Question 3 of 10
Use the quadratic formula to find both solutions to the quadratic equation
given below.
2x²+x-1=0
Answers
Answer:
x=1/2 or x=−1
Step-by-step explanation:
The solution to the quadratic equation is x = -1 or 1/2
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
2x² + x - 1 = 0 be equation (1)
And , roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
On simplifying , we get
x = [ -1 ± √ ( 1 )² - ( 4 ) ( 2 ) ( -1 ) ] / 4
x = [ -1 ± √ ( 1 + 8 ) ] / 4
x = [ -1 ± 3 ] / 4
So , the two values of x are
x = ( -1 - 3 ) / 4
x = -1
And , x = ( -1 + 3 ) / 4
x = 1/2
Therefore , the values of x are -1 or 1/2 respectively
Hence , the roots of the quadratic equation are -1 or 1/2 respectively
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Related Questions
Anasia is a basketball player who regularly shoots sets of 2 free-throws. Suppose that each shot has probability
0.7 of being made, and the results of the shots are independent.
The table below displays the probability distribution of X, the number of shots that Anasia makes in a set of 2
attempts.
2
X=of makes 0 1
P(X)
0.09 0.42
0.49
Given that r = 1.4 makes, find the standard deviation of the number of shots that Anasia makes.
Round your answer to two decimal places
shots
Answers
Answer:
0.65
Step-by-step explanation:
The required standard deviation is 0.65
Given data is,
Computation:
[tex]\varepsilon_x\times P(X=x)=0\times 0.09+1\times0.42+2\times0.49\\=0.42+0.98\\=1.4[/tex]
Now,
[tex]E(X^2)=0^2\times 0.009+1^2\times 0.42+2^2\times 0.49\\=0.42+1.96\\=2.38\\\sigma ^2=E(X^2)-(E(X))^2\\=2.38-(1.4)^2\\=0.42\\\sigma =\sqrt{0.42}\\=0.65[/tex]
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Triangles practice, need help.
Answers
Using the pythagorean Theorem formula (a^2 + b^2 + c^2) Plug in A and B (13, and 13).
(13)^2 + (13)^2 = c^2
13 • 13 + 13 • 13 = c^2
169 + 169 = c^2
v/338 = v/c^2 (square root them both)
Then you can have your answer for y, hope this helps
Betsy works from 6:00 AM to 12:00 PM, takes an unpaid lunch break from 12:00 PM to 1:00pm, then works from 1:00 PM to 3:30 PM. How many hours did Betsy work?
Answers
Answer:
9 hours and 30 mins
Step-by-step explanation:
Betsy works for about 9 hours 30 minutes daily.
What are mathematics operations?
A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Calculating time of Betsy total work for getting paid :
Betsy Working from 6:00 AM to 12:00 PM = 6 hour
Betsy takes an unpaid lunch break from 12:00 PM to 1:00pm = 1 hour
Betsy Working from 1:00 PM to 3:30 PM = 2.5 hour
Now adding-up all the time = 6 + 1 + 2.5 hour = 9.5 hours or 9 hours 30 minutes.
Therefore, Betsy works for about 9 hours 30 minutes daily.
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Why is it so hard for people to learn math?
Answers
Answer:
I don't know, I kind of wonder the same thing sometimes. But everyone understands things at a different rate, so that's why I'm here helping people by answering their questions and doing my best to explain how I got there.
thank you for the free points though :)
Answer:
because they are over thinking easy thing and getting stressed out.
Step-by-step explanation:
this is what happened to me
Tom drove at a constant speed of 50 miles per hour for 2.5 hours.
Albert drove at a constant speed of 65 miles per hour for 2 hours.
Who drove farther? How many more total miles did he drive?
Use the equation d =r xt to solve.
drove farther. He drove
more total miles.
Answers
Answer:
Albert by 5 more miles
Step-by-step explanation:
Tom: 50 * 2.5 = 125 miles
Albert: 65 * 2 = 130 miles
Albert drove for more miles
130-125 = 5 miles
Albert drove for 5 more miles
Introduction to nonlinear models
Complete the table below.
Answers
Answer:
The table will be:
x y = 2x² y = 2ˣ
0 0 1
1 2 2
2 8 4
Step-by-step explanation:
Given the non-linear equations
y = 2x²
y = 2ˣ
When x = 0y = 2x²
y = 2(0)² =0
y = 2ˣ
y = 2⁰ = 1
When x = 1y = 2x²
y = 2(1)² = 2
y = 2ˣ
y = 2¹ = 2
When x = 2y = 2x²
y = 2(2)² = 8
y = 2ˣ
y = 2² = 4
Thus, the table will be:
x y = 2x² y = 2ˣ
0 0 1
1 2 2
2 8 4
write the slope intercept form of the equation of each line
Answers
Answer:
y=1/5x+3
Step-by-step explanation:
Slope-intercept form is written as y=mx+b, with mx representing slope and b representing the y-intercept.
Referring to the line on the graph, find where the line crosses the y-axis and you get 3 for your y-intercept. Now, to get the slope start from the point of the y-intercept (0,3) and choose another point. For example, choose (5,4)
Remember rise over run. Start from the y-intercept and count up and over until you get to (5,4). When doing this, you get 1/5
Equation is: y=1/5x+3
the perimeter of a rectangle is 8x+10. if the length is 2x+8 what is the width?
Answers
Answer:
Step-by-step explanation:
8x+10 - 4x+16 = 4x-6
w= 2x-3
HELP PLEASE AND THANK YOU!!
Answers
Ten times a number increased by four is no more than twenty-five.
Answers
Answer:
10x + 4 < 25
Step-by-step explanation:
The correct answer is:
10x + 4 < 25
Today only, a suit is being sold at a 15% discount. The sale price is $391.
What was the price yesterday?
Answers
Answer:
$460.
Step-by-step explanation:
[tex]Percentage\ change = (\frac{Original\ Price\ - Discounted\ Price}{Original\ Price})100\\\\15=(\frac{x-391}{x})100\\\\15x=(x-391)100 \\\\15x/100=x-391\\0.15x=x-391\\391=x-0.15x\\391=0.85x\\391/0.85=x\\460=x\\[/tex]
So the price yesterday was $460
Please help if you can :(
Answers
Answer:
its b
Step-by-step explanation:
SO 2 chairs are left out. If there are 4781 chairs, find the
The cost of levelling a square lawn at 32 per sq. metre is 3 6272. Find its one side. Also find the cost of
fencing it at 3 per meter.
Answers
Answer:
u need 2321 chairs
Step-by-step explanation:
there u go
PLEASE HELP ASAPPPP!!???
Answers
Answer:
I dont know what does the long question requires.If is the question of 17 problem then i have explained and solved .If not then I dont know what to do.
The cost of an limited edition figurine starts at $255 and it increases in value by 8% each year. What is the growth or decay rate as a decimal? What is the initial value? Write an exponential model that represents the cost f (t) of the figurine t years after it's bought. After 6 years the figurine's value is ?
Answers
Answer:
Growth rate = 8% = 0.08
Initial value (Po) = $255
F(t) = Po* e^rt
F(t) = $412.09897
Step-by-step explanation:
Given that:
Initial cost = $255
Rate of increase per year (r) = 8% = 0.08
Growth rate :
Final amount = Initial amount * (1 + rate)^time
Growth rate = 8% = 0.08
Initial value (Po) = $255
Exponential model for the cost :
F(t) = Initial value * e^(rate * time)
F(t) = Po* e^rt
Value after 6 years :
F(t) = Po* e^rt
t = 6
F(t) = 255 * e^(0.08*6)
F(t) = 255 * 1.6160744
F(t) = $412.09897
If you ride your bike around the block that is 20 meters returning to the exact point where you started your displacement is___m?
A 0m
B20m
Answers
kind of stuck here , & yeah I need help , please help omg-
Answers
Answer: (4,-6) , do u need help on the bottom question?
Step-by-step explanation:
A museum recorded that it had 988 visitors in 4 hours .What is the unit rate in visitors per hour?
Answers
Answer:
247
Step-by-step explanation:
247 visitors per hour
Here is a list of numbers:
20, 8, 6, 11, 3, 15, 11 ,20 ,12 ,13
State the median.
Answers
Answer: 18
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
1. Arrange the numbers from least to greatest.
3,6,8,11,11, 12,13,15, 20
2. Start from the two ends and cross them off until you're left with what's in the middle.
6,8,11,11,12,13,15
8,11,11,12,13
11,11,12
11
3. The median is 11 because that is the number you are left with.
20a + 20b + 4c + 6c - 4b - 2a
Answers
Answer:
18a, 16b, 10c
Step-by-step explanation:
you can’t add variables together so this is the simplestform
which of these expressions represent a 15% tip on a $20 meal? which represent the total bill?
Answers
Answer:
3
Step-by-step explanation:
20x0.15
= 3
Answer:
Well I didn't understand this question to well, but I think 15% of a $20 meal is ($3.00). OR
20x0.15
= 3
Step-by-step explanation:
I hope this helped! :)
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality. \,<\sqrt{32}<\,< 32
Answers
Answer:
Could you retype the equation so it isn't jankey?!
Step-by-step explanation:
Avery is making a necklace for her mothers birthday. She uses 1 1/20 strings of black beads and 1 4/5 more strings of gray beads than black beads. How many strings of gray beads did she use?
.
Answers
Answer:
She used 2 17/20 strings of grey beads
Step-by-step explanation:
Here, we want to know the number of grey beads used
To calculate this, we simply add up the black beads number with the number of grey beads
Mathematically, that will be;
1 1/20 + 1 4/5
= 21/20 + 9/5
= (21 + 36)/20
= 57/20 = 2 17/20
The answer to this question
Answers
Answer:
divide 9 and 21
Step-by-step explanation:
if you divide 9 and 21 u will get ur answer
work out 1/2×7 write your answer mixed
Answers
Answer:
1/2 x 7= 3.5
Step-by-step explanation:
A boat traveled 300 miles in 15 hours. What rate did the boat travel in miles
per hour?
1. 2
2. 20
3. 30
4. 285
Answers
Answer:
2.20 ms
Step-by-step explanation:
distance divided by time
300÷15=20
Use the drop-down menus to complete the solution to the equation cos(pie/2-x)=square root 3/2 for all possible values of x on the interval [0,2pie].
Answers
Answer:
0
1
sin
3
3
Step-by-step explanation:
These are the answers in order from every blank
The value of cos(π/2) is 0 sinπ/2 is 1 further sinx = √3/2 thus x = π/3,2π/3.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
As per the given trigonometric equation,
cos(x)cosπ/2 + sin(x)sinπ/2 = √3/2
Since, cosπ/2 = 0 and sinπ/2 = 1
cos(x)(0)+ sin(x)(1) = √3/2
sinx = √3/2
sinx = sin π/3 = sin 2π/3.
Hence "The value of cos(π/2) is 0 sinπ/2 is 1 further sinx = √3/2 thus x = π/3,2π/3".
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anyone help please will give brainliest
Answers
9514 1404 393
Answer:
7. y = f(x +2) -7
8. y = -f(x -5)
9. y = f(-x) +3
Step-by-step explanation:
The general transformation can be written ...
y = a·f(b·(x -c)) +d
'a' is the vertical expansion factor. A negative value means the graph is reflected over the x-axis.
'b' is the horizontal compression factor. A negative value means the graph is reflected over the y-axis.
'c' is the number of units of right-shift.
'd' is the number of units of up-shift.
__
7. 2 left and 7 down means (c, d) = (-2, -7), so the transformed function is ...
y = f(x +2) -7
__
8. reflected over x and 5 right means (a, c) = (-1, 5), so the transformed function is ...
y = -f(x -5)
__
9. reflected over y and up 3 means (b, d) = (-1, 3), so the transformed function is ...
y = f(-x) +3
_____
The graph shows an asymmetrical function that makes it possible to tell what the transformations are. The original is dashed orange. The various y-values correspond to the problem numbers. You can see that the transformations match the problem statements.
Which matrix represents the total expected?
O A.
[20
24
20
8
2201
264
220
88
B.
200
240
200
80
E.
[240]
288
240
96
C.
(210)
250
210
90
Answers
Answer: the answer is B
Step-by-step explanation:
You add the A,B,C numbers together for the soda for example,
Cola: 70(A) + 30(B) + 100(C) = 200
Now you just continue that for the other sodas hope this helps :)
If a baseball travels at 90 mi/h, how many seconds does it take to travel 60 ft.?
Answers
Answer:
0.458 seconds
Step-by-step explanation:
dont get mad when its wrong
0.458 seconds
You already know that the ball travels at 90 mi/hr. 60.5 1/475200 = 0.00012732 hours. This is still a small number so express it in seconds. 0.0076389 minutes = 60 0.0076389 = 0.458 seconds. (this from google btw)