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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Please help me ASAP
Answer:
x ≤ -17
Step-by-step explanation:
What is the value of x in the equation 2(x−3)+9=3(x+1)+x?
a. x = −3
b. x = −1
c. x = 0
d. x = 3
Answer:
x=0
Step-by-step explanation:
1st Step(Plug in 0 for x): 2(0-3)+9=3(0+1)+x
2nd Step(Simplify): 2*(-3)+9=3*(1)+x
3rd Step(Multiply): -6+9=3+x
4th Step(Add): 3=3+x
5th Step(Subtract 3 from both sides): x=0
For any questions saying what is the value of x in the equation, just plug in one of the options from a,b,c,d. And work from there
What is the probability of choosing an ace from a standard deck of 52 playing ?
Answer:
48/52
Step-by-step explanation:
The probability of picking up an ace in a 52 deck of cards is 4/52 since there are 4 aces in the deck. The odds of picking up any other card is therefore [tex]52/52 - 4/52 = 48/52.[/tex]
I hope this helps and have a great day!
Alicia has 7 paintings she wants to hang side by side on her wall.
2. If Alicia only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.
3. In how many ways can Alicia arrange 4 out of the 7 paintings? Show your work.
The question is an illustration of permutation and combinations.
The number of ways she can choose 4 out of the 7 paintings is 35The number of ways she can arrange 4 out of the 7 paintings is 840The given parameters are:
[tex]\mathbf{n = 7}[/tex]
[tex]\mathbf{r = 4}[/tex]
(a) Choose 4 of 7 paintings
Choosing 4 of 7 paintings implies combination.
So, we have:
[tex]\mathbf{^nC_r = \frac{n!}{(n - r)!r!}}[/tex]
Substitute values for n and r
[tex]\mathbf{^7C_4 = \frac{7!}{(7 - 4)!4!}}[/tex]
[tex]\mathbf{^7C_4 = \frac{7!}{3!4!}}[/tex]
Expand
[tex]\mathbf{^7C_4 = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4 !}}[/tex]
[tex]\mathbf{^7C_4 = 35}[/tex]
Hence, the number of ways she can choose 4 out of the 7 paintings is 35
(b) Arrange 4 of 7 paintings
Arranging 4 of 7 paintings implies permutation.
So, we have:
[tex]\mathbf{^nP_r = \frac{n!}{(n - r)!}}[/tex]
Substitute values for n and r
[tex]\mathbf{^7P_4 = \frac{7!}{(7 - 4)!}}[/tex]
[tex]\mathbf{^7P_4 = \frac{7!}{3!}}[/tex]
Expand
[tex]\mathbf{^7P_4 = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!}}[/tex]
[tex]\mathbf{^7P_4 = 840}[/tex]
Hence, the number of ways she can arrange 4 out of the 7 paintings is 840
Read more about permutation and combinations at:
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2. An architect is reading a plan that is drawn on a scale of 0.75 inches to 1 foot. If the plan says that a room is 12 feet high, how high is the roof in the drawing?
Answer:
9 Inches
Step-by-step explanation:
1 feet is 0.75 inches
12 feet will be 0.75 * 12 = 9 inches
Therefore,it 9 inches.
Answer:
9 inches
Step-by-step explanation:
12 * 0.75 = 9
Answer: 9
Multiply out and simplify:
(x-8) (x-7)
To expand the brackets, each term in the first bracket must be multiplied by each term in the second bracket and then simplified:
(x-8) (x-7) = (x × x) - (7 × x) - (8 × x) + (8×7)
= x² - 7x - 8x + 56
= x² - 15x + 56
Answer: x^2-15x+56
Step-by-step explanation:
1-Distribute
x(x-7)-8(x-7)
2-Distribute
x^2-7x-8(x-7)
3-Distribute
x^2-7x-8x+56
4-Combine like terms
x^2-15x+56
Write a possible polynomial function in factored form with roots 0, -2, and 7. Group of answer choices
f(x)=(x+1)(x+2)(x−7)
f(x)=x(x+2)(x−7)
f(x)=x(x−2)(x+7)
f(x)=(x+2)(x−7)
Answer:
2nd option
Step-by-step explanation:
Given x = a is a root of a polynomial function then (x - a) is a factor
Given roots are x = 0, x = - 2, x = 7 , then corresponding factors are
(x - 0) , (x - (- 2) ) , (x - 7) , that is
x , (x + 2) , (x - 7)
The polynomial function f(x) is then the product of the factors, so
f(x) = x(x + 2)(x - 7)
PLEASE HELP IT’S DUE TMR
Answer:
13) 29.75
14) P : P
Step-by-step explanation:
13)
4 ------ 17
7 ------ x
4x = 7*17
4x = 119
x = 29.75
14) A square is a square it has all sides the same, so p : p is the ratio
Find the slope of the line containing the points (-2,-1) and (3,4).
Answer:
Step-by-step explanation:
[tex]\frac{4-(-1)}{3-(-2)}[/tex] =[tex]\frac{5}{5}[/tex]= 1
find the missing values in the ratio table then write the equivalent ratios
PLS HURRY!!
Answer:
1. 10
2. 4, and the bottom row is 21
3. divide the bottom by 4. you get 8
4. top row is 15 and bottom row is missing 6
A game you wanted was discounted 45% and now costs $26.29 what did the game cost before the discount
Answer: I think its $58.4
guys pls help me!!!!!!
Answer:
48 degrees
Step-by-step explanation:
Answer: 6.8
Step-by-step explanation:
nnxj
guys pls help me!!!!!
jamie is 3 years less than three times Andys age. In five years the sum of their ages will be 59.How old are they now
Answer:
Andy : 13 years old and
Jamie: 36 years old
Step-by-step explanation:
Andy = x
Jamie = 3x - 3
In 5 years:
(X+5)+(3x-3+5) = 59
4x + 7 = 59
4x = 59 - 7
x = 52/4
x = 13
How many times larger than 2 x 102 is 2 x 108?
Answer:
1 x 106
Step-by-step explanation:
200,000,000 divided by 200 is equal to 1,000,000
find the value of x using the triangle
Answer:
x=13
Step-by-step explanation:
See attached image. If you have any questions, let me know!
help yall
Solve and graph the absolute value inequality: 2x + 1) 5.
Answer:
x=2
Step-by-step explanation:
2x=5-1
2x=4
x=4/2
simplify 4/2 to 2, x=2
Answer:
B is the answer
The inequality is −
3≤x≤2
Step-by-step explanation:
What is the most appropriate method to solve the quadratic equation x²−16=0?
B. By factoring
A. By extracting the square root
C. By completing the square
D. By using the quadratic formula
Which of the following is correctly written in Standard Form?
A.) -6x + 3y = 8
B.) y = 6/5x + 4
C.) 6x - 2y = 4
D.) 6/5x + 3y = 8
HELP NEEDED PLZ
How many solutions are there to this equation?
4(x-5)=3x+7
A. 1
B. infinitely many
C. 0
Answer:
1
Step-by-step explanation:
4x-20=3x+7
x=27
Please help fast
What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
Answer:
I'm only able to see a black square instead of any image. Could you resend it?
Which numbers are between -7 and 2 on a number line? Circle all that apply.
A. 2.1
B. -1
C. 0
D. -7.5
E. 3.5
F. -6.4
G. -8
Answer: See below
Step-by-step explanation:
A. 2.1 No (2.1>2)
B. -1 Yes
C. 0 Yes
D. -7.5 No (-7.5<-7)
E. 3.5 No (3.5>2)
F. -6.4 Yes
G. -8 No (-8<-7)
Pls answer question thx
There is a total of 53 Yr 11 students. 18 in math 13 in science making 31 students, leaving 22 Year 11 students for english. 37 total students picked english, so that makes 15 the remaning amount which is put into the Yr12 students.
There are 100 students total. 53 of which are Yr 11 students leaving 47 to be Yr12 students.
12 Yr 12 students chose science, 15 Yr 12 kids chose english, leaving 20 Yr12 students to have chosen math.
12+15+20=47 Yr 12 students.
22+18+13=52 Yr 11 students.
15 Yr 12 students chose english.
20 Yr 12 students chose math.
12 Yr 12 students chose science.
There are 47 Yr 12 students total.
22 Yr 11 students chose english.
18 Yr 11 students chose math.
13 Yr 11 students chose science.
There are 53 Yr 11 students.
What is the answer of this
Answer:
[tex]\frac{25}{32}[/tex]
Step-by-step explanation:
Rode here on the bus
Now you're one of us
It was magic hour
Counting motorbikes
On the turnpike
One of Eisenhower's
Live your life on a merry-go-round
Who starts a fire just to let it go out?
(dreams tonite lol)
Which type of parent function is f(x) = ?
A. Square root
B. Reciprocal
C. Quadratic
D. Cube root
SUNMIT
Answer:
Write properties of function:
x intercept/zero: x = 0
Step-by-step explanation:
Write properties of function: Write properties of function:
x intercept/zero: x = 0
Answer: Write properties of function:
x intercept/zero: x = 0
can someone please help
Answer:
the slope is -8
Step-by-step explanation:
4/5 - 3/8
plz help me might give brainlist
Answer:
17/40
Step-by-step explanation:
4/5-3/8=32/40-15/40
=17/40
Answer:
Solution:
17/40 Alternative form 0.425
Step-by-step explanation:
Explanation how:
Write all numerators above the least common denominator 40
32-15/40
hope to help
estimate 1.75 * 12.5
Answer:
21.875, round as needed.
Step-by-step explanation:
1.75 * 12.5
21.875
You can also round to:
21.88
21.9
22
Just depends on what your teacher is asking
The height of a cylinder is 4 millimeters.The circumference of its base is 10 pi mm
[tex]\\ \sf\longmapsto C=10\pi mm[/tex]
[tex]\\ \sf\longmapsto 2\pi r=10\pi mm[/tex]
[tex]\\ \sf\longmapsto 2r=10[/tex]
[tex]\\ \sf\longmapsto r=5mm[/tex]
h=4mm[tex]\\ \sf\longmapsto Volume=V=\pi r^2h[/tex]
[tex]\\ \sf\longmapsto V=\pi (5)^2(4)[/tex]
[tex]\\ \sf\longmapsto V=\pi 25(4)[/tex]
[tex]\\ \sf\longmapsto V=100\pi mm^3[/tex]
volume is 100pi mm³.
What is volume?In mathematics, volume is the space taken by an object.
Here, given that,
The height of a cylinder is 4 millimeters.=h
The circumference of its base is 10 pi mm=2r*pi
So, we get,
r=5
Volume =pi*r²*h
=100pi mm³
Hence volume is 100pi mm³.
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What is an equation in point slope form for the line perpendicular to..
Answer:
b
Step-by-step explanation:
And since we're perpendicular to y is equal to 3x plus 9, we know the slope of the two lines that are perpendicular
K times 3 is minus 1, so k is minus 1/3,
Only b and c match. Plug in the point negative 6,5.
The answer is b.
