) and (-3) both negative
The products of each of the two factors are therefore;
5 × 3 = 15 (Positive product)
(-5) × (-3) = 15 (Positive product)
6B. An example that refutes Francisco's claim is the product of two imaginary numbers 5·i and 3·i where i = √(-1) as follows;
5·i × 3·i = 15·i² = 15×i×i = 15 × √(-1) ×√(-1) = 15×(√(-1))² = 15 × (-1) = -15
Therefore;
5·i × 3·i = -15 which is a negative number and therefore refutes Francisco's claim
6C. Francisco could rewrite his statement as follows;
When two or more real factors are multiplied and they have the same sign, the product is positive
To make it always true.
(a) Which of the following has only one subset? (1)
(i) {2} (ii) { } (iii) {Ǿ} (iv) None of these
Answers
Answer:
Option (i)
Step-by-step explanation:
{2} has only 1 subset i.e. {2} and no other subset. While { } or ∅ has no subset.
HELP ME PLEASE HELP ME HELP ME PLEASE
Answers
Answer:
no, because the remainder is 126Step-by-step explanation:
if x+3 is a factor, then -3 is a root of expression, and the remainder would be 0
calculating remainder:
[tex]-3(-3)^3+6(-3)^2+6(-3)+9=-3\cdot(-27)+6\cdot9-18+9=\\\\=81+54-9=126[/tex]
Can someone please help me I really need help please help me thank you
Answers
Answer: x=14
Step-by-step explanation: The total is 180 degrees. The right angle is 90, the given angle is 76, so x is 14.
Which relation defined by a mapping diagram is not a function?
Answers
Answer:
C
Step-by-step explanation:
Sam bakes a variety of biscuits. 1/3
are peanut, 12 are raisin and the
remaining 12 were oat. How many
biscuits are baked?
Answers
Answer: 36
Step-by-step explanation:
Let the no. of biscuits be x
Peanuts will be 1/3x
So,
1/3x + 12 + 12 = x
1/3x + 24 = x
x + 72 = 3x
x-3x = -72
x = 72/2 = 36
Peanut biscuits will be 1/3 * 36 = 12
Total no. of biscuits baked were 12+12+12 = 36
Arc CD is One-fourth of the circumference of a circle. What is the radian measure of the central angle?
StartFraction pi Over 4 EndFraction radians
StartFraction pi Over 2 EndFraction radians
2π radians
4π radians
Answers
Answer:
[tex]\frac{\pi }{2}[/tex]
Step-by-step explanation:
Since the arc is [tex]\frac{1}{4}[/tex] of the circumference, then
central angle = [tex]\frac{1}{4}[/tex] × 2π ← angle in whole circle
central angle = [tex]\frac{2\pi }{4}[/tex] = [tex]\frac{\pi }{2}[/tex]
Answer:
B. [tex]\frac{\pi }{2}[/tex] radians
Step-by-step explanation:
Edge 2021
TIME REMAININ
y = -6x+2
-12x - 2y = -4
How many solutions does this linear system have?
Answers
Answer:
Infinitely many solutions.
Step-by-step explanation:
y = -6x + 2
Add 6x to both sides
6x + y = 2
-12x - 2y = -4
Divide each term by -2
6x + y = 2
Since both equations are actually exactly the same, this linear system will have infinitely many solutions.
Hope this helps!
16 - 4y when y is 4
Some plzzzzz helppppp!!!!
Answers
Answer:
0
Step-by-step explanation:
To solve this equation, first find out 4y, which equals 16. Then do the full equation, 16-16=0.
Answer:
Let 16-4y=0
Substracting 16 on both sides
16-16-4y=-16
-4y=-16
4y=16
y=4
Rebutting the value of y
=16-4(4)
=16-16
=0
Step-by-step explanation:
I hope this will help you :)
2) The marked price of a laptop is Sh.47500. Mimo bought the laptop after the shopkeeper allowed her a
discount of 5°. If the shopkeeper made a profit of 25%, calculate the price at which the shopkeeper
bought the laptop from the manufacturer.
(3 marks)
Answers
Explanation:
Find the amount that amino bought:
47500 x 5/100 = 2375
47500 - 2375 =45125
Find the amount of profit the shopkeeper made:
45125 x 25/100 = 11281.25
Find the amount that the shopkeeper buy from the manufacturer:
45125 - 11281.25 = 33843.75