What is the solution to the inequality?
Express yourself in interval notation.
Answers
Answer:
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \frac{20}{23}\:\\ \:\mathrm{Decimal:}&\:x\ge \:0.86956\dots \\ \:\mathrm{Interval\:Notation:}&\:[\frac{20}{23},\:\infty \:)\end{bmatrix}[/tex]
Step-by-step explanation:
[tex]-\frac{2}{3}\left(2x-\frac{1}{2}\right)\le \frac{1}{5}x-1[/tex]
Expand [tex]-\frac{2}{3}\left(2x-\frac{1}{2}\right)\le \frac{1}{5}x-1[/tex] [tex]-\frac{4}{3}x+\frac{1}{3}[/tex]
[tex]-\frac{4}{3}x+\frac{1}{3}\le \frac{1}{5}x-1[/tex]
[tex]\mathrm{Subtract\:}\frac{1}{3}\mathrm{\:from\:both\:sides}[/tex]
[tex]-\frac{4}{3}x+\frac{1}{3}-\frac{1}{3}\le \frac{1}{5}x-1-\frac{1}{3}[/tex]
[tex]Simplify[/tex]
[tex]-\frac{4}{3}x\le \:-\frac{4}{3}+\frac{1}{5}x[/tex]
[tex]\mathrm{Subtract\:}\frac{1}{5}x\mathrm{\:from\:both\:sides}[/tex]
[tex]-\frac{4}{3}x-\frac{1}{5}x\le \:-\frac{4}{3}+\frac{1}{5}x-\frac{1}{5}x[/tex]
[tex]Simplify[/tex]
[tex]-\frac{23}{15}x\le \:-\frac{4}{3}[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-\frac{23}{15}x\right)\left(-1\right)\ge \left(-\frac{4}{3}\right)\left(-1\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\frac{23}{15}x\ge \frac{4}{3}[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}15[/tex]
[tex]15\cdot \frac{23}{15}x\ge \frac{4\cdot \:15}{3}[/tex]
[tex]Simplify[/tex]
[tex]23x\ge \:20[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}23[/tex]
[tex]\frac{23x}{23}\ge \frac{20}{23}[/tex]
[tex]\mathrm{Simplify}[/tex]
Hence the final answer is [tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \frac{20}{23}\:\\ \:\mathrm{Decimal:}&\:x\ge \:0.86956\dots \\ \:\mathrm{Interval\:Notation:}&\:[\frac{20}{23},\:\infty \:)\end{bmatrix}[/tex]
Related Questions
A circular flower bed is 17 m in diameter and has a circular sidewalk around it that is 3 m wide. Find the area of the sidewalk in square meters. Use 3.14 for π.
Answers
Step-by-step explanation:
A-a
A=3.14x10x10
=314m^2
a=3.14x8.5x8.5
=226.865m^2
=314-226.865
=87.135m^2
. Mr. Donut wants to paint a donut on the wall of his restaurant. The diameter of the outside edge of the donut will be 22 inches. The area of the hole of the donut will be 78.5 square inches. How much area will need to be painted if only the donut needs to be painted? Use 3.14 for π.
Answers
Answer:
The area needed to be painted is approximately 301.44 square inches.
Step-by-step explanation:
The shape of a donut is represented by two concentrical circles, whose area is described by the following formula:
[tex]A =A_{g}-A_{s}[/tex] (Eq. 1)
Where:
[tex]A[/tex] - Total area of the donut, measured in squared inches.
[tex]A_{g}[/tex] - Area of the greater circle, measured in square inches.
[tex]A_{l}[/tex] - Area of the lesser circle, measured in square inches.
By using the definition of the area of the circle, we expand the equation above:
[tex]A = \frac{\pi}{4}\cdot D^{2}_{ext} - A_{s}[/tex] (Eq. 1b)
If we know that [tex]\pi = 3.14[/tex], [tex]D_{ext} = 22\,in[/tex] and [tex]A_{s} = 78.5\,in^{2}[/tex], the area needed to be painted is:
[tex]A = \frac{(3.14)\cdot (22\,in)^{2}}{4}-78.5\,in^{2}[/tex]
[tex]A \approx 301.44\,in^{2}[/tex]
The area needed to be painted is approximately 301.44 square inches.
The first week, there were 10 students in a teacher’s classroom. The next week, there were 13 students in the same teacher's classroom. What is the percent increase of the number of students?
Answers
Answer:
130% increase
Step-by-step explanation:
A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied at least one hour for the test. The remaining twelve students admitted that they had not studied for the test at all. The test results (expressed as a percent) for the two groups are shown below.
Studied :
87
,
100
,
94
,
79
,
92
,
100
,
95
,
83
,
89
,
99
,
100
,
91
,
89
,
95
,
100
,
93
,
96
,
83
Did Not Study :
82
,
72
,
45
,
91
,
58
,
83
,
65
,
87
,
90
,
77
,
73
,
89
Part 1: Calculate the mean of the group that studied, rounded to the nearest tenth.
Part 2: Calculate the mean absolute deviation of the group that studied, rounded to the nearest tenth.
Part 3: How many of the scores (from the group that studied) are within one mean absolute deviation of the mean.
Answers
Step-by-step explanation:
part1
the mean value is
(87+100+94+79+92+100+95+83+89+99+100+91+89+95+100+93+96+83) / 18
= 1665 / 18 = 92.5
part2
this is the sum of the absolute value of the differences bergen the individual sites and the mean value divided by the number of data points :
(5.5+7.5+1.5+13.5+0.5+7.5+2.5+9.5+3.5+6.5+7.5+1.5+3.5+2.5+7.5+0.5+3.5+9.5)/18
= 94/18 = 5.222222222... ≈ 5.2
part3
how many scores are less than 5.2 away (plus or minus) from the mean value ? in other words, how many differences in the part2 calculation were smaller than or equal to 5.2 ?
there are 9 scores meeting that criteria :
94, 92, 95, 89, 91, 89, 95, 93, 96
Suppose line segment XY has one endpoint at X(0,0). If (3,4) is the midpoint of XY, what are the coordinates of point Y?
Answers
Midpoint (3,4)
Y (6,8)
Write an explicit formula for an, the n
term of the sequence 38, 44, 50,....
Answer: an =
Answers
The sequence 38, 44, 50,.... is an arithmetic sequence
The explicit rule of the sequence is an = 32 + 6n
How to determine the explicit formula?The sequence 38, 44, 50,.... is an arithmetic sequence with the following parameters:
First term, a1 = 38
Common difference, d = 6
The explicit rule is calculated as:
an = a1 + (n - 1) * d
This gives
an = 38 + (n - 1) * 6
Evaluate the product
an = 38 - 6 + 6n
This gives
an = 32 + 6n
Hence, the explicit rule of the sequence is an = 32 + 6n'
Read more about arithmetic sequence at:
https://brainly.com/question/6561461
find the slope of the line whose angle of inclination is 60
Answers
Answer:
Slope (m) = tanθ
=tan60
=√3
Hence the slope is √3
I think it will help you
In January, a store sold 3 scarves for $14.10. In March, it sold 5 scarves for $22.90. In which month did a scarf cost the least?
Answers
In January, a store sold 3 scarves for $14.10.
so 1 scarf = 14,10 : 3 = $4,7
In March, it sold 5 scarves for $22.90.
so 1 scarf = 22.90 : 5 = $4.58
In which month did a scarf cost the least?
in march
Which is the equation of the function?
f(x) = 3]x] + 1
f(x) = 3x - 11
f(x) = (x + 1
f(x) = 1 |x-11
Answers
Answer:
4
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Brayden and his cousin Kayla live twenty miles away from each other. On the same day, Brayden recorded 1.046 inches of rain at his house and Kayla recorded 1.062 inches of rain at her house. Whose house received fewer inches of rain that day?
Answers
ZA and 23 are supplementary angles. If m
ZB = (4x + 3)º, then find the measure of ZA.
Answers
Answer:
Since they are supplementary angles which add up to 180 degrees the measure of ZA must be 157 degrees.
Step-by-step explanation:
HALP!!!!!!!!!!! brainiest for first answer!
Answers
Answer:
1. no
no because 2:3 is not equal to 3:22.50
2. Yes
the constant proportionality is 3=4.35
Step-by-step explanation:
How much do
Jennie sam if she
got 340 for
Babysitting, plus a
15% tip
Answers
First determine 15% of 340. Multiple 15 (as decimal) by 340.
0.15 x 340 = 51
Find the total amount she earns by adding these values.
51 + 340 = 391
Therefore, she will make $391.
the awenser is three
hundred and fifty five dolars
Look at the photo attached number 36
Answers
Answer:
a. Check Mark
b. Check Mark
c. No Check Mark
d. No Check Mark
e. No Check Mark
Step-by-step explanation:
1 hour = 60 minutes
1/4 X 60 min = 15
9 pages every 15 minutes
9 X 4 = 36
36 pages in an hour
what is the answer? does anyone like maths because I don't?
Answers
Answer:
8 cm
Step-by-step explanation:
Th smaller rectangle is a scaled down version of the bigger rectangle. The smaller rectangle is 1/2 the size of the large one.
So we will multiply 4 by 2 to get 8 cm
Your correct answer is 8 cm :)
Hope this helps!
Please rate and mark brainliest!!
Have a great day!!
Answer:
the ratio of rectangle 1 the same with rectangle 2 so as you see in the photo the area of rectangle 2 equal 4×2 which we find it obviously of similar ratio
How do you know a table is linear?
How do you know an equation is linear?
How do you know a graph is linear?
Answers
Answer:
You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear.
An equation is considered linear, if it is in the form of. y = mx + b. where m is the slope of the equation, and b is the y-intercept.
First of all the shape of the graph is a straight line. Every linear graph is nothing more than a straight line so if there is any curves in it, it's not linear. The other way to tell is look at its equation.
Step-by-step explanation:
Please help me! there is a picture
Answers
Answer:
B
Step-by-step explanation:
½=20*x
x=½*1/20
x=1/40
Evaluate 100−x^2 , when x is 6 *
Answers
Answer:
64
Step-by-step explanation:
100-6^2
6^2=36
100-36=64
Hope this helps :)
what is 8 times 7..................
Answers
Answer: the answer is 56
Step-by-step explanation: its 56 because if you multiply 8 times 5 you get 45 then add 8 to 45 you get 48 now add 8 to 48 you 16 carry the 1 over tje 4 you get 56
Yee yee yee
Find the value of x.
A.
74°
53°
Answers
Answer:
74
Step-by-step explanation:
Melissa went for a drive in her new car. She drove at a speed of 25.6 miles per hour for 2 hours. For how many miles did she drive?
Answers
Answer:
51.2 miles
Step-by-step explanation:
25.6 x 2= 51.2
WILL GIVE BRAINLIEST IF CORRECT PLEASE ANSWER!!!!!
Christian wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box. If all the triangles are equilateral, how much wrapping paper did he use, in square inches?
Answers
The amount of wrapping paper he use is 62.4 square inches
How to calculate the surface area of a prismThe formula for calculating the total surface area is expressed as:
Area = 4(area of triangle)
Find the area of the triangle
A = 0.5(6)(5.2)
A =3(5.2)
A = 15.6 square inches
TSA = 4(15.6)
TSA = 62.4 square inches
Hence the amount of wrapping paper he uses is 62.4 square inches
Learn more on total surface area here: https://brainly.com/question/1297098
What is the value of w?
Answers
Answer:
37°
Step-by-step explanation:
angles in a triangle add up to 180 degrees.
if two sides have the same length, an isosceles triangle is formed. the angles corresponding to the sides that have the same length are the same therefore, as FH = HG, ∠HFG = ∠FGH
180° = ∠HFG + ∠FGH + ∠FHG
= 106° + ∠HFG + ∠HFG
= 106° + 2* ∠HFG
subtract 106 from both sides to isolate the unknown and its coefficient
74° = 2*∠HFG
divide both sides by 2 to isolate the unknown
37° = ∠HFG = ∠FHG = w
Joel has a vintage comic book worth $360. According to a dealer, the value of this particular comic book will increase by 5% each year. How much will the comic book be worth in 15 years?
Answers
The worth of the comic in 15 years is $784.41.
What is the worth of the comic?If the value of the comic is increasing it means it is appreciating in value. As a result of the appreciation, the price of the comic increases with the passage of time.
FV = P (1 + r)^n
FV = Future value P = Present value R = interest rate N = number of years$360 x (1.05)^15 = $784.41
To learn more about future value, please check: https://brainly.com/question/18760477
Answer:
The final answer is 748.41
Step-by-step explanation:
i need this now asap
Answers
Answer:
141.3
Step-by-step explanation:
π x 6 (3 + 4.5
I really need answers for this
Answers
Answer:
1. [tex]-tan (x)[/tex]
2[tex]-san(x)[/tex]
3. [tex]cos (x)[/tex]
4. [tex]tan (\pi +3)[/tex]
Step-by-step explanation: May God bless you and your family during spring break
Maria invests £4500 in a savings account for 3 years.
The account pays simple interest at a rate of 1.8% per year.
Work out the total amount of interest Maria gets by the end of the 3 years.
Answers
Answer:
Rm243
Step-by-step explanation:
Rm4500 × 0.018 × 3
=Rm243
Please mark as brainliest;)
Answer:
243
Step-by-step explanation:
(4500*1.8*3)/100
=243
A pair of designer sneaker was purchased for $120. Since they were purchased, their price has increased by 15%. What is the new price?
Answers
Answer:
$138
Step-by-step explanation:
120x1.15=$138
Answer this, please!
Help!!!
Answers
Answer:
It is 45.8° because it is a straight line so straight line is 180°.
In ΔABC, If AB=BC and ∠B=40∘,what is the measure of ∠C?
Answers
Answer:
70
Step-by-step explanation:
all angles in a triangle add up to 180
if two sides are equal their angles are equal
180-40
140÷2
70