show your solution need an answer, please need an answer, please.
complete answer pls:(
Answers
Answer:
1. x = -1
2. y = -1, y = 2
3. y = -½ + i [tex]\frac{\sqrt{3} }{2}[/tex]; y = -½ - i [tex]\frac{\sqrt{3} }{2}[/tex]
4. x = -3; x = -6
Step-by-step explanation:
I will only produce work for questions 1 through 4, and you could follow the same steps for questions 5 and 6 so that you could learn and get used to solving quadratic equations. I am practically using the same techniques in solving questions 1 through 4 anyway.
1.) x² + 2x + 1 = 0
where a = 1, b = 2, c = 1
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = 2² - 4(1)(1) = 4 - 4 = 0
This means that the equation has one real root.
Next, determine the factors of the quadratic equation.
Use the perfect square trinomial factoring technique:
u² + 2uv + v² = (u + v)²
From the equation, x² + 2x + 1 = 0
where a = 1, b = 2, c = 1
Find factors with product a × c and sum b:
Possible factors:
product a × c : 1 × 1 = 1
sum b : 1 + 1 = 2
Therefore, the binomial factors of x² + 2x + 1 = 0 is (x + 1)²
To find the roots, set x = 0:
x + 1 = 0
Subtract 1 from both sides to isolate x:
x + 1 - 1 = 0 - 1
x = -1 (This is the root of the equation).
2) y² - y - 2 = 0
where a = 1, b = -1, and c = -2
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (-1)² - 4(1)(-2) = 9
Since b² - 4ac > 0, then it means that the equation will have two real roots.
From the equation, y² - y - 2 = 0
where a = 1, b = -1, and c = -2:
Find factors with product a × c and sum b:
Product a × c :
1 × -2 = -2
-1 × 2 = -2
Sum b:
1+ (-2) = -1
-1 + 2 = 1
Therefore, the possible factors are: 1 and -2:
(y + 1) (y - 2)
To find the roots, set y = 0:
y + 1 = 0
Subtract 1 from both sides:
y + 1 - 1 = 0 - 1
y = -1
y - 2 = 0
Add 2 to both sides:
y -2 + 2 = 0 + 2
y = 2
Therefore, the roots of the quadratic equation, y² - y - 2 = 0 are: y = -1 and y = 2.
3.) y² + y + 1 = 0
where a = 1, b = 1, and c = 1
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (1)2 - 4(1)(1) = -3
Since b² - 4ac < 0, then it means that the equation will have two complex roots.
Use the Quadratic Formula:
[tex]y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]y = \frac{-1 +/- \sqrt{1^{2} - 4(1)(1)} }{2(1)}[/tex]
[tex]y = \frac{-1 +/- \sqrt{1 - 4} }{2}[/tex]
[tex]y = \frac{-1 +/- \sqrt{-3} }{2}[/tex]
[tex]y = \frac{-1 +/- i\sqrt{3} }{2}[/tex]
Therefore, the roots of the quadratic equation, y² + y + 1 = 0 are:
y = -½ + i [tex]\frac{\sqrt{3} }{2}[/tex]; y = -½ - i [tex]\frac{\sqrt{3} }{2}[/tex]
4) x² + 9x + 18 = 0
where a = 1, b = 9, and c = 18.
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (9)2 - 4(1)(18) = 9
Since b² - 4ac > 0, then it means that the equation will have two real roots.
Use the Quadratic Formula:
[tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]x = \frac{-9 +/- \sqrt{9^{2} - 4(1)(18)} }{2(1)}[/tex]
[tex]x = \frac{-9 +/- \sqrt{9} }{2}[/tex]
[tex]x = \frac{-9 + 3}{2}; x = \frac{-9 - 3}{2}[/tex]
[tex]x = \frac{-6}{2}; x = \frac{-12}{2}[/tex]
x = -3; x = -6
Therefore, the roots of the quadratic equation, x² + 9x + 18 = 0
are: x = -3 and x = -6.
Related Questions
Rewrite 2/9 + 5/12 with a common denominator
Answers
36 divided by 9 times 2 is 8
36 divided by 12 times 5 is 15
Washing his dad's car alone, Aidan takes 6 hours. If his dad helps him, then it takes 2 hours. How long does it take Aidan's dad to wash the car by himself?
Answers
Answer:
Step-by-step explanation:
If he washes his dads car alone it takes 6hrs, If his dad helps him it takes 2hrs.
6-2= 4
4hrs?
I dont understand the question lol.
somone plz help me will make brainlest if is right
Answers
9514 1404 393
Answer:
y = 1/5
Step-by-step explanation:
Divide both sides of the equation by the coefficient of the variable.
7 = 35y
7/35 = (35y/35)
1/5 = 1y
y = 1/5
_____
A number divided by itself is 1. A number multiplied by 1 is unchanged.
To get from 35y to 1y, or y, divide by 35. That gives you (35/35)y = 1y = y.
Whatever you do to one side of the equation must also be done to the other side. Dividing 7 by 35 gives 7/35 = (7/7)×(1/5) = 1/5.
YALL PLSSSSSSSS HELP IM SHAKING I NEED HELP PLSS
Answers
Answer:
someone is adding dont worrie
Step-by-step explanation:
Choose an equation that would be used to solve
0 = -x^2 + 10x -8
(x+25)^2 = -8
(x-5)^2 = 17
(x-10)^2 = 25
Answers
The equation that would be used to solve the function is (x+5)^2 = 17
Given the quadratic equation -x^2 + 10x -8 = 0
This can also be written as:
-x^2 + 10x -8 = 0
x^2 - 10x + 8 = 0
x^ 2- 10x = -8
The coefficient of x is -10
Half of the coefficient of -10 = -10/2 = -5
Square the result = 5^2 = 25
Add 25 to both sides of the equation
x^2 - 10x + 25 = -8 + 25
x^2 - 10x + 25 = 17
(x+5)^2 = 17
Hence the equation that would be used to solve the function is (x+5)^2 = 17
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A basketball player made 40% of the shots she attempted, if she attempted 60 shots how many did she make?
Pls help ASAP
Answers
Answer:
80 shots were taken by the basketball player
Step-by-step explanation:
Answer:
she made 20 shots 40% of 60 is 20
NEED HELP ASAP What is the equation of the function in standard form? WILL GIVE BRAINLYEST TO CORRECT ANSWER
Answers
Answer:
i can ans it
(-4,-1,-12)
Each container of Twizzlers holds 105 pieces. Each
student will receive 1 Twizzler with their lunch. If
there are 1250 students in the school, how many
containers does the school need to buy for each
student to receive 1 Twizzler?
Answers
Answer:
The school would need to buy 12 containers for each student to receive 1 Twizzler.
Step-by-step explanation:
1250/105 = 11.9 or 12
what is 5+6? Show your work
Answers
Answer:
11
Step-by-step explanation:
2+2+1(5)+3+3(6) =11
Check all solutions to the equation. If there are no solutions, check 'None."
x2=-4
Answers
Answer:
-2 is the only answer
Step-by-step explanation:
You know the answer can't be a positive number because a positive multiplied by a positive is a positive number. It is not 0 because 0 X anything is 0. -16 x 16 is way to high. But, -2 x 2 = -4
There are no real solutions
Option F is correct.
What is an imaginary number?An imaginary number is a number that, when squared, has a negative result. Essentially, an imaginary number is the square root of a negative number and does not have a tangible value.
Given equation
[tex]x^{2} =-4[/tex]
Apply square root on both sides of the equation
[tex]\sqrt{x^{2} } =\sqrt{-4}[/tex]
[tex]x=2i[/tex]
2i is imaginary number.
There are no real solutions
Hence, Option F is correct.
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What is 4.312 x 100
Answers
any decimal times a multiple of 10 means that the decimal will move to the right based on the number of zeros
therefore
4.312 * 100 = 431.2
hope this helps
Answer:
431.2
Step-by-step explanation:
[tex] \\ 4.312 \times 100[/tex]
[tex] \\ = \frac{4312}{1000} \times 100[/tex]
[tex] \\ = \frac{4312}{10} [/tex]
[tex] \\ = 431.2[/tex]
How many tens are
there in 350?
Answers
Answer:
35 because 35 times ten equals 350
Step-by-step explanation:
A square-shaped park has an area of 400 ft2. What are the dimensions of the park? Write and solve an equation.
Answers
Answer:I think 200ft2
Step-by-step explanation:
Kylie just accepted a job at a new company where she will make an annual salary of $43000. Kylie was told that for each year she stays with the company, she will be given a salary raise of $5000. How much would Kylie make as a salary after 6 years working for the company? What would be her salary after tt years?
Answers
Answer:5600
Step-by-step explanation:
Because I just did it
Solve for w
Please help :)
THANK U
Answers
Answer:
w=12
Step-by-step explanation:
[tex]5=\frac{w}{-4} +8\\\\-3=\frac{w}{-4}\\12=w[/tex]
Answer:
12
If you ever have a problem like that, just search for it on the internet. It will give you the answer so you don't have to waist your points on here.
(I hope that didn't sound mean :)
A coat usually sells for $62.95. It is on sale for 10% off.
What is the sale price?
Answers
Answer:
Hii, okay so the sale price is $56.66, Hope this helps
Step-by-step explanation:
There was 5/8 of a pie in the fridge. Daniel ate 1/4 leftover. How much of a pie did he have
Answers
Answer:
Therefore, 15 / 32 of the pie is left in the fridge.
write the equaion of a line in slope-intercept form if the slope is 1/5 and the y-intercept is -9 explain please
Answers
Answer:
[tex]y = \frac{1}{5} x - 9[/tex]
Step-by-step explanation:
The slope-intercept form is y = mx + b, where:
m = slope
b = y-intercept.
The slope (m) tells you the steepness of the line. It is the average rate of change which measures how the y-value changes for each one-unit change in the x-value. Hence, slope [tex]= \frac{rise}{run}[/tex]. So the given slope of 1/5 means that for every 1 unit change in the y-value, the x-value changes by 5 units (you go up 1 unit, and "run" 5 units to the right).
Next, the y-intercept is the point on the graph where it crosses the y-axis, and has the coordinates, (0, b). It is also the value of y when x = 0. Since you're given the y-intercept of -9, then that means that it is the y-coordinate of (0, b). So, it becomes (0, -9).
Now that we have our slope (m ) = 1/5, and the y-intercept (b ) = -9, we can write the equation of the line as:
[tex]y = \frac{1}{5} x - 9[/tex]
(I'm also including a screenshot of the line where it shows the y-intercept of (0, -9) on the graph).
Please mark my answers as the Brainliest if you find my explanations helpful :)
please help me asap and show your work
Answers
Answer:
We need a question
Step-by-step explanation:
Write four hundred thirty-five thousand, two hundred two in standard form.
Answers
Answer:
four hundred thirty-five thousand : 435,000
two hundred two : 202
Consider the inequality shown
4x+ax-14>-24
What is the highest integer value of a when x=-2
Answers
4x + ax - 14 > - 24
(4 + a)x - 14 > - 24
Add both sides 14
(4 + a)x - 14 + 14 > - 24 + 14
(4 + a)x > - 10
put the given value instead of x ( x = - 2 )
(4 + a)( - 2 ) > - 10
Divide both sides by - 2
Hint :When we multiply or divide the sides of an inequality by a negative number, the direction of the inequality changes which means < changes to > , and > changes to <
(4 + a)( - 2) ÷ ( - 2 ) < - 10 ÷ ( - 2 )
(4 + a) < 5
4 + a < 5
Subtract both sides 4
4 - 4 + a < 5 - 4
a < 1
Thus the highest integer value of a is:
a = 0
Sara started her homework at 5:30pm and finished it at 6:15pm.how much time did she take to finished her homework
Answers
Answer:
she took 45 mins on homework.
Answer:
45 min hope you get it right
Can someoe help?
7x-24=6x-2
Answers
Answer:
[tex]7x - 24 = 6x - 2 \\ collecting \: like \: terms \: \\ 7x - 6x = - 2 + 24 \\ 1x = 22 \\ x = \frac{22}{1} \: \: or \: \: x = 22[/tex]
Answer:
x = 22
Here's how i got it ^u^
7x - 24 = 6x - 2
Step 1: Subtract 6x from both sides.
7x - 24 = 6x - 2
- 6x - 6x
x - 24 = - 2
Step 2: Add 24 to both sides.
x - 24 = - 2
+ 24 + 24
which TA-DA!!! it equals x = 22
An airplane takes 5 hours to travel a distance of 3400 kilometers against the wind. The return trip takes 4 hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?
Answers
find the value of y. 7y + y - 2y =18
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
y=3
Step-by-step explanation:
if you are to put this on a graph the would be Linear
Plato!!! Please help ~_~
Type the correct answer in the box. If necessary, use / for the fraction bar.
A solid wooden block in the shape of a rectangular prism has a length, width, and height of 3/8 centimeter, 1/8 centimeter, and 5/8 centimeter,
respectively,
The volume of the block is (——)
cubic centimeter.
The number of cubic wooden blocks with a side length of 1/8 centimeter that can be cut
from the rectangular block is(—)
Answer goes in the (—)
Answers
Answer:
V = 3/8 * 1/8 * 5/8 cm^3 = 15 / 512 cm^3
Since all sides are evenly divisible by 1/8 and v = (1 / 8)^3 = 1 / 512 cm^3
N = V / v = (15 / 512) / (1 / 512) = 15 blocks
Example: cut 1/8 by 5/8 into 5 blocks
Cutting 1/8 by 5/8 could be done 3 times for a total of 15 blocj\ks
how do you prove that vertical angles are ⩭
Answers
Answer:
congruent
Step-by-step explanation:
If two angles are vertical angles, then they're congruent
hope it helps
mark me brainliest
Evaluate.
-3+ (9+6) : (-3)
o 4
0-2
0 - 4
оо
1
2.
3
4
5
6
7
Answers
Answer:
-8
Step-by-step explanation:
brackets first division second and addition third
The correct solution of the expression -3 + (9+6) ÷ (-3) is,
⇒ - 7
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ -3 + (9 + 6) ÷ ( -3 )
Now, We can simplify the expression by using BODMAS rule as;
⇒ - 3 + (9 + 6) ÷ ( -3 )
⇒ - 3 + 12 ÷ (- 3)
⇒ - 3 - 4
⇒ - 7
Thus, The correct solution of the expression -3 + (9+6) ÷ (-3) is,
⇒ - 7
Learn more about the mathematical expression visit:
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Seven more than twice a number is greater than negative nineteen. Find all numbers that make this statement true.
The answer is I (Type an inequality using x as the variable.)
Answers
Answer:
Hey there,
Let the unknown number be x
Here they say that ,
Seven more than twice a number,
2x + 7
Is greater than,
2x + 7 >
Negative 19,
2x + 7 > -19
Now solve for x
[tex]2x + 7 > - 19 \\ 2x > - 19 - 7 \\ 2x > - 26 \\ \frac{2x}{2} > \frac{ - 26}{2} \\ x > - 13[/tex]
So,
All the numbers which are greater than (-13) makes this statement true.
Examples
[tex]x = { - 12, - 11, - 10, - 9...} \\ [/tex]
Hope this helps you.
Let me know if you have any other questions :-):-)
All numbers that makes, the statement "Seven more than twice a number is greater than negative nineteen" True, are the numbers greater than -13.
Let us denote the unknown number as "x",
The given statement can be translated into an inequality as follows:
7 + 2x > -19,
Now, to solve for "x," we separate the variable by subtracting 7 from both sides of the inequality,
We get,
2x > -26
Divide both sides by 2:
We have,
x > -13
Therefore, any number greater than -13 would make the statement "Seven more than twice a number is greater than negative nineteen" true.
In interval notation, this would be written as (-13, ∞), indicating all real numbers greater than -13.
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Find what 2/4 is multipled by to to get 2/4 divided by 12. Then solve the problem. Do not reduce your answer.
Answers
Answer:
Step-by-step explanation:
