Answers
Answer:
x = 3Step-by-step explanation:
given:
f(x) = g(x)
f(x) = x³ - 3x² + 2
g(x) = x² - 6x + 11
find: the value of x
solution:
as given f(x) = g(x) equate each side x³ - 3x² + 2 = x² - 6x + 11 combine similar terms and equate to zero: x³ - 4x² + 6x - 9 = 0 solve by factoring: (x - 3) (x² - x + 3) use the Zero factor principle: x - 3 = 0 x = 3 for x² - x + 3 = 0 ----this is a complex solution.
therefore, the value of x = 3
Step-by-step explanation:
[tex]
\underline{\bf{Given\::}}
Given:
\underline{\bf{To\:find\::}}
Tofind:
\underline{\bf{Explanation\::}}
Explanation:
\boxed{\bf{\frac{1}{f} =\frac{1}{v} -\frac{1}{u} }}}}
\begin{gathered}\longrightarrow\sf{\dfrac{1}{-10} =\dfrac{1}{v} -\dfrac{1}{-30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-10} +\dfrac{1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{-3+1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\cancel{\dfrac{-2}{30} }}\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-15} }\\\\\\\longrightarrow\sf{v=-15\:cm}\end{gathered}
⟶
−10
1
=
v
1
−
−30
1
⟶
v
1
=
−10
1
+
30
1
⟶
v
1
=
30
−3+1
⟶
v
1
=
30
−2
⟶
v
1
=
−15
1
⟶v=−15cm
\boxed{\bf{M \:A \:G \:N\: I \:F \:I \:C\: A\: T \:I \:O\: N :}}
MAGNIFICATION:
\begin{gathered}\mapsto\sf{m=\dfrac{Height\:of\:image\:(I)}{Height\:of\:object\:(O)} =\dfrac{Distance\:of\:image}{Distance\:of\:object} =\dfrac{v}{u} }\\\\\\\mapsto\sf{m=\cancel{\dfrac{-30}{-15}} }\\\\\\\mapsto\bf{m=2\:cm}\end{gathered}
↦m=
Heightofobject(O)
Heightofimage(I)
=
Distanceofobject
Distanceofimage
=
u
v
↦m=
−15
−30
↦m=2cm
Thus;
The magnification will be 2 cm .
[/tex]
Related Questions
3 (4x - 2) - 30 = -6 (6 - 2x) - 20
A.Infinite Solutions/Identity
B.No Solution
C.x = 0
D.x = 1
show work please
Answers
Answer:
B.
Step-by-step explanation:
3(4x-2)-30=-6(6-2x)-20
12x-6-30=-36+12x-20
12x-36=12x-56
Solve for b: 3ab = -7
Answers
Since we are solving for b, you need to get it by itself. So you would divide both sides by 3a. That would leave b= -7/3a.
Hope this helps!!
Scott wrote the number 39 on the board and said that it was a prime
number because it was an odd number. Is he correct? Explain why
or why not.
Answers
Please show your work? A pool of possible candidates for a student council consists of 14 freshmen and 9 sophomores. How many different councils consisting of 5 freshmen and 7 sophomores are possible?
28,828,800
1,352,078
72,072
943,286,400
Answers
Answer:
28,828,800
Step-by-step explanation:
There are 72,072 ways of choosing different councils consisting of 5 freshmen and 7 sophomores
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, A pool of possible candidates for a student council consisting of 14 freshmen and 9 sophomores.
∴ 5 freshmen out of 14 freshmen can be chosen in [tex]^{14}C_5[/tex] ways and 7 sophomores can be chosen out of 9 sophomores in [tex]^{9}C_7[/tex] ways.
So, The no. of different councils consisting of 5 freshmen and 7 sophomores are possible is,
= [tex]^{14}C_5\times^{9}C_7[/tex] ways.
= 14!/(14 - 5)!×5! × 9!/(9 - 7)!×7! ways.
= 14×13×12×11×10/120 × 9×8/2 ways.
= 2002× 36 ways.
= 72,072.
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How many times larger is 5 * 10 ^ 2 5 * 10 ^ -2
Answers
Answer:
Step-by-step explanation:
Substitute the given value into the function and evaluate.
5 ⋅ 10 ^2 = 500
5 ⋅ 10^ − 2 = 0.05
Hope This Helps!
Please Mark Brainliest If You Want!
It Helps A lot! ;)
PLEASEEEEEEEEEEEEEEEEEEEE HURRYYYYYYYYYYYYYYYYYYYYYYYYYYYY SOMEONEEEE
Answers
Answer: C = 30 - 3t
Step-by-step explanation: he starts with 30 therefore having 30 on day 0 and he eats 3 daily so day 1 would be 27 day 2 24 and so on
9=4(s-3)
Help me what’s the correct answer?
Answers
Answer:
s=5 1/4
Step-by-step explanation:
Have a wonderful day
Sally's soccer team played 25 games and won 17 of them. What percent did the team win
Answers
Answer:
68%
Step-by-step explanation:
Answer:
Sally's soccer team won 68% of the games they played.
which representation does not show y as a function of x
Answers
Eighth grade
W.15 Find the number
You have prizes to reveal! Go
How many solutions does this equation have?
-4p + 8 = -2p
no solution
one solution
infinitely many solutions
Answers
Answer:
one solution because you combine like terms and your answer is p=4
First to awnser will the question correct will get brainlyist
Ashley was out at a restaurant for dinner when the bill came. She wanted to leave a tip of 12%. What number should she multiply the cost of the meal by to find the total plus tip in one step?
Answers
Answer:
x 1.12
Step-by-step explanation:
Total meal plus 12% tip in one step.
12% as a fraction is .12
Multiply the cost of the meal by 1.12 To get the total cost including tip.
x 1.12
the sum of three consecutive odd integers is 57. what are three integers.
Answers
Answer:
17,19,21
Step-by-step explanation:
Let x be the smallest integer
x+x+2+x+4=57
3x+6=57
3x=57-6
3x=51
x=51/3
x=17
17,19,21
What is the equation of the line that passes through the point (-8, 3) and has a
slope of -1/4
Answers
Answer:
-1/4x + 1 ( If this is wrong then ignore this)
Step-by-step explanation:
The formula for a problem like this is y - y1 = m(x - x1). The x coordinate, -8 is the x1 and the y coordinate 3 is x1. So the equation is y - 3 = -1/4(x + 8)
Equation:
y - 3 = -1/4(x + 8)
y - 3= -1/4x - 2
y = -1/4x + 1
Therefore the equation for the line is y = -1/4x + 1
Given parameters:
Slope of the line = [tex]-\frac{1}{4}[/tex]
Coordinates of the points = (-8, 3)
Unknown:
Equation of the line = ?
Solution:
To find the equation of the line, we must note that any straight line can be represented by the equation;
y = mx + c
where x and y are the coordinates
m is the slope
c is the y-intercept of the line
Input the parameters and solve for c;
x = -8 and y = 3;
3 = [tex]-\frac{1}{4}[/tex] x (-8) + c
3 = 2 + c
c = 1;
So the equation of the line is ;
y = [tex]-\frac{1}{4}[/tex]x + 1
multiply through by 4;
4y = -x + 4
The equation of the line is 4y = -x + 4
1. f(x) = 2^-2x + 3
T-chart:
End behavior:
2. f(x) = (½)^ (x - 1)
T-chart:
End behavior:
3. j(x) = -2 (3/2)^x
T-chart:
Asymptotes:
End behavior:
4. g(x) = -3x
T-chart:
End behavior:
Answers
Step-by-step explanation:
Make sure all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.
Select the correct answer.
The product of two numbers, x and I + 3, is 550. Which equation could be solved to find the value of the smaller number, x?
CA. 12 + 3.1 = 550
B. 12 + 3 = 550
C. 31 + 3 = 550
D. 322 = 500
Reset
Next
Answers
Answer:
the answer on plato is x^2+3=500
Please answer correctly !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!
Answers
Answer:
1) B
2) A
Step-by-step explanation:
B because we use pemdes and for 2 they answers are both equivalent
Answer:
1) B. Add/subtract the same quantity to/from both sides
2) Yes
Step-by-step explanation:
To answer Part B, we have to answer to equation.
Step 1- Add x to both sides of the equation.
4x+2= 6-x
+x +x
5x+2= 6
Step 2- Subtract 2 to both sides of the equation.
5x+2= 6
-2 -2
5x= 4
Step 3- Divide 5 to both sides of the equation.
5x= 4
5 5
This gives us 4/5 or 0.80.
So, the answer is yes to Part B.
Hope this helps!
PLEASE ANSWER NEED HELP BAD AND IM OUT OF POINTS T-T
To determine whether they used the same number of tiles, set the two expressions equal to each other and solve for x. Is there a solution for x? Why or why not? If there is a solution, what is it?
Here is the equation stuff to solve:
Expression for the number of tiles Bruce used : 5x+2
Expression for the number of tiles Felicia used : 5x + 5
How could you change the equation so it has infinitely many solutions? What would infinitely many solutions mean in terms of the situation?
Answers
To determine whether they used the same number of tiles, set the two expressions equal to each other and solve for x. Is there a solution for x? Why or why not? If there is a solution, what is it?
5x +2 = 5x + 5 (subtract 5x and 2 on both sides)
0 = 3 No solution
How could you change the equation so it has infinitely many solutions?
Have 2 or 5 change because they need to be equal to each other. Its fine what you put as long as the equal sign is the same as the other side like 3 = 3 for example or 5 = 5, something like that. Once they have the same end then you can substitute the number to x.
What would infinitely many solutions mean in terms of the situation?
x represents the number of tiles they used
Find the GCF of 38 and 49.
Answers
Answer:1
Step-by-step explanation:
I found the factors and prime factorization of 38 and 49. The biggest common factor number is the GCF number. So the greatest common factor 38 and 49 is 1
Answer: The greatest common factor is 1
Step-by-step explanation:
49 is not even like 38 so the only one they have together in 1.
3/8 divided by 2/5??
Answers
Answer:
15/16
Ste
Step-by-step explanation:
Keep, Change, Flip.
(1) Keep the first fraction, 3/8.
(2) Change the sign from a division sign to a multiplication sign.
(3) Flip the last fraction, 2/5 --> 5/2.
(4) Multiply across.
3/8 x 5/2= 15/16
The 3/8 divided by 2/5 is equal to 15/16.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
To divide 3/8 by 2/5:
(3/8) ÷ (2/5) = (3/8) × (5/2)
Now, let's multiply the numerators and denominators:
(3 × 5) / (8 × 2) = 15/16
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Enter the fraction as a decimal.
1
8
The fraction as a decimal is
Answers
Answer: 0.125
Step-by-step explanation:
Answer:
0.125
1/8
= 0.125
= 12.5%
PLEASE HELP FAST
write an inequality and solve it
Answers
Answer:
1>2x
Step-by-step explanation:
1>2x
1/2= one half
2x/2= x
one half>x
Please help with this, it's due today and I don't really understand it.
Answers
Answer:
Check description
Step-by-step explanation:
First: work out the difference (increase) between the two numbers you are comparing. Then: divide the increase by the original number and multiply the answer by 100. % increase = Increase ÷ Original Number × 100. If your answer is a negative number, then this is a percentage decrease.
State the solutions of the equation |x| + 2 = 4.
Answers
I think thats 2
Because 2+2=4
explanation: if you plug in 2 or -2 or x, then it would always become 2. this is because if you take the absolute value of any number, then it would become positive. this makes the equation true because 2 + 2 = 4
Hi Krystal, when you submit this form, the owner will be able to see your name and email address,
1. A is located ( 1,-1) and B is located (4,4) Find the coordinates of point p that partition
AB in the ratio 1:4. 03
Enter your answer
I
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Answers
Answer:
hi Krystal , I am Felicia
The value of w varies directly with z. If z = 4, then w = 12. What is the value
of w when z = 6? (TEKS: A2D)
Answers
Answer:
18
Step-by-step explanation:
w varies directly with z, let k be the constant of proportionality, hence this can be represented by the equation:
w = kz
When z = 4, w = 12, hence we need to find the value of the constant of proportionality, substituting:
12 = 4k
Dividing both sides by 4:
12/4 = 4k/4
k = 3
Therefore the equation becomes:
w = 3z
The value of w when z = 6 is given as:
w = 3(6)
w = 18
Emmett buys an emerald pendant priced at $527.50. Shipping and handling are an additional 12% of the price. How much shipping and handling will Emmett pay?
Answers
A rancher built a cattle fence in the shape of a triangle.
From one corner, the fence will go 200 yards south.
Then, the fence will turn at a right angle and go 120 yards west.
From there, the fence goes straight back to its starting point.
To the nearest yard, how much fencing did the rancher use?
Answers
Answer:
it is 480 yards!
Step-by-step explanation:
Answer:
480
Step-by-step explanation:
Aaron invested $7,500 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 8 years?
Answers
Answer:
\text{Compounded Continuously:}
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
P=7500\hspace{35px}r=0.015\hspace{35px}t=8
P=7500r=0.015t=8
Given values
A=7500e^{0.015(8)}
A=7500e
0.015(8)
Plug in
A=7500e^{0.12}
A=7500e
0.12
Multiply
A=8456.22638685
A=8456.22638685
Use calculator (with e button)
A\approx 8500
A≈8500
Round to nearest hundred dollars
Step-by-step explanation:
The amount of money to the nearest hundred dollars that would be in the account after 8 years is $60,900.
What is the future value of the account?The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate7500 x e^0.015 x 8 = $60,900
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need help with this please
Problem-solving Ava and Ben set the alarms on their phones to sound at 6:30 am
Both alarms sound together at 6:30 am.
Ava's alarm then sounds every 24 minutes.
Ben's alarm then sounds every 30 minutes.
Use the lowest common multiple to find out when both alarms next sound
together.
Answers
Answer:
08:30 am
Step-by-step explanation:
30 * 1 =30 24 * 1 = 24
30* 2 = 60 24 * 2 = 48
30 * 3 = 90 24 * 3 = 72
30 * 4 = 120 24 * 4 = 96
24 * 5 = 120
The lowest common multiple ist 120.
06:30 am + 120 min = 08:30 am
-5 ( x + 7) = -5x + 35
Answers
Step-by-step explanation:
Let's solve your equation step-by-step.
−5(x+7)=−5x+35
Step 1: Simplify both sides of the equation.
−5(x+7)=−5x+35
(−5)(x)+(−5)(7)=−5x+35(Distribute)
−5x+−35=−5x+35
−5x−35=−5x+35
Step 2: Add 5x to both sides.
−5x−35+5x=−5x+35+5x
−35=35
Step 3: Add 35 to both sides.
−35+35=35+35
0=70
Answer:
There are no solutions.
Answer:
x= no solution
Step-by-step explanation:
-5(x+7)=-5x+35
-5x-35=-5x+35
+5x +5x
-35= 35
+35 +35
0=70
x=no solution
When x doesn't equal anything, and 0 doesn't equal 0, there is no solution to make the equation true. When 0=0, x can equal any value.