What is the justification for each step in solving the inequality?
−2(x+1)≥3x+8−2(x+1)≥3x+8
Select from the drop-down menus to correctly justify each step.
2nd picture is the dropdown box answers
Answers
The first step is getting rid of the brackets using the distributive property.
The second and third steps is isolating the term containing the x on one side of the inequality using addition or subtraction property of order
The last step is getting rid of the coefficient of the x using the multiplication or division property of order.
So, the correct order of choices is:
1- distributive property.
2- addition or subtraction property of order
3- addition or subtraction property of order
4- multiplication or division property of order.
Second step: Addition property of order, because we are adding 2 to both sides (or Subtraction: we are subtracting -2 to both sides)
Third step: Subtraction property of order, because we are subtracting 3x to both sides of the inequality.
Fourth step: Division property of order, as we are dividing both sides by -5.
(or multiplication property of order: we are multiplying both sides by -1/5
Related Questions
the angle of elevation to the top of a 20 story sky scraper is measured to be 2 degrees from a point on the ground 5,280 from the building what is the height of the sky scraper to the nearest hundred foot
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make sure your calculator is in Degree mode.
−4x−y+4 when x=−1/4 and y=3 .
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1 - 3 + 4
-2 + 4
2
The bird house in your friend's yard casts a shadow that is 14 feet long. Your friend is 5 feet tall and casts a shadow that is 3.5 feet long. What is the height of the bird house?
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then difference between the cubes of two numbers is twice the value of the perfect square of a possitive Intiger
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For example, the difference between 2² and 4² = 12, which is twice the number 6, which is √36
The difference between 2² and 6² = 32, which is twice the number 16, which is a perfect square.
So choose depending on your interpretation of the question... ;-)
When the expression -5x^2+20x-17 is written in the form $a(x+d)^2+e$, where a, d, and e are constants, then what is the sum a+d+e?
PLEEEASE HELP
Answers
-5x^2+20x-17
=-5(x^2-4x)-17
=(-5(x-2)^2+20) -17
=-5(x-2)^2+3
So a=-5, d=-2, e=+3
a+d+e=-5-2+3=-4
What two consecutive whole numbers that square root of 86 lies between
Answers
sqrt(86) = 9.273
which is between 9 & 10
Identify a counterexample to disprove n3 ≤ 3n2, where n is a real number.
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The quantity on the left hand side will be positive for any [tex]n>3[/tex], so suppose consider [tex]n=4[/tex].
Now,
[tex]4^3=64[/tex]
but
[tex]3(4)^2=48[/tex]
and [tex]64\not\le48[/tex]
"The correct counterexample to disprove the inequality [tex]\( n^3 \leq 3n^2 \)[/tex]for real numbers [tex]\( n \)[/tex]is any real number[tex]\( n \)[/tex]greater than 3.
To find a counterexample, we need to show that there exists at least one real number[tex]\( n \)[/tex] for which the inequality [tex]\( n^3 \leq 3n^2 \)[/tex] does not hold. Let's solve the inequality to find the values of[tex]\( n \)[/tex] that satisfy it:
[tex]\[ n^3 \leq 3n^2 \][/tex]
[tex]\[ n^3 - 3n^2 \leq 0 \][/tex]
[tex]\[ n^2(n - 3) \leq 0 \][/tex]
The critical points of this inequality are [tex]\( n = 0 \) and \( n = 3 \)[/tex]. We can divide the real number line into three intervals:[tex]\( n < 0 \), \( 0 \leq n \leq 3 \)[/tex], and[tex]\( n > 3 \).[/tex]Let's test each interval:
1. For[tex]\( n < 0 \), \( n^2 \)[/tex] is positive, but [tex]\( n - 3 \)[/tex] is negative, so the product [tex]\( n^2(n - 3) \)[/tex]is negative, and the inequality holds.
2. For [tex]\( 0 \leq n \leq 3 \)[/tex], both [tex]\( n^2 \) and \( n - 3 \)[/tex] are non-negative, so the product [tex]\( n^2(n - 3) \)[/tex]is non-positive, and the inequality holds.
3. For [tex]\( n > 3 \)[/tex], both [tex]\( n^2 \)[/tex] and [tex]\( n - 3 \)[/tex] are positive, so the product[tex]\( n^2(n - 3) \)[/tex] is positive, and the inequality does not hold.
Therefore, any real number [tex]\( n \)[/tex] greater than 3 will serve as a counterexample to the inequality[tex]\( n^3 \leq 3n^2 \)[/tex]. For instance, if we take [tex]\( n = 4 \),[/tex] we get:
[tex]\[ 4^3 \leq 3 \cdot 4^2 \][/tex]
[tex]\[ 64 \leq 48 \][/tex]
This statement is false, as 64 is not less than or equal to 48. Thus, \( n = 4 \)[tex]\( n = 4 \)[/tex] is a valid counterexample."
Matrix's van holds 14 gallons of gas and can be driven 25 miles per gallon. His next road trip is 1,050 miles away. How many times will his ban need to be filled up to make the trip?
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On his next trip, he'll be driving it for 1050 miles, how many tanks is that?
well, how many times does (14*25) go into 1050? 1050/(14*25) that many.
Divide (67 gallons 2 quarts)÷3
A) 21 gallons 1 quart
B) 22 gallons 3 quart
C) 21 gallons 3 quart
D) 22 gallons 1 quart
E) NONE
Answers
E) None is correct.
To solve this problem, we need to divide the total volume of 67 gallons 2 quarts by 3.
Convert the total volume to only quarts since both gallons and quarts are involved in the problem. There are 4 quarts in a gallon.
67 gallons = 67 * 4 quarts = 268 quarts
Add the additional 2 quarts: 268 quarts + 2 quarts = 270 quarts
Divide the total quarts by 3 to find the result:
270 quarts ÷ 3 = 90 quarts
Convert the result back to gallons and quarts. Since there are 4 quarts in a gallon:
90 quarts ÷ 4 = 22 gallons with a remainder of 2 quarts
A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 60,000.
(a) What was the initial size of the squirrel population?
Answers
To find the initial size of the grey squirrel population, we used the exponential growth formula. After calculating, we determined that the initial population size was 1,875 squirrels.
Explanation:The student asked how to find the initial size of a grey squirrel population that doubles every 7 years and now has a population of 60,000 after 35 years.
To calculate the initial population size, we'll use the formula for exponential growth: P(t) = P0 × (2t/T), where P(t) is the population at time t, P0 is the initial population size, 2 is the base because the population doubles, t is the number of years, and T is the time it takes for the population to double.
The problem gives us 35 years (t) and a doubling time (T) of 7 years. Plugging these into the equation, we have 60,000 = P0 × (235/7). Simplifying, we get 60,000 = P0 × 25 or 60,000 = P0 × 32. Dividing both sides by 32, we find the initial population size is 1,875 squirrels.
Thus, the initial size of the grey squirrel population was 1,875.
Factor the polynomial. x2 - 6x + 9 A) (x - 9)(x - 1) B) (x - 3)(x + 3) C) (x + 9)(x + 1) D) (x - 3)(x - 3)
Answers
x -3
x -3
D) (x - 3) (x -3) is your answer
To check, do your FOIL
x(x) = x^2
x(-3) = -3x
-3(x) = -3x
-3(-3) = 9
x^2 -6x +9 True
hope this helps
[tex]x^2 -6x+9 =(x-3)(x-3) The correct answer is option D[/tex]
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I added a picture that will help you in the future and I recommend you to memorize them. At least, write them in your notebook.
~Credit to google image~
What is the LCM of 4,8,14?
Answers
M of 4 are 4,8,12,16,20,24,28,32,36,40,44,48,52,56
M of 8 are 8,16,32,48,56,64
M of 14 are 14,28,42,56
I hope this helps you
Answer:
The LCM of 4, 8, and 14 = 56
Step-by-step explanation:
Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.
Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, (56), 60, 64
Multiples of 8:
8, 16, 24, 32, 40, 48, (56), 64, 72
Multiples of 14:
14, 28, 42, (56), 70, 84
Hope this helps!
Are the functions linear or nonlinear? Column A Column B 1. 72 = x3 + y 2. y + 1 = 5(x – 9) 3. 7y + 2x = 12 4. 4y = 24 A. linear B. nonlinear
Answers
Function 1:
72 = x³ + y ⇒ rearranging to make 'y' the subject we have
y = -x³ + 72
This function has 'x³' not 'x', so this function is non-linear
---------------------------------------------------------------------------------------------------------------
Function 2:
y + 1 = 5(x - 9) ⇒ Multiplying out and simplify like terms
y + 1 = 5x - 45
y = 5x - 45 - 1
y = 5x - 46
This form is exactly the same with y = mx + c so the function is a linear function
----------------------------------------------------------------------------------------------------------------
Function 3
7y + 2x = 12
7y = 12 - 2x
7y = -2x + 12
y = ⁻²/₇ x + ¹²/₇
This function does follow the form of linear function so it is a linear function
------------------------------------------------------------------------------------------------------------
Function 4
4y = 24
y = 24/4
y = 6
This function does not have the 'x' term, it means the function is non-linear
Answer:
72=x3+y: nonlinear
y+1=5(x−9): linear
7y + 2x = 12: linear
4y = 24: linear
I know because I took the k12 test.
Hich equation correctly applies the distributive property?
A. −2.5⋅0.6⋅5.8=−2.5⋅5.8⋅0.6
B. −1.5⋅(6⋅1.25)=(−1.5⋅6)⋅1.25
C. (0.7⋅0.7)+(0.7⋅0.9)+(0.7⋅0.2)=0.7⋅(0.7+0.9+0.2)
D. 70+2.028=(70⋅2)+(70⋅0.02)+(70⋅0.008)
Please answer fast!
Answers
3 divided by what equals 5
Answers
1st step: Write this as an algebraic equation
3/x=5
2nd step: Multiply by x on both sides
3=5x
3rd step: Divide both sides by 5
3/5=x
So your answer is 3/5 or 0.6
Find the minimum length of u × v when u = 5 j and v is a position vector of length 4 in the xy-plane.
Answers
what 3 digits are in the units period?
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If x2 - 4 = 45, then x could be equal
Answers
Describe the set of all points p(x,y) in a coordinate plane that satisfy the given condition
Answers
The line x = -2 is a vertical line passing through point (-2, 0) on the x axis.
The set of points satisfying x = -2 are all the points on the coordinate plane which lies on the vertical line crossing point -2 on the x-axis.
Part B:
The line y = 5 is a horizontal line passing through point (0, 5) on the y axis.
The set of points satisfying y = 5 are all the points on the coordinate plane which lies on the horizontal line crossing point 5 on the y-axis.
Part C:
The line x = 0 is the y axis.
The set of points satisfying x ≥ 0 are all the points on the coordinate plane to the right of the y-axis.
Part D:
The set of points satisfying xy > 0 are all the points on the coordinate plane which lies on the 1st quadrant and all the points on the coordinate plane which lies on the 3rd quadrant.
Part E:
The line y = 0 is the x axis.
The set of points satisfying y < 0 are all the points on the coordinate plane that are below the x-axis.
Part F:
The line x = 0 is the y axis.
The set of points satisfying x = 0 are all the points on the coordinate plane that lie on the y-axis.
Part G:
The line y = -2 is a horizontal line passing through point (0, -2) on the x axis.
The set of points satisfying y = -2 are all the points on the coordinate plane which lies on the horizontal line crossing point -2 on the y-axis.
Part H:
The line x = 4 is a vertical line passing through point (4, 0) on the x axis.
The set of points satisfying x = 4 are all the points on the coordinate plane which lies on the vertical line crossing point 4 on the x-axis.
Part I:
The set of points satisfying x / y < 0 are all the points on the coordinate plane which lies on the 2nd quadrant and all the points on the coordinate plane which lies on the 4th quadrant.
Part J:
The line xy = 0 are the x-axis and the y-axis.
Therefore, the set of points satisfying xy = 0 are all the points on the coordinate plane which lies on the x-axis and all the points on the coordinate plane which lies on the y-axis.
Part K:
The line y = 1 is a horizontal line passing through point (0, 1) on the y axis.
The set of points satisfying y > 1 are all the points on the coordinate plane which lies above the horizontal line crossing point 1 on the y-axis.
Part L:
The line y = 0 is the x axis.
The set of points satisfying y = 0 are all the points on the coordinate plane that lie on the x-axis.
The set of all points p(x,y) in a coordinate plane that satisfy the given condition refers to the graph that represents the change of y as a function of x.
Explanation:In a rectangular (Cartesian) xy-coordinate system, a point in a plane is described by a pair of coordinates (x, y). The set of all points p(x,y) that satisfy the given condition refers to the plotted or sketched graph that represents the change of y as a function of x. Using the given table of points (1,5), (2,10), (3,7), and (4,14), we can plot these points on a graph and connect them to see how y values change with different x values.
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Expanded form of 6985062 using exponential notation
Answers
6,000,000 +900,000 +80,000 +5,000 +0 +60 +2
cory earns 52.50 in 7 hours. find the unit rate
Answers
divide the two:
52.50 / 7 = 7.50 per hour
Under what conditions can the t-distribution be correctly employed to test the difference between two population means?
Answers
Final answer:
The t-distribution is employed when testing the difference between two population means if the data come from a simple random sample and the population is approximately normally distributed or the sample size is large. It is also used when the population standard deviation is unknown, and a one-tailed or two-tailed test is conducted based on expectations about the direction of the mean difference.
Explanation:
Conditions for Using the t-Distribution to Test Differences Between Two Means
The t-distribution is appropriately used to test the difference between two population means under specific conditions. Firstly, your data must be obtained from a simple random sample. Secondly, the sample should come from a population that is approximately normally distributed, or the sample size should be large enough to compensate for non-normality. This is because the t-test relies on the assumption of normality, especially with smaller sample sizes (<30). If the sample size is small and the population distribution is unknown or not normal, the use of a t-test may not be appropriate without transformation or other techniques to meet the assumptions.
It is also essential to use the t-distribution when the population standard deviation is unknown, and as a result, the sample standard deviation is used as an estimate. Moreover, the t-test can adapt to various research scenarios, considering that it is designed to handle different levels of variability and data types. This flexibility makes the t-distribution a key tool for many scientific studies where the variance is not known ahead of time.
In hypothesis testing, the direction of the mean difference is considered, such as when conducting a one-tailed test or a two-tailed test. A one-tailed test is conducted when an expectation about the direction of the difference exists, while a two-tailed test is used to determine if there is any statistically significant difference between group means without a predefined direction. Lastly, when employing the t-test for paired data, the assumption is that the population from which the differences are drawn is normally distributed.
Solve the equation. What does “m” equal?
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What is the future value of $1400 saved at i=11.41%, compounded annually in 1 year?
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Which of the following symbols correctly completes this comparison? 5 + 10 + 13 ? 13 + 10 + 5 = < > ≠
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The correct symbol to complete the expression is,
⇒ 5 + 10 + 13 = 13 + 10 + 5
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The expression is,
⇒ 5 + 10 + 13 ? 13 + 10 + 5
Now,
Since, The expression is,
⇒ 5 + 10 + 13 ? 13 + 10 + 5
From LHS;
⇒ 5 + 10 + 13 = 28
From RHS;
⇒ 13 + 10 + 5 = 28
So, We get;
The correct symbol to use is,
⇒ 5 + 10 + 13 = 13 + 10 + 5
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a sporting good store sells golf balls and boxes each box has 4 compartments of golf balls each compartment has three golf balls the store sold 37 boxes on Friday and 42 boxes on Saturday how many golf balls did the store sell in all
Answers
First you find out how much golf balls are in each box. If there are 4 compartments with 3 balls in each you multiply them to get 12 golf balls in 1 box.
If the store sells 37 and 42 boxes you add them to get 79 boxes. So to find the amount of golf balls you multiply 79 and 12 to get 948.
The store sold a total of 948 balls on Saturday and Friday.
Given that,
A sporting good store sells golf balls and boxes each box has 4 compartments of golf balls each compartment has three golf balls the store sold 37 boxes on Friday and 42 boxes on Saturday how many golf balls did the store sell is to be detrmined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
A sporting goods store sells golf balls and boxes each box has 4 compartments of golf balls each compartment has three golf balls
Implies
each box has = 3 x 4 = 12 balls
Total box sold = 37 + 42 = 79
Total balls = 79 * 12 = 948
Thus, the store sold a total of 948 balls on Saturday and Friday.
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Which expression is equivalent to 18a+12b+9a+24b ?
Answer Choices
* 63ab
* 30a+33b
* 27a+36b
* 21a+42b
Answers
27a+36b, Because 18a+9a=27a 12b+24b=36b,so the correct answer is 27a+36b.
The correct expression is equivalent to 18a+12b+9a+24b is,
⇒ 27a + 36b
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 18a + 12b + 9a + 24b
Now, We can simplify as;
⇒ 18a + 12b + 9a + 24b
⇒ 18a + 9a + 12b + 24b
⇒ 27a + 36b
Thus, The correct expression is equivalent to 18a+12b+9a+24b is,
⇒ 27a + 36b
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A keycode must contain 2 letters and 3 numbers. The letters may be any letter of the alphabet. The numbers should be any number from 0 to 9. How many different keycode combinations are there?
Answers
The digits from 0 to 9 are a total of 10.
A keycode contains 2 letters, and 3 numbers, for example:
AB 598; MM 139; NT 498; ...
So there are 26 possible choices for the first letter, which can combined with any of the 26 possible choices for the second letter, so there are a total of
26*26=676 possible pairs of letters.
Similarly, the 10 possible choices for the first number, which can be combined with the 10 possible choices for the second number, and the 10 possible choices for the third number make a total of :
10*10*10=1,000 possible triples of numbers.
Any of the 676 possible pairs of letters can be combined with any of the possible 1,000 triples of numbers. This makes a total of
676*1,000=676,000 keycodes.
Answer: 676,000
Answer:
There is 676,000 combinations
Step-by-step explanation:
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suppose you have 192 marbles in groups of 15 marbles each. find the number of groups of marbles that you have. write the quotient with the remainder written as a fraction. explain what the fraction part of your answer means
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the fraction ia there because ( i think) 8 people have one less marble
A map has a scale of 1 inch to 15 miles . If 2 cities are 3.4 inches apart on the map , what is the actual distance between the 2 cities ?
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