Graph the solution to this inequality on the number line.
−8 + x < −3
(Please answer this question by taking a screenshot of the number line and drawing a number line where it needs to go)
Answers
A graph of the solution to this inequality (x < 5) is shown on the number line in the image attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for the comparison of two (2) or more numerical data, numerals, and variables that are contained in an algebraic equation, especially based on the following inequality symbols:
Less than (<).Greater than or equal to (≥).Greater than (>).Less than or equal to (≤).Generally speaking, a number line is a type of chart which primarily decreases in numerical value towards the right from zero (0) and increases in numerical value towards the left from zero (0).
Next, we would solve the given inequality by adding eight to both sides as follows;
−8 + x < −3
−8 + x + 8 < −3 + 8
x < 5
Therefore, the solution is x is less than five.
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Related Questions
. A team of movers are unloading a truck. One of the movers stays in the truck and places
the boxes on a ramp, so they slide down to the other members of the team. One box
has a mass of 34.9 kg. The mover places the box on the ramp, which is 24.7° below
horizontal. If the coefficient of friction between the box and the ramp is 0.211, how
quickly will the box accelerate down the ramp?
Answers
The box will accelerate down the ramp at a rate of 0.063 m/s²
To find the acceleration of the box down the ramp, you can use the equation:
a = g sin(θ) - (μ g cos(θ)) / m
In this equation, "a" is the acceleration of the box, "g" is the acceleration due to gravity (9.8 m/s²), "θ" is the angle of the ramp with respect to the horizontal, "μ" is the coefficient of friction between the box and the ramp, and "m" is the mass of the box.
Plugging in the values that you know, you get:
a = 9.8 × sin(24.7) - (0.211 × 9.8 × cos(24.7)) / 34.9
This simplifies to:
a = 4.095 - 1.87/ 34.9 = 0.063 m/s²
Thus, the box will travel down the ramp at a speed of 0.063 m/s².
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The length of a rectangle is the sum of the width and 2. The area of the rectangle is 63 square units. What is the width, in units, of the rectangle?
Answers
The width of the given rectangle is; 7 units
How to find the area of a rectangle?Let the length of the rectangle be x and let the width be y.
We are told that the length of a rectangle is the sum of the width and 2. Thus;
x = y + 2
Now, formula for area of rectangle is;
A = length * width
Thus;
A = y(y + 2)
Now, we are told that the area is 63 square units and as such;
y(y + 2) = 63
y² + 2y - 63 = 0
Factorizing gives us;
(y + 9)(y - 7) = 0
Thus; y = 7
x = 7 + 2
x = 9
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Question 1 (Multiple Choice Worth 2 points)
(02.07 MC)
Solve -3x2 + 30x - 90 = 0.
Ox=5 ± 2i√5
Ox=5±i√5
Ox=10 ± 2i√5
Ox=10 ± i √5
Answers
Answer: Choice 2. x = 5 ± i √5
Step-by-step explanation:
Use the formula
(b/2)^2
in order to create a new term. Solve for x by using this term to complete the square.
Hope this helps!
Find an equation for the line below. Please help!
Answers
Answer:
Step-by-step explanation:
y=1/3x-13/3
Okay so we have the points (1,-4) and (-5,-6).
Slope = (-6+4 ) / (-5-1)
Slope = -2/-6
Slope = 1/3
y=mx+b
m=1/3
Now let's take a point from the equation, and use the slope to determine b.
-4=1/3(1)+b
b=-4 1/3
Now let's combine our elements.
y=1/3x-13/3
The radius of a circle is 3 feet. What is the circle's area? Use 3.14 for .
Answers
Answer: [tex]A = 28.26 ft^2[/tex]
Step-by-step explanation:
The formula for the area of a circle is: A = π[tex]r^2[/tex]
We need to plug in the values from the question into the formula.
r = 3 feetuse 3.14 for π[tex]A = (3.14)(3)^2[/tex]
A = (3.14)(9)
A = 28.26
Don't forget the units! Since we found the area of the circle, we need to square the units.
[tex]A = 28.26 ft^{2}[/tex]
Laila wants to create a data display to clearly show the median salary, the highest
salary, and the lowest salary of the 685 employees at her company. She is trying to
decide whether she should create a dot plot, a box plot, or a histogram of the salaries.
A sample of the data is shown below.
$25,745; $26,512; $27,322; $27,750; $29,820; $32,500; $35,448; $52,020; $63,485; $87,167
Which graph should Laila choose? Explain your reasoning by completing the sentences. Click the
arrows to choose an answer from each menu.
A dot plot Choose...
A box plot
Choose...
A histogram Choose...
So Laila should create (
Choose.
to display the data.
Answers
A Histogram from the menu should be used.
What is a histogram?A histogram is a bar graph-like representation of data that buckets a range of outcomes into columns along the x-axis. The y-axis represents the number count or percentage of occurrences in the data for each column and can be used to visualize data distributions.
Given data is $25,745; $26,512; $27,322; $27.750; $29,820; $32,500; $35,448; $52,020; $63,485: $87,167
We know that Histograms are graphs that are preferred to determine any probability distribution of data. So, the Median, maximum value, and lowest value can be easily demonstrated in "Histogram graphs"
Thus, Histograms should be used.
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In the diagram below, what are AC and BC?
Answers
We can see here that AC and BC are:
AC = 5cm
BC = 3cm
What is triangle?A triangle is a three-sided polygon, and it is one of the basic shapes in geometry. In a triangle, three straight lines, called sides, are connected end-to-end to form the shape. The point where two sides meet is called a vertex, and there are three vertices in a triangle.
There are several types of triangles, each with their own specific properties. The most common classification of triangles is based on their side lengths.
An equilateral triangle is a triangle in which all three sides are of equal length.An isosceles triangle is a triangle in which two sides are of equal length.A scalene triangle is a triangle in which all three sides have different lengths.Using Sine Rule, we have:
[tex]\frac{a}{Sin A} = \frac{b}{Sin B}[/tex] where:
Sin A = Sin 30° = 0.5
Sin B = Sin 80° = 0.9848
a = x cm
b = 5cm
Thus, inserting the the above values into the Sine Rule equation, we have:
[tex]\frac{x}{0.5} = \frac{5}{0.9848}[/tex]
Cross-multiplying, we have:
0.9848x = 5×0.5
0.9848x = 2.5
∴ x = 2.5 ÷ 0.9848 = 2.538cm
≈ 3cm.
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A large mall conducted a survey to estimate how much money people planned to spend during the Christmas season. The survey included 5 questions asked of randomly selected shoppers between 10 AM and 4 PM on a weekday during the month of August. The survey estimate of $250 per shopper was much lower than the actual average of $400 spent per shopper from the previous Christmas season. Do you think this result reliably indicates that sales will be lower for the upcoming Christmas? Can you identify any other reason the $250 average is so far below the previous $400 figure?
Answers
August surveys may not adequately represent Christmas buyers' intentions. Surveying customers on a weekday between 10 AM and 4 PM may not capture the spending intentions of all demographic groups, resulting in a skewed sample.
It's also vital to consider economic situations, customer preferences, and promotional bargains when predicting consumer spending.
What is a survey?Generally, It is possible that the survey results do not accurately predict the actual spending during the Christmas season. Surveying shoppers in August, several months before the Christmas season, may not accurately reflect the shopping plans of consumers closer to the holiday. Additionally, surveying shoppers during a weekday and between the hours of 10 AM and 4 PM may not capture the spending plans of all demographic groups, potentially leading to a biased sample.
Another reason why the survey estimate of $250 is so far below the previous $400 figure could be due to the fact that the survey only asked 5 questions. This may not have been enough to gather enough information about the spending habits and intentions of the shoppers surveyed.
It's also worth noting that there are many different factors that can influence consumer spending, such as economic conditions, changes in consumer preferences, and the availability of promotional deals, so it's important to consider these other factors as well when trying to predict future spending.
In conclusion, the survey results do not provide a reliable indication of the sales for the upcoming Christmas. Without more information about the survey methodology and the results, it's difficult to determine the reasons for the discrepancy between the survey estimate and the actual spending from the previous Christmas season.
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Copy and complete the statement.
1. If HG = HK, then ____ = ____
2. If KHJ = KJH, then ____ = ____
Please add explanation as to why
Answers
Answer:
If HG = HK, then HG = HK. This statement is true by definition, as both sides of the equation are equal to the same value.
If KHJ = KJH, then KHJ = KJH. This statement is also true by definition, as both sides of the equation are equal to the same combination of letters.
a number k multiplied by 6 is greater than 11
Answers
Answer:
k should equal 2 and above
Step-by-step explanation:
A product of 6 is 12 which is 6 * 2 so therefore k should equal anything above 2
Choose the fraction that is equivalent to a terminating decimal between 0.25 and 0.50.
Multiple choice question.
A)
13
B)
49
C)
720
D)
1325
Answers
The fraction that is equivalent to a terminating decimal between 0.25 and 0.50 is given as follows:
C. 7/20.
How to convert a fraction to a decimal number?A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:
Fraction = x/y.
The terms that represent x and y are listed as follows:
x, which is the top term of the fraction, is called the numerator.y, which is the bottom term of the fraction, is called the denominator.Hence the conversion from fraction to decimal for each item in this problem is given as follows:
1/3 = 0.3333, which is a non-terminating decimal.4/9 = 0.4444, which is a non-terminating decimal.7/20 = 0.35, which is a terminating decimal between 0.25 and 0.50.13/25 = 0.52, which is a terminating decimal, however is not between 0.25 and 0.50.This means that the correct option is given by option C.
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What percent of the surface area of the ottoman is green? (Not including the bottom)? PLS HELP! :(
Answers
The required answer is,
Percentage of green = 37%.
What is surface area of a cylinder?The surface area of a cylinder can be defined as the total space covered by the flat surfaces of the bases of the cylinder and its curved surface.
A=2πrh+2πr2
r Radius
h Height
Here, we have,
Surface area of a cylinder = πr² + 2πr h
With r = 22 and h = (6 + 10) = 16
Area = π * 22² + 2 * π * 22 * 16
Area = 1520.728 + 2211.968
Area = 3732.696 in²
Now,
Percentage of green = surface area of green ÷ total surface area
Surface area of green = 2πr h
Surface area of green = 2 * π * 22 * 10
Surface area of green = 1382.48
Percentage of green = 1382.48 / 3732.696 * 100%
Hence, the required answer is,
Percentage of green = 37%
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Find the area of the shape.
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Answers
The area of the shape as shown in the diagram is 50.24 squared unit.
What is area?Area can be defined as the region bounded by a plane shape.
To calculate the area of the shape, we use the formula below.
Formula:
A = ∅πr²/360Where:
A = Area of the shaper = Radius of the circle the shape was formed fromπ = PieFrom the question,
GIVEN:
r = 8 ∅ = 90°π = 3.14Substitute these values into equation 1
A = 90×3.14×8²/360A = 50.24 squared unitHence, the area is 50.24 squared unit.
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10
Select the correct answer.
This rational inequality can be used to determine the number of seconds, x, that a beginning ice-skater can skate before losing his or her footing.
>13
If Charlene has never ice-skated before, which inequality describes the number of seconds she can expect to skate before losing her footing?
O A. 6>x>6.5
OB. x<6
O c. x<0
O D. 6
OE. x <6
Reset
Next
Answers
The solution of the given inequality is x<6.5. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is x/x-6 >13.
Multiply x-6 on both the sides of an inequality, we get
x>13(x-6)
x>13x-78
Add 78 on both the sides of an inequality, we get
x+78>13x
Subtract x on both the sides of an inequality, we get
78>12x
12x<78
x<6.5
Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
This rational inequality can be used to determine the number of seconds, , that a beginning ice-skater can skate before losing his or her footing. x/x-6 >13 If Charlene has never ice-skated before, which inequality describes the number of seconds she can expect to skate before losing her footing?
A. 6>x>6.5
B. x<6
C. x<0
D. x<6.5
E. x<6
Which expression is equivalent to
O
O
0443
O√45
112
314
2
2
?
Answers
Answer:
✓2^5
Step-by-step explanation:
use the concept of indixes.
so;
By the power rule;
= (2^1/2)^2 *(2^3/4)^2
=2*(2^3/2)
2^(1+3/2)
2^5/2
✓2^5.
The value of solution of the expression is,
⇒ [tex]\sqrt{2^{5} }[/tex]
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,
⇒ [tex](2^{1/2} * 2^{3/4} )^{2}[/tex]
Now, We can simplify as;
⇒ [tex](2^{1/2} * 2^{3/4} )^{2}[/tex]
⇒ [tex](2^{(5/4) } )^{2}[/tex]
⇒ [tex](2^{5/2} )[/tex]
⇒ [tex]\sqrt{2^{5} }[/tex]
Thus, The value of solution of the expression is,
⇒ [tex]\sqrt{2^{5} }[/tex]
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A city has a population of 370,000 people. Suppose that each year the population grows by 6.25%. What will the population be after 8 years? Round your answer to the nearest whole number.
Answers
Answer:
Step-by-step explanation:
6.25 X 8 = 50.000 then add 370,000 + 50.000 = 420,000
4(-p-3q)+9q-10(6q+3p)
Answers
Answer:
-34p-63q
Step-by-step explanation:
Simplify
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Combine like terms
Find the two values that would make the inequality true
Answers
An inequality's solution is a value that makes the inequality true. There are various ways to resolve an inequality.
What values make the inequality true?The solution set is the collection of all possible solutions to an inequality. The meaning of the symbol / is "is not greater than or equal to." A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics.
So inequality results from an imbalance. in order to demonstrate that substituting one or more variables into an inequality or equation "works out". This means that the equation or inequality can be reduced to a true statement.
A number sentence proves that two numerical expressions are equal. When two numerical expressions are equivalent, a number sentence is said to be true (that is, both evaluate to the same number). Otherwise, it is alleged to be false.
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A gardener has a rectangular flowerbed. The length of the flowerbed is 5 feet more than the width. The perimeter of the flowerbed is 70 feet. Which equation can be used to find the width w in feet
Answers
Answer:
75 = 4w
Step-by-step explanation:
Let w = width
Let w + 5 = length
Let p = perimeter ( Perimeter is given: 70 ft. )
Write the formula to find the perimeter of a rectangle
p = 2 ( l + w )
Sub the numbers in
70 = 2 [(w+5) + (w)]
Simplify the equation
70 = 2 (2w + 5)
70 = 4w + 5
75 = 4w
Chang added some chlorine to the water in the pool . The chlorine evaporated at a fixed rate every week. The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks
Answers
The function that best shows the relationship between n and f(n) is;
f(n) = 24(0.5)ⁿ⁻¹
How to solve function tables?The function table below that shows the amount of chlorine is;
n 1 2 3 5
f(n) 24 12 6 3
Where f(n) is the amount in ounces, that was left in the pool after n weeks:
We can see that the value of f(n) is decreasing as n increases from the table.
Due to the fact that f(n) does not have common difference. Let us attempt tp see if it has a common ratio;
12/24 = 0.5
6/12 = 0.5
3/6 = 0.5
Using the formula for the nth term of a geometric progression is;
aₙ = arⁿ⁻¹
Where;
a represents the first term = 24
r represents the common ratio = 0.5
Thus, the equation of the function is;
f(n) = 24(0.5)ⁿ⁻¹
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Assuming the pattern continues, what is S12 for the series
−6 − 14 − 22 − 30 − …?
A. -608
B. -600
C. -564
D. -94
Answers
Answer:
-600 is the sum of the arithmetic SERIES till [tex]S_{12}[/tex]
Step-by-step explanation:
Since this is a SERIES you would use the finite arithmetic SERIES formula
which is [tex]S_{n} = \frac{n}{2} (2a_{1} +d(n-1))[/tex]
[tex]S_{12} = \frac{12}{2} (2(-6) + -8(12-1))[/tex]
[tex]S_{12} = 6(-12 + -8(11))[/tex]
[tex]S_{12} = 6(-12 + -88)[/tex]
[tex]S_{12} = 6(-100)[/tex]
[tex]S_{12} = 600[/tex]
Therefore, the sum of the SERIES would be -600. Hope this helps!
Determine the value of b.
b3 = 64
b = 21.3
b = ±21.3
b = 4
b = ±4
Answers
Answer:
b = 4
Step-by-step explanation:
b^3=64
3√b = √64
b = 4
Answer:
b = 4
Step-by-step explanation:
In what time will a sum of
money double itself at 9% per
year if interest is calculated
annually?
Please explain step by step to help me understand and be able to do this on my own in the future
Answers
It will take 9 years to double the money at 9% per annum
What is Compound Interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given:
let P = 100
Interest = 100
Apply formula of interest
Interest= (P x R x T) ÷ 100
100= (100x 9 xT )÷100
T= 11.11 years
In case of annually compounded interest let us assume that Rs 100 to[tex](1.09)^ 9 =(1.09)^T[/tex] become 200 . Apply formula
A=P[tex](1+R/100)^T[/tex]
200=100 [tex](1+9/100)^T[/tex]
200=100 [tex](109/100)^T[/tex]
2 = [tex](109/100)^T[/tex]
[tex](1.09)^ 9 =(1.09)^T[/tex]
On Comparing
T= 9 years.
Hence, It will take 9 years.
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A school band has `70` students.
`50\%` of them are sixth graders, `30\%` are seventh graders, and the rest are eighth graders.
How many band members are 6th graders and how many are 7th grader
Answers
7th - 21 members
Answer:
Step-by-step explanation: Half of 70 is 35 so there are 35 Sixth-grader and then you do 70 multiplied by 30% and get 21
10 pints is equal to how many quarts?
Answers
10 pints is equal to 5 quarts.
Given that there are 10 pints.
We need to convert pints to quarts.
To convert pints to quarts, we need to keep in mind that there are 2 pints in 1 quart.
Given that we have 10 pints, we can divide this value by 2 to obtain the equivalent amount in quarts:
10 pints / 2 pints per quart
= 5 quarts
Therefore, 10 pints is equal to 5 quarts.
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I need to see the steps to the question. I see the answer but, I am still confused, the question is: What is the future value of a $1,000 annuity payment over six years if interest rates are 10%/
Answers
The future value of the $1000 annuity payment is $7,715.61.
What is the future value?An annuity is when a series of payment is made over a period of time. The future value of the annuity would be a function of the amount deposited each year, the interest rate earned and the duration of the investment.
Future value = Quarterly deposit x annuity factor
Annuity factor = (1 + r)^n] - 1} / r
Where:
r = interest rate n = number of periods = 6Future value = 1000 x [{(1 + 0.1^(6} - 1 ] / 0.1 = $7,715.61
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4000 times 73 plus 42 minus 34 equals what? I need help
Answers
Answer:
Step-by-step explanation:
1st. 4000x73+292000
2nd. 292000+42+292042
3rd. 292042-34=292008
Tiana shares a granola bar with her brothers. They each get one piece of the bar. What fraction names one part?
Answers
The fraction that names one part of the granola bar shared by Tiana and her 3 brothers is c. 1 / 4.
How to find the fraction ?Tiana has 3 brothers and they all shared a piece of the granola bar. This means that the number of people who shared the granola bar is:
= Tiana + 3 brothers
= 4 people
With each of them getting a piece of the granola bar, it means that the fraction that names one part of the bar is:
= Number of granola bars / Number of people
= 1 / 4
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The full question is:
Tiana shares a granola bar with her 4 brothers. They each get one piece of the bar. What fraction names one part?
1 / 21 / 81 / 41 / 32. In the computer lab, there are 2 PC for every 10 Mac computers. If the computer lab has a total of 24 computers,
how many are Macs?
Answers
Step by Step:
We have a ratio here, 2 PC for every 10 Mac, so the ratio can be written as 2:10
Which is simply comparing the number of pc(2) to the number of macs(10), next with the ratio 2:10 we take the total amount of devices which is 12 in this ratio( 2 PC and 10 Macs) then u write it as 2/12:10/12.. so in 12 computers 2 are pc and 10 are mac.. in the next case we have 24 computers so it’s the double of 12 so double macs and double pc.. So 20 Mac and 4 PC
The scenes and the graph relate to the reaction of X₂(g) (black) with Y₂(g) ( orange ) to form XY(g).
(a) If reactants and products are in their standard states, what quantity is represented on the graph by x?
(b) Which scene represents point 1? Explain. (c) Which scene represents point 2 ? Explain.
Answers
The point that is marked X on the graph is the standard free energy of the reaction.
What is the standard free energy of the reaction?Let us note that when we talk about the standard free energy of the reaction what we mean here is the energy of the reaction that is free to be able to do work. In the case of the standard change in the free energy, we are looking at the change of the free energy of the standard states of the substance.
The graph as we have it is trying to show the reaction profile and the reaction profile would give the difference between the free energy of the products and the reactants and this is the standard change in free energy.
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