The solution of the inequality is 1<x<2.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
According to the given statement;
2 < 3x - 1 < 5
or, 2 + 1 < 3x - 1 + 1 < 5 + 1
or, 3 < 3x < 6
Divide the whole by 3, we get
or, 3/3 < (3/3)x < 6/3
or, 1 < x < 2
hence, the solution of the inequality is 1<x<2.
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Susan Marciano invested part of her 29000 bonus in a fund that paid an 11
% profit and invested the rest in stock that suffered a 4% loss. Find the amount of each investment if her overall net profit was 2740.
The amount invested in the in account that had an 11% profit is $26,000
The amount invested in the in account that had a 4% loss is $3,000.
What are the linear equations?a + b = 29,000 equation 1
0.11a - 0.04b = 2740 equation 2
Where:
a = amount invested in the account that had an 11% profit
b = = amount invested in the account that had a 4% loss
How much was invested in each account?
Multiply equation 1 by 0.11
0.11a + 0.11b = 3190 equation 3
Subtract equation 2 from equation 3
0.15b = 450
Divide both sides of the equation by 0.15
b = 3000
Subtract 3000 from 29,000
a = 29,000 - 3,000 = 26,000
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HELP URGENT how many minutes does it take for omar to print the pages on tuesday?
An equation that models the amount of time Omar spends printing on Tuesday is: 135 = 30 × m, where m be the amount of time, in minutes.
We have been given Omar uses a laser printer that prints 30 pages per minute.
So, the rate of printing = 30 pages/ minute
On Monday, he prints 8 pages.
Omar prints a total of 143 pages on Monday and Tuesday.
So, the number of pages printed on Tuesday are:
143 - 8 = 135
So On Tuesday, Omar prints 135 pages.
let m be the amount of time, in minutes, he spends printing on Tuesday.
We need to find an equation to model the amount of time Omar spends printing on Tuesday.
number of pages printed = (rate of printing) × (amount of time, in minutes)
Using this formula for given example, we get an equation,
135 = 30 × m
Therefore, an equation that models the amount of time Omar spends printing on Tuesday is: 135 = 30 × m, where m be the amount of time, in minutes.
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Your question was incomplete. Please refer the content below
Omar uses a laser printer that prints 30 pages per minute. on Monday, he prints 8 pages. on Tuesday, he prints more pages. Omar prints a total of 143 pages on Monday and Tuesday. let m be the amount of time, in minutes, he spends printing on Tuesday. part a create an equation using m to model the amount of time Omar spends printing on Tuesday.
I NEED HELP WITH QUESTION PLEASE!!
What is the inverse of f(x)
(x) = (x-4)² for x ≥ 4?
Answer:
4th choice [tex]\bold{f^{-1}(x) = \sqrt{x} + 4}[/tex]
Step-by-step explanation:
Definition of the inverse of a function
A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing. We can write this in terms of the composition of f and g as g(f(x))=x. The domain of f becomes the range of g and the range of f becomes the domain of g
To solve for the inverse of the function [tex]f(x) =\left(x-4\right)^2[/tex]
Let [tex]y=\left(x-4\right)^2[/tex]
[tex]\mathrm{Replace}\:x\:\mathrm{with}\:y[/tex] [tex]\text{ and replace }\:y\:\mathrm{with}\:x[/tex]
[tex]x=\left(y-4\right)^2[/tex]
Switch sides
[tex]\left(y-4\right)^2=x[/tex]
Take square roots on both sides
[tex]y-4=\pm\sqrt{x}[/tex]
Add 4 on both sides to solve for y
[tex]y = \pm\sqrt{x} + 4[/tex]
We have two solutions
[tex]y=\sqrt{x}+4,\:y=-\sqrt{x}+4[/tex]
To determine which one of these to be chosen not that in the given choices we can eliminate the first two since x cannot be negative
The third choice can also be eliminated since
[tex]-\sqrt{x} + 4[/tex] is a decreasing function for [tex]x \ge 0[/tex]
So the last answer choice is correct and the inverse of[tex]f(x) = (x-4)^2[/tex]
is given by [tex]f^{-1}(x) = \sqrt{x} + 4[/tex]
Answer:4th choice [tex]\bold{f^{-1}(x) = \sqrt{x} + 4}[/tex]
Note
Domain of (x-4)² is [4, ∞) since x ≥ 4 and (x-4)² cannot be negative
Range of (x-4)² is [0, ∞)
Domain of [tex]\sqrt{x}\:+\:4[/tex] is [0, ∞)
Range of [tex]\sqrt{x}\:+\:4[/tex] is [4, ∞)
so indeed the domain of (x-4)² has become the range of [tex]\sqrt{x}\:+\:4[/tex] and the range of (x-4)² has become the domain of [tex]\sqrt{x}\:+\:4[/tex]
Find the quotient of x^5 − 2x^3 + 1 / x^2 − 6 by any appropriate method. Given that the initial expression is of the form a(x)/b(x) , rewrite the quotient in the form q(x)+r(x)/b(x) , noting that r(x) could possibly be zero. Identify q(x) , r(x) , and b(x) .
q(x)=
r(x)=
b(x)=
The quotient in the form q(x)+r(x)/b(x) which is equal to the x^3 +4x +(24x +1 divided by x^2 − 6), and the identification q(x) , r(x) , and b(x) are as follow :q(x) = x^3 +4x
r(x) = 24x +1
b(x) = x^2 − 6
Given details in the following question are as follows:
x^5 − 2x^3 + 1 is divided by x^2 − 6
By using the divisor method :
x^5 − 2x^3 + 1 / x^2 − 6 = x3 +(4x^3+1 is divided by x^2 − 6)
= x^3 +4x +(24x +1 divided by x^2 − 6)
where we can see that the q(x) +r(x)/b(x) is equal to the x^3 +4x +(24x +1 divided by x^2 − 6)
q(x) = x^3 +4x
r(x) = 24x +1
b(x) = x^2 − 6
The quotient in the form q(x)+r(x)/b(x) which is equal to the x^3 +4x +(24x +1 divided by x^2 − 6)
What is the divisor method?A divisor divides a number into equal groups. The number that is being divided is called the dividend and the number that divides it is called the divisor.
Divisor Formula
The divisor formula is formed for two situations - with or without a remainder:
If the remainder is 0, then Divisor = Dividend ÷ Quotient.
If the remainder is not 0, then Divisor = (Dividend - Remainder) ÷ Quotient
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The quadrilateral ABCD is to be reflected across the line y = x, as shown in the diagram, to give a new quadrilateral, A'B'C'D'
B
A
7
6
5
4
3
4
-2
-3
-4
-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8
-5
-6
D
-7
y=x
What are the coordinates of A?
Using translation concepts, the coordinates of A' are given as follows:
A' (6,-2).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule for a translation over the line y = x is given by:
(x,y) -> (y,x).
The coordinates of A are (-2,6), hence the coordinates of A' are given as follows:
A' (6,-2).
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pls help with math. :(
Answer:
I would say 9 miles
Step-by-step explanation:
He would have to be HAULING it to run 6 miles in 8 minutes lol.
But, I think it's 9 miles
Answer:
Tom will run 9 miles in 12 minutes.
Step-by-step explanation:
A decimal number has 2 digits to the right of it's decimal point. If we round it to the nearest tenth, the result is 18.6. What is the maximum possible value of this decimal ?
This number can have a maximum value of 18.64.
What are decimal numbers?The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. Non-recurring (non-repeating or terminating, for example), recurring (repeating or non-terminating, for example), and decimal fractions are the three types of decimals (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).So, when rounded to the nearest tenths, the number is 18.59.
Now, look at the number to the right of it.If that number is 5 or higher, we round the 5 to a 6.But if that number is 4 or lower, the number remains a 5.18.55 rounded to the nearest tenths equals 18.6 (because the number to the right of 5 is 5, we round up to 18.6)18.54 rounded to tenths = 18.5 (because the number to the right of the 5 is 4, so we round it to 18.5).Therefore, this number can have a maximum value of 18.64.
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1. A 5 pound bag of dog treats cost $15.80. What is the uni
cost of the dog treats per pound?
Answer: $3.16 per pound
Step-by-step explanation:
$15.8/5=$3.16 per pound
Write the following numbers
In order from least to greatest
[(3/4), -(√5), -3, 2.5 and 0] when arranged in ascending order will be in the order of [tex][(-3),-(\sqrt{5}),0,\frac{3}{4},2.5][/tex].
As per question statement, we are provided with 5 random numbers:
[(3/4), -(√5), -3, 2.5 and 0].
We are required to rearrange the above mentioned numbers in their ascending order.
We know from basic mathematical knowledge that, any number of integer or fraction with a negative sign is less than Zero or any other positive number.
Here, we have two negative quantities [-(√5) and (-3)]. Since [tex]4 < 5 < 9\\or, \sqrt{4} < \sqrt{5} < \sqrt{9} \\or,2 < \sqrt{5} < 3\\or,(-2) > [-(\sqrt{5})] > (-3)\\or,(-3) < [-(\sqrt{5})] < (-2)[/tex]
That is, we have established our required relation between the negative numbers.
We also know that, zero is the midpoint of the number line and any other positive number is greater than zero while any negative number is less than zero. Hence, [tex][(-3) < -(\sqrt{5}) < 0][/tex] and [tex](0 < \frac{3}{4}),(0 < 2.5)[/tex].
Now, between (3/4) and 2.5, since (3/4) is a proper fraction, it means that (3/4) is less than 1, and since (1 < 2.5), therefore, [tex](\frac{3}{4} < 2.5)[/tex].
Hence, [(3/4), -(√5), -3, 2.5 and 0] when arranged in ascending order will be in the order of [tex][(-3),-(\sqrt{5}),0,\frac{3}{4},2.5][/tex].
Ascending Order: In mathematics and also in any field of daily life, arranging a set of values starting with the least one, then the second least, then the third least and so on till the greatest value is known as an Ascending Order.To learn more about Ascending Order, click on the link below.
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60 PTS, BRAINLIEST, 5-STAR, THANKS.
Consider the following polygon. Determine the measure of both angles A and B. Show your work. (Note: image is not drawn to scale)
Step-by-step explanation:
Add everything and then equate it to 360 and when you have found x, substitute it in A and B
15 Points help ASAP!!!
v Simplify This equation v
6 ⋅ 7 - 3^2 ⋅ 9+4^3
Answer42 - 2197
Step-by-step explanation:
Use function notation to write the equation of the line.
please help
Answer:
f(x)=3
Step-by-step explanation:
equal to y=3 because the lime is horizontal meaning each point has the same y value
Raymond has saved $50, and Felicia has saved $30. Each week, Felicia saves $15 and Raymond saves $10.
The following is true:
n=the number of weeks
R= the amount Raymond saves
F=the amount Felicia saves
Create equations to represent how much Raymond and Felicia will save after n weeks.
Answer:
50+10n for Raymond and 30+15n for Felicia
Step-by-step explanation:
N is for the amount of weeks times the amount saved per week then add the amount saved in the beginning.
ESTIMATE CUBE ROOTS
Which two integers is
3 v12 between?
Answer:
between 2 and
Step-by-step explanation:
Answer:
between
2 and
Step-by-step explanation:
simplify the expression (x-2) (3x4)
Question 4 of 10
One spring, a group of students measured rainfall totals at their school. This
chart shows how many inches of rain the students measured each month.
How much total rainfall did they receive at their school that spring?
MONTH
March
April
May
Subtracting Decimals in Word Problems
RAINFALL
1.1
4.1
6.1
Answer:
11.3
Step-by-step explanation:
1.1 + 4.1 = 5.2
5.2 + 6.1 = 11.3
The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels
since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005,
the figure was 374 parts per million. Find the increase in carbon dioxide levels and the percent of increase.
Round to the nearest tenth of a percent.
Increase carbon dioxide levels:
Percent increase:
196
Submit Question
parts per million
Question Help: Video Message instructor
Answer: The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959. At that time, there were 313 parts per million of carbon dioxide in the atmosphere. In 2005, the figure was 383 parts per million.
Step-by-step explanation:
4 is multipled by the difference of 5 and a number.
Answer:
Four times the difference of a number and 5 means equates to: 4(x-5), with x being the unknown number. You also know that this equation is equal to the number, x, increased by 4. So you now know that 4(x+5) is equal to (x+4
A bathtub is filled with 38 1/2 gallons of water. If 2 3/5 gallens splash out, how much water is left in the tub
Answer: 35.9
Step-by-step explanation:
Answer:
The answer would be 35 9/10 gallons of water left.
Aircraft A has 127 seats more than aircraft B. If their total number seats it 505, find the number of seats for each aircraft
In linear equation ,316 is the number of seats for each aircraft .
What are instances of linear equations?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Aircraft B: x seats
Aircraft A: x+ 127 (127 more than B)
Total seats on both is 505.
So, x+127+x = 505
Combine like terms
2x+127 = 505
Subtract by 127 both sides
2x = 505-127 = 378
Divide by 2 on both sides
x = 189 seats (B)
x + 127 =189 + 127 = 316 (A)
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A spinner with 6 equally sized slices has 2 blue slices, 1 red slice, and 3 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a blue slice?
Write your answer as a fraction in simplest form.
Answer:
3/6
Step-by-step explanation:
i think
Describe the path of a baseball in terms of the forces, balanced or unbalanced, that are acting on it.(1 point)
The baseball is at rest in the pitcher's glove, meaning the forces are balanced. The forces are unbalanced during the pitcher's windup and release since the ball is moving. The forces remain unbalanced while the ball is traveling through the air at a constant speed. The forces only return to being balanced once the ball makes contact with the catcher's glove, preventing it from moving.
The baseball is at rest in the pitcher's glove, meaning the forces are balanced. The forces are unbalanced during the pitcher's windup and release since the ball is moving. The forces remain unbalanced while the ball is traveling through the air at a constant speed. The forces only return to being balanced once the ball makes contact with the catcher's glove, preventing it from moving.
The baseball is at rest in the pitcher's glove, meaning the forces are balanced. The forces are unbalanced during the pitcher's windup and release. The forces remain unbalanced while the ball is traveling through the air at a constant speed and when the ball hits the catcher's glove and slows down. The forces only return to being balanced once the ball is completely at rest in the catcher's glove.
The baseball is at rest in the pitcher's glove, meaning the forces are balanced. The forces are unbalanced during the pitcher's windup and release. The forces remain unbalanced while the ball is traveling through the air at a constant speed and when the ball hits the catcher's glove and slows down. The forces only return to being balanced once the ball is completely at rest in the catcher's glove.
The baseball is at rest in the pitcher's glove, meaning the forces are balanced. The forces are unbalanced during the pitcher's windup and release since the ball is moving. They then return to being balanced while the ball is traveling through the air at a constant speed. The forces become unbalanced when the ball hits the catcher's glove and slows down. They then return to being balanced once the ball is completely at rest in the catcher's glove.
The baseball is at rest in the pitcher's glove, meaning the forces are balanced. The forces are unbalanced during the pitcher's windup and release since the ball is moving. They then return to being balanced while the ball is traveling through the air at a constant speed. The forces become unbalanced when the ball hits the catcher's glove and slows down. They then return to being balanced once the ball is completely at rest in the catcher's glove.
The baseball is at rest in the pitcher's glove, meaning the forces are balanced, and remain balanced during the pitcher's windup since the ball is still in contact with the glove. During the release, the forces become unbalanced and remain unbalanced as the ball travels through the air at a constant speed. The forces become balanced again the moment the ball makes contact with the catcher's glove.
The path of the ball in terms of the balanced or unbalanced forces that act on it is described by the following option;
The baseball is at rest in the pitcher's glove, meaning the forces are balanced. The forces are unbalanced during the pitcher's windup and release since the ball is moving. They then return to being balanced while the ball is traveling through the air at a constant speed. The forces become unbalanced when the ball hits the catcher's gloves and slows down. They then return to being balanced once the ball is completely at rest in the catcher's gloveHow can the path of the baseball be described?According to Newton's laws of motion, a body remains at rest or maintains a uniform motion in a straight line unless unbalanced forces are acting on it.
Therefore;
The forces are balanced when the ball is at rest in the pitcher's glove.
While the ball is made to move during the pitcher's windup and release, the forces are unbalanced.
The forces are balanced while the ball is traveling at a constant speed (uniform motion).
When the ball's speed is changed as it hits the catcher's gloves, the forces are unbalanced.
When the ball is at rest in the catcher's gloves, the forces are balanced.
The correct option is therefore the 6th option
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−t+(5−t) 3; when t=3
Answer: 3
Step-by-step explanation:
t=3
−t+(5−t) 3=
−t+(5−t)*3=
−t+3(5−t)=
−3+3(5−3)=
-3+15-9=
12-9=3
Hence, the answer is 3.
Answer:
Given t = 3,
[tex]\sf -t + (5 - t) * 3\\-3 + (5 - 3) * 3\\5 - 3\\= 2\\= -3 + 2\\= 1\\= 1 * 3\\= 3[/tex]
Therefore, your answer is 3.
Joyce's dad packs her lunch and always packs a yogurt. Joyce knows there are five yogurts in the refrigerator: one raspberry, two strawberry, one blueberry, and one vanilla. Her dad usually reaches into the refrigerator and randomly grabs a yogurt. which flavor is she most likely to have in her lunch today?
She is most likely to get strawberry in her lunch today.
This problem can be understood if we know the concept of probability.
In probability we just have to calculate what are the chances of any favorable outcome to occur by dividing with the total number of outcomes.
Here, Joyce's dad packs her lunch with one Yoghurt everyday.
And there are 5 yoghurts in the refrigerator.
The probability of getting raspberry flavor = 1/5
The probability of getting a strawberry flavor is = 2/5
The probability of getting a blueberry flavor is = 1/5
The probability of getting vanilla flavor is = 1/5
So, the highest probability is of getting strawberry flavor.
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Help please asap!!!!
A, perpendicular line
What is the image of the point (-10, 6) after a 90 degree counterclockwise
rotation?
After a 90-degree counterclockwise rotation of the point (-10, 6); the image point will be (- 6, - 10) .
As we all know, when a point ( x, y ) rotates counterclockwise, then the new coordinates of the given point are ( -y, x ).
Here the given point is (-10, 6) , where x = -10 and y = 6 ; as we know after rotation new x will be -6 and new y will be -10 .
So, after rotation the new coordinates will be ( -6 , -10 ) .
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1/2 of the candles on Claire's birthday cake are pink of the candles are green. The rest 2/10 are red What fraction of the candles is red?
According to the solving the fraction of the candles is red = 7/10.
What exactly is a fraction in mathematics?A fraction is a portion of a whole. In arithmetic, each number is represented as a quotient, which is the numerator divided by the denominator. In a simple fraction, are both integers. A complicated fraction contains a fraction in either the numerator or denominator.
How do you calculate a fraction?To calculate a fraction of either a number, divide it by the fraction's denominator, then multiply the result by the fraction's numerator. For example, if we wanted to figure out what 3/8 of 24 is, we might divide 24 by 8. (the denominator of the fraction).
According to the given data:Let 1 would be the total,
So,
2/10 are green.
1/2 of 1 is 1/2, so 1/2 candles are pink.
1/5+1/2.
1/5+1/2 = red candles
there is ultimately 7/10 candles that are red.
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I understand that the question you are looking for is:
1/2 of the candles on Claire's birthday cake are pink. 2/10 of the candles are green. The rest are red. What fraction of the candles is red?
The equation of the line that goes through the point (2,2) and is parallel to the line going through the points (-1,6) and (1,5) can be written in the form y=mx+b where m is what and b is what?
Answer:
m = -1/2b = 3Step-by-step explanation:
You want the slope-intercept equation of the line through (2, 2) and parallel to the line through (-1, 6) and (1, 5).
SlopeThe parallel line will have the same slope. The slope is given by the equation ...
m = (y2 -y1)/(x2 -x1)
m = (5 -6)/(1 -(-1))
m = -1/2
InterceptWe need to find the y-intercept of the desired line. Solving the equation for "b", we get ...
y = mx +b
b = y -mx . . . . . . . subtract mx to find b
b = 2 -(-1/2)(2) . . . . use m=-1/2 and (x, y) = (2, 2)
b = 2 +1
b = 3
The equation we want is ...
y = -1/2x +3
The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10.
. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
Answer: The height of the water was 2 inches before any water was added.
Translate the following into an expression or equation.
Five more than twice a number.
Answer: 5>x
Step-by-step explanation: hope this right
Answer: 2x+5
Step-by-step explanation:
Five more is adding 5
Twice a number would be 2 times something so we use a variable as "a number"