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
which are the following statements is 6×7 = 42
Answer:
A and B are both correct
Step-by-step explanation:
the definitions of the following words are:
factor- a number or quantity that when multiplied with another produces a given number or expression.
multiple- a number that can be divided by another number without a remainder.
6 multiplied with 7 equals 42
42 divided by 7 equals 6
another way of phrasing it:
7 and 6 are factors of 42
and
42 is a multiple of both 7 and 6
hope this helped!
Answer:
42 is a multiple of 7.
6 is a factor of 42
Step-by-step explanation:
What is the percent of change from 56 t0 22
idea 34 I did 56-22 0.0
Answer:
I think it is -60.71428571 percent.
need help with please
Answer:
(1,2)
Step-by-step explanation:
So, if y= 2x...
2x= 8x-6
-6x= -6
x= 1
y=2x
y= (2)(1)
y=2
(1,2)
what's the area of the circle
Answer:
3.14
Step-by-step explanation:
Find and interpret the standard deviation of the set of data. 7. {6, 8, 2, 3, 2, 9}
Answer:
3.1
Step-by-step explanation:
can someone please help with this? real answer only please......ive asked multiple questions today becuz i dont really understand the assignment, please help
9y - 2x = 0 in slope intercept form.
Answer:
y=2/9x
Step-by-step explanation:
I hope this helps
Step-by-step explanation:
9y-2x=0
9y=2x
y=(2/9)x
I'll give you brainiest if you help me.
Answer:
88 degrees.
Step-by-step explanation:
Since AB is equal to BC, ABC is an isosceles triangle. Therefore, the angle of B will be 180-39-39=102 degrees. As the angle of a straight line is 180 degrees, take 180-102-32=46 degrees. This 46 degrees is angle B. Since DEB is an isosceles triangle, 180-46-46=88 degrees. 88 degrees is angle E which is your answer. Edit: (Just added on the explanation.)
Please helppp thanksss
Hello Kitty has created a new system of conversion for the residents of Kitty Nation. The standard for measurement of length in Kitty Nation is that 8 lenthii = 30 inches and 4 gianthii = 478.8 lenthii. If a design to be sent to Kitty Nation is 294.3 feet long, how many gianthii long will it be? (Include units)
Answer:
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In a population of adults the proportions of people in various marital status are: Single:35%, Married: 60%, Divorced: 5%. A person is selected at random. If that person is not divorced find the probability that he or she is single.
Answer:
7/20 0r 0.35
Step-by-step explanation:
Probability of been single = percentage of single adult / sum of percentages
sum of percentages = 35 + 60 + 5 = 100
35/100 = 7/20 or 0.35
i need help with this
Answer:
A) 9 inches per minute
Step-by-step explanation:
36 inches in 4 minutes
36/4 = 9 inches per minute
Please answer all of them! SHOW WORK!!
Plsss help I’m super stuck on this
Answer:
its b
Step-by-step explanation:
took the quiz
Answer:
I would go with D
Step-by-step explanation:
You can look at the graph and answer it
HELP ASAP!!!
Two random samples were taken to determine how often people in a community listen to the local radio station each month.
The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20.
The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12.
Which statements are true? Check all that apply.
The second sample is random.
The second sample is likely to be more representative of the population.
The first sample is likely to be more representative of the population.
The second sample will give a better representation because is it larger.
The first sample will give a better representation because it is smaller.
Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
Answer:
The answers to this question are 1,2,4,6. Hope this helps you
Step-by-step explanation:
the CN Tower of Toronto, Canada is 553 M tall. how tall is the tower in cm
Answer:
The answer is 55,300.
Step-by-step explanation:
There are 100 centimeters in one meter so you can multiply by 100 to get the answer. I hope this helps! Have a great rest of your day!
There are 12 brown hair teachers and 20 blond hair teachers. For every blank blond teachers there are blank brown teachers
Answer:
For every 5 blonde teachers there are 3 brown teachers.
Step-by-step explanation:
Here we have to find the ratio of blonde teachers to brown teachers
Blonde : Brown
20: 12
10:6
5:3
For every 5 blonde teachers there are 3 brown teachers.
This can be further evaluated
Blonde : Brown
5:3
dividing both sides by 5
1: 3/5
For every 1 blonde teachers there are 3/5 brown teachers. It means that the brown teachers are 2/5 less than the blonde teachers.
1-2/5= 3/5
20* 3/5= 12
Hellllllllllllllllllllppppppppppppppppppppppppp
Answer:
According to two brainly answer choices it should be Choice A.
15/6
Step-by-step explanation:
SOURCES:
https://brainly.com/question/16451231
https://brainly.com/question/16811984
THIS IS THE WORK OF ANOTHER BRAINLY USER NOT MINE
In this question, we are to get the total number of hours that Irina used in watching the movie which does not include the term used for airing the commercials.
Now to calculate this, let us first take a look at the shaded segmented bar. We can see that out of the 6 horizontal bars, 5 were shaded. What this means is that 5/6 of the hours went into airing the movie while 1/6 of the hour went into airing commercials
Now, mathematically the number of hours she viewed the movie without the commercials can be calculated by adding all these 5/6 hour in the 3 hours
Mathematically that would be 5/6 + 5/6 + 5/6 = 3 (5/6) or simply 3 * 5/6 = 5/2 = 15/6 hours
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En una carrera participaron 7000 personas entre hombres y mujeres y 5000 personas entre mujeres y niños. Si han corrido 3000 mujeres ¿cuantas mujeres participaron en total?
Answer:
9000 personas en total participaron de la carrera.
Step-by-step explanation:
En este caso, planteo las siguientes variables:
x: cantidad de hombres que participaron de la carrera.y: cantidad de niños que participaron de la carrera.En una carrera participaron 7000 personas entre hombres y mujeres. Si han corrido 3000 mujeres, entonces se puede interpretar mediante la siguiente expresión:
3000 + x= 7000
Entonces, resolviendo se obtiene que participaron la siguiente cantidad de hombres:
x= 7000 - 3000
x= 4000
En la carrera también participaron 5000 personas entre mujeres y niños. Entonces se puede interpretar mediante la siguiente expresión:
3000 + y= 5000
Resolviendo se obtiene que participaron la siguiente cantidad de niños:
y= 5000 - 3000
y= 2000
Para calcular la cantidad de personas en total que participaron de la carrera, debes sumar la cantidad de hombres, mujeres y niños. Esto es:
4000 hombres + 3000 mujeres + 2000 niños= 9000 participantes
9000 personas en total participaron de la carrera.
A small tree was planted at a height of 5 feet. The tree has been planted for 16 months, and is now 61 feet tall. Which equation could
be used to find x, the average number of feet the tree grew each month?
A. 5x + 16 = 61
B.16x + 5 = 61
C. 61x + 5 = 16
D. 16x + 61 = 5
Answer:
B
Step-by-step explanation:
please help me !!!!!!!!!!!!
Answer:
The answer is D
Step-by-step explanation:
A 180 rotation on 1,1 which is the center will rotate it onto itself.
In December, a car salesman sold 60 cars. In January, he only sold 24. Find the percent decrease in his monthly sales.
Answer: 45.6
Step-by-step explanation:
60 - (24% × 60) =
60 - 24% × 60 =
(1 - 24%) × 60 =
(100% - 24%) × 60 =
76% × 60 =
76 ÷ 100 × 60 =
76 × 60 ÷ 100 =
4,560 ÷ 100 = 45.6
Plss I need this rnnn
Answer:
25
Step-by-step explanation:
25 is the answer because the sum of angles add up to 90
Which line has the steepest graph?
Answer:
I think it is the fourth one
[tex]y = \frac{1}{8} x + 9[/tex]
Step-by-step explanation:
I hope that is useful for you :)
Pls help me on this what is the correct answer
Answer:
C 61,705
Step-by-step explanation:
10.9% of 35,000 = 3,815
3,815 x 7 = 26,705 (interest is added per year and 3,815 is the interest amount)
35,000 + 26,705 = 61,705 ( the original loan plus the interest for 7 years)
Find the area of the figure.
40.8 cm2
1128 cm2
47.52 cm2
33.7 cm2
Answer:
answer is 47.52 cm2
Step-by-step explanation:
follow me please
the other answers I already did I just need the division answers
Answer:
6÷41 equals 0.14634146341
6÷21 equals 0.28571428571
6÷43 equals 0.13953488372
6÷37 equals 0.16216216216
6÷20 equals 0.3
Step-by-step explanation:
Hope this helps
Pls help I have this homework !! bye I will mark you the best or brainliest!!
Answer:
90-54w
Step-by-step explanation:
18(5−3w)=
18*5=90 , 18*3w= 54w =
so simplified it would be = (90-54w)
Please mark me as brainliest :D
Find the intercepts of the linear function: -3 = 3y – 3.2
Answer:
The given line is a horizontal one, with slope 0 and y-intercept (0, -2/3)
Step-by-step explanation:
To find the y-intercept, set x = 0 (which is the y-axis) and find y:
-3 = 3y - 3.2
Add 3.2 to both sides, to isolate 3y:
0.2 = 3y
Dividing both sides by 3 yields y = 0.06667
The given line is a horizontal one, with slope 0 and y-intercept (0, -2/3)