The single inequality:
y > |x + 2|
Can be rewritten into:
y > x + 2
y > -x - 2
So the second option is the correct one.
How to decompose the inequality into two ones?
Remember that an absolute value equation like:
|x + a| = b
Can be rewritten as:
x + a = b
x + a = -b
So the inequality:
y > |x + 2|
Also can be rewritten into two equations, which are:
y > x + 2
-y < x + 2
The direction of the sign changes in the second one because the sign of the variable in the left changes.
Then if we multiply both sides by -1 of the second inequality, we get:
y > -x - 2
Then the two inequalities are:
y > x + 2
y > -x - 2
So the correct option is the second one.
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work. (4 points)
From the given sequence, it is found that:
a) It is a geometric sequence, as the ratio between consecutive terms is the same.
b) Station 5 will be completed in 48 minutes.
c) Station 9 will be completed in 768 minutes.
What is a geometric sequence?In a geometric sequence, the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by the following rule:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In the context of this problem, the ratio between consecutive terms is given by:
r = 24/12 = 12/6 = 6/3 = 2.
Hence it is a geometric sequence.
Applying the recursive formula, the time for Station 5 is the time for Station 4 multiplied by the common ratio of 2, hence:
24 x 2 = 48 minutes.
The first term of the sequence is of 3, hence the explicit formula is given by:
[tex]a_n = 3(2)^{n-1}[/tex]
Hence the time for the 9th station, in minutes, is given as follows:
[tex]a_9 = 3(2)^{8} = 768[/tex]
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Which expression is equivalent to 2.5 + 3a
5.5a - 29.5
3a - 32
3a - 27
5.5a - 10.5
Mak
20 9.5?
Answer:d
Step-by-step explanation:
Work out the area of this semicircle.
Take to be 3.142 and write down all of the digits given by your calculator.
18 cm
Answer:
A = 127.251 cm²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( where r is the radius )
the area (A) of a semicircle is then
A = [tex]\frac{1}{2}[/tex] πr²
given diameter = 18 then r = 18 ÷ 2 = 9 cm , so
A = 0.5 × 3.142 × 9² = 0.5 × 3.142 × 81 = 127.251 cm²
If a and b are the roots of 2x²+3x-1=0,find the values of a³-b³
Answer:
Step-by-step explanation:
Your equation has two complex roots, a=-3/4+sqrt(23)/4*i and b=-3/4-sqrt(23)/4*i. Calculate (x-a³/b³)*(x-b³/a³) and simplify it to get that expression. It will be a bit tedious, but the result is quite nice.
a³/b³=1001/1024+45*sqrt(23)/1024*i
b³/a³=1001/1024-45*sqrt(23)/1024*i
Notice that these are complex conjugates (which isn’t surprising, because a and b were complex conjugates). That’s why the result (x-a³/b³)*(x-b³/a³) will be a polynomial with real coefficients!
If you have complex conjugate roots c+di and c-di, you always get (x-(c+di))*(x-(c-di))=x²-2cx+c²+d², where c and d are real numbers.
It is -2c=-2*1001/1024=-1001/512, and
c²+d²=(1001/1024)²+(45*sqrt(23)/1024)²=1048576/1048576=1.
There are 20 balloons in Emma's hand. Four-fifths are red
balloons. How many red balloons are in Emma's hand?
Answer:
16
Step-by-step explanation:
4/5=0.8
20*0.8=16
look at attachment please MATHHHHHHHHHHHHHHHHH
Answer: 89%
[tex]\frac{0.89}{1}*\frac{100}{100} = \frac{89}{100}[/tex]
The mass of a textbook is approximately 0.0165 metric tons. If this number were written in scientific notation, what would the
exponent be?
If the number were written in scientific notation, the exponent will be -2.
What is scientific notation?Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.
The number of times a number is multiplied by itself is referred to as its exponent.
In this case, the mass of a textbook is approximately 0.0165 metric tons. It should be noted that this will be 1.65 × 10^-2. The exponent is -2.
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A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number less than 7.The probability of rolling a number less than 7 is
Probability is the quantitative measure of the likelihood of the occurrence of an event.
It is mathematically expressed as:
[tex]P=\frac{number\text{ of selected outcome}}{number\text{ of total outcome}}[/tex]We can decide to call the set of numbers below 7 "A".
A = {1, 2, 3, 4, 5, 6}
|A| = 6
We call the universal set, the set containing all the numbers rollable "U"
|U| = 12
Our probability is therefore:
[tex]undefined[/tex]w=0.75f.
What does 0.75 tell us in this situation?
Answer:
it should be in the ratio of 3:4
Step-by-step explanation:
100w= 75f
w/f = 75/100
= 3/4
= 3:4
What is the value of x?
Answer:
x=27
Step-by-step explanation:
easy 8th grade math
with explanation pls
Answer:
x: (40,0)
y:(0,30)
Step-by-step explanation:
hope this helped
have a good day :)
8x-5x+21 = 36-6y
Write the equation so that y is a function of x.
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex].
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Given Data
Function
8x-5x+21 = 36-6y
6y = 36 - 21 - 8x +5x
6y = -3x + 15
y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
The equation so that y is a function of x is y = [tex]\frac{-1}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
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At the school 460 of the students walk to school.
1The number of students who take public transit is 20% of the number of students who walk. How many students take public transit?
2The number of students who bike to school is 5% of the number of students who walk. How many students bike to school
3The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
Answer:
92 public transit
23 bike
Step-by-step explanation:
460 / 5 = 92
460 / 20 = 23
two trains leave the station at the same time, one heading west and the other east. the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours, what is the rate of the westbound train?
if the two trains are miles apart after hours, then the rate of the westbound train is 79 miles per hour
two trains leave the station at the same time, one heading west and the other east.
the westbound train travels miles per hour slower than the eastbound train. if the two trains are miles apart after hours,
what is the rate of the westbound train?
Allow the westbound train to be "w" and the eastbound train to be "e". We can make the following equation:
4 (e + (e - 12)) = 680
4 (2e + 12) = 680
8e - 48 = 680
8e = 728
e = 91 mph
e - 12 = w
91 - 12 = w
79 = w
Therefore, the westbound train travels at 79 miles per hour.
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The diagram below shows the first four of a series of designs that an artist draws on artwork.
The artist wants to use a design with a maximum of 15 shaded circles. What number of design should the artist use?
Using an arithmetic sequence, the number of design that the artist should use is:
b. Design 6.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
The sequence for the number of circles is:
(4, 6, 8, ...)
Hence the common difference is given by:
d = 8 - 6 = 6 - 4 = 2.
Then the rule for the nth term is:
[tex]a_n = 4 + 2(n - 1)[/tex]
As the first term is of 4.
The maximum number is of 15 shaded circles, hence:
4 + 2(n - 1) ≤ 15
4 + 2n - 2 ≤ 15
2 + 2n ≤ 15
2n ≤ 13
x ≤ 6.5.
Hence the maximum number is of 6, meaning that Design 6 is chosen, given by option b.
Missing informationThe complete problem is given by the image at the end of the answer.
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NEED HELP ASAP WILL MARK BRAINLIEST
Answer:
b -3
Step-by-step explanation:
t-3(4-t)=-24 multiply
t-12+3t=-24 simplify
4t-12=-24 plus 12 on both side
4t=-12 divide 4 on both side
t=-3
(1 × 10¹)(8 × 10^4) help
Answer:
800000
Step-by-step explanation:
(1 x 10^1) = 10
(8 x 10^4) = 80000
10 x 80000 = 800000
Math for Homework
Question Help Challenge You buy 1.09 pounds of apples, 0.99pounds of grapes, and 1.29 pounds of oranges. What is your total bill?
Grocery Store Prices
Item
Cost
Apples
$0.99 per
pound
Grapes
$1.19 per
pound
$1.09 per
Oranges
Savvar Egge Rigid muiago
Your total bill is $
(Round to the nearest cent as needed.)
Clasroom Continks Schoonet: math
which best describes why you might want to rewrite a literal equation?
To solve for a different indicated variable.
To solve for the variable x.
To solve for a different number.
To solve for the variable y.
Sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
What are literal equations?A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. Multiple letters or variables make up a literal equation. Examples include the formula for calculating speed (v = Dt) and the area of a circle (A = r₂).So, as in the description, it is given that A literal equation is one that is mostly made up of letters.
Therefore, sentence (A) "to solve for a different indicated variable" best describes why we might want to rewrite a literal equation.
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The correct question is given below:
Which best describes why you might want to rewrite a literal equation?
(A) To solve for a different indicated variable.
(B) To solve for the variable x.
(C) To solve for a different number.
(D) To solve for the variable y.
2y - 16 = 12 solve for y and simplify your answer as much as possible
Answer:
y = 14
Step-by-step explanation:
2y - 16 = 12
add 16 to both sides:
2y - 16 + 16 = 12 + 16
2y = 28
divide both sides by 2:
2y/2 = 28/2
y = 14
Answer: y = 14 is the solution.
Alan is ordering uniforms for his flag football team. Each uniform costs $14. All orders over $150 receive a 15% discount.
If Alan buys 12 uniforms, what will be the cost?
Answer:
$142.80
Step-by-step explanation:
smarts
Can someone help me please
The next correct step of the following elimination method is (C) subtract to eliminate 'x'
What is the elimination method?The elimination method involves taking one variable out of the system of linear equations by using addition or subtraction along with multiplication or division of the variable coefficients. The problem is reduced to solving a single variable equation using the elimination method. Finding the values of x and y without changing the equations is fairly challenging. The x s cancel out and the x is removed from the equations when they are added together. As a result, it is known as the "elimination method."So, the next correct step of the elimination method:
We can see that in both equations, '-3x' is the same and this means we will cancel the x variable.Then, option (A) and option (D) is incorrect.
We know that (+ -) is always (-) but (- -) is always (+).And we need to make if -3x and +3x to cancel the 'x' variable.Thus, the correct option will be an option (C).
Therefore, the next correct step of the following elimination method is (C) subtract to eliminate 'x'
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PLEASE HELP I AM GROUNDED AND MY MOTHER IS SO MAD AT ME FOR MY GRADE
Answer: b=116, c=64
Step-by-step explanation:
how do i convert (x+3)(x-4) to standard form
Answer:
solving the bracket
x×x = x²
x×-4= -4x
3×x= 3x
3×-4= -12
x²-x-12=0
Zach and Ginny are building model cars. Ginny's car is 2 more than 3 times the length of Zach's car. The sum of the lengths of both cars is 30 inches. Write an equation to determine the lengths of Zach's and Ginny's cars. A. 3x+2=30B. x+2+3x=30C. 2x+3=30D. x+2x+3=30
We can represent the length in Zach's car model by x
Since we have been given that Ginny's car is 2 more than 3 times the length of Zach's car, then we can get the expression as follow
[tex]\begin{gathered} 3\text{ times the length of Zach's car is} \\ 3\times x=3x \\ \end{gathered}[/tex][tex]\begin{gathered} 2\text{ more than 3 times the length of Zach's car will be} \\ 2+3x \end{gathered}[/tex]Therefore,
Ginny's model will be 2 + 3x
Next, we are told that the sum of the lengths of both cars is 30 inches
Then
[tex]\begin{gathered} Zach\text{+}Ginny=30 \\ x+2+3x=30 \end{gathered}[/tex]Therefore,
The answer is
[tex]x+2+3x=30[/tex]Thus, the answer is Option B
Create a division equation that represents the question: How many \frac{3}{8} are in \frac{5}{4} ?
The division equation that represents number of 3/8 in 5/4 is 10/3 = x.
Given,
Fractions : 3/8 and 5/4
We have to find a division equation for number of 3/8 in 5/4
Number of 3/8 in 5/4 = x
Now,
Number of a in b = b/a
So here,
Number of 3/8 in 5/4, x = 5/4 / 3/8
Number of 3/8 in 5/4, x = 5/ 3/2
Number of 3/8 in 5/4, x = 5 × 2 / 3
Number of 3/8 in 5/4, x = 10/3
That is,
The division equation that represents number of 3/8 in 5/4 is 10/3 = x.
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A race car driver
travels 34 ft in the first second of a race.
If the driver travels 3.5 additional feet each
subsequent second, how many feet did the
driver travel in 52 s?
The number of distance in feet the driver travel in 52 seconds is 216 feet.
How to find the distance in feet the driver can travel in a particular time?The race car driver travels 34 feet in the first second of a race.
The driver travels 3.5 additional feet each subsequent second.
The number of feet the driver travel in 52 seconds can be solved as follows:
Therefore,
the distance travel = 34 + 3.5x
where
x = number of time in seconds the driver travelsTherefore,
the distance travel = 34 + 3.5(52)
the distance travel = 34 + 182
the distance travel = 216 feet
Therefore, if the driver travels 34 feet in the first seconds of the race and travels an additional 3.5 feet each subsequent second, the number of distance in feet the driver will travel in 52 seconds is 216 feet.
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A group of friends wants to go to the amusement park. They have no more than $155 to spend on parking and admission. Parking is $18, and tickets cost $24 per person, including tax. What is the maximum number of people who can go to the amusement park?
Answer:
5
Step-by-step explanation:
155-18=137
137/24=5.70833333
5 people are able to join max
Find the length of the missing side.
Answer:
13 cm
Step-by-step explanation:
You can use the pythagorean theorem to solve this problem. The pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where and b are the legs of a right triangle and c is the hypotenuse.
In the problem, we are given two legs, 12 and 5, so we can substitute them in for a and b and solve from there:
[tex]5^2+12^2=c^2[/tex]
[tex]25+144=c^2[/tex]
[tex]c^2=169[/tex]
[tex]c=13[/tex]
The missing side is 13 cm long
When 4a-a is simplified it’s equivalent to
Answer: 3a
Step-by-step explanation: 4a - 1a = 3a