Answer:
9.5 < x < 15
Step-by-step explanation:
The possible values of x for the given problem lies in (-infinity, -1.33) ∪ (9.5, 15).
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
Given that,
The sides of the triangle are as follows,
CD = x - 4, DE = 3x + 21 and CE = 6x - 13.
There can be three cases for the given problem.
Case 1,
The longest side of the triangle is CE = 6x - 13.
Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,
6x - 13 < x - 4 + 3x + 21
=> 6x - 13 < 4x + 17
=> 6x - 4x < 17 + 13
=> 2x < 30
=> x < 15
Case 2,
The longest side of the triangle is DE = 3x + 21.
Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,
3x + 21 < 6x - 13 + x - 4
=> 3x + 21 < 7x - 17
=> 7x - 3x > 21 + 17
=> x > 38/4
=> x > 9.5
Case 3,
The longest side of the triangle is CD = x - 4.
Since the sum of the two sides of a triangle is always greater than the longest one, the following inequality can be written for the given triangle,
x - 4 < 3x + 21 + 6x - 13
=> x - 4 < 9x + 8
=> x - 9x > 8 + 4
=> x < -1.33
Thus, the range of the values of x is intersection of x < 15, x > 9.5 and x < -1.33, which is equivalent to (-infinity, -1.33) ∪ (9.5, 15).
Hence, the range of possible values of x lies in the interval (-infinity, -1.33) ∪ (9.5, 15).
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Add the two expressions.
−4.2x+3 and 2.5x−6
write an equivalent expression to present patricia total earnings this week 7h + 135 + 5h = ?h + ?
Answer: 12 h + 135
Step-by-step explanation: 7h +135 + 5h = ?h + ?
7h +5h +135
=12h +135
So u combine like terms together which are 7h and 5h which gives you 12 h.And then you have 135 left,so you add 12h to 135.
Ps.If you don't know what like terms are.I will explain down below.
Like terms are variable that are the same.For an example 4y and 3y are like terms .Another example is 1/3 xy and 6xy .
Hope this helps :) and if it does please give brainliest .
Taylor bought a painting for 1 million yen
Answer:
Yen is the currency of Japan
Steven hiked 3/8 mile in 1/4 hour. How fast did he hike, in miles per hour?
3/23
2/3
1 1/2
4
What is the inverse of the function f(x) = 1/4x-12?
Answer:
[tex]\huge\boxed{f^{-1}(x)=4x+48}[/tex]
Step-by-step explanation:
In order to find the inverse of a function, we need to follow a couple of steps.
Step 1: Write the function as [tex]y=mx+b[/tex] Step 2: Swap all x and y values Step 3: Solve for y Step 4: Replace y with [tex]f^{-1}(x)[/tex]We can follow these steps to find the inverse of this function.
Step 1: We can just replace the f(x) with y, making our function [tex]y=\frac{1}{4}x-12[/tex].
Step 2: We can swap where the x and y values are, making our equation
[tex]x = \frac{1}{4}y-12[/tex]
Step 3: We can now solve for y.
[tex]x = \frac{1}{4}y-12[/tex] [tex]x + 12 = \frac{1}{4}x[/tex] [tex]4x+48 =y[/tex]We now have the function as [tex]y = 4x+48[/tex].
Step 4: We can now replace the y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x) =4x+48[/tex]
Therefore the inverse of [tex]f(x) = \frac{1}{4}x-12[/tex] is [tex]f^{-1}(x) =4x+48[/tex].
Hope this helped!
A restaurant orders corn tortillas and flour tortillas. The ratio of the number of corn tortillas is 4:5. What is the ratio of the nunber of flour tortills to the total number of tortillas?
Answer:
Pretty sure 5:9.
Step-by-step explanation:
The total tortillas are 9. The total number of flour tortillas is 5. You get 5:9.
Hope I helped! :) Sorry if it's wrong :( Have an amazing day!!
Answer:
Step-by-step explanation:
I don't think you've provided the correct information. When you write the ratio of corn tortillas is 4:5, it doesn't make sense. It should be a ratio of one thing to another. Is it a ratio of corn tortillas to flour tortillas?
1. What is the range of y = x2 - 1, given the domain of (-2,-1, 0, 1, 2}?
I
I'm tryna figure out the same question
Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she
drinks ina week?
There are 16 cups in a gallon
Answer:
7×0.5= 3.5 cups of water
Step-by-step explanation:
7×0.5 is the expression used to find how many cups she drank in a week
A garden has the form of a right triangle. One leg of the triangle is formed by a 2000-ft long sea wall. The hypotenuse of the triangle is 400 ft longer than the other leg. What are the dimensions of the garden?
Answer:
[tex]H = 5200[/tex] - Hypotenuse
[tex]S_1 = 2000[/tex] - Leg 1
[tex]S_2 = 4800[/tex] - Leg 2
Step-by-step explanation:
Represent the dimensions as:
[tex]H = Hypotenuse[/tex]
[tex]Other\ Legs = \{S_1,S_2\}[/tex]
So, we have:
[tex]S_1 = 2000[/tex]
[tex]H = 400 + S_2[/tex]
Required
Determine the dimensions
Apply Pythagoras theorem
[tex]H^2 = S_1^2 + S_2^2[/tex]
This gives:
[tex](400 + S_2)^2 = 2000^2 + S_2^2[/tex]
Open bracket
[tex]160000 + 800S_2 + S_2^2 = 4000000 + S_2^2[/tex]
[tex]160000 + 800S_2 = 4000000[/tex]
Collect Like Terms
[tex]800S_2 = 4000000 - 160000[/tex]
[tex]800S_2 = 3840000[/tex]
Solve for S2
[tex]S_2 = \frac{3840000}{800}[/tex]
[tex]S_2 = 4800[/tex]
Recall that:
[tex]H = 400 + S_2[/tex]
[tex]H = 400 + 4800[/tex]
[tex]H = 5200[/tex]
Hence, the dimensions are:
[tex]H = 5200[/tex]
[tex]S_1 = 2000[/tex]
[tex]S_2 = 4800[/tex]
What's -3(x – 4) =
A. -3x + 12
B. -3x + 4
C. -3x - 4
D. -3x - 12
Answer:
Step-by-step explanation:
-3(x-4)= multiply -3 with each term in parenthesis
-3x+12 choice A
Definition: This is an approximate calculation of quantity or degree or worth.
Example: Bill Gates net worth is about 75 billion dollars.
Answer:
estimation
Step-by-step explanation: Just got it correct thanks to the person in the other answers comments
HELPPPPPPPLLL
You-tube music channel plays 4 rap songs to 2 pop songs. The ratio is 4:2. Based on the information provided, how many rap songs does You-tube play for every 8 pop songs? How many pop songs does You-tube play for every 12 rap songs?
Answer:
16
Step-by-step explanation:
4:2
2x4 = 8
4x4=16
2. 5²- 4 +3 • (9 • 2) /2=
3. 4³ - 4(8-7) +12=
4. 6(5 +4) + 4 – 3 •4 =
5. 10²- 4 + 1 • (9 • 2) /2 =
6. 32 -5 + 8 / 2 • 5 =
7. 3² • (1+4) + 4 – 3 • 4 =
8. 9² • (1+4) + 7 – 3 • 4 =
9. 3³ - (2+4) + 5 – 3 • 3 =
10. (2 + 5) – 3 + 4 • 2 + 1³ =
2) 48
3) 72
4) 48
5) 105
6) 47
7) 37
8) 400
9) 17
10) 13
I hope this helps! Let me know if I get anything wrong so I can fix it.
A JIT system uses kanban cards to authorize movement of incoming parts. In one portion of the system, a work center uses an average of 105 parts per hour while running. The manager has assigned an inefficiency factor of .35 to the center. Standard containers are designed to hold 3 dozen parts each. The cycle time for parts containers is about 90 minutes. How many containers are needed
Answer: 6 Containers are needed
Step-by-step explanation:
The ideal number of Kanban cards can be calculated using the following formula;
N = (DT × ( 1 + X)) / C
where N is total number of container,
D is panned usage rate of using work Centre
T is Average waiting time for replenishment of parts plus average production for a container of parts,
X is policy variable set by management that reflects possible inefficiency in the system ,
C is capacity of standard container.
Now, given that;
D = 105 parts
T = 90min = 90/60 = 1.5 hrs
X = 0.35
C = 3 × 12parts = 36 parts
so; we substitute
N = (105×1.5 × ( 1 + 0.35)) / 36
N = 212.626 / 36
N = 5.9063 ≈ 6
Therefore 6 Containers are needed
The students in a class were each asked to name their favorite meal of the day. The results are shown in this percentage bar graph. Which table could be represented by the percentage bar graph?
Answer:
bar graph??? we need a pic
The requried table that represents the bar graph is table H.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
The total number of students is 30,
Now,
10% of students take lunch,
So the number of students who take lunch,
= 10% of 30
= 3
Similarly,
Number of students who takes Breakfast = 9
Number of students who takes super = 18
Thus, the requried table that represents the bar graph is table H.
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What is the value of b?
Answer:
interior angle of a hexagon = 720
straight line is a 180 degree angle.
180- 116 = 64
a=64
180- 82 = 98
116 + 98 + 90 = 304
720 - 304 = 416
416/3 =138.666666
b=138.666666
that's as far as I could get not 100%
pls hurry I need this. can y'all answer this ?
Pythagorean theorem question:)
Answer:
14.21
Step-by-step explanation:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
hellllllllllllllllllllllllllllppppppppppppppppp
Answer:
11
Step-by-step explanation:
2.2x 5 = 11
Stations 1, 2, and 3 are bus stations. The equation y = 160x represents the number of people that go to Station 1, where y is the total number of people and x is the number of hours since opening. The table shows the same relationship for Station 2, and the graph shows the relationship for Station 3.
Answer:
station three for part a and 2,064 for part b
Step-by-step explanation:
i got the answer correct
Estimate the sum by rounding each number to the nearest tenth: 0.214 +0.61
The estimate of the sum by rounding each number to the nearest tenth is 0.8
How to estimate the sum by rounding each number to the nearest tenth?Estimation is a method used for calculating the approximate value of a quantity (just to get a 'rough answer')
In estimation 1, 2,3, and 4 are rounded down while 5, 6, 7, 8 and 9 are rounded up.
Rounding each number to the nearest tenth:
0.214 = 0.2
0.61 = 0.6
The sum = 0.2 + 0.6 = 0.8
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A cable car suddenly slackens while crossing an 86 m wide gorge. The cable makes an angle of depression of 57 degrees at one end and 40 degrees at the other end. How long is the cable that holds the car?
Answer:
I took the test its 63
Step-by-step explanation:
please mark brainliest
Estimate the sum of 6107 and 2960 to the nearest thousand.
How u do this
Answer:
9,000
Step-by-step explanation:
You would add it together.
6107 + 2960 = 9,067
You round the thousand (9) to the 0.
The rule is that if any number next to the one your rounding is higher then 5 or is 5 then the rounding number will go up, if its 4 or below if won't go up but stay the same.
9,067 would not go up but stay the same because of the rule.
Estimations are guesses from the mind so an exact answer wouldn't work but its whatever.
What’s the answer for step 5 and 6
Answer:
Step-by-step explanation:
Step 4) AW = PW
Step 5) ΔAWB ≅ ΔPWR {A A S}
Step 6) RW ≅ BW {corresponding sides of congruent triangles are congruent}
Is the binomial a factor of the polynomial function?
f(x)=x^3+4x^2-25x-100
Select Yes or No for each binomial.
Binomial Yes No
(x-5)
(x+2)
(x-4)
binomial (x+11) answer
What is the slope of the line graphed on the coordinate plate? (1,-2) (0,6)
Answer:
m = -8 (Two points slope form)
Step-by-step explanation:
y = -8x + 6
write an equation that describes the function
Answer:
x+7
Step-by-step explanation:
Hope this helps!
Please mark me brainliest if possible. :)
What is the explicit formula for the geometric sequence with this recursive formula? { a1 = -7 an = an-1 • (1/3)
9514 1404 393
Answer:
an = -7(1/3)^(n-1)
Step-by-step explanation:
The explicit formula for a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
The multiplier in the recursion relation is the common ratio: 1/3. The first term is given as a1 = -7. Putting these in the general formula, we have ...
an = -7·(1/3)^(n-1)
i am thinking of a number x. What algebraic expression represents "eight less than three times this number "?
Answer:
3x-8
Step-by-step explanation:
3x is three times the number, -8 is 8 less.
When this 3-digit number is rounded to the nearest hundred, it rounds to 400. The digit in the ones place is the fourth odd number you count beginning with 1. The sum of the digits is 12. What is the number?
Answer: 417
Step-by-step explanation:
Since the digit in the ones place is the fourth odd number that the person count beginning with 1, then the digit will be 7.
This means the number will be:
____ _____ 7. The number in the units and hundreds place are still unknown. But since the addition of the three numbers gives 12, and approximating to the nearest hundred gives 400. Then the number will be 417.
Check: 4 + 1 + 7 = 12
417 = 400 to nearest hundred