Answers
Answer:
C.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define
x² - 5x + 7 = 0
Step 2: Identify Variables
a = 1
b = -5
c = 7
Step 3: Find solutions
Substitute [Quad Formula]: [tex]x=\frac{5\pm\sqrt{(-5)^2-4(1)(7)} }{2(1)}[/tex]Evaluate Exponents: [tex]x=\frac{5\pm\sqrt{25-4(1)(7)} }{2(1)}[/tex]Evaluate Multiplication: [tex]x=\frac{5\pm\sqrt{25-28} }{2}[/tex]Evaluate Subtraction: [tex]x=\frac{5\pm\sqrt{-3} }{2}[/tex]Factor: [tex]x=\frac{5\pm\sqrt{-1} \sqrt{3} }{2}[/tex]Simplify: [tex]x=\frac{5\pm i\sqrt{3} }{2}[/tex]The solutions to the equation x² - 5x + 7 = 0 are:
x = (5 + i√3) / 2 or x = (5 - i√3) / 2
Option C is the correct answer.
We have,
To find the solutions of the quadratic equation x² - 5x + 7 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For the given equation, the coefficients are:
a = 1
b = -5
c = 7
Substituting these values into the quadratic formula,
x = (-(-5) ± √((-5)² - 4(1)(7))) / (2(1))
Simplifying further:
x = (5 ± √(25 - 28)) / 2
x = (5 ± √(-3)) / 2
Since the discriminant (the value inside the square root) is negative, √(-3) is imaginary, meaning there are no real solutions to this quadratic equation.
The solutions exist in the complex number system.
So,
√-1 = i
x = (5 ± i√3) / 2
This can be written as,
x = (5 + i√3) / 2
and
x = (5 - i√3) / 2
Thus,
The solutions to the equation x² - 5x + 7 = 0 are:
x = (5 + i√3) / 2 or x = (5 - i√3) / 2
Learn more about solutions of equations here:
https://brainly.com/question/545403
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Related Questions
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. Draw the possibility diagram of the product of the two numbers appearing on the die in each throw Use the possibility diagram to calculate the probability that the product of the two numbers is A prime number Not a perfect square A multiple of 5 Less than or equal to 21 Divisible by 4 or 6
Answers
Answer:
(a)See below
(b)I) 0.125 (ii)0.828125 (iii)0.234375 (iv) 0.625 (v)0.65625
Step-by-step explanation:
When an 8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.
The sample space is:
[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]
PART A
The sample space of the product a*b of each pair forms the required possibility diagram.
This is given as:
[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]
PART B
I) A prime number
The number of products that gives prime numbers = 8
The probability that the product is a prime number
[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]
ii) Not a perfect square
Number of products that results in perfect squares =11
The probability that the product is not a perfect square
[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]
iii) A multiple of 5
Number of products that are multiples of 5=15
The probability that the product is a multiple of 5
[tex]=\dfrac{15}{64}\\=0.234375[/tex]
iv) Less than or equal to 21
Number of products which are less than or equal to 21=40
The probability that the product less than or equal to 21
[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]
v) Divisible by 4 or 6
Number of products divisible by 4 or 6= 42
The probability that the product is divisible by 4 or 6
[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]
A fair dice is rolled 3 times in a row. The outcomes are shown below. Calculate the probability of all three events occurring. Roll Outcome 1st 5 2nd factor of 6 3rd more than 1
Answers
Answer:
5/54
Step-by-step explanation:
probability of the dice being 5 = 1/6
probability of the dice being a factor of 6 = 4/6
probability of the dice being more than 1 = 5/6
1/6 * 4/6 = 4/36
4/36 * 5/6 = 20/216
20/216 simplified to lowest is equal to 5/54
PLEASE HELP IMAGE ATTACHED!!
Answers
Answer:
Step-by-step explanation:
Parallel lines have same slope
19) y = x - 4
m = 1 ; (2, 3 )
Equation: y - y₁ = m(x- x₁)
y - 3 = 1(x - 2)
y - 3 = x -2
y = x - 2 + 3
y = x + 1
20) 2x + 3y = 3
We have to write in y = mx + b form
3y = - 2x - 3
[tex]y=\frac{-2}{3}x-\frac{3}{3}\\\\y=\frac{-2}{3}x-1\\\\m=\frac{-2}{3}[/tex]; (-6, -1)
[tex]y-[-1]=\frac{-2}{3}(x-[-6])\\\\y+1=\frac{-2}{3}(x+6)\\\\y+1=\frac{-2}{3}x+\frac{-2}{3}*6\\\\y+1=\frac{-2}{3}x-4\\\\y=\frac{-2}{3}x-4-1\\\\y=\frac{-2}{3}x-5[/tex]
for perpendicular lines, m2 = -1/m1
21) y = 2x+ 5
m1 = 2
[tex]m_{2}=\frac{-1}{2}[/tex]; (-2,8)
[tex]y-8=\frac{-1}{2}(x-[-2])\\\\y-8=\frac{-1}{2}(x+2)\\\\y-8=\frac{-1}{2}x+2*\frac{-1}{2}\\\\y-8=\frac{-1}{2}x-1\\\\y=\frac{-1}{2}x-1+8\\\\y=\frac{-1}{2}x+7[/tex]
22) x+ 4y = 8
4y = -x + 8
[tex]y=\frac{-1}{4}x+\frac{8}{4}\\\\y=\frac{-1}{4}x+2\\\\m_1=\frac{-1}{4}\\\\m_{2}=4\\\\[/tex]
m2 = 4; (-2,-11)
y - [-11] = 4(x -[-2])
y + 11 = 4 (x + 2)
y + 11 = 4x + 8
y = 4x + 8 - 11
y = 4x - 3
Set up the problem, but use a calculator to find the number of outcomes for the permutation. Eight horses run a race. In how many ways can the first three finishers turn out?
Answers
Explanation:
Label the slots A,B,C for first through third place.
There are 8 choices for slot A, 7 for slot B, and 6 for slot C. We start with 8 and count our way down until we get to the final slot. Then we multiply out those values
8*7*6 = 336
There are 336 ways to select three people from a pool of eight overall.
-----------------
If you want to use the permutation formula, then your steps might look like this
[tex]_n P _r = \frac{n!}{(n-r)!}\\\\_8 P _3 = \frac{8!}{(8-3)!}\\\\_8 P _3 = \frac{8!}{5!}\\\\_8 P _3 = \frac{8*7*6*5!}{5!}\\\\_8 P _3 = 8*7*6\\\\_8 P _3 = 336\\\\[/tex]
Note how the 5! terms cancel out on the second to last step, leaving behind the expression 8*7*6 which was found earlier.
Describe the transformation from the parent function of f ( x ) = x 2 to g ( x ) = 6 x 2.(Need answer in less than 2 hours!)
Answers
Answer: (b) vertical stretch by a factor of 6
Step-by-step explanation:
Consider h(x) = A(x - h)² + k
A is the vertical stretch by a factor of Ah is the horizontal shift (positive = right, negative = left)k is the vertical shift (positive = up, negative = down)f(x) = x²
g(x) = 6x²
↓
vertical stretch by a factor of 6
what is the solution to this inequality x/10+6≥8
Answers
Answer:
x ≥ 20
Step-by-step explanation:
First, we want to isolate x. We can start to do that by subtracting 6 to both sides.
x/10≥2
Now, we multiply each side by 10.
x ≥ 20
That's the answer, all values above or equal to 20 are solutions.
Answer:
The answer is x_> 20
Step-by-step explanation:
Yvette graphs the equivalent ratios shown in the table. Pineapples 1 2 3 4 Oranges 5 10 15 20 Yvette graphs is (10, 2), which other ordered pair will she graph? (2, 1) (3, 15) (15, 20) (20, 4) helpppppppppppppppp meeeeeee
Answers
Answer:
Yvette plotted (10, 2) because for 10 oranges you have 2 pineapples. Similarly, she would plot (20, 4) for the same reason.
Answer:
20,4
Step-by-step explanation:
edge
Which of the following proves ALMN= AOPQ?
Answers
Answer:
Step-by-step explanation:
From the figure attached,
Given : LM ≅ OP
PQ ≅ MN
NL ≅ QO
To Prove : ΔLMN ≅ ΔOPQ
In the triangles LMN and OPQ,
Statements Reasons
1). LM ≅ OP 1). Given
2). PQ ≅ MN 2). Given
3). NL ≅ QO 3). Given
4). ΔLMN ≅ ΔOPQ 4). By SSS property of congruence
Solve for x
12:15 = x 5
36
060
Answers
Answer:
x = 12:15=×5
36
060
Step-by-step explanation:
12:15=0
x=0
Answer:
4
Step-by-step explanation:
Divide the left side by 3
12:15
12/3 : 15/3
4:5
x would be 4
5776 students are sitting in an auditorium in such a manner that there are as many as
students in a row as there are rows in the auditorium.. How many rows are there in the
auditorium?(76)
Answers
Answer:
Hope it will helpful.Follow for more answers.
Manuel need to say more than $75 for a class trip. he already has $24 and will save an equal amount each week for the next 6 weeks. Which any quality can be used to determine how much money Manuel should save each week?
Answers
Answer:
the answer is D!
Step-by-step explanation:
I took that quiz :)
Jose has a family of 4. Is it more reasonable for Jose to purchase 3 pounds of potatoes for his family’s meal tonight or 13 pounds of potatoes?
Answers
Answer:
3
Step-by-step explanation:
1) 2a × 2b 2) 3a × 2b × 2a 3) 2a × 4b × b 4) 3b × 2a × b 5) 3a × 2b × 2c 6) 2a × 3b × b × c 7) a × 4b × 2a × 2c 8) 3a × 3b × 3c
Answers
Step-by-step explanation:
1) = 4ab
2) 12a2b
3) 8ab2
4) 6ab2
5) 12abc
6) 6ab2c
7) 16a2bc
8) 27abc
20 points help babes!!!!!
Answers
Answer:
Brainliest if correct!
Step-by-step explanation:
6561
9^4
the first one!!!
The price of a watch is £230. In a sale this price is reduced by 16%. Calculate the sale price
Answers
Answer:
£193.2solution
Marked Price(MP)=£230
Discount percent=16%
Now,
[tex]discount \: amount = discount \: of \: mp \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 16 \: of \: 230 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{16}{100} \times 230 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 36.8 \\ selling \: price = mp - \: discount \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 230 - 36.8 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 193.2[/tex]
hope this helps...
Good luck on your assignment...
Answer:
£193.2
Step-by-step explanation:
MP= £230
SP= MP - 16%= MP*0.84= £230*0.84= £193.2
What is the value of x in the diagram below? Id necessary, round your answer to the nearest tenth of a unit.
Answers
Answer:
30.1
Step-by-step explanation:
Multiply 17/18 by the reciprocal of -289/324.
Answers
Answer:
18/17
Step-by-step explanation:
the negative reciprocal of -289/324 is 324/289. When it is multiplied by 17/18 you get 18/17 as the answer.
Answer:
[tex] - 1 \frac{1}{17}[/tex]
Step-by-step explanation:
[tex]Reciprocal \: of \: - \frac{289}{324} = - \frac{324}{289} \\ \\ \frac{17}{18} \times (- \frac{324}{289} ) \\ \\ = \frac{17}{18} \times (- \frac{18 \times 18}{17 \times 17} ) \\ \\ = - \frac{18}{17} \\ \\ = - 1 \frac{1}{17} \\ [/tex]
Find the range of value of x for which: x-3/x+3>0
Answers
answer x>1/2 (sqrt(21) - 3)
x>0.791288
Question 9 - (3 marks available)
By rounding to 1 significant figure, estimate the answers to these questions:
a) 17 * 82
b) 54 x 671
c) 207 x 643
Answers
Answer: a) 1,600
b) 35,000
c) 120,000
Step-by-step explanation:
First, round each number to one significant digit (the first digit).
Then multiply them.
a) 17 --> rounds to 20
82 --> rounds to 80
20 x 80 = 2 x 8 with two zeros
= 1 6 0 0
b) 54 --> rounds to 50
671 --> rounds to 700
50 x 700 = 5 x 7 with three zeros
= 3 5 0 0 0
c) 207 --> rounds to 200
643 --> rounds to 600
200 x 600 = 2 x 6 with four zeros
= 1 2 0 0 0 0
Given f(x)= √7x and g(x) = 1/x-8 which value is in the domain of f^o g
Answers
Answer:The right answer is -8.
Step-by-step explanation:
///// PLZZZZZZZZZ HLPPPPPPPPPP MEEEEEEEEEEEEEEEEEE ////// WHAT IS THE SLOPE OF THE BELOW IF NECESSARY ENTER YOUR ANSWER AS A FRACTION IN LOWEST TERMS USING THE SLASH (/) AS THE FRACTION BAR DO NOT ENTER YOUR ANSWER AS A DECIMAL NUMBER OR AN EQUATION.
Answers
Answer:
1/6
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
= (6-3)/(12 - -6)
= (6-3)/(12+6)
= 3/18
=1/6
PLEASE HELP I DONT KNOW WHAT TO DO !! I APPRECIATE IT IF YOU HELP ME !
Answers
Answer:
x = ±20
Step-by-step explanation:
x^2 -1=399
Add 1 to each side
x^2 = 399+1
x^2 = 400
Take the square root of each side
sqrt(x^2) = ±sqrt(400)
x = ±20
What is the equation of the graph line with in standard form X=-3Y =-3X +Y=-3X-Y= -3
Answers
Answer:6
Step-by-step explanation:
Find the constant of variation k for the direct variation.
A . K = -2
B . K = 2
C . K = -0.5
D . K= -1.5
Answers
Answer:
K = -2
Step-by-step explanation:
If y varies directly as x, k (constant) can be found by dividing the y-coordinate by the x-coordinate.
[tex]k = \frac{2}{-1} = -2[/tex]
Answer:
B
Step by step explanation
what is the measure of
Answers
Answer:
the measure of this is
Step-by-step explanation:
cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese cheese
An experimental population of fruit flies increases according to the law of exponential growth. There were 60 flies after the 2nd day of the experiment and 360 flies after the fourth day. How many flies were there in the original population?
Answers
Answer:
There were 10 flies originally
Step-by-step explanation:
Since we have an exponential growth, we will be having a constant percentage of increase and we can set up the increase at any day using the following equation;
V = I(1+r)^d
where V is the number of flies on a particular day
I is the initial number of flies
r is the constant increase in percentage
and d is the number of days.
So we have for the second day;
60 = I(1+r)^2 ••••••(i)
For the fourth day, we have;
360 = I(1+r)^4 ••••••••(ii)
divide equation ii by i; we have;
360/60 = (1+r)^4/(1+r)^2
6 = (1+r)^2
(√6)^2 = (1+r)^2
1 + r = √6
r = √6 - 1
So we can substitute the value of r in any of the equations to get I which is the initial number of flies
Let’s use equation 1
60 = I(1 + r)^2
60 = I(1 + √6 -1)^2
60 = I(√6)^2
60 = 6I
I = 60/6
I = 10 flies
If f(x) = x and g(x) = 2x + 7, what is g(x)
when x = -6?
Answers
Answer:
g(-6) = -5
Step-by-step explanation:
g(x) = 2x + 7
Let x = -6
g(-6) = 2(-6) +7
= -12 +7
= -5
Answer:
-5
Step-by-step explanation:
g(x) = 2x + 7
Put x as -6.
g(-6) = 2(-6) + 7
g(-6) = -12 + 7
g(-6) = -5
0.0995 rounded to 3 decimal places
Answers
Answer:
0.100
Step-by-step explanation:
0.0995 has 4 decimal places
5>4 so round up
9 turns to 10, the 1 is "added on" to the number ahead
9 turns to 10 again, the 1 is "added on" to the number ahead
0 turns to 1
you are left with 0.100
Answer:
0.100
Step-by-step explanation:
Three decimal places: 0. 0 / 9 / 9 / 5
Rounding number: 0. 0 / 9 / 9 / 5
Since it is 5, add 1 to the second 9. This will result to 0 while adding 1 to the first 9. Again, this would result to 10 which will add 1 to the next number, 0.
0.1000
Since the question wants you to round three places, you were not told to remove the zeros in those decimal places. So only remove the last 0.
0.100 is the answer
Solve for d.
4d – 4 = 5d - 8
Answers
Answer:
d = 4
Step-by-step explanation:
4d - 4 = 5d - 8
Add -5d and 4 on both sides.
4d - 5d = - 8 + 4
- 1d = - 4
Divide -1 into both sides.
d = -4/-1
d = 4
Three-fifths of the members of the Spanish club are girls. There are a total of 30 girls in the Spanish club.
Which statements can be used to solve for x, the total number of members in the Spanish club? Select three options
Answers
Problem: You do not have an attached picture. Though, I can help you out with this question.
So, three-fifths of the members are girls. There are 30 of girls. We can immediately make an equation using "x".
3/5x=30
3/5x × 5/3=30 × 5/3
x=50
Thus, there are 50 members in total. Though if x is too hard for you, you may substitute it by using another variable.
Variable in here is x.