Given the equations x^2 + 8x + 12 = 0 and 3x + 6 = 0, what is the common
solution?
Answers
[tex] {x}^{2} + 8x + 12 = 0 \\ = > {x}^{2} + 6x + 2x + 12 = 0 \\ = > x(x + 6) + 2(x + 6) = 0 \\ = > (x + 2)(x + 6) = 0 \\ = > x = - 2 \: \: or \: \: - 6[/tex]
[tex]3x + 6 = 0 \\ = > 3x = - 6 \\ = > x = \frac{ - 6}{3} \\ = > x = - 2[/tex]
Here, the common solution is -2.
Answer:
x = -2.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Related Questions
8-kg lead brick falls from a height of 1.6 m.
(a) Find its momentum as it reaches the ground.
Ikg-m/s
(b) What Impulse is needed to bring the brick to rest?
N-s
(c) The brick falls onto a carpet, 2.0 cm thick. Assuming the force stopping it is constant, find the average force the carpet exerts on the brick
N
(d) If the brick falls onto a 6,0 cm foam rubber pad, what constant force is needed to bring it to rest?
Answers
The magnitude of the impulse needed to bring the brick to rest is given by the initial momentum of the brick.
The correct responses are;
(a) 44.8 kg·m/s(b) 44.8 N·s(c) 6,278.4 N(d) 2,092.8 NReasons:
The velocity of the brick as it reaches the ground is given by the formula;
v² = 2·g·h
v = √(2·g·h)
Where;
h = The height of the brick, h = 1.6 m
g = The acceleration due to gravity ≈ 9.81 m/s²
Therefore;
v ≈ √(2 × 9.81 m/s² × 1.6 m) ≈ 5.6 m/s
(a) Momentum = Mass × Velocity
The momentum of the brick = 5.6 m/s × 8 kg = 44.8 kg·m/s
(b) Impulse = Force × Δt = Mass × Δv
Mass × Δv = 8 kg × (5.6 m/s - 0) = 44.8 kg·m/s = 44.8 N·s
Therefore, the impulse = 44.8 N·s
(c) The distance over which the carpet stops the brick = 2.0 cm = 0.02 m
Initial energy in the brick, E = m·g·h
Which gives;
E = 8 kg × 9.81 m/s² × 1.6 m = 125.568 J
Energy = Force × Distance
[tex]\displaystyle Force \ carpet \ exerts \ on \ brick, \ F = \frac{125.568 \, J}{0.02 \, m} = \mathbf{ 6,278.4 \, N}[/tex]
The average force the carpet exerts, F = 6,278.4 N
(d) If the brick falls on a foam which is 6.0 cm (thickness), we have;
Distance = 6.0 cm = 0.06 m
Therefore;
[tex]\displaystyle Force, \, F = \frac{125.568 \, J}{0.06 \, m} = \mathbf{2,092.8 \, N}[/tex]
The constant force needed to bring the brick to rest is, F ≈ 2,092.8 N
Learn more about force and energy here:
https://brainly.com/question/6366228
https://brainly.com/question/528149
468 divided by 3 step by step solution
Answers
Answer:
156Step-by-step explanation:
468 ÷ 3
= 156
hope u liked the answer :)
#keep learningHow i can answer this question?, NO LINKS, if you answer correctly i'll give u brainliest!
Answers
Answer:
9
Step-by-step explanation:
The coefficient is always the number before the variable (X).
Answer:9
Step-by-step explanation:
The coefficient is always by the variable (the number or letter)
Please help, we're supposed to be writing an equation from the table here. But I don't know.
Answers
Answer:
y = 3x - 3
Step-by-step explanation:
This more of a guess than a reality of method. You have to try and guess which number when multiplied by 4 will give 9. It won't happen directly.
The best clue is provide by (0,-3).
So let's start with a general linear equation.
y = mx + b
If you put in 0 for x then mx disappears and you are are left with y = - 3
That means that b = - 3
So now you have
y = mx - 3
Now try another one
y = mx - 3
y = 9
x = 4
9 = mx - 3
9 = 4m - 3 Add 3 to both sides
9+3 = 4m-3+3 Combine
12 = 4m Divide by 4
12/4 = 4m/4
3 = m
So the equation you want so far, is y = 3x - 3 Does it work for anything else?
Try - 3 , - 12 . If it works for this, it should work for anything.
y = 3*-3 - 3
y = -9 -3
y = - 12
and it does work, so that's your answer.
A freight ship has been moving at 19 miles per hour for the past 2 days. Hugo recorded that the ship moved 155 miles yesterday and 92 miles today. For how many hours has Hugo been keeping track of the ship?
Answers
Answer:
13 hours
Step-by-step explanation:
155 + 92 = 247
247 / 19 = 13
Can someone please help !!
Answers
Officer Brimberry wrote 32 tickets for traffic violations last week, but only 12 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent. [The percent decrease is___%
Answers
Answer:
62.5 %
Step-by-step explanation:
you have to subtract 32-12, which equals 20
then divide 20 by the original amount (20/32)
20/32= .625, then you have to multiply to get the final answer...hope this helped!
Solve for W if:
4w^2+9w=-2
Answers
Hope it helps
The image below represents a Function. Describe what is happening in this "machine".
Answers
Answer:
The input is being multiplied by 10.
This can be represented with the function x * 10 = y with x representing the input and y representing the output.
Step-by-step explanation:
Select the four equivalent expressions to 4x^2 - 4x -24
A - 2x^2 - 2x - 12
B - 4(x^2 - x - 6)
C - 4(x - 3)(x + 2)
D - (2x - 2x)^2 - 24
E - (4x - 12)(x +2)
F - (x - 3)(4x + 8)
Answers
Answer:
b. 4(x^2 - x - 6)
c. 4(x - 3)(x + 2)
e. (4x - 12)(x +2)
f. (x - 3)(4x + 8)
hope it helps :)
mark brainliest!!
Solve for percent error: At a school production, the drama club advisor
predicted that there would be 200 people on the first night. Find the
percent error if 250 people attend.
Answers
Answer:
25 %
Step-by-step explanation:
Error = (actual - predicted) / (predicted)
= (250-200) / 200
= 50 / 200
= 0.25
multiply by 100 to conver to a percent
25 %
pls help on my maths
Answers
Given:
[tex]A = 25[/tex]Let's simplify.
=> [tex]25 = \frac{22}{7} r^{2}[/tex]=> [tex]\frac{25}{\frac{22}{7} } = \frac{\frac{22}{7}r^{2} }{\frac{22}{7\\} }[/tex]=> [tex]\frac{7(25)}{22} = r^{2}[/tex]=> [tex]\sqrt{\frac{25(7)}{22}}= \sqrt{r^{2}}[/tex]=> [tex]\sqrt{\frac{25(7)}{22}}= r[/tex]=> [tex]r = 2.82[/tex] (Estimated)Therefore, r ≈ 2.82.
Hoped this helped.
Answer:
r= 5/√ π
or
r=2.820948 or simplified =2.82
Step-by-step explanation: it could be either one of these
a *blank* *blank* trinomial has only one element in the solution set
Answers
Answer:
a solution set trinomial has only one element in the solution set
Step-by-step explanation:
Point A=(7,9) is dilated from the origin by scale factor of r=11. what are the coordinates of point A
Answers
Answer:
42 and 54
Step-by-step explanation:
A quadratic. equation will always have an irrational solution since there is a square root in the quadratic formula. True or False?
Answers
Answer:
False
Step-by-step explanation:
If the square root can be simplified to a rational number the solution will not be irrational.
Answer:
False
Step-by-step explanation:
Consider reducible quadratic equations. They have rational solutions.
Evaluate to function for the given value of X
Answers
[tex]\text{Given that,}\\\\\\f(x) = 9x^3 -x^2 +2 \\\\f(2) = 9(2^3) - 2^2 +2\\\\~~~~~~~ = 9(8) -4 +2 \\\\~~~~~~~= 72 -2 \\\\~~~~~~~=70[/tex]
how do you know how many points are needed to make a graph of a polynomial function from a table? are there a safe number of points to make the graph of any polynomial function? if so, what is that number? please help, explain well if possible
Answers
Step-by-step explanation:
You need a arbitrary points that will help you determine the sketch of the graph. I say use at most 5 points but you just need to know the following
The exterma: The maximum/minimum points on a certain interval.
The zeroes: What values willTheorem, Factoring, and more to help you find the zeroes.
Increasing and decreasing behavior between the consective zeroes: How the function behaves around consective zeroes. It must be above or below x axis between the zeroes.
And finally, the end behavoir: How the function behaves as x approaches infinity and negative infinity. Does the function increases or decreases.
That it. If you need an example, just ask me
Katarina bought a package of 500 stickers. 25% of the stickers are hearts. The remaining stickers are stars. Select all the statements that are true.
Answers
Answer: 125 hearts and 375 stars
Step-by-step explanation:
25% of 100 is 25. Take 100 and x it by 5. 100 x 5 is 500 making 25 x 5 125. That being said 125 hearts and 375 stars
Answer:
125 hearts and 375 stars
Step-by-step explanation:
A man left 1⁄2 of his property to his wife 1/3 of the remainder to his eldest
son and the rest to be divided equally among his five younger children,
each of whom got p60,000. How much did his wife get?
Answers
Answer: p800,000
Step-by-step explanation:
1/2 to wife
1/3 to eldest son, and
Rest(x) to 5 youngest children
(1/2) + (1/3) + x = 1 [The sum of the shares will equal 1 estate]
(3/6) + (2/6) + x = 1
(5/6) + x = 1
x = (1/6); to be divided among the 5 youngest children
We find that each young child receives p60,000. That group of five received 5*(60,000) = p300,000, which represents (1/6) of the total estate (Estate).
We can write: (1/6)*(Estate) = p300,000
Estate = p1,800,000
The wife hauled in 1/2 of this, so she received p800,000.
help please 6(l+3)<3(2l+6)
Answers
Answer:
No solution
Step-by-step explanation:
Expand and simplify both expressions:
6l+18 < 6l+18
6l+18-18 < 6l+18-18
6l < 6l
0 < 0
Therefore, there is no solution
what is 7.5% as a fraction
Answers
Answer:
15/2
Step-by-step explanation:
hope it helps (•‿•)
If Delta FGH sim Delta KJH find FH .
Answers
Answer:
39
Step-by-step explanation:
Two triangles are similar so we can use the similarity ratio to calculate the value of x this way we can find the length of FH
(x+8)/32 = (4x-25)/52 cross multiply expressions
52x + 416 = 128x - 800 export like terms to the same side of equation
416 + 800 = 128x - 52x
1216 = 76x divide both sides by 76
16 = x then the length of FH
4*16 - 25 = 39
Please help me and If your answer is wrong or not appropreat I will report it
Simplify (-2x^(3)y^(7))^(2)(3x^(2)y^(2))^(5)
Answers
Answer:
972 x^16 y^24
Step-by-step explanation:
Simplify the following:
(-2 x^3 y^7)^2 (3 x^2 y^2)^5
Multiply each exponent in -2 x^3 y^7 by 2:
(-2)^2 x^(2×3) y^(2×7) (3 x^2 y^2)^5
2×7 = 14:
(-2)^2 x^(2×3) y^14 (3 x^2 y^2)^5
2×3 = 6:
(-2)^2 x^6 y^14 (3 x^2 y^2)^5
(-2)^2 = 4:
4 x^6 y^14 (3 x^2 y^2)^5
Multiply each exponent in 3 x^2 y^2 by 5:
4 x^6 y^14×3^5 x^(5×2) y^(5×2)
5×2 = 10:
4×3^5 x^6 y^14 x^(5×2) y^10
5×2 = 10:
4×3^5 x^6 y^14 x^10 y^10
3^5 = 3×3^4 = 3 (3^2)^2:
4×3 (3^2)^2 x^6 y^14 x^10 y^10
3^2 = 9:
4×3×9^2 x^6 y^14 x^10 y^10
9^2 = 81:
4×3×81 x^6 y^14 x^10 y^10
3×81 = 243:
4×243 x^6 y^14 x^10 y^10
4 x^6 y^14×243 x^10 y^10 = 4 x^(6 + 10) y^(14 + 10)×243:
4×243 x^(6 + 10) y^(14 + 10)
14 + 10 = 24:
4×243 x^(6 + 10) y^24
6 + 10 = 16:
4×243 x^16 y^24
4×243 = 972:
Answer: 972 x^16 y^24
Answer:
972x^(16)y^(24)
Step-by-step explanation:
Hope it correct !!
Without doing any calculations, is positive or negative?
Explain your reasoning.
Answers
Answer:
what is positive or negative???
brainliest if correct
Solve.
−49x+2.4=6
Enter your answer as a decimal or as a mixed number in simplest form in the box.
x =
$\text{Basic}$
Answers
Step-by-step explanation:
[tex] - 49x + 2.4 = 6 \\ - 49x = 6 - 2.4 \\ - 49x = 3.6 \\ x = \frac{3.6}{ - 49} \\ x = - \frac{18}{245} = - 0.0735[/tex]
20 Points Please Help
Answers
That’s all I know from this I apologize, I’m only a freshman in hs lol
Good luck and Merry Christmas, happy holidays
Solve the equation.
7- 3n = 11n+ 2
Answers
3n-11n=11n+2-11n
The table below shows the number of minutes a household phone is used daily based on the number of household members.
Which equation best models this set of data?
A. P = -20.2x^2 - 1.3
B. P= -20.2x - 1.3
C. P= 20.2X^2 + 1.3
D. P= 20.2x + 1.3
Answers
I'm pretty sure the answer would be D) P = 20.2x + 1.3 but the answer should be P = 19.2x + 1.3, but it isn't listed so it would be D
9 + (-6) = 3 is this correct
Answers
Answer:
yes u are correct,it's does equal that
HELPPP ASAPPPPPPPPPPP
Answers
I can't see it can you retake the picture please so I can try to help if I know it?