Given:
The equation is:
[tex](x-3)^2+2(x-3)-8=0[/tex]
To find:
The value of x.
Solution:
We have,
[tex](x-3)^2+2(x-3)-8=0[/tex]
Substitute [tex]x-3=u[/tex].
[tex]u^2+2u-8=0[/tex]
Splitting the middle term, we get
[tex]u^2+4u-2u-8=0[/tex]
[tex]u(u+4)-2(u+4)=0[/tex]
[tex](u-2)(u+4)=0[/tex]
Using zero product property, we get
[tex]u-2=0\text{ and }u+4=0[/tex]
[tex]u=2\text{ and }u=-4[/tex]
Now, substitute [tex]u=x-3[/tex].
[tex]x-3=2\text{ and }x-3=-4[/tex]
[tex]x=2+3\text{ and }x=-4+3[/tex]
[tex]x=5\text{ and }x=-1[/tex]
Therefore, the correct option is b.
The solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
Quadratic equationFrom the question, we are to determine the solution of the given equation
(x - 3)² + 2(x - 3) - 8 = 0
First, we will expand the equation and clear the brackets
[tex](x - 3)^{2} + 2(x - 3) - 8 = 0[/tex]
[tex](x - 3)(x - 3) + 2(x - 3) - 8 = 0[/tex]
[tex]x^{2} -6x + 9 +2x - 6 - 8 = 0[/tex]
Simplifying
[tex]x^{2} -4x - 5 = 0[/tex]
Factorizing, we get
[tex]x^{2} -5x +x- 5 = 0[/tex]
[tex]x(x-5)+1(x- 5) = 0[/tex]
[tex](x+1)(x-5)= 0[/tex]
Then,
x + 1 = 0 or x - 5 = 0
x = -1 or x = 5
Hence, the solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
Learn more on solving Quadratic equations here: https://brainly.com/question/8649555
If fixed cost of 20 article is 500 and variable cost for each article is 40. Find the total cost function? Also ,find the total cost of 90 articles?
Answer:
Cost function = 40a + 500
Cost of 90 articles = $4,100
Step-by-step explanation:
The fixed cost is $500 and it will.not change regardless of production level.
The Variable cost is $40 and increases by every additional unit produced.
Assume the number of articles produced is a.
Cost function would be:
Total cost = Variable cost * Number of articles + Fixed cost
TC = 40a + 500
Using this, the cost of 90 articles is:
= 40 * 90 + 500
= $4,100
What is the volume of a sphere having a diameter of 6 cm?
Please help fast 15 points math homework
Answer:
Letter C
Step-by-step explanation:
Five examples of how circles and their radii be used in other content areas
Thanks for the points but i hope you have a great day and find your answer
What is the value 8x=5x+21
)) What is 538 rounded to the nearest ten? 500 535 ))
Step-by-step explanation:
540 because it I think or 535 but I I think it's 540
HELPPPPPPPPPPPP PLEASEEEE
Answer:
H. 13.5 in²
Step-by-step explanation:
[tex]V=LWH/3[/tex]
[tex]V=(3)(3)(4.5)/3[/tex]
[tex]V=13.5 in^{2}[/tex]
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hope it helps...
have a great day!!
As she drove down the icy road, Mrs. Campbell slammed on her brakes. Her car did a 360. Explain what happened to Mrs. Campbell's car.
Answer:
Step-by-step explanation:
Her car doing a 360 means that the car turned in a manner akin to going round a full circle. This is because, she was moving on an icy way. Ice have been known to be slippery, and thus, stepping on the brakes unexpectedly would have made the car tilt a bit, which then increased to turning sideways, and an eventually full circle turning. This full circle turning is what is being referred to as 360
Find the value of the ratio.
Can someone help please???
Answer:
SOH CAH TOA.....Cosine=adj/hyp...... __cosX=16/30___
SOH CAH TOA,,,,,, Tangent= opp/adj-------- Tan X=36/27
Step-by-step explanation:
Find the product. 1.5m6(-2m2)4
9514 1404 393
Answer:
24m^14
Step-by-step explanation:
It looks like you want to simplify ...
[tex]1.5m^6(-2m^2)^4=(1.5)(-2)^4(m^6)(m^{2\cdot4})\\\\=(1.5)(16)m^{6+8}=\boxed{24m^{14}}[/tex]
__
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
Solve.
-25 - (-5) = 0
PLLLSSS
Answer:
-20=0
Step-by-step explanation:
Answer: -20=0
Step-by-step explanation:
-25 - (-5) = 0
-25+5=0
-20=0
Marking brainliest
What colors should I add?
Answer:
Maybe some red, lime green, tan-ish brown, blue, crimson, navy blue
Step-by-step explanation:
The total cost to play paintball can be represented by the expression (48x+54). If Rocco and five friends split the cost equally, what is the cost for each person
Answer:
8x + 9
Step-by-step explanation:
The total number of people splitting the cost equally = Rocco and five friends = 6 people
The total cost to play paintball can be represented by the expression (48x+54)
The cost for each person is calculated as: The total cost to play paintball/ Total number of people
= (48x+54)/6
= 48x/6 + 54/6
= 8x + 9
Therefore, the cost for each person is
8x + 9
The price of a tablet was increased from $180 to $207. By what percentage was the price of the tablet increased?
A.33%
B.8%
C.27%
D.15%
Answer:
D. 15%
Step-by-step explanation:
Find the percent increase by dividing the difference in prices by the original price
27/180
= 0.15
So, the percent increase was 15%
The correct answer is D. 15%
could someone please check my work! no files please and thank you!
Answer:
It looks fine well done
PLSSSSS HELP!!!!!!!!!
Answer:
x=30º
∠CAB=60°
∠ACB=80°
Step-by-step explanation:
Because the angles of every triangle add up to 180º, we know that:
[tex]2x+20+2x=180-40\\ 4x=180-40-20\\ 4x=180-60\\ 4x=120\\ x=\frac{120}{4}[/tex]
x=30º
Plug that in for x on both angles, and you will get
∠CAB=60°
∠ACB=80°
Terri is beginning a science experiment in his lab instructions called for 227 mg of potassium what is the difference between this amount and 1 gram
Answer:
773 mg
Step-by-step explanation:
1 gram = 1000 mg so the difference is:
1000 - 227
= 773 mg.
Find the volume of the rectangular pyramid.
16 ft
-Ft--
2 ft
7 ft
Figure not drawn to scale.
Answer:
ft 3
Complete the steps to solve the equation - 15x - 11 = - 56.
- 15x - 11 = -56
Write the original equation.
Apply the Addition Property
of Equality.
- 15x =
X = ?
Romeo has captured many yellow-spotted salamanders. He weighs each and
then counts the number of yellow spots on its back. Which trend line best fits
the data?
Answer: D.
Step-by-step explanation:
Answer:
It's D
Step-by-step explanation:
I took the AP3X quiz and got it right. Just make sure you don't just click D on your end without looking at the graph in the question.
What is the value of c in the equation below?
24.22= a^b = 0
Answer:
There's no c in your uploaded question
The function f (x) is a PLEASE HELP ME. quadratic function.
How does the graph of f (x + 4) compare to the graph of f (x)?
A. It is shifted 4 units up.
B. It is shifted 4 units down.
C. It is shifted 4 units to the left.
D. It is shifted 4 units to the right.
Answer:
It is shifted 4 units down
5 for every $2.50 10 for every ?
Answer:
5 dollars
you do 2.50 x 2 because 5 x 2 makes 10, and you have to do what you do to one side, to the other.
Substitution.
-3x - 2y = -12
y = 5x - 7
Answer:
-3x-2(5x-7)=-12
-3x-10x+14=-12
-13x+14=-12
-13x=-16
x=2
The current population of Rochester is 211,000 and is decreasing at a rate of 4.1% every ten years. Which function can be used to find the population 30 years from now?
Answer:
211,000(0.97)t
Step-by-step explanation:
Firstly; Write the exponential decay function for this situation.
y = a(1 – r)t Write the formula.
= 211,000(1 – 0.041)t Substitute 1700 for a and 0.03 for r.
= 211,000(0.97)t Simplify.
Next; Find the population in function.
y = 1700 Substitute 12 for t.
≈ 1180 Use a calculator and round to the nearest whole number.
The population in 30 years function will be approximately 211,000(0.97)t.
Antwan earned $9 for 1/2 of an hour of babysitting. At this rate, how much would Antwan make in 1 hour?
Answer:
$18
Step-by-step explanation:
double the value of 9 to get 18
10. Solve for y. 3y + 6p = 9r
Answer is y = 3r - 2p
help m.e please please
Answer:
(-3, -4)
Step-by-step explanation:
The solution is where the two lines intersect. Therefore, the x-coordinate is -3, and the y-coordinate is -4.
Another way to solve this would be to set the to equations equal to each other, so 2x+2 = -4. Therefore, 2x = -6, and x = -3. And from the second equation, y = -4.
pls help ill mark you brainliest
Answer:
if i am not mistaking it got to be c
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
First you subtract 325 from 75 then divide the answer by 10
A group of students was randomly divided into two subgroups. One subgroup took a test in the morning, and the other took the same test in the afternoon. This table shows the results. Pass Fall Total Morning 28 75 Afternoon 53 22 75 Total 81 69 150 Compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon. Draw a conclusion based on your results.
Answer:C
Step-by-step explanation: I believe it is C according to my calculations
Answer:C
Step-by-step explanation: