To solve a one-variable-inequality, isolate the variable on one side of the inequality. This can be done by using the four mathematical operations.
What is the four mathematical operations?
The four mathematical operations include the following:
AdditionSubtractionMultiplicationDivisionThese operations can be used to solve equations, inequalities, and more.
[Solving] Simplifying the inequality:Given inequality:
c – 12 > –1As stated in the previous section, let's isolate the variable (c) using the four mathematical operations. Clearly, we have to add both sides by 12 of the inequality as "c" is being subtracted by 12. Therefore, we get:
⇒ c – 12 + 12 > –1 + 12⇒ c > –1 + 12Simplify the right-hand-side to obtain the simplified inequality:
⇒ c > 11Therefore, option B is the correct/best choice.
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can anybody help me find what 11x-21=
The following lines are parallel. 6x + 3y = 7 and y = -2x + 3
True
False
Answer:
True
Step-by-step explanation:
• Parallel lines have equal slopes
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
6x + 3y = 7 ( subtract 6x from both sides )
3y = - 6x + 7 ( divide terms by 3 )
y = - 2x + [tex]\frac{7}{2}[/tex] → in slope- intercept form
with slope m = - 2
y = - 2x + 3 ← is in slope- intercept form
with slope m = - 2
since both lines have equal slopes then they are parallel lines
Analyze the diagram below and complete the instructions that follow.
Solve for y.
11
21
24
42
The value of y is 11 if the measure of the angle (x + 6y) is 90 degree and x = 24 option first is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other known as parallel lines.
We have a perpendicular line shown in the picture.
The measure of the angle (4x - 6) is equal to 90 degree.
4x - 6 = 90
4x = 96
x = 24
Similarly, the measure of the angle (x + 6y) is equal to 90 degree:
x + 6y = 90
Plug x = 24
24 + 6y = 90
y = 11
Thus, the value of y is 11 if the measure of the angle (x + 6y) is 90 degree and x = 24 option first is correct.
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the gomez family drove 476 miles in 7 hours. what was their average speed, in miles per hour?
The average speed is 68 miles per hour
How to determine the average speed?The given parameters are:
Distance = 476 miles
Time = 7 hours
The average speed is calculated as:
Speed = Distance/Time
So, we have:
Speed = 476 miles/7 hours
Evaluate
Speed = 68 miles per hour
Hence, the average speed is 68 miles per hour
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The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 0.69(1.03)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04
Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)
Answer:
A) 3%
B) Product A
Step-by-step explanation:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Part A
Product A
Assuming the function for Product A is exponential:
[tex]f(x) = 0.69(1.03)^x[/tex]
The base (b) is 1.03. As b > 1 then it is an increasing function.
To calculate the percentage increase/decrease, subtract 1 from the base:
⇒ 1.03 - 1 = 0.03 = 3%
Therefore, product A is increasing by 3% each year.
Part B
[tex]\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100[/tex]
To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:
[tex]\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%[/tex]
Check using different two consecutive values of f(t):
[tex]\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%[/tex]
Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.
Although the question has not asked, we can use the given information to easily create an exponential function for Product B.
Given:
a = 10,100b = 1.01n = t - 1 (as the initial value is for t = 1 not t = 0)[tex]\implies f(t) = 10100(1.01)^{t-1}[/tex]
To check this, substitute the values of t for 1 through 4 into the found function:
[tex]\implies f(1) = 10100(1.01)^{1-1}=10100[/tex]
[tex]\implies f(2) = 10100(1.01)^{2-1}=10201[/tex]
[tex]\implies f(3) = 10100(1.01)^{3-1}=10303.01[/tex]
[tex]\implies f(4) = 10100(1.01)^{4-1}=10406.04[/tex]
As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.
There were 35 children and 10 adults in a picnic. What is the ratio of children to the total number of people in the picnic?
Answer:
7/9 ( or 7:9)
Step-by-step explanation:
Children = 35
Total people = 35 + 10 = 45
ratio Children / total people = 35/45 = 7/9
PQ = 15cm and QR = 17cm. Calculate the perimeter of PQR.
can u please tell if the figure is a right angled triangle??...cuz in order to find the perimeter, Pythagoras theorem must be applied but it's only for right angled triangle...so specify please
3(2x − 8) – 11x
equivalent to
Answer:
-5x - 24
Step-by-step explanation:
3(2x − 8) – 11x =
Distribute the 3.
= 6x - 24 - 11x
Combine like terms.
= -5x - 24
If geometry symbol represented as small triangle with three sides. abc a geometry symbol represented as small triangle with three sides. dec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
Answer:
D. X=1
Step-by-step explanation:
It's clear if you work through it just use substitution and you'll get the same answer yourself
55 mi / h = ____ ft / s
Answer:
80.6ft/s
Step-by-step explanation:
[tex]\frac{55mi}{h} * \frac{5280ft}{1 mi}* \frac{1h}{3600s} = 80.6ft/s[/tex]
A biologist watches and records the number of hippos that visit a particular
watering hole over a 30-day period. What method is the scientist using to
collect data?
OA. Observational study
OB. Survey
C. Control
D. Experiment
The correct answer is option A which is Observational study.
What is an observational study?This is an example of an observational study because the biologist is not interfering or interacting with the subjects of the study but just watching and registering data (recording with cameras).
The biologist is not conducting an experiment because (he is not setting up special conditions to register different responses to drive conclusions), and the biologist is not making any survey (questionnaires for example).
Therefore the correct answer is option A which is Observational study.
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Which of these polygons can be formed by the cross-section created when a plane intersects a pyramid? Select all that are possible.
square
pentagon
circle
rectangle
When a plane intersects a pyramid, the cross-section of polygon created is
Square andRectangleTo answer the question whe need to know what polygons are.
What are polygons?Polygons are shapes with 3 or more sides.
What is a pyramid?A pyramid a four-sided solid with triangular sides and a square base.
What polygons are formed by the cross-section created when a plane intersects a pyramid?When a plane intersects a pyramid parallel to its base, the cross-section created by the plane is a squareAlso, when a plane intersects a pyramid at an angle to its base, the cross-section formed is a rectangle.So, when a plane intersects a pyramid, the cross-section of polygon created is
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Avani has a loyalty card good for a discount at her local hardware store. The item she wants to buy is priced at $17, before discount and tax. After the discount, and before tax, the price is $15.64. Find the percent discount.
The percentage discount on the item will be equal to 8%.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Price of the item before tax and discount = $17After discount and before tax price is = $15.64The percentage of the discount will be calculated as:-
Percentage discount = ( 17 - 16.64 ) / ( 17 )
Percentage discount= ( 1.36 ) / ( 17 )
Percentage discount = 0.08 x 100 = 8%
Therefore the percentage discount on the item will be equal to 8%.
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Question 11 of 17
What are the coordinates of the point that is of the way from A to B?
Step-by-step explanation:
b l think so
17. Find the height of a rectangular room that
measures 4.7 m long and 3.2 m wide, if
the space within it is 33.84 m³.
Answer:
the height: h=2,25
Step-by-step explanation:
volume of rectangular box = wide*long*the height
----> the height = volume of rectangular box / ( wide*long) = 2,25
give me 5 stars and hearts^^
Kelly bought a pair of sneakers for $35.00. She also bought a pile of different laces. Each set of laces, l, costs $3.00. Write a variable expression to show how Kelly could calculate her total cost.
Answer:
35 + 3x
Step-by-step explanation:
we mark the number of sets of laces as x, each pf those costs 3$, so in total - 3x$
we add that to the 35$ of the shoes and get:
35+3x
The largest number of Oscars received by a film in year X was 4. This was different in previous years. Below is a probability distribution for the number of Oscars per Oscar winning film. What is the standard deviation of this distribution
The standard deviation of the given discrete distribution, considering it's formula, is of 1.195.
How to find the mean and the standard deviation of a discrete distribution?The mean is given by the sum of the multiplications of each outcome by it's probability.The standard deviation is given by the square root of the sum of the squares of each outcome subtracted by the mean, multiplied by it's probability.Researching this problem on the internet, the distribution is given by:
P(X = 1) = 0.56.P(X = 2) = 0.23.P(X = 3) = 0.11.P(X = 4) = 0.05.P(X = 5) = 0.03.P(X = 6) = 0.02.Hence the mean is given by:
E(X) = 0.56(1) + 0.23(2) + 0.11(3) + 0.05(4) + 0.03(5) + 0.02(6) = 1.82.
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{0.56(1-1.82)^2+0.23(2-1.82)^2+0.11(3-1.82)^2 + \cdots + 0.02(6-1.82)^2} = 1.195[/tex].
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Please help fast!!!
Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
5 x 2/3 =
Find the equation of the parabola that has zeros of x = - 6 and x = 6 and a yintercept of (0, 4) .
rne subtracted 6x3 2x
find the difference.
from -3.x3 +
4x - 7. Use the drop-down menus
to identify the steps Lorne used
(-3x' + 5x7,+ 4x - 7) + (-6x3 + 2x -3)
(-3x°) + 5x2 + 4x + (-7) + (-6x3) + 2x + (-3)
[(-3x*) + (-6x°)] + [4x + 2x] + [(-7) + (-3)] + [5x2)
-9x° + 6x + (-10) + 5x2
-9x' + 5x2 + 6x - 10
Four students are trying to determine what number must replace the question (x^2)^?=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? In words explain why.
Joe is correct as the unknown number is 6.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
Given :
[tex](x^2)^?=x^4\times x^8[/tex]
Let the question mark exponent outside the bracket be y, which needs to be determined
[tex](x^2)^y=x^4\times x^8[/tex]
Simplify the equation by applying exponent rules to either side of the equation:
Apply the rule [tex](a^b)^c = a^{b \times c}[/tex]
[tex](x^2)^y=x^4\times x^8[/tex]
[tex](x)^{2y}=x^4\times x^8[/tex]
Now apply [tex]a^b \times a^c = a^{b+c}[/tex]
[tex](x)^{2y}=x^{4+8}\\\\(x)^{2y}=x^{12}[/tex]
So, the base is the same the exponent will be the same also,
2y = 12
y = 6
Hence, Joe is correct as the unknown number is 6.
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which expression is the equivalent to the given expression
(3m-4)³(3m³)
Answer:
81m^6 - 323 m^5 + 432m^4 - 192m^3
Step-by-step explanation:
Comment
If you are given choices, you should list them please. Otherwise we cannot be certain our answers are taken far enough.
The general formula for expanding a binomial raised to the third power is
(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
Solution
To modify the general formula to suit this problem, let
a = 3m
b = - 4
When that is done, the general equation becomes
(3m)^3 - 3* (3m)^2 * 4 + 3 * 3m * 4^2 - 4^3
(3m - 4)^3 = 27m^3 - 108 m^2 + 144m - 64
Multiply everything in the 4-nomial by 3m^3
(27m^3 - 108 m^2 + 144m - 64)3m^3
81m^6 - 323 m^5 + 432m^4 - 192m^3 which is your answer. I see why you didn't include it, with other (incorrect) possibilities.
How many factors does 16 have
Answer:
5
Step-by-step explanation:
1,2,4,8,16 total 5 factors
Can someone help me with question 3? I like to see the working and answer on paper, that would be more helpful, I’m in a hurry
The steps to draw all the three angles have been explained.
What is an Angle ?An angle is made by two rays that have one common end point known as vertex.
To make an angle congruent to the one given , the angle has to be copied
For making both ∠XYZ and∠ UVW , following steps will be followed.
Draw two rays separately and name it YZ and VW .Take a compass and draw a free hand arc from the point B and E and with the same measure draw a free hand arc from the point Y and V respectively.Take the compass to the angle ABC and DEF again , from the point where the arc intersects BC and EF , cut an arc on the ray AB and DE .With the same measure , keep the compass on the point the free hand arc intersected on the ray YZ and VW , cut the arc by the new arc .The point where both the arc intersects will be joined form the end points , Y and V , to form an angle.The angle formed will be copy of ∠ABC and∠ DEFNow to draw RST = ABC + DEF
Draw the angle ABC and repeat the steps to draw DEF taking , AB ray as the base of the angle.The angle obtained will be RST.
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The proportional relationship between two variables, y and z, is represented by y = 11/2z. What is the constant of proportionality from z to y?
Answer:
Step-by-step explanation:
Comment
The constant you want is just the reciprocal of the constant you have been given. You can show it this way
y = 11/2 z Multiply both sides by 2
2y = 11z Divide both sides by 11
Answer
2/11 y = z
what is 11x2 – 4x = 1?
Answer:
x=5 1/4 or 5.25
Step-by-step explanation:
11x2-4x=1
22-4x=1
22-1-4x=
21-4x=
21=4x
x=5 1/4 or 5.25
Answer:
Using the formula of quadratic equation, we find x = 0.534 and x = -0.17.
Step-by-step explanation:
It is a quadratic equation.
11x² - 4x - 1 = 0
Find the determinant of the quadratic equation.
D = b² - 4ac
D = 16 + 44
D = 60
One of the values of x will be
x = (-b+√D)/2a
x = (4+2√15)/22
x = 0.534
The second value will be
x = (-b-√D)/2a
x = (4-2√15)/22
x = -0.17
The two values of x, from the quadratic formula are 0.534 and -0.17.
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The graph of which function has a minimum located at (4, –3)?
f(x) = one-halfx2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = one-halfx2 – 4x + 5
f(x) = 2x2 – 16x + 35
The parabola with the minimum at (4, -3) is the third option:
[tex]y = 0.5*x^2 - 4x + 5[/tex]
Which of the given parabolas has a minimum at (4, -3)?
Remember that for a parabola of the form:
[tex]y = a*x^2 + b*x + c[/tex]
If a > 0, the minimum is at the x-value of the vertex:
[tex]x = \frac{-b}{2a}[/tex]
If a < 0, there is no minimum (so we discard option 2).
Taking the third option:
[tex]y = 0.5*x^2 - 4x + 5[/tex]
The x-value of the vertex is:
[tex]x = \frac{-(-4)}{2*0.5} = 4[/tex]
As expected.
To get the y-value of the vertex (and minimum) we just evaluate the parabola equation in x = 4.
[tex]y = 0.5*(4)^2 - 4*4 + 5 = -3[/tex]
So the minimum is at (4, -3), as expected, so that is the correct option.
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If the price of an apple is Rs. 40, find the number of apples that can be brought for Rs. 200.
Answer:
5
Step-by-step explanation:
Divide 200 by 40 to get 5.
Answer:
ig 5 Apples can be Brought with Rs. 200
Step-by-step explanation:
Rs. 40 = 1 apple
Rs. 200 = ? Apple
therefore 5 apples can be brought...
Hope it Helps!!!
light a flashes every 5 seconds Light b flashes every 6 seconds light c flashes every 7 seconds work out how long it will take for all of them to flash
Answer:
210 seconds
Step-by-step explanation:
LCM of 5,6 and 7
The maximum number of turning points of a 9th degree polynomial is?
Answer:
8
Step-by-step explanation:
this was actually in my book and it came in today's test as well but I got 14/20 and failed lol
