Answers
[tex]\bf \cfrac{|3v-1|}{5}\ge 4\implies |3v-1|\ge 20\implies \begin{cases} +(3v-1)\ge 20\\ -(3v-1)\ge 20 \end{cases}\\\\ -------------------------------\\\\ +(3v-1)\ge 20\implies 3v-1\ge 20\implies 3v\ge 21\implies v\ge \cfrac{21}{3} \\\\\\ \boxed{v\ge 7}\\\\ -------------------------------\\\\[/tex]
[tex]\bf -(3v-1)\ge 20\implies -3v+1\ge 20\implies -3v\ge 19 \\\\\\ \stackrel{\textit{negative division, the sign changes}}{v\le \cfrac{19}{-3}}\implies \boxed{v\le -\cfrac{19}{3}}\\\\ -------------------------------\\\\ 7\le v\le -\cfrac{19}{3}[/tex]
Related Questions
Why, if two wrongs don't make a right, do two negatives make a positive in mathematics?
Answers
So, we can’t directly compare wrong with that of negative. Let me give an example. Let’s just think of Terrorism. Do you think there are positive and negative sides of terrorism? Mostly the answer would be no. There is no such things as positive and negative when we think of terrorism. But here we can directly say that Terrorism is always wrong whenever and wherever we talk about it.
I think now I have cleared your doubts about difference between wrong and negative. That’s why we can never say that two wrong can make a right. I hoped this helped!!
Final answer:
In mathematics, two negatives make a positive due to the rules of multiplication and addition. This rule is a fundamental property of mathematics and is consistent across various mathematical operations and contexts.
Explanation:
In mathematics, two negatives make a positive due to the rules of multiplication and addition. When two negatives are multiplied, the negative signs cancel each other out and result in a positive product. For example, (-4) x (-3) = 12, where both numbers are negative but the product is positive.
The same concept applies to addition as well. When two negative numbers are added, the negative signs combine and result in a negative sum. However, when two negative numbers are multiplied, the negative signs cancel out and produce a positive product.
It's important to note that this rule is a fundamental property of mathematics and is consistent across various mathematical operations and contexts.
An area of 16m^2 can be covered by 1.5 litres of pain. How many litres are needed to cover 20m^2?
Answers
Solve for x.
[tex]16:1.5=20:x[/tex]
[tex]16/1.5=20/x[/tex]
Cross Multiply.
[tex]16*x=20*1.5[/tex]
Simplify.
[tex]16x=30[/tex]
Divide both sides by 16.
[tex](16x)/16=(30)/16[/tex]
Simplify.
[tex]x=1.875[/tex]
1.875 litres of pain would be required to cover an area of 20 meters².
Hope this helps.
-Benjamin
If PQ bisects CX at point J, and if JX = 4y and CJ = y+9 find y
Answers
4y=y+9
-y -y
3y=9
divide by 3
y=3
By setting the given equations equal to each other (JX = CJ), we can create a new equation (4y = y +9). This equation simplifies to 3y = 9, giving a solution of y = 3.
Explanation:The problem you're facing deals with bisecting line segments, which is a topic under Geometry. Remember, if a segment bisects another, that means it divides the second segment into two equal parts. In this case, PQ bisects CX at point J, so JX = CJ.
We're also given that JX = 4y and CJ = y + 9. Because JX = CJ, we can set the two equations equal to each other and solve for y:
4y = y + 9
By subtracting y from both sides, we get
3y = 9
Finally, by dividing both sides by 3, we solve for y, which is 3
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a family pays $19 each month for internet access. next mont, the cost will increase by 5% because of the equipment fee. After this increase, what will be the cost for the internet
Answers
So the cost would be $19.95
The cost for the internet after an increase is $19.95.
Given that,
The family pays $19 each month. And, the cost should be increased by 5%.Based on the above information, the cost for the internet after an increase is
= $19 + 5% of $19
= $19 + $0.95
= $19.95
Therefore we can conclude that the cost for the internet after an increase is $19.95.
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Xavier is a salesperson who is paid a fixed amount of $455 per week. He also earns a commission of 3% on the sales he makes. If Xavier wants to earn more than $575 in one week, how many dollars (x) in sales must he make?
Answers
The answer is c reason I now this is cause I had this on my test
The price of a bracelet increase from $170 to $200 A Mother's Day what is the percent of increase in the price rounded to the nearest percent
Answers
The percentage of increase:
(30/170)*100=17.6471%
Peter is reading a 193-page book. he has read three pages more than one-fourth of the number of pages he hasn't yet read. how many pages has he not yet read? 147 144 152 141
Answers
"He has read three pages more than one-fourth of the number of pages he hasn't yet read." The first key phrase here is "he has read." What this means is that the number of pages he's read, which we've named [tex]m[/tex], is equal to everything in the rest of the sentence. "Thee pages more than" means that we're going to be adding 3 to whatever the next quantity described is, which, in this case, is "one-fourth of the number of pages he hasn't yet read." We already established earlier that "the number of pages he hasn't yet read" is [tex]193-m[/tex], so one-fourth of that would be [tex] \frac{1}{4} (193-m)[/tex]. Putting everything together, we get the following equation:
[tex]m= \frac{1}{4} (193-m)+3[/tex]
To solve for [tex]m[/tex], we might first want to eliminate the fraction 1/4 by multiplying both sides of the equation by 4, obtaining
[tex]4m=193-m+12[/tex]
Solving for m, we get:
[tex]4m=193+12-m\\5m=205\\m=41[/tex]
Now that we have m, it's a simple matter to solve for [tex]193-m[/tex]:
[tex]193-41=152[/tex]
So, he has not yet read 152 pages.
if two angles are supplementary, then it adds up to 180 degrees True or false?
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___________________________
True; by definition, if two angles are supplementary, their measures add up to 180 degrees.
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starting from 105 feet away a person on a bicycle rides toward a checkpoint and then passes it.the rider is traveling at a constant rate of 35 feet per second.The distance between the bicycle and the checkpoint given by the equation is D=|105-35t|.at what times is the bike 60 feet away from the checkpoint?
A.1.3 sec and 2.6 sec
B.1.3 sec and 4.7 sec
c.1.1 sec and 2.6 sec
d.4.7 sec and 9.4 sec
WHO EVER ANSWERS IT FIRST AND RIGHT GETS BRAINIEST
Answers
Answer:
The correct option is B.
Step-by-step explanation:
It is given that starting from 105 feet away a person on a bicycle rides toward a checkpoint and then passes it.the rider is traveling at a constant rate of 35 feet per second.
The distance between the bicycle and the checkpoint given by the equation
[tex]D=|105-35t|[/tex]
We have to find the times at which the bike 60 feet away from the checkpoint.
Substitute D=60 i the given equation.
[tex]60=|105-35t|[/tex]
[tex]\pm 60=105-35t[/tex]
Case 1:
[tex]60=105-35t[/tex]
Subtract 105 from both the sides.
[tex]60-105=-35t[/tex]
[tex]-45=-35t[/tex]
Divide both sides by -35.
[tex]1.2857=t[/tex]
[tex]t\approx 1.3[/tex]
Case 2:
[tex]-60=105-35t[/tex]
Subtract 105 from both the sides.
[tex]-60-105=-35t[/tex]
[tex]-165=-35t[/tex]
Divide both sides by -35.
[tex]4.71428=t[/tex]
[tex]t\approx 4.7[/tex]
The bike is 60 feet away from the checkpoint at 1.3 sec and 4.7 sec. Therefore the correct option is B.fore the correct option is B.
1/6d + 2/3 = 1/4(d-2)
Answers
1/6d + 2/3 = 1/4(d-2)
1/6d + 2/3 = 1/(4d-8)
Multiplying both sides by 1/(4d-8)
(4d-8/6d) + 2/3 = 1
Multiplying both sides by 6d
(4d - 8) + 2/3 = 6d
4d - 24/3 + 2/3 = 6d
4d - 22/3 = 6d
-2d = 22/3
2d = -22/3
d = -11/3
Help me reduce this please!!!
Answers
Are they divisible by 3?
Add the digits of 45. 4 + 5 = 9. Since 9 is divisible by 3, 45 is divisible by 3.
Add the digits of 567. 5+6+7 = 18. Since 18 is divisible by 3, 567 is divisible by 3.
Now we divide the numerator and denominator by 3.
45/3 = 15
567/3 = 189
We have this now:
45/567 = 15/189
We need to try to reduce it more.
15 is divisible by 3 and 5.
189 is divisible by 3.
15/3 = 5
189/3 = 63
45/567 = 15/189 = 5/63
5 is prime and divisible only by 1 and 5.
63 is not divisible by 5.
The fraction cannot be reduced any more.
Answer: 5/63
can you help me round 3,418,913 to the nearest thousand
Answers
Xy has endpoints at x(2,-3) and y(-1,2). What is the length of xy
Answers
The perimeter of a rectangular garden is 98 feet. the length of the garden is 4 feet more than twice the width. what is the length of the garden?
Answers
Length: 4+2x
Perimeter=x+x+4+2x+4+2x=6x+8
6x+8=98
x=15
Length=4+2(15)=34 feet
What is the ratio 42 to 48 as a fraction in simplest form?
Answers
How do u you a irrantional number from a rational number?
Answers
Irrational numbers can be written as a decimal but not as a fraction.
3 is rational, but \sqrt{3} is irrational.
what is x ⋅ x ⋅ x = ?
Answers
Think of it like this:
x ⋅ 1 = x^1
x ⋅ x = x^2
Therefore x ⋅ x ⋅ x = x^3.
Hope this helps! :)
∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 . What is the value of x? Enter your answer in the box.
Answers
6x=30
x=5
Answer:
5 is the answer
Step-by-step explanation:
I'm from K12
9 different coin combinations that equal 76 cents
Answers
multiply 2/7 with its additive inverse
Answers
Answer: -2/7.
Why is the answer -2/7?
When you add 2/7 + (-2/7) the answer will be 0.
This is why -2/7 is the additive inverse.
Find the distance between the given points . find the midpoint of the segment with the given endpoints. round to the nearest tenth, if necessary
Answers
In △ABC, the coordinates of vertices A and B are A(1,−1) and B(3,2). For each of the given coordinates of vertex C, is △ABC a right triangle?
Select Right Triangle or Not a Right Triangle for each set of coordinates.
C(0,2) right triangle or not a right triangle?
C(3,-1) right triangle or not a right triangle?
C(0,4) right triangle or not a right triangle?
Answers
Answer:
C(0,2) - Not A Right Angle
C(3,-1) - Right Angle
C(0,4) - Right Angle
I took the unit test and after this was the correct and answer. Hope this helps :))
Final answer:
To determine if △ABC is a right triangle, we can use the distance formula to calculate the lengths of the sides of the triangle. By comparing the squares of these lengths, we can determine if △ABC is a right triangle. For the given coordinates of vertex C, △ABC is not a right triangle.
Explanation:
To determine if △ABC is a right triangle, we need to check if the square of the length of the longest side is equal to the sum of the squares of the other two sides. Using the distance formula, we can find the lengths of AB and AC for each set of coordinates for vertex C. We then compare the squares of these lengths to determine if △ABC is a right triangle.
For C(0,2), the distance between A(1,-1) and C is √((0-1)^2 + (2-(-1))^2) = √(1 + 9) = √10. The distance between B(3,2) and C is √((0-3)^2 + (2-2)^2) = √(9 + 0) = 3. The longest side is AB with length √(2^2 + 3^2) = √(4 + 9) = √13. Since √13 is not equal to √10 + 3, △ABC is not a right triangle.
Following the same calculations for C(3,-1) and C(0,4), we find that △ABC is also not a right triangle for both cases. Therefore, the answer for all three sets of coordinates is Not a Right Triangle.
Vehicle a averages 14 miles per gallon of gasoline, and vehicle b averages 36 miles per gallon of gasoline. at these rates, how many more gallons of gasoline does vehicle a need than vehicle b to make a 1,008-mile trip?
Answers
Final answer:
Vehicle A requires 72 gallons and vehicle B requires 28 gallons for a 1,008-mile trip. Therefore, vehicle A needs 44 more gallons of gasoline than vehicle B for the trip.
Explanation:
To calculate the number of gallons of gasoline each vehicle needs for the trip, we would divide the total distance of the trip by the miles per gallon (mpg) that each vehicle gets. Then, to find out how many more gallons of gasoline vehicle A needs than vehicle B, we subtract the gallons of gasoline used by vehicle B from the gallons used by vehicle A.
First, we find the gallons needed for vehicle A:
Vehicle A: 1,008 miles ÷ 14 mpg = 72 gallonsNext, we calculate the gallons needed for vehicle B:
Vehicle B: 1,008 miles ÷ 36 mpg = 28 gallonsFinally, we determine how many more gallons vehicle A requires than vehicle B:
Additional gallons needed by vehicle A: 72 gallons - 28 gallons = 44 gallons
What are the excluded values of x for x^2-9x/x^2-7x-18
Answers
The excluded values are those values of x for which the denominator, [tex]x^2-7x-18[/tex], becomes zero.
So, we need to factorize the expression [tex]x^2-7x-18[/tex].
To factorize the expression, we can use the grouping method. Write -7x as -9x+2x to create 4 terms, as follows:
[tex]x^2-7x-18=(x^2-9x)+(2x-18)=x(x-9)+2(x-9)[/tex].
The, factorizing (x-9), we have (x-9)(x+2).
This expression becomes 0 for x=-2, or for x=9.
Answer: {-2, 9}
The excluded values of x for x^2-9x/x^2-7x-18 are -2 and 9
The expression is given as:
x^2-9x/x^2-7x-18
Set the denominator of the expression to 0
x^2-7x-18 = 0
Expand the above expression
x^2 + 2x -9x -18 = 0
Factorize the expression
x(x + 2) -9(x +2) = 0
Factor out x + 2
(x -9)(x +2) = 0
Solve for x
x = 9 and x = -2
Hence, the excluded values of x for x^2-9x/x^2-7x-18 are -2 and 9
Read more about quadratic functions at:
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there are 13 animals in the barn some are ducks and some are pigs there are 42 legs in all how many of each animal are there (ducks have 2 legs and pigs have 4)
Answers
1=6(2 legs from the duck, 4 legs from the pig)
2=12(4 legs from the ducks, 8 legs from the pigs)
3=18(6 legs from the ducks, 12 legs from the pigs)
4=24(8 legs from the ducks, 16 legs from the pigs)
5=30(10 legs from the ducks, 20 legs from the pigs)
6=36(12 legs from the ducks, 24 legs from the pigs)
7=42(14 legs from the ducks, 28 legs from the pigs)
A manufacturer wants to design an open-top box having a square base and a surface area of 120 square inches. what dimensions will provide a box with maximum volume?
Answers
The dimensions √30 inches square and 4 inches high will provide a box with maximum volume.
What are maxima and minima?The Maxima and minima of a function are the extremes within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
It is given that:
A manufacturer wants to design an open-top box having a square base and a surface area of 120 square inches.
Let's suppose x is the base edge length and h is the box height.
x² + 4xh = 120
h = (120 - x²)/(4x)
h = 30/x - x/4
Volume = x²(30/x - x/4) = 30x - x³/4
dV/dx = 0
30 - x² = 0
x = √30
h = 120/x² = 120/30 = 4 inches
The box is √30 inches square and 4 inches high.
Thus, the dimensions √30 inches square and 4 inches high will provide a box with maximum volume.
Learn more about the maxima and minima here:
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a writer gets paid monthly at a rate of $300 for each article she completes last moth she wrote 11.8 articles how much money did she get paid last month? show your work
Answers
so if she wrote 11.8 articles, she would get paid :
300 * 11.8 = $ 3540 <==
Answer:
She got paid last month $3540 .
Step-by-step explanation:
This problem can be solve by rule 3, knowing that she gets paid for each article a rate of $300.
1 article ------- $300
11.8 article----- x
Next you have to calculate the value of x as follows:
[tex]x=\frac{11.8*300}{1}[/tex]
x=3540
She got paid last month $3540.
John and Tim are looking at the equation the square root of the quantity of 3 times x minus 4 equals square root of x . John says that the solution is extraneous. Tim says the solution is non-extraneous. Is John correct? Is Tim correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences. (10 points)
Answers
3x - 4 = sqrt(x)
where 'sqrt' is shorthand for 'square root'
Let's solve the equation. To do so, we square both sides. Then we get everything to one side
3x - 4 = sqrt(x)
(3x - 4)^2 = (sqrt(x))^2
9x^2 - 24x + 16 = x
9x^2 - 24x + 16-x = x-x
9x^2 - 25x + 16 = 0
Now use the quadratic formula. See the attached image for those steps.
After using the quadratic formula the two possible solutions are x = 1 or x = 16/9
We need to check each possible solution to see if it is extraneous or not.
----------------------------
Checking x = 1
3x - 4 = sqrt(x)
3*1 - 4 = sqrt(1)
3 - 4 = 1
-1 = 1
The final equation is false, so x = 1 is not a true solution
x = 1 is extraneous.
So far, John is correct; however, we need to see the nature of the possible solution x = 16/9
So let's check it
----------------------------
Checking x = 16/9
3x - 4 = sqrt(x)
3*(16/9) - 4 = sqrt(16/9)
48/9 - 4 = 4/3
16/3 - 4 = 4/3
16/3 - 12/3 = 4/3
(16 - 12)/3 = 4/3
4/3 = 4/3
The last equation is true, so x = 16/9 is a proper solution.
This solution is considered non-extraneous. So Tim is also correct
----------------------------
They are both correct because there are two possible solutions. One of which is extraneous (x = 1) and the other is non-extraneous (the fraction x = 16/9)
Is this right? Domain and range of a function
Answers
Need some geometry help
Answers
that means
angle AFB is 27 + 2 = 29
angle BFC is 2(27) + 12 = 66
and angle CFD is 2(27) or 54
so hmmmm, you'd know which one isn't there.