Choose the compound inequality that can be used to solve the original inequality |3x – 5| > 10.
A. –10 < |3x – 5| < 10
B. 3x – 5 > –10 or 3x – 5 < 10
C. 3x – 5 < –10 or 3x – 5 > 10
D. –10 < 3x – 5 < 10
Answers
Compound inequality is the combination of more than one inequality.
The compound inequality from [tex]|3x - 5| > 10[/tex] is:
(c) [tex]3x - 5 < -10[/tex] or [tex]3x - 5 > 10[/tex]
Given that:
[tex]|3x - 5| > 10[/tex]
When the above inequality is split, we have the following inequalities:
[tex]3x - 5 > 10[/tex]. [tex]3x - 5 < -10[/tex]So, the result of the split is:
[tex]3x - 5 < -10[/tex] or [tex]3x - 5 > 10[/tex]
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How do i know that the variable x has a uniform distribution function?
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lisha is making headbands using ribbon. she would like to make 12 head bands. Each one requires 15.5 inches of ribbon. She estimates that she will need to buy 160 inches of ribbon is her estimate reasonable? Explain your reasoning and lol I'm not in college i just did that
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15.5 * 12 = 186
Her estimate is not reasonable.
186-160 = 26
She still needs 26 more ribbons.
A college freshmen must take a science course, a humanities course and a mathematics course. If she may select any of 6 science courses, any of 4 humanities and any of 4 mathematics courses, how many ways can she arrange her program? Make a tree diagram and list the possibilities.
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How many times does 1/2 fit into 30
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30 ÷ [tex] \frac{1}{2} [/tex]
To divide by a fraction, multiply by its reciprocal (find reciprocal by flipping the fraction)
Ex. 30 * 2
Multiply 30 by 2 to get 60.
A 20-foot cable hangs from the top of a building that is 50 feet high. if the cable weighs 2 pounds per foot, how much work is done in lifting up the entire cable to the top of the building?
Answers
40*50=2000
2000/60=33.33
about 33 hours by lifting by hand
To find the work done in lifting the entire cable to the top of the building, multiply the weight of the cable by the height of the building.
Explanation:To calculate the work done in lifting the entire cable to the top of the building, we need to find the weight of the cable. The weight of the cable can be found by multiplying the length of the cable (20 feet) by its weight per foot (2 pounds per foot). Therefore, the weight of the cable is 20 feet × 2 pounds per foot = 40 pounds.
The work done in lifting the cable to the top of the building is equal to the product of the weight of the cable and the height of the building. So, the work done is 40 pounds × 50 feet = 2000 foot-pounds.
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a line that intersects the points (-23,-17) and (-13,-7), find the slope, now fill in the missing inputs to the slope-intercept formula -17=1(?)+b or (?)=(-13)+b
Answers
slope = (y2-y1) / (x2-x1)
The given points are (-23,-17) and (-13,-7), therefore:
y2 = -7
y1 = -17
x2 = -13
x1 = -23
Substitute with these values to get the slope as follows:
slope (m) = (-7--17) / (-13--23) = 1
The formula of the slope-intercept is:
y = mx+b where m is the slope and b is the intercept.
Using the point (-23,-17), the formula would be:
-17 = 1(-23) + b
Using the point (-13,-7), the formula would be:
-7 = 1(-13) + b
120 × a = 2889 what is the product
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2889 divided by 120 to get your answer.
24.075
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Hi, How do you find the first and second derivatives of the function.
y=(x^2-7/63x) (x^4+1/x^3)
I think for the first derivative dy/dx it's 2/63x-3/63x^-3+4/9x^-5 but I'm not sure, and I have no clue for the second derivative d^2y/dx^2.
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The first hand derivative of the function is [tex]6x^5 - \frac{35}{63}x^4 - \frac{1}{x^2} - \frac{4}{63x^3}[/tex] and the second derivative is [tex]30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]. To find the first derivative, apply the product rule to the given function. Then, differentiate the first derivative to obtain the second derivative. Simplify each step carefully.
To find the first derivative of the given function [tex]y = \left( x^2 - \frac{7}{63}x \right) \left( x^4 + \frac{1}{x^3} \right)[/tex], we'll use the product rule, which states that if [tex]y = u(x) \cdot v(x)[/tex], then [tex]y' = u' \cdot v + u \cdot v'[/tex].
First, define u(x) and v(x) as following:
[tex]u(x) = x^2 - \frac{7}{63}x = x^2 - \frac{1}{9}x[/tex][tex]v(x) = x^4 + \frac{1}{x^3}[/tex]Compute u'(x):
[tex]u'(x) = 2x - \frac{1}{9}[/tex]Compute v'(x):
[tex]v'(x) = 4x^3 + (-3)x^{-4} = 4x^3 - \frac{3}{x^4}[/tex]Apply the product rule: [tex]y' = u' \cdot v + u \cdot v'[/tex]
Thus,
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex]Simplify this expression step-by-step to find the first derivative.
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= \left(2x \cdot x^4 + 2x \cdot \frac{1}{x^3} - \frac{1}{9} \cdot x^4 - \frac{1}{9} \cdot \frac{1}{x^3} \right)[/tex][tex]&\quad + \ \left( x^2 \cdot 4x^3 - x^2 \cdot \frac{3}{x^4} - \frac{1}{9}x \cdot 4x^3 + \frac{1}{9}x \cdot \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= 2x^5 + \frac{2}{x^2} - \frac{1}{9}x^4 - \frac{1}{9x^3} \\[/tex] [tex]&\quad + \ 4x^5 - \frac{3}{x^2} - \frac{4}{9}x^4 + \frac{1}{3x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{1}{x^2} - \frac{5}{9}x^4 + \frac{2}{9x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{5}{9}x^4 - \frac{1}{x^2} + \frac{2}{9x^3}[/tex]To find the second derivative, differentiate the first derivative, carefully differentiating each term:
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Answers
and
have a difference (x - y) of (=) 25.
So, x + y = 53 and x - y = 25.
Solve one equation for a variable. We'll solve for x in the first equation.
x + y = 53 Subtract y from both sides
x = 53 - y
Substitute x for (53 - y) in the second equation.
x - y = 25 Substitute (53 - y) in the x spot
53 - y - y = 25 Combine like terms (-y and -y)
53 - 2y = 25 Subtract 53 from both sides
-2y = -28 Divide both sides by -2
y = 14
Now, find x by plugging this y-value (14) into the first equation.
x + y = 53 Substitute y for 14
x + 14 = 53 Subtract 14 from 53
x = 39
Check both of your answers by plugging them into the original equations.
x + y = 53 Plug in your numbers (39 and 14)
39 + 14 = 53 Add
53 = 53
x - y = 25 Plug in your numbers (39 and 14)
39 - 14 = 25 Subtract
25 = 25
So, your answers are x = 39 and y = 14 .
In an x-y plot of an experiment what is usually plotted on the x axis?
a. the independent variable, which is the parameter that was manipulated.
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How would I find a given triangle where: A=0.1, B=1 and c=9? Thanks in advance.
C=
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make sure your calculator is in Radian mode.
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B. 2/3+9.26
C. sqrt of 45 + sqrt of 36
D.14.3... + 5.78765239...
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You swim 121 out of 1,000 meters. How can you write this as a decimal
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0.121
The number in decimal form will be 0.121 meters.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that you swim 121 out of 1,000 meters. The decimal for the number will be written by dividing the number by 1000.
Decinmal form = 121 / 1000
Decimal form = 0.121 meters
Therefore, the decimal form of the number will be 0.121 meters.
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Estimate instantaneous rate of change of the point indicated p(x) = 3x^2-5, x = 2
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Ordering Least to greatest 2 9/11, 4/5, 2.91, 0.9
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HELP! solve for p p+10/p-7=8/9
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use the cross method solve the equation.
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Hope this helps.
You would like to join a fitness center. Fit-N-Trim charges $80 per month. Fit-For-Life charges a one tim e membership fee of $75 and $55 per month. The lines shown in the graph represent the cost y to attend each fitness center for x months. Are the lines parallel?
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y=55x+75
They are not parallel
What is 164% of 25? I have no idea and im in the middle of a test XDDD
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Simplify 6 - 23 + (-9 + 5) · 2
A. -10
B. -12
C. 6
D. -8
I've been told the answer is A. -10, but I need to know how to get that answer.
Thanks.
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at least u tried to help but the answer is -10 bro
John throws a rock straight down with speed 12 m/s from the top of a tower. the rock hits the ground after 2.37 s. what is the height of the tower? (air resistance is negligible)
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The tower is 28.44 meters tall.
A boat was sailing for 4 hours and covered 224 miles. A jet is ten times as fast as the boat. Find the jet’s speed.
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224 ÷ 4 = 56
56 mi/1 h
Next, you would multiply the number of miles the boat traveled, 56, by 10.
56 x 10 = 560
The jet flew 560 mi/per hour
I hope this helps!
56 x 10 = 560 miles per hour
A 27 oz bottle of a new soda costs $2.25. What is the unit rate, rounded to the nearest tenth of a cent?
Answers
1 / x =
Divide 2.25 by 27 to get
.08 dollars per ounce
The unit rate is the cost per ounce of soda. By dividing the total cost by the total ounces, we get the price per ounce in dollars ($0.08333), and converting this to cents gives us $8.3 cents per ounce.
Explanation:The term unit rate refers to a rate in which the second term is 1. In this case, we want to find out how much 1 ounce of soda costs.
First, you want to divide the total cost of the bottle by the total ounces in the bottle. So you divide $2.25 by 27. The answer you get is the price of one ounce of soda in dollars. When calculating it, you get approximately $0.08333.
To get the rate in cents, convert the dollars to cents by multiplying by 100 (since 1 dollar is 100 cents). The answer ($8.33) is the cost of one ounce to the nearest tenth of a cent.
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Solve for x.
−5x−4(x−6)=−3
Answers
-5x -4x + 24 = -3 Subtract 24 from both sides, collect like terms
-9x = -27 Divide both sides by -9
x= 3
-5x -(4x-6) = -3
-5x -4x + 24 = -3
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One side of a rectangle is 3 inches shorter than the other side, and the perimeter is 54 inches. Which of the following equations could be used to determine the dimensions of the rectangle
Answers
Side B: x-3
Perimeter: 2(l+w)
54"=2(x+x-3)
54"=2(2x-3)
54"=4x-6
54-6=4x
48/4=x
12=x
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Hope I helped :)
what is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16? y = –4 y = –2 y = 4 y = 6
Answers
It's always a good idea to use parentheses for clarity; it reduces or removes the need for guessing.
Here is my interpretation of your equation:
-8/2y-8=5/y+4 - 7y+8/y^2-16 becomes
-8 / (2y-8) = 5 / (y+4) - 7y + 8 / (y^2-16) (note use of parentheses)
Factoring all of the denominators results in:
-8 / [2(y-4)] = 5 / (y+4) - 7y + 8 / [(y-4)(y+4)]
The LCD is 2(y-4)(y+4). You must multiply each and every term in the above equation by this LCD to clear fractions:
-8(y+4) = 5(2)(y-2) - 7(y+4)(y-4) + 8/2
Then -8y - 32 = 10y -20 -7y^2 + 4
I believe the "-7y^2" term is incorrect.
In retrospect, you could simply substitute each of the given answers (y-values), one at a time, to determine which, if any, makes the equation true:
-8 / (2y-8) = 5 / (y+4) - 7y + 8 / (y^2-16) (note use of parentheses)
Let's test y = 4. Is this a solution? Subst. 4 for y in the above equation, we get:
-8 / (8-8) and several more terms. No, 4 is not a solution, because
-8 / (0) is undefined. Eliminate y = 4 as a solution. Try y = -4 and the other given possible solutions. Do any of them make this equation true?
Answer:
d. 6
Step-by-step explanation:
just took the pretest:) have such a fantastic day loves, you're doing AMAZING!
Multiple choice strategy: some students have suggested that if you have to guess on a multiple-choice question, you should always choose
c. carl, the student, wants to investigate this theory. he is able to get a sample of past tests and quizzes from various teachers. in this sample there are 110 multiple-choice questions with four options (a, b, c, d). the distribution of correct answers from this sample is given in the frequency table below. correct answer frequency a 22 b 26 c 38 d 24
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Come up with the answer in your head before looking at the possible answers, this way the choices given on the test won't throw you off or trick you.
Eliminate answers you know aren't right.
Read all the choices before choosing your answer.
If there is no guessing penalty, always take an educated guess and select an answer.
Don't keep on changing your answer, usually your first choice is the right one, unless you misread the question.
In "All of the above" and "None of the above" choices, if you are certain one of the statements is true don't choose "None of the above" or one of the statements are false don't choose "All of the above".
In a question with an "All of the above" choice, if you see that at least two correct statements, then "All of the above" is probably the answer.
A positive choice is more likely to be true than a negative one.
Usually the correct answer is the choice with the most information.
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Have all of your study material in front of you: lecture notes, course textbooks, study guides and any other relevant material.
Find a comfortable and quiet place to study with good lighting and little distractions
(try avoiding your own bed, it is very tempting to just lie down and take a nap).
Start out by studying the most important information.
Learn the general concepts first, don't worry about learning the details until you have learned the main ideas.
Take notes and write down a summary of the important ideas as you read through your study material.
Take short breaks frequently. Your memory retains the information that you study at the beginning and the end better than what you study in the middle.
Space out your studying, you'll learn more by studying a little every day instead of waiting to cram at the last minute. By studying every day, the material will stay in your long-term memory but if you try to study at the last moment, the material will only reside in your short-term memory that you'll easily forget.
Make sure that you understand the material well, don't just read through the material and try to memorize everything.
If you choose to study in a group, only study with others who are serious about the test.
Test yourself or have someone test you on the material to find out what your weak and strong areas are. You can use the review questions at the end of each chapter or practice tests the teacher may give out as well as other materials.
Listening to relaxing music such as classical or jazz on a low volume can relieve some of the boredom of studying.
Don't study later than the time you usually go to sleep, you may fall asleep or be tempted to go to sleep, instead try studying in the afternoon or early evening. If you are a morning person try studying in the morning.
Jeff invests an amount at 4% interest compounded annually. After 3 years, he has $1687.30. What was the original amount Jeff invested?
$1500
$1200
$1450
$750
Answers
:
To find the effect of 4% annual interest over 3 years, take 1.04 and raise it to the third power:
1.04³ = 1.125
Divide the final amount, 1687.30 by 1.125 to find the principal amount:
1687.30 ÷ 1.125 = ~1500
Answer is A.
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Answers
because she sold 24 cupcakes for $3 then you would multiply 24 and 3 to get the amount of money she made