Please Please help! I am so beyond stuck. I have figured out what is wrong with the first step but I cant figure out what is going on with the second one!
Answers
Answer:
[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]
Step-by-step explanation:
So we have the equation:
[tex]|-4x+1|>3[/tex]
First, note that since the sign is greater than, this is an or inequality (not an "and" inequality). This is the student's first mistake.
So, let's solve this inequality.
Case 1:
[tex]-4x+1>3[/tex]
Subtract 1 from both sides:
[tex]-4x>2[/tex]
Divide both sides by -4:
[tex]x<-\frac{1}{2}[/tex]
The student did not flip the sign when doing this step, hence the incorrect answer.
You correctly spotted the student's mistake. Nicely done!
Case 2:
[tex]-4x+1<-3[/tex]
This is what you're missing: for this second instance, we must flip the sign to less than right away. This is because we are essentially multiplying the 3 by a negative. So, we must flip the sign in order to be correct.
Now solve. Subtract 1 from both sides:
[tex]-4x<-4[/tex]
Divide both sides by -4. Since we're dividing by a negative, flip the sign:
[tex]x>1[/tex]
So, our solutions are:
[tex]x<-\frac{1}{2}, x>1[/tex]
As mentioned previously, this is an or inequality. Therefore, our final answer is:
[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]
Edit: Improved Answer
Related Questions
A tire shop had to fill 3 1/2 tires with air. It took a small air
compressor 3 3/5 seconds to fill them up. How long would it take to fill 3 tires?
Answers
Answer: 3 seconds
Step-by-step explanation: the pump fills 1 tire per second
3 3/5 = 18/5
(7/2)/3 = (18/5)/t
3(18/5) = (7/2)t
54/5 = (7/2)t
108/35 = t
t = 3 3/35
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. Find the following sums without using a calculator or a formula. Hint: Apply the procedure used by Gauss. (See the Math Matters on page 31.) (a) 1 + 2 + 3 + 4 + . . . + 397 + 398 + 399 + 400 (b) 1 + 2 + 3 + 4 + . . . + 542 + 543 + 544 + 545 (c) 2 + 4 + 6 + 8 + . . . + 72 + 74 + 76 + 78
Answers
Calculus 2 master needed; stuck on evaluating the integral please show steps [tex]\int {sec(x/2)tan^5(x/2)} \, dx[/tex] I am thinking that we want to split up the tan^5, making [tex]\int {sec(x/2)tan^2 tan^3(x/2)} \, dx[/tex] and then [tex]\int {sec(x/2)*sec^2x-1* tan^3(x/2)} \, dx[/tex] but I am not sure this is correct. Can anyone help? The thing I am unsure of is that tan^3 is still odd, so would we do the same thing again and factor so we will be left with just tanx?
Answers
Answer:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]
Step-by-step explanation:
We want to find the integral:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left({\frac{x}{2}\right)dx[/tex]
First, perform the substitution y = x / 2. This yields:
[tex]\displaystyle dy = \frac{1}{2} \, dx \Rightarrow dx = 2\, dy[/tex]
Hence, the integral becomes;
[tex]\displaystyle =2\int \sec y\tan^5 y \, dy[/tex]
Next, as you had done, let's expand the tangent term but to the fourth:
[tex]\displaystyle =2\int \sec y\tan^4 y\tan y\, dy[/tex]
Recall that:
[tex]\tan^2(y)=\sec^2(y)-1[/tex]
Hence:
[tex]\displaystyle =2\int \sec y(\sec^2 y-1)^2\tan y\, dy[/tex]
We can use substitution once more. This time, let u = sec(y). Hence:
[tex]\displaystyle du = \sec y \tan y \, dy[/tex]
Rewrite:
[tex]\displaystyle =2\int \left((\sec^2y-1)^2\right)\left(\sec y \tan y\right)dy[/tex]
Therefore:
[tex]\displaystyle = 2\int (u^2 - 1)^2\, du[/tex]
Expand:
[tex]\displaystyle =2\int u^4-2u^2+1\, du[/tex]
Reverse Power Rule:
[tex]\displaystyle = 2\left(\frac{u^5}{5} - \frac{2u^3}{3} + u\right) + C[/tex]
Simplify:
[tex]\displaystyle = \frac{2u^5}{5} - \frac{4u^3}{3} + 2u + C[/tex]
Back-substitute:
[tex]\displaystyle = \frac{2\sec^5 y }{5}-\frac{4\sec^3 y}{3}+2\sec y+C[/tex]
Back-substitute:
[tex]\displaystyle =\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec \left(\frac{x}{2}\right)+C[/tex]
Therefore:
[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]
Answer:
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) ) + C
3 5
Step-by-step explanation:
∫sec(x/2) tan⁵(x/2) dx
apply u substitute u = x/2
= ∫sec(u) tan⁵(u) * 2du
= 2 * ∫sec(u) tan⁴(u) tan(u) du
= 2 * ∫sec(u) (tan²(u))² tan(u) du
= 2 * ∫sec(u) (-1 + sec²(u))² tan(u) du
apply u substitute v = sec(u)
= 2 * ∫(-1 + v²)² dv
expand
= 2 * ∫1 - 2v² + v⁴ dv
sum
= 2 (v - 2v³ + v⁵ )
3 5
substitute it back
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) )
3 5
add constant to the solution.
= 2 (sec (x/2) - 2sec³(x/2) + sec⁵(x/2) ) + C
3 5
By switching service providers, a family’s telephone bill decrease from about $50 a month to about $46. What was the percent of decrease?
Answers
Answer:
92%
Step-by-step explanation:
Given segment AB with points (-4, 8) and (6, 3) respectively. Find the coordinates of point P that partitions Segment AB in the ratio 3:2. The answer should be entered in the form (x,y) with out any spaces between characters.
Answers
Answer:
The coordinates of point P are (2,5)
Step-by-step explanation:
We know that point P divides AB internally in the ratio 3:2, that is AP/PB = 3/2,
we thus use the formula for internal division.
Let A = (x₁, y₁) = (-4, 8), B = (x₂, y₂) = (6, 3) and P = (x, y)
So x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
where m = 3 and n = 2
Substituting the values of the x coordinates of A and B into x, we have
x = (mx₂ + nx₁)/(m + n)
x = (3 × 6 + 2 × (-4))/(3 + 2)
x = (18 - 8)/5
x = 10/5
x = 2
Substituting the values of the y coordinates of A and B into y, we have
y = (my₂ + ny₁)/(m + n)
y = (3 × 3 + 2 × 8)/(3 + 2)
y = (9 + 16)/5
y = 25/5
y = 5
Therefore, the coordinates of point P are (2,5)
If for two non-zero vectors a,b : ∣a+b∣=∣a−b∣ then angle between them is:______a. 0b. 45c. 60d. 90
Answers
Answer:
[tex]90^\circ[/tex]
Step-by-step explanation:
Given two non zero vectors, [tex]\vec a, \vec b[/tex].
Let the angle between the two vectors = [tex]\theta[/tex]
Given that:
[tex]|\vec a+\vec b|=|\vec a-\vec b|[/tex]
Let us have a look at the formula for magnitude of addition of two vectors:
[tex]|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}[/tex]
Where [tex]\theta[/tex] is the angle between the two vectors.
formula for magnitude of subtraction of two vectors:
[tex]|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}[/tex]
As per the given condition:
[tex]\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}[/tex]
Squaring both sides:
[tex]a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ[/tex]
So, the angle between the two vectors is: [tex]90^\circ[/tex]
(4³)² simplified can anyone help
Answers
Answer:
4096
Step-by-step explanation:
Answer:
4096
Step-by-step explanation:
4 to the third power is 64 and 64 to the 2nd power is 4096 so that should be your answer
Can some body check my math on this one(question #6) I think it’s n=26 am I right?
Answers
Answer:
[tex]n=26[/tex]
Step-by-step explanation:
So we have the equation:
[tex]-413.4=-15.9n[/tex]
To figure out the value of n, divide both sides by -15.9. The right will cancel. Thus:
[tex]n=(-413.4)/(-15.9)[/tex]
Use a calculator:
[tex]n=26[/tex]
So, the answer is 26.
So, yes, you are very correct!
Answer:
n=26
Step-by-step explanation:
We are given the equation:
[tex]-413.4=-15.9n[/tex]
We want to solve for the unknown variable, which is n. Therefore, we must isolate n on one side of the equation.
n is being multiplied by -15.9. The inverse of multiplication is division. Divide both sides of the equation by -15.9
[tex]\frac{-413.4}{-15.9} =\frac{-15.9n}{-15.9}[/tex]
[tex]\frac{-413.4}{-15.9}=n[/tex]
[tex]26=n[/tex]
Let's check our solution. Plug 26 in for n and solve.
[tex]-413.4=-15.9n[/tex]
[tex]-413.4=-15.9(26)[/tex]
Multiply -15.9 and 26.
[tex]-413.4=-413.4[/tex]
This checks out, so we know our solution is correct.
The solution to this equation is n=26 and you are correct!
Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation
represents all numbers of points, p, a player may have after his or her first turn of the game?
O p = 4
O p = -4
O pl = 4
Op = -4
Answers
Answer:
Equation to represent all number of points = |4|
Step-by-step explanation:
We are told that a player either wins or loses 4 points during each turn. This means a player could either gain 4 points or loose 4 points. When writing this in Mathematical terms its means either -4 or +4.
Now, since possible number of turns is -4 or 4, then we can represent this with the absolute value symbol.
Thus, it's |4|
1.
Adrienne and Michelle are two hairstylists at a new age salon. They pay two different monthly
fees to rent a station at the salon.
The graph below represents Adrienne's profit she makes each month based on the number of
haircuts she performs.
Answers
Answer:
$50 is profit because every $50 it intersects.
X would be the $50 so 10x50=500-150=which would be $350.
I think this is right hope this helps!
What is the value of the 5 in the number 975,178
Answers
Answer:
thousands place
Step-by-step explanation:
Simplify: 2 + 7(1 - 3x)
2 + 14x
16x
9-27x
9 - 21x
Answers
Answer:
9 - 21x
Step-by-step explanation:
Simplify the following:
7 (1 - 3 x) + 2
Hint: | Distribute 7 over 1 - 3 x.
7 (1 - 3 x) = 7 - 21 x:
7 - 21 x + 2
Hint: | Add the numbers in -21 x + 2 + 7 together.
Add like terms. 2 + 7 = 9:
9 - 21 x
Hint: | Factor out the greatest common divisor of the coefficients of 9 - 21 x.
Factor 3 out of 9 - 21 x:
Answer: 3 (3 - 7 x)
(of the given solutions it's the only correct one, but can be further simplifued to 3 (3 - 7 x)
In need of some major help!!
Answers
The answer to your question is 4.8 kilometers. Brainliest?
Answer:
1.86
Step-by-step explanation:
cleveland has 64 fl Oz of orange juice how many pints of orange juice does cleveland have??
Answers
Answer:
4 pints
Step-by-step explanation:
16 oz in a pint
in 1971 the us dollar became part of the total fiat system meaning what?
Answers
Answer:
Step-by-step explanation:
Unit rate for 150 students in 3 classes.
Answers
Answer:
Step-by-step explanation:
150 students/3 classes= 50 students per class
David noticed that locker 49 was changed exactly 3 times it was opened by Student one closed by student seven and open my Student 49 what other lockers were changed exactly 3 times what is the relationship between these numbers
Answers
Answer:
The other lockers that were changed exactly 3 times are:
Locker 1 and Locker 7
Step-by-step explanation:
Question: What other lockers were changed exactly 3 times?
Answer: Lockers 1 and 7
How?
Locker 1 was opened by a student other than student 1; it was closed by a student other than student one; and it was opened by student 1.
Same happened with Locker 7.
The relationship between these numbers is an associative relationship.
Jack is running back on his football team. The first play he gained 12 yards, second play loss 15 yards, third play gained 25 yards, and fourth play loss 2 yards. What was his total gains or losses?
Answers
Answer:
20
Step-by-step explanation:
The total gains of Jack if, In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards is 20 yards.
What is Subtraction?The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards.
Assume the gains can be denoted by positive and loss by negative,
Gains = 12 yards, 25 yards.
Total gain = 12 + 25 = 37 yards
Loss = -15 yards, -2 yards
Total loss = -15 + (-2) = -17 yards
Calculate the total gain as shown below,
Total gain = total gain + total loss
Total gain = 37 + (-17)
Total gain = 20 yards.
To know more about subtraction:
https://brainly.com/question/28008319
#SPJ2
x2+9-8x in standard form
Answers
Answer:
x^2 - 8x + 9
Step-by-step explanation:
Please write x2+9-8x as x^2 + 9 - 8x. The " ^ " indicates exponentiation.
Next, please write x^2 + 9 - 8x in descending powers of x:
x^2 - 8x + 9
Which of the following fractions is greater than 2/5 and less than 3/5 ?
Answers
Answer:the answer would be 2.5/5
the sum of 5x and 8x is less than the sum of 4x and -7
Answers
Answer:
false or not true
Step-by-step explanation:
5x + 8x < 4x + -7
combine like terms
13x<4x+-7
4x divided by 4 -7 divided by 4
x= -7/4
13x<-7/4
If 1,000 gallons of oil cost $4,861, what is the cost of 35 gallons
Answers
Answer:
$170.14
Step-by-step explanation:
4,861 / 1,000 = $4.861 per gallon
35 x $4.681 = $170.135, so you need to round up to the nearest penny
Step-by-step explanation:
For 1000 gallons=$4861
For 1 gallon =$4861/1000
For 35 gallons=$4861/1000 x 35=170.135
John invests $200 at 4.5% compounded annually. About how long will it take for John’s investment to double in value?
Answers
Answer:
The number of years needed is 15.75 years.
Step-by-step explanation:
The investment amount (present value) = $200
Interest rate =4.5%
Double of investment = $400
Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.
Future value = present value ×(1+interest rate)^n
400 = 200×(1+4.5%)^n
N = 15.75 years
The number of years required to double the amount is 15.75 years.
TRUE OR FALSE: When two lines intersect then they create 4 linear pairs
Answers
Which is the graph of y<2x-1
Answers
Answer:
the last one is the only one with a y intercept of -1
Step-by-step explanation:
Jamie is sewing her own dress for the school dance. She bought 2 1/4 yards of fabric. The total cost was $10. What was the cost per yard?
Answers
Answer:
$4.44
Step-by-step explanation:
Cost per yard = $10/2.25
= $4.44 (nearest cent)
the answer $ 4.44
explanation :
so first of all you need to divide 10 by 2 1/4
when you divide both number you'll get 4 4/9
4 4/9 can also be written as 4.44444444444
which is also 4.4 recurring
now we can round this off
when you round it off, you should round it off to two decimal points cause the answer should be in dollars
you should get 4.44 as an answer
so the answer will be $ 4.44
really hope that helped :)
2+3+4+3+3+3x3x3x3x3x3x3x3x3x3x3x3x3x3
Answers
Answer:4782984
Step-by-step explanation:
Answer:4782984
Step-by-step explanation:
*BRAINLIEST* The lines below are parallel. If the slope of the green line is 8/5, what is the slope of the red line?
Answers
Any two parallel lines always have the same slope (but different y intercepts)
The equation of the green line is y = (8/5)x+6
The equation of the red line is y = (8/5)x-3
Slope intercept form is y = mx+b with m as the slope and b as the y intercept.
The slopes must be the same so that each time the line goes up some amount, we move to the right the same amount. Think of a set of stairs to possibly visualize what I mean. If the slopes are different (even slightly), then the lines will intersect at some point and we wouldn't have parallel lines.
Which number is less than 8.3507
O A 8,503
OB. 8.305
O c. 8,530
D. 8.355
Answers
can you find two fractions that multiply together to make 12/20 can you find two fractions that multiply together to make 12/35
Answers
Answer:
4/5*3/4&6/7*2/5
Step-by-step explanation:
4/5*3/4=12/20
6/7*2/5=12/35