Tentukan nilai x yang memenuhi ketidaksamaan. |3x + 12| < 2 |x - 6|
Answer:
x∈(-24, 0) ⇒ -24 < x < 0Step-by-step explanation:
|3x + 12| < 2 |x - 6|
|3(x + 4)| < 2 |x - 6| ⇒ -4 and 6 are "zeros"
1°. x∈(-∞, -4> ⇒ |3x + 12| = - (3x + 12) and 2|x - 6| = -2(x-6)
-(3x + 12) < -2(x - 6)
-3x - 12 < -2x + 12
-x < 24
x > -24 ∧ x∈(-∞-4> ⇒ x∈(-18, -4>
2°. x∈(-4, 6) ⇒ |3x + 12| = 3x+12 and 2|x - 6| = -2(x-6)
3x + 12 < -2(x - 6)
3x + 12 < -2x + 12
5x < 0
x < 0 ∧ x∈(-4, 6) ⇒ x∈(-4, 0)
3°. x∈(6, ∞) ⇒ |3x + 12| = 3x+12 and 2|x - 6| = 2(x-6)
3x + 12 < 2(x - 6)
3x + 12 < 2x - 12
x < -24
x < -24 ∧ x∈(6, ∞) ⇒ x∈∅
x∈1°∪2°∪3°
x∈(-24, -4>∪(-4, 0)∪∅
x∈(-24, 0) ⇒ -24 < x < 0
A company rents out 19 food booths and 30 game booths at the county fair. The fee for a food booth is $100 plus $9 per day. The fee for a game booth is $50 plus $8 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
Answer:
2500 + 215d
Step-by-step explanation:
What is the area or rectangle xbcy
Paula used these steps to solve an equation: Step 1: Step 2: Step 3: Step 4: Step 5: Between which two steps did Paula use the division property of equality?
Answer:
Step 4
Step-by-step explanation:
Paula used these steps to solve an equation:
Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -9.5
Between which two steps did Paula use the division property of equality?
Step 1: -4(x + 8) - 2x = 25
Opening the parenthesis
Step 2: -4x – 32 - 2x = 25
Combining x-terms
Step 3: -6x – 32 = 25
Adding 32 to both sides
Step 4: -6x = 57
Dividing both sides by -6
Step 5: x = -9.5
The Division Property of Equality states that: when both sides of an equation are divided by the same nonzero number, both sides remain equal.
The rule applies to step 4 where both sides of the equation is divided by -6(nonzero number) giving us x = -9.5
This means from the equation, x is equal to -9.5 and -9.5 is equal to x
The correct answer is step 4
Answer:it is step 4 and 5 hope this helps
Step-by-step explanation:
Find the value of X round to the nearest tenth. I need help.
Answer:
x ≈ 22.1°
Step-by-step explanation:
Using the law of cosines, then
cosC = [tex]\frac{a^2+b^2-c^2}{2bc}[/tex]
with a = 19, b = 14, c = 8 and C = x, thus
cos x = [tex]\frac{19^2+14^2-8^2}{2(19)(14)}[/tex]
= [tex]\frac{361+196-64}{532}[/tex]
= [tex]\frac{493}{532}[/tex], thus
x = [tex]cos^{-1}[/tex] ([tex]\frac{493}{532}[/tex] ) ≈ 22.1° ( to the nearest tenth )
A student solved the equation 7 = 3(t - 1) - 2(t - 3) as shown below. Assume there is a value for t that satisfies the equation. Provide a justification for each step of the solution process. LaTeX: 7\:=\:3\left(t-1\right)-2\left(t-3\right)7 = 3 ( t − 1 ) − 2 ( t − 3 ) LaTeX: 7\:=\:3t\:-3-2t\:+67 = 3 t − 3 − 2 t + 6.
Answer: 7
Step-by-step explanation: You first distribute 3, and -2. This gets you 7 = 3t -3 -2t +3. Then you add like terms which gets you, 7 = t.
Nate runs 8 miles each week. Write an expression for the number of miles he runs in n weeks. Find the number of miles Nate runs in 5 weeks.
Total miles = number of miles per week x number of weeks:
Total = 8n
For 5 weeks, replace n with 5:
Total = 8(5) = 8 x 5 = 40 miles
Answer:
8x, 40 miles
Step-by-step explanation:
He runs 8 miles each week.
8 miles x week
8 x week
To replace week, use a variable, commonly x.
8x
For 5 weeks, plug in the numbers.
x = 5
8 x 5 = 40
40 miles
Hope this helped, please mark Brainliest for everyone to see! :)
hector worked monday, tuesday and thursday from 9:00 am to 4:30 pm with a half hour lunch each day. How many total hours did he work?
Dave has $15 to spend on an $8 book and two birthday cards(c) for his friends. how much can he spend on each card if he buys the same card for each friend?
Please do not use the equal sign, we're using the greater than >, or less than sign< !
Answer:
each card cost = $3.5
Step-by-step explanation:
to spent $15 = $8 + 2cards
$15 = $8 + 2C
$15 - $8 = 2C
$7 = 2C
C = $7 / 2
C = $3.5
therefore each card cost = $3.5
Answer:
$3.50 per card
Step-by-step explanation:
15 = 8 + 2x
x = 7 / 2
x = 3.50
What is the value of x in the equation below? One-third (12 x minus 24) = 16 2 6 8 10
Answer:
The correct answer is b. 6
Answer:
6
Step-by-step explanation:
^_^ yep
If (x + 5)/2 is an integer, then x must be?
once again why is it so dumb???
Answer: vrey suptuidddd
Step-by-step explanation:
Point O is on line segment NP Given OP = 4x - 5 , NP = 3x + 4 , and NO = 2x - 3 determine the numerical length of OP .
Answer: 11 units.
Step-by-step explanation:
Given: Point O is on line segment NP.
i.e. NP is the combination of NO and OP.
i.e. NP = NO+OP (1)
Since , OP = 4x - 5 , NP = 3x + 4 , and NO = 2x - 3
Substitute these values in (1), we get
[tex]3x + 4 = 2x - 3 + 4x - 5[/tex]
[tex]\Rightarrow\ 3x+4=2x+4x-3-5\\\\\Rightarrow\ 3x+4=6x-8\\\\\Rightarrow\ 6x-3x=8+4\\\\\Rightarrow\ 3x=12\\\\\Rightarrow\ x=\dfrac{3}{12}=4[/tex]
i.e. x= 4
Now, OP = 4(4)-5= 16-5= 11 units
Hence, the numerical length of OP is 11 units.
(n^(4))/(n^(4)) what does that equal?
Answer:
the answer would be 1 happy to help ya :)
Step-by-step explanation:
find the perimeter of the triangle to the nearest unit A(-2,3) B(2,1) C(-2,1)
Answer:
10 units
Step-by-step explanation:
We can find the length of the hypotenuse of this right triangle using the Pythagorean theorem.
AB² = AC² +BC²
AB² = 2² +4² = 20
AB = √20 ≈ 4.47
Then the perimeter is ...
P = AB +BC +CA = 4.47 +4 +2 = 10.47
P ≈ 10 units
Can someone please tell me if this makes sense in English?, is well written and I have used the expressions well? Please I was learning English.
Dear Grievance Manager
I am writing this letter to bring your attention that I am not satisfied with your quality of sending services at "Adornet".
The last month, on 30th July exactly, I bought in a online way in "Adornet" because i live in other country. It was a collectiable necklace, that had an hourglass in its center.
The managers told me that the order should arrive in two weeks, but it arrived in three and a half weeks. I have been a regular client of your business but now I am complety disappointed, becuase when i received the package i notice that it was in bad condition and I found that the hourglass was broken. The way they packed it had been a lot more sloppy than the other times I shopped here.
i called to the shop the same day and I mentioned that they did not pack the necklace with due protection, but the shop assistant refuse to change it or make a refund. She said that it wasn't a store fault.
Please, I have always been satisfied with your services, but this time I think I'm entitled to a refund of my money and I would like to know how I can get it back. I look forward to hearing fron you soon.
Yours truly.
Gaby D.C
Answer:
Well Written
Step-by-step explanation:
Great Job
What number is 7 units to the left of -1?
Answer:
-8 I think on a graph right
Answer:
-8
Step-by-step explanation:
on a number line -1 is one unit away add we just add 7 units. To get -8!
Is 65 + -58 positive or negative?
Let f(x) = x + 7 and g(x) = x − 4. Find f(x) ⋅ g(x). (1 point
Step-by-step explanation:
f o g(x)
= f(x - 4)
= (x - 4) + 7
= x + 3.
7 kilogramos cuanto miligramos son
Answer:
7e+6
Step-by-step explanation:
7e+6 miligramos
algebraic expression for 5 minus the product of y and 3
Answer:
5 - 3y
Step-by-step explanation:
Step 1: Convert product of y and 3 into numbers
Product = multiply
y = y
3 = 3
3y
Step 2: Convert 5 minus into numbers
minus = subtract
5 - 3y
Answer:
5-3y
Step-by-step explanation:
David bought two video games and a DVD. One video game cost $32.50 and the other video game cost $45.35. David spent a total of $115.65. How much did the DVD cost?
Answer:
$37.80
Step-by-step explanation:
Add the cost of the 2 video games together to get 77.85
Subtract 77.85 from the total, $115.65
$37.80
Hope this helps :-)
30 pts and will mark brainiest.
please explain.
Answer:B
Step-by-step explanation:
X+2 divide 3x^4-x+2=
3x^3-6x^2+12x-25=
52=
52/x+2
the answer is d. its simple,the reason of that is because you would set up the synthetic division using the coefficients of the numerator and the root of the denominator. divide using the rules for synthetic division.
3x 4 cubed- 6x3 cubed +12x 2 cubed-24x-z+48+ 2(z-47) over x+2
Evaluate \dfrac{e}{4}+2f-3 4 e +2f−3start fraction, e, divided by, 4, end fraction, plus, 2, f, minus, 3 when e=12e=12e, equals, 12 and f=\dfrac12f= 2 1
I have same question and I need help
What is the value of a in the equation 5 a minus 10 b equals 45, when b equals 3?
Answer:
15
Step-by-step explanation:
5a - 10b = 45
5a - (10×3) = 45
5a - 30 = 45
5a = 45 + 30
5a = 75
a = 15
0.18 repeating fraction in the simplest form.
Answer:
2/11
Step-by-step explanation:
Let's say our fraction is x = 0.1818181818...
The trick is to multiply x by 10²=100 in this case, since there are two repeating digits, and then subtract the original x.
So, in fact you are subtracting 0.181818 from 18.181818 which effectively cancels the entire bit after the decimal point.
You get:
100x - x = 18
Which you can solve:
99x = 18
x = 18/99 = 2/11
A, b, and c are collinear, and B is between a and c. The ratio of AB to AC is 1:2. If A is at (7,-1) and B is at (2,1) what are the coordinates of point C
Answer:
C(-3,3)
Step-by-step explanation:
Given
A = (7,-1)
B = (2,1)
AB:AC = 1:2
Required
Determine the coordinates of C
Since, B is between A and C; we need to determine ratio BC as follows;
[tex]AB:AC = 1:2[/tex]
Convert to division
[tex]\frac{AB}{AC} = \frac{1}{2}[/tex]
AC = AB + BC;
[tex]\frac{AB}{AB + BC} = \frac{1}{2}[/tex]
Cross Multiply
[tex]2 * AB = 1 * (AB + BC)[/tex]
[tex]2 AB = AB + BC[/tex]
[tex]2AB - AB = BC[/tex]
[tex]AB = BC[/tex]
Divide both sides by BC
[tex]\frac{AB}{BC} = 1[/tex]
Rewrite as
[tex]\frac{AB}{BC} = \frac{1}{1}[/tex]
Write as ratio
[tex]AB:BC = 1:1[/tex]
Next is to determine the coordinates of C as follows;
Because B is between both points. we have:
[tex]B(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where
[tex]m:n = AB:BC = 1:1[/tex]
[tex]B(x,y) = B(2,1)[/tex]
[tex]A(x_1,y_1) = A(7,-1)[/tex]
So; we're solving for x2 and y2
[tex]B(2,1) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where
Solving for x2;
[tex]x = \frac{mx_2 + nx_1}{m+n}[/tex]
[tex]2 = \frac{1 * x_2 + 1 * 7}{1+1}[/tex]
[tex]2 = \frac{x_2 + 7}{2}[/tex]
Cross Multiply
[tex]2 * 2 = x_2 + 7[/tex]
[tex]4 = x_2 + 7[/tex]
[tex]x_2 = 4 - 7[/tex]
[tex]x_2 = -3[/tex]
Solving for y2;
[tex]y = \frac{my_2 + ny_1}{m+n}[/tex]
[tex]1 = \frac{1 * y_2 + 1 * -1}{1+1}[/tex]
[tex]1 = \frac{y_2- 1}{2}[/tex]
Cross Multiply
[tex]2 * 1 = y_2 - 1[/tex]
[tex]2 = y_2 - 1[/tex]
[tex]y_2 = 2 + 1[/tex]
[tex]y_2 = 3[/tex]
Hence, the coordinates of C are: C(-3,3)
Is this sum rational or irrational? Explain.
1.12 + 18/7 (1 point)
The sum is rational because both 1.12 and 18 are rational, and the sum of rational numbers is rational.
The sum is irrational because 1.12 is irrational, and the sum of a rational number and an irrational number is irrational..
The sum is rational because both 1.12 and 18 are positive, and the sum of positive numbers is rational.
The sum is irrational because 18 is irrational, and the sum of a rational number and an irrational number is irrational.
Answer: The sum is irrational because 18/7 is irrational, and the sum of a rational number and an irrational number is irrational
Step-by-step explanation:
Given the two numbers :
1.12 and 18/7
1.12 is a rational number as it is a not a non-terminating decimal and can accurately be expressed in the form a/b, where a and b are integers, thus 1.12 is equivalent to 112 / 100
18/7 on the other hand is an irrational number as it is a non-terminating decimal.
Hence, takingbthe sum of both numbers (rational and irrational) results in an irrational output.
18 / 7 = 2.57142857....
Taking the sum of both,
1.12 + 2.57142857... = 3.69142857... ; which is irrational
Answer:
The sum is irrational because 18/7 is irrational, and the sum of a rational number and an irrational number is irrational.
Step-by-step explanation:
Question 5 of 10
Which of the following functions best describes this graph?
Answer:
A
Step-by-step explanation:
The function that best describes the graph is y = x²-9x+1+20
What is function?A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).
Given that, a graph, we need to find its function,
The parabola is intersecting the x-axis at 4 and 5, therefore, the function in the option having value of equal to 4 and 5 is the function of the graph,
So, the first function is =
y = x²-9x+20
Put y = 0,
x²-9x+20 = 0
Factorizing the equation to get the values of x,
x²-9x+20 = 0
x²-4x-5x+20 = 0
x(x-4)-5(x-4) = 0
(x-5)(x-4) = 0
Therefore,
x = 5, 4
Since, the function is having solutions x = 5 and x = 4, therefore, the graph is of the function y = x²-9x+20.
Hence, the function that best describes the graph is y = x²-9x+1+20
Learn more about function, click;
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How can I solve this quadratic equation by factoring?
First set the equation equal to 0 by subtracting n from both sides.
That leaves us with 8n² - 11n = 0.
Since the GCF on the left is n, we can
factor it out to get n(8n - 11) = 0.
So either n = 0 or 8n - 11 = 0.
Solving for n in the second equation, we get n = 11/8.
So our solution is {0, 11/8}.