Solve the Quadratic
2x^2–5x-8=0
Solution 1:
Solution 2:
[tex]2x^2 -5x-8 =0\\\\\implies x = \dfrac{ -(-5) \pm \sqrt{(-5)^2 - 4\cdot 2 \cdot (-8)}}{2 \cdot 2}\\\\\\\implies x = \dfrac{5 \pm \sqrt{89}}{4}\\\\\\\text{Hence}~ x = \dfrac{5 + \sqrt{89}}{4},~~ x = \dfrac{5 - \sqrt{89}}{4}[/tex]
Answer:
[tex]\sf \boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]
[tex]\sf \boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]
✰Step-by-step explanation✰ ⤵[tex]\sf 2x^2-5x-8=0[/tex]
☁ We'll solve this equation using The Quadratic Formula:
[tex]\boxed{\sf \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
A= 2, b= -5, c= -8
[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}}{2\times \:2}[/tex]
[tex]\mapsto \sf \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}[/tex]
[tex]**\sf \left(-5\right)^2=5^2[/tex]
[tex]\mapsto \sf \sqrt{5^2+4\times \:2\times \:8}[/tex]
[tex]\mapsto \sf \sqrt{5^2+64}[/tex]
[tex]\mapsto \sf \sqrt{89}[/tex]
______________
[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{89}}{2\times \:2}[/tex]
☁ Now, we'll Separate solutions, first, we'll solve the equation when ± is plus:
[tex]\mapsto \sf \cfrac{-\left(-5\right)+\sqrt{89}}{2\times \:2}[/tex]
☁ Multiply 2*2 =4
[tex]\boxed{\sf \cfrac{5+\sqrt{89}}{4}}[/tex]
_________________
☁ Now solve the equation when ± is minus:
[tex]\mapsto \sf \cfrac{-\left(-5\right)-\sqrt{89}}{2\times \:2}[/tex]
☁ Multiply 2*2 =4
[tex]\boxed{\sf \cfrac{5-\sqrt{89}}{4}}[/tex]
[tex]\sf Solution \:1:\boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]
[tex]\sf Solution \:2:\boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]
☁❅☁❅☁☁❅☁❅☁☁❅☁❅☁❅☁
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Find the value of X Show all work
(2x+6)
36
(4x-18)
Answer:
X=30
Step-by-step explanation:
(2X + 6) + 36 = (4X- 18)
36=4X-18-2X-6
36=2X-24
2X = 60
X = 30
wELCOME
This is the ANSWER
2x-3y=5.5
What is the solution to the system of equations shown above
Answer:
⸻⸻⸻⸻⸻
Solving
2X + 3Y = 5.5
⸻⸻⸻⸻⸻
Simplifying
2X + 3Y = 5.5
⸻⸻⸻⸻⸻
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
⸻⸻⸻⸻⸻
Add -3y to each side of the equation.
2x + 3y + -3y = 5.5 + -3y
⸻⸻⸻⸻⸻
Combine terms: 3y + -3y = 0.
2x + 0 = 5.5 + -3y
2x = 5.5 + -3y
⸻⸻⸻⸻⸻
Divide each side by 2.
x = 2.75 + -1.5y
⸻⸻⸻⸻⸻
Simplifying.
x = 2.75 + -1.5y
⸻⸻⸻⸻⸻
What is the degree of each polynomial?
(x^2 - y)^2 Degree _______
8x^4-5x^7+4c^5 Degree ______
x^2y^3/3+2x^3+8x^3 Degree ______
x^4 +2x^3-6x^4-17 Degree ______
-x^2+7x-4x Degree _____
x^7+y^8+x^7-y^8 Degree_____
Answer:
A- 4
B- 5
C- 8
D- 4
E- 2
F- 7
I'm 99% sure these are right!! I hope this helps :(
ok. 4. 62 decreased by 2 7 co 8 anolo 5. 14 increased by 14
Answer: Arachidonic acid (AA, sometimes ARA) is a polyunsaturated omega-6 fatty acid 20:4(ω-6), or 20:4(5,8,11,14).
Step-by-step explanation: It is structurally related to the saturated arachidic acid found in cupuaçu butter.[3] Its name derives from the New Latin word arachis (peanut), but it is important to note that peanut oil does not contain any arachidonic acid.[4]
Evaluate the expression using the values given.
4y(y + x); use x= 3/2, and y = -5/4
Answer:
-5/4 or -1 1/4
Step-by-step explanation:
Okay! We'll take this problem one part at a time so that the process is less confusing and less difficult. Here's what our expression looks like when we replace x with 3/2 and y with -5/4:
[tex]4(-\frac{5}{4} )(\frac{3}{2} +-\frac{5}{4} )[/tex]
Looks a little scary! We can start by working within the parentheses and adding the two fractions together. First, we have to make each fraction have the same denominator, so we can multiply each fraction by 3/2 to get both our fractions a denominator of 4.
[tex]\frac{3}{2} *\frac{2}{2} =\frac{6}{4}[/tex]
[tex]\frac{6}{4} + -\frac{5}{4} =\frac{1}{4}[/tex]
Now, our expression is a little easier to work with. It looks like this now:
[tex]4(-\frac{5}{4} )(\frac{1}{4})[/tex]
First, let's multiply 4 by -5/4. Then, we'll take that product and multiply it by 1/4 to get our final answer.
[tex]\frac{4}{1} * -\frac{5}{4} =-\frac{20}{4} =-5[/tex]
Alright, this is our simplest expression yet. What's -5 times 1/4?
[tex]-\frac{5}{1} * \frac{1}{4} =-\frac{5}{4}=-1\frac{1}{4}[/tex]
So our answer is -5/4, or -1 1/4. Hopefully that's helpful! :)
Solve this problem and show the steps with check steps confirming answer is correct.
4x-7=2x+15
Answer: X=11
Step-by-step explanation:
Add 7 to both sides of the equation 4x-7=2x+15
4x-7+7=2x+15+7
Simplify
Add the numbers :4x -7 + 7 = 2 x + 15 + 7
Add the numbers:4 x = 2x + 15+7
down
4x=2x+22
Subtract
2 2 x 2 x from both sides of the equation
4 x = 2x +22 4x - 2x = 2x +22- 2x
Simplify
2x = 2x +22-2x
Divide both sides of the equation by the same term
2x = 22 2x/ = 22/2 x =22/2x =22/2 x=11
What is the mean? 3 8 7 2 9 6 6 7
Answer:
6
Step-by-step explanation:
To find the mean, you add up all the numbers and divide that by the number of numbers there are.
In this case, the total is [tex]3+8+7+2+9+6+6+7=48[/tex]
There are 8 numbers.
Thus, the mean is 48 ÷ 8 = 6
Hey there!
When you hear/see the word “mean” in mathematics it usually means “average” or “total”.
Formula: sum of the total numbers ÷ total numbers in the data plot
YOUR EQUATION:
3 + 8 + 7 + 2 + 9 + 6 + 6 + 7 ÷ 8
= 11 + 7 + 2 + 9 + 6 + 6 + 7 ÷ 8
= 18 + 2 + 9 + 6 + 6 + 7 ÷ 8
= 20 + 9 + 6 + 6 + 7 ÷ 8
= 29 + 6 + 6 + 7 ÷ 8
= 35 + 6 + 7 ÷ 8
= 41 + 7 ÷ 8
= 48 ÷ 8
= 6
Therefore, your mean is: 6
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A school has 320 girls and 250 boys
The probability that a girl is left handed is 0.2
The probability that a boy is left handed is 0.1
Estimate the umber of left handed students in the school.
Guided Practice
Write the equation of the parabola in vertex form. The vertex is (3, 2) and the parabola passes through the point (0, 38). Create a rough sketch of the graph to use as a visual aid.
A.
y = 4(x + 3)2 + 2
B.
y = (x + 3)2 + 2
C.
y = 19(x − 2)2 + 3
D.
y = 4(x − 3)2 + 2
Answer:
D.
y = 4(x − 3)^2 + 2
Step-by-step explanation:
A. y = 4(x + 3)^2 + 2 = ( − 3 , 2 )
B. y = (x + 3)^2 + 2 = ( − 3 , 2 )
C. y = 19(x − 2)^2 + 3 = ( 2 , 3 )
D. y = 4(x − 3)^2 + 2 = ( 3 , 2 )
The following triangles are similar triangles with some dimensions specified. Find the measures of the other sides.
Answer:
116°
Step-by-step explanation:
(Angle sum property of a triangle = 180°)
angle A + angle C + angle ABC = 180°
66° + 50° + angle BAC = 180°
116° + angle ABC = 180°
angle ABC = 180° - 116°
angle ABC = 64°
angle ABD + angle ABC = 180°
angle ABD + 64° = 180°
angle ABD = 180° - 64°
angle ABD = 116°
So, the measure of the unknown angle is 116°
12
Fill in the blank: What's the length of the missing
side?
Ilype your answer
Answer:
13
Step-by-step explanation:
Using Pythagoras Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute values of a and b:
[tex]5^2+12^2=25+144=169[/tex]
[tex]c^2=169\\c=13[/tex]
The length of the missing side is 13.
Sara earns $12.75 per hour at her job. She works 18 hours each week. While at work, she parks her car in a garage that charges $10.50 every 3 hours.
After paying for parking, how much does Sara earn each week?
A.$198.00
B.$229.50
C.$166.50
D.$261.00
9514 1404 393
Answer:
C. $166.50
Step-by-step explanation:
The rate Sara pays for parking is ...
$10.50/(3 hours) = $3.50 /hour
So, Sara's net pay, after paying for parking, is ...
$12.75/hour - 3.50/hour = $9.25 /hour
If she works 18 hours per week, her net earnings are ...
(18 h)($9.25/h) = $166.50 . . . . weekly earnings
a prism is a 3d shape with the same _______ all the way through
Answer:
cross-section
Step-by-step explanation:
prism is a type of three-dimensional (3D) shape with flat sides.
It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.
According to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like iced coffee, and 22% like both hot and iced coffee. The Venn diagram displays the coffee preferences of the customers.
Answer:
0.08
Step-by-step explanation:
the orange circle is all people who like iced coffee, since we want the probability of liking only iced coffee, we need to look at the part of the orange circle not overlapping with the blue circle. this is 0.08
What is the sum in 1 1/3+ 2 1/3 + 3 2/3 + 4 1/2 + 5 1/2 + 6 3/4
Answer:
17.999999999999999
Step-by-step explanation:
Answer:
25 and 1/12
1/3+1/3+2/3+1/2+1/2+3/4 = 4 and 1/12
6+5+4+3+2+1 = 21
helppppppppppppppppppppp!
Answer:
1:3
Step-by-step explanation:
Since your scaling down you divide the smaller number by the larger number
7/21=1/3
=1:3
Hope this helps :)
−3 ≤ n < 2
−2 < m < 4
n and m are integers.
Given that n = m, write down all the possible values of n.
_1,0,1 are possible value of n
Where does -3/7 belong on the Venn diagram
A) integers
B) natural numbers
C)rational numbers
D) irrational numbers
Answer:
rational
Step-by-step explanation:
3. A certain container of mouthwash usually costs $2.99 at a store. If it is on sale for 20% off how much does the mouthwash cost now?
A. $2.75
B. $2.77
C. $2.40
D. $3.74
Answer:
the answer is D Because
Step-by-step explanation:
so I will say about $3.74
Alguém me ajuda pfv rápido
Answer:
9.72
Step-by-step explanation:
1.8 x 1.8 x 3 = 9.72
This is a glucose molecule. How many hydrogen atoms are in a molecule of glucose? A) 10. B) 11. C) 12. D) 13
Answer:
12 for sure
Step-by-step explanation:
I just know
Henry steps onto an elevator at the first floor. He goes up to the 9th floor and then comes down 2 floors. He then goes up 4 floors and down 6 floors. What floor is Henry on?
Answer:
He is on the 5th floor
Step-by-step explanation:
9 - 2 = 7
7 + 4 = 11
11 - 6 = 5
Answer:
he goes 1 +9=10
10-2=8
8+4=12
12-6=6
so he is ont the sixth floor
i need help on this math problem
Answer:
Step-by-step explanation:
Slope: 3/1 (positive: line go uphill)
y-intercept: -5
Place your pencil on the vertical line (y) on -5. Go up 3 units and 1 to the right, repeat and trace the line (actually you only need two points to trace a line)
Add 1, multiply by 2. 2 First
Answer:
2+1×2=6
6+1×2=14
14+1×2=30
And so on
A tortoise is walking in the desert. It walks 5.12 meters in 2 minutes. What is its speed?
Answer:
2.61 meters per minute
Step-by-step explanation:
All you have to do is divide by 2!
The speed of the tortoise is 2.56 meters per minute.
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given, A tortoise is walking in the desert.
It walks 5.12 meters in 2 minutes.
The speed meter per minute;
5.12/2
= 2.56 meters per minute.
Therefore, 2.56 meters per minute is the speed of the tortoise.
To learn more about the speed;
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HELP!
due tommorow , KS3 year 8
Answer:
Perimeter = (Length + Width)×2
=(17.8cm + 4.6cm)×2
=(22.4 × 2)cm
= 44.8cm
The perimeter of a triangle is 71 cm. If the longest side of the triangle is 8 cm longer than five times the shortest side and the third side is 7 cm less than four times the shortest side. How long is the longest side of the triangle?
Answer:
43 cm
Step-by-step explanation:
If the longest side of the triangle is 8 cm longer than five times the shortest side
5s + 8
the third side is 7 cm less than four times the shortest side
4s - 7
The perimeter of a triangle is 71 cm
s + (4s - 7) + (5s + 8) = 71
Combine like terms
10s + 1 = 71
Subtract 1 from both sides
10s = 70
divide both sides by 10
s = 7
---------------------------------
How long is the longest side of the triangle
5s + 8
5(7) + 8
35 + 8
43
We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)
Evaluate the information given by the pilot.
Show calculations to support your answer.
Answer:
Step-by-step explanation:
500 mph with a flight time of 10 hours and 20 minutes [(20 min)*(1 h/60 min) = 0.333 hr]
Distance = Speed * Time
Time = 10.333 hours
Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles
The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles. That is a 4.3% reduction from the pilot's numbers. Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.
My preference would be to trust the pilot's data. I don't know where Mark got his math education.
Please help please please help me help please
Answer:
y = 9/10x - 7/5
Step-by-step explanation:
Slope = 9/10
Point (6,4)
y-intercept = 4 - (9/10)(6) = 4 - 54/10
= - 7/5