The equation with only one unique solution is 9 − |2x − 1| = 9, with the solution x = 1/2. D.
To determine which equation has only one unique solution, let's analyze each equation:
|3 − x| = 3
In this equation, the absolute value term represents a distance.
By setting up two cases, where the absolute value is positive and negative, we can find the solutions.
Case 1:
3 - x = 3
Solving for x, we have x = 0.
Case 2:
x - 3 = 3
Solving for x, we have x = 6.
Thus, this equation has two solutions.
|x − 2| − 7 = 7
Similar to equation A, the absolute value term represents a distance.
By adding 7 to both sides, we have |x - 2| = 14.
This equation implies that the distance between x and 2 is 14.
There are two possible values for x: x = 2 + 14 = 16 and x = 2 - 14 = -12.
This equation has two solutions.
-4|x| + 1 = -3
To solve this equation, we isolate the absolute value term:
-4|x| = -4
Dividing both sides by -4:
|x| = 1
The absolute value of any number is always positive or zero.
The equation |x| = 1 has two solutions: x = 1 and x = -1.
9 − |2x − 1| = 9
The absolute value term represents a distance.
Subtracting 9 from both sides, we have |2x - 1| = 0.
The only way the absolute value of a real number can be equal to zero is if the number inside the absolute value is zero.
Thus, we set 2x - 1 = 0 and solve for x:
2x - 1 = 0
2x = 1
x = 1/2
Equation D has only one unique solution: x = 1/2.
For similar questions on unique solution
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Simplify (a – b)(a2 – 5ab + 2)
Answer:
5ab^2-6a^2b+a^3-2b+2a
Step-by-step explanation:
The simplified expression of expression (a – b)(a² – 5ab + 2) is a³ – 6a²b + 5ab² + 2a – 2b
What is Expression?An expression is combination of variables, numbers and operators.
To simplify the expression (a – b)(a² – 5ab + 2), we need to apply the distributive property, which states that:
(a + b)(c + d) = ac + ad + bc + bd
Using this property, we can multiply the two binomials as follows:
(a – b)(a² – 5ab + 2) = a(a² – 5ab + 2) – b(a² – 5ab + 2)
Now we can distribute the terms of each binomial:
= a³ – 5a²b + 2a – a²b + 5ab² – 2b
Simplifying the terms, we can combine like terms:
= a³ – 6a²b + 5ab² + 2a – 2b
Therefore, the simplified expression is a³ – 6a²b + 5ab² + 2a – 2b
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What is -(x + 4) - 3x = x in Distributive property?
Answer:
x = -4/5
Step-by-step explanation:
Original equation: -(x+4)-3x=x
Remember distributive property allows us to get rid of the parenthesis by bringing a multiplication from outside to inside a parenthesis.
-(x+4) = -x-4
= -x-4-3x=x
Now we combine like terms in this case we have (-x) and (-3x)
= -4x-4=x
Subtract x from both sides
= -4x-4=x
-x -x
----------------
-5x-4=0
Add 4 to both sides
-5x-4=0
+4 +4
---------------
-5x=4
Our final step is to divide both sides by -5
-5x=4
---- ----
-5 -5
x = -4/5
Hope this helps!!!
Solve:
4x + 1.21 > 5
HELP ME PLEASE
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x > 0.9475[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]4x + 1.21 > 5\\\rule{150}{0.5}\\\rightarrow 4x + 1.21 - 1.21 > 5 - 1.21\\\\\rightarrow 4x > 3.79\\\\\rightarrow \frac{4x>3.79}4}\\\\\rightarrow \boxed{x > 0.9475}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
How many solutions does the nonlinear system of equations graphed below have?
A. One
B. Four
C. Two
D. Three
Answer:
There are three possible types of solutions for a system of nonlinear equations involving a parabola and a line.
Step-by-step explanation:
The functions j(x)=x−1 and k(x)=3x+1 intersect at:
A. Infinitely many points
B. 2 points
C. 1 point
D. There are no intersection points
Answer:
C
Step-by-step explanation: for j(x) = k(x)
My English is not good, please forgive me
When Zack checked his solution, it didn’t work. What was his mistake?
In step 1, he should have used the multiplication property of equality.
In step 2, he should have a constant of – 4 on the right side.
In step 3, he should have divided both sides by StartFraction 6 Over 4 Endfraction.
In step 4, the answer should be positive.
Answer: its c In step 3, he should have divided both sides by StartFraction 6 Over 4 Endfraction.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
an artist spent 3/5 of an hour painting 1/4 of a mural. how kuch of the mural will be completed in one hour how long will it take to complete one mural
Answer:
2.4hrs or 2hrs 24 minutes
Step-by-step explanation:
3/5 × 4/1 = 12/5
60÷5=12
12×12=144
144÷60=2.4hrs
ebgjwbjhkjfhdsn wmiuehdbnsmkji
Answer:
im srry what
Step-by-step explanation:
DYK?
— Pretty face is everywhere, but a woman who cheer you up at your weakest and stay after knowing about your flaws and bad sides are rare, so you better keep her dude!.
#moodchallenge
I need help ASAP!!! (please look at the image and explain how you got the answer, please and thanks)
Answer:
114
Step-by-step explanation:
so lets call shelf 1 x
shelf 2 is twice size + 18 of shelf 1 so it is 2(x)+18
shelf 3 is 12 less than shelf 1 so x-12
shelf 4 is four more so x+4
Add them all together and it should be 5x+10= 2.5 m or 250 cm
Solve for x using cm
then plug into shelf 2 equation
A bottle of grape juice costs 6.50$ of you buy 6 bottles you can get 10%discount workout how much you save if you buy 6 bottles
Molly has 3 pounds of blueberries. She is freezing the berries into 1 half pound portions. How many smaller portions of blueberries will Molly make
Answer:
6 smaller portions
Step-by-step explanation:
1 pound (lb) = 16 ounces (oz)
3 lbs = 48 oz
1/2lb = 8oz
48oz (total)/8oz (amount in each portion) = 6 portions
guys pls help me!!!!!!
Answer:
[tex]x = 67[/tex]
Step-by-step explanation:
[tex]x = 67[/tex]
[tex]Alternate \:Intrerior \: Angles[/tex]
What is 45% of 345? Please help me I’m failing math
Answer:
155.25
Step-by-step explanation:
Answer:
155.25
Step-by-step explanation:
Since 45% is equal to 0.45, simply multiply 0.45 x 345 and youll get 155.25
The price of a notebook has risen to $3.45 today. Yesterdays price was $3.20. find the percentage increase, round your answer to the nearest tenth of a percent.
Answer:
7.8%
Step-by-step explanation:
Yesterday’s price =$3.20
Today’s price =$3.45
Increase =today’s price - yesterday’s price
That’s $3.45 - $3.20
= $0.25
Percentage increase = increment /yesterday’s price x 100%
That’s $0.25/$3.20 x 100%
0.0781 x 100%
7.81
7.8%
Your last 4 test scores are 65, 70, 80 and
70. If you want to finish with a 74
average, what do you need to get on your
fifth test?
Answer:
Step-by-step explanation:
74*5 = 370
370 - 65 - 70 -70 -80 = 85
So. you need to get 85 on your fifth test.
If 40 meters of a cloth costs Rs 1940 how many meters can be bought for Rs 727.5
Plz explain
Answer:
15
Step-by-step explanation:
suppose x is the no. of cloth that can be bought in rs 727.5
then cost of 1meter cloth is rs 727.5×.....(i)
and cost of 40mtr cloth is rs 1940
then 1mtr cloth is 1940/40....(ii)
so from i and ii
we get
727.5/x = 1940/40
Solve for x: 16 = x + 32
Answer:
-16
Step-by-step explanation:
Use everyone's favourite thing: ALGEBRA!!!
16=x+32
16-32=x
-16=x
Hope that helps
Step-by-step explanation:
16=x+32
16-x=32
-x=32-16
-x=16
X=-16
3 ft
10 ft
Perimeter:
Area:
Step-by-step explanation:
The area = 3 × 10 = 30
The perimeter = 2(3 + 10) = 26
please give me a brainliest answer
what is the equation for the line that is perpendicular to the x-axis and passes through the point (4, -7)?
Step-by-step explanation:
perpendicular means to cross at a right angle (90 degrees).
so, any line perpendicular to the x-axis is parallel to the y-axis.
and any line parallel to the y-axis has only a defining x value. all points on that line have the same x value (while any value for y from -infinity to +infinity is valid).
the y-axis itself is
x = 0
the specified point here has an x value of 4.
so, the line we are looking for is
x = 4
to point out : this is NOT a function, because for the same x value we get more than 1 valid y values.
Pls help
bobik: yes, or no
Answer:
yes
Step-by-step explanation:
Answer:
?? Yes??
Step-by-step explanation:
please help me do this
Answer:
125
Step-by-step explanation:
add 21 and 34. with that you get 55. then subtract 180 from 55 then get 125
10 greater than less than, or equal to 5? Explain
Answer:
greater than because 10 is further to the right on a numberline than 5
Step-by-step explanation:
HELP
In order to isolate the variable term in the equation 6 -2x = -3 using the subtraction property of equality, which number
should be subtracted from both sides of the equation?
-3
3
6
-2
- How are the functions y = x and y = x + 4 related? How are their graphs related?
Answer:
Either horizontal translation 4 units to the left or vertical translation UP 4 units
Step-by-step explanation:
Solve the equation x2-81 = 0.
Answer:
40.5
Step-by-step explanation:
x2 - 81 = 0 --> + 81 to both sides
2x = 81 --> divide by 2 on both sides
x = 40.5
Answer:
2x-81=0
2x=0+81
2x=81
x=81
2
x=40.5 ANSWER.
MARK ME AS A BRAINLIST PLZ.
PLEASE HELP WILL MARK BRAINLIEST!
Answer:
P of rectangle = 2(L + W)
21 units = 2(n units + W)
21 units = 2nunits + 2W
21 = 2n + 2W
2W = 21 - 2n
W = 21 - 2n units.
2
on simplifying
10.5 - n units
The width of the rectangle is units (10.5 - n) units.
When using empirical data (data and information collected by scientists in an experiment), sometimes, that data will not form a perfect line on a graph. When this happens, the line that is created using a linear regression is known as the “Line of Best Fit.” The following speed data was collected from a car moving with a constant acceleration.
Time (s) Velocity (m/s)
2 13.1
4 19.8
6 28.1
8 34.6
What is the Line of Best Fit for this data? Perform a linear Regression on this table to find the equation.
Based on your equation, what was the car’s approximate initial velocity (at time=0)?
If the car continued at the same acceleration (meaning the slope of the line does not change), how fast would it be going in 15 seconds?
Answer:
98.25
Step-by-step explanation:
60% of a mussems fossils are from the jurassic period if the number of fossils from the jurassic period is 15 what is the total of number of fossils ate the musuem ?
The total number of fossils at the museum are, 25
what is green and blue? HELP
Answer:
green horizontal asymptote: y = -2
blue horizontal asymptote: y = -4
Step-by-step explanation: Exponential functions have a horizontal asymptote
What are the values of v and w ?
Answer:
V = 72 & W = 72
Step-by-step explanation:
All angles of a triangle will be equivalent to 180 degrees.
We start by subtracting first.
180 - 36 = 144
Look back at the triangle. FG and HG are congruent, which means the values of V and W will be the same.
The last step is to divide.
144 / 2 = 72
V = 72 & W = 72