Answers
As a single inequality, we can write the solution of the given compound inequality as → x ≥ 8.
What are two types of inequalities?There are two types of inequalities -
Strict inequalities : The inequalities that have < or > symbol between the L.H.S and R.H.S.
Slack inequalities : The inequalities that have ≤ or ≥ symbol between the L.H.S and R.H.S.
Given in the question are two inequalities as mentioned below -
-2x - 3 < -1 and -2x - 3 ≤ -11
In this question → -2x - 3 < -1 is a strict inequality and -2x - 3 ≤ -11 is a slack inequality. We will solve them one by one.
Inequality - 1
- 2x - 3 < - 1
Add 3 on both sides -
- 2x - 3 + 3 < - 1 + 3
- 2x < 2
Multiply by -1/2 on both sides -
x > - 1
Inequality - 2
-2x - 3 ≤ -11
Add 3 on both sides -
-2x ≤ -8
Multiply by -1 on both sides -
2x ≥ 8
Divide by 2 on both sides -
x ≥ 8
Now, we have two inequalities -
x > - 1 and x ≥ 8
We can write it as one equality -
x ≥ 8
Therefore, as a single inequality, we can write the solution of the given compound inequality as → x ≥ 8.
[Graph is attached at the end]
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Related Questions
What is the x-value of the solution of
x + y = 7 , 3x - 2y = 11 ?
Answers
The x-value of the solution of x + y = 7 , 3x - 2y = 11, is equal to 5.
The given equations are linear equations in two variables since there are two unknown variables present in these equations.
Considering equation number one to be, x + y = 7
and equation number two to be, 3x - 2y = 11
By rearranging the first equation, the value of x can be considered to be:
x + y = 7
x = 7 - y
Adding this value of x in the second equation for the solution of y;
3 (7 - y) - 2y = 11
21 - 3y - 2y = 11
Rearranging,
21 - 11 = 3y + 2y
10 = 5y
y = 10 ÷ 5
y = 2
By adding this value of y to the first equation, the value of x can be found as follows,
x + y = 7
As y = 2
x + 2 = 7
x = 7 - 2
x = 5
Hence, the value of x is calculated to be 5.
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Question content area top
Part 1
Solve the compound inequality
Answers
Answer:
It's C
Step-by-step explanation:
Trust me bro
Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.
(-2,6),(0,2),(1,0)
Answers
Using the definition of slope, the points (-2 , 6), (0 , 2), and (1 , 0) are collinear.
Three or more points are said to be collinear if they lie on a single straight line.
To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.
m = (y2 - y1)/(x2 - x1)
Getting the slope of each pair of points:
(-2 , 6) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - 6)/(0 - -2)
m = -4/2
m = -2
(0 , 2), and (1 , 0)
m = (y2 - y1)/(x2 - x1)
m = (0 - 2)/(1 - 0)
m = -2/1
m = -2
(-2 , 6) and (1 , 0)
m = (y2 - y1)/(x2 - x1)
m = (0 - 6)/(1 - -2)
m = -6/3
m = -2
Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is equal with each other, then they are collinear.
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need help in factorization
Answers
Hence , on factorization given equation 2x² + 5xy/3 - 2y² gives ( 2x + 3y)(3x -2y) .
Factorisation of AN algebraical expression means that writing the given expression as a product of its factors.We have given an equation 2x² + 5xy/3 - 2y² .
On simplification , we get
2x² + 5xy/3 - 2y² = 0
6x² + 5xy - 6y² = 0
By splitting in the middle term , we can write 5xy as ( 9 - 4 ) xy
6x² + (9xy - 4xy ) - 6y² = 0
( 6x² + 9xy ) - (4xy + 6y²) = 0
3x ( 2x + 3y) - 2y (2x + 3y ) = 0
( 2x + 3y)(3x -2y) = 0
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Factor each expression that can be factored. For an expression that cannot be factored into a product of two binomials, explain why. x²+2 x+1 .
Answers
The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
⇒ x² + 2x + 1
Factorize the expression, then the factor of the expression will be
⇒ x² + x + x + 1
⇒ x(x + 1)x + 1(x + 1)
⇒ (x + 1)(x + 1)
⇒ (x + 1)²
The product of two binomials will be (x + 1) and (x + 1).
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Cadence went to the amusement park and paid $14.25 for a souvenir refill cup. Refills cost $1.25 each. If Cadence spent a total of $23, how many refills did she get?
Answers
Answer:
Cadence had gotten 7 refills.
Step-by-step explanation:
$14.25 + $1.25r = 23$
23 - 14.25 = 8.75
8.75/1.25 = 7
r = 7
I just need help with this problem and more!! 3. What is the perimeter of the figure shown below, which is not drawn to the scale?
Answers
Answer:
8x+12
Step-by-step explanation:
To find the Perimeter, we need to add all 4 sides together. In this case, we would do:
x+4+x+4+3x+2+3x+2
Now, we have to combine like terms.
x+x+3x+3x=8x.
4+4+2+2=12
The final answer would be 8x+12 or 12 +8x.
You can put whichever answer you want because it doesn't matter.
Hope this helps!
:D
Suppose an MP3 player cost 499 in 2003 and 249.99 in 2009 .
b. Based on the data, how much does the price drop per year?
Answers
Per year price drop is -41.50$
The cost of an MP3 player in the year 2003 is = $ 499
The cost of an MP3 player in the year 2009 is = $ 249.99
The price drop per year will be –
We need to subtract the base year price from that of the current year price and divide that by the difference between the base year and the current year
The year that serves as the standard against which subsequent values are measured is referred to as the base year.
The term "current year" refers to the fiscal year that has already begun but has not yet completed its cycle.
So,
(499-249.99) / (2003-2009)
249.01 / -6 = -41.50 $
Hence per year price drop is -41.50$
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PLS!!!! Read the following excerpt.
The poison arrow frog, which resides in the tropical forests of South America, has enough toxicity on its skin that a dart rubbed across the surface of the body can kill a small mammal.
Which of the following sentences uses an ellipsis correctly?
1 "The poison arrow frog … has enough toxicity on its skin … "
2 "The poison arrow frog … has enough toxicity on its skin that a dart rubbed across the surface can kill a small mammal."
3 "The poison arrow frog, which resides in the tropical forests of South America … has enough toxicity on its skin that a dart rubbed across the surface of the body can kill a small mammal."
4 "The poison arrow frog, which resides in the tropic forests of South America, … that a dart rubbed across the surface of the body can kill a small mammal."
Answers
Answer:
"The poison arrow frog... has enough toxicity in its skin that a dart rubbed on the surface can kill a small mammal.
Step-by-step explanation:
An ellipsis is a punctuation mark that indicates the interruption of thought and has great power of suggestion. They are also used, for example, in interrupting a character's speech.
The sentence which uses ellipsis correctly is: "The poison arrow frog ... has enough toxicity on its skin ... ".
As per the passage, which defines the ellipsis, that the poison arrow frog who resides in the tropical forest of the South America has enough toxicity on its skin that a dart rubbed across the surface of the body which can kill a small mammals.
The given passage is a missing punctuation marks which defines the ellipsis. In this the thoughts are in the interruption face as well as in the power of suggestion. In this, the suggestions are very important because it is killing the mammals which are resided at the surface.
What is ellipsis?
Ellipsis has number of dots in a sentences or a phrase which define the intention of a passage as well as author. It is also called as punctuation marks with three dots.
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Rachel found this rate of change for the scenario represented in the table
What can you conclude from her work? Check all that apply
Answers
THE FUNCTION IS CONTINOUS - True
We see from the table that for every hour given, there will be a value of juice (cups). The graph would have been a linear graph between the time 4 hours and 8 hours with no jump or holes in the chart.
TIME REPRESENTS THE DEPENDANT VARIABLE - False
Time is the independent variable as it does not depend on any other value. The number of cups, on the other hand, depends on the number of hours, hence is a dependent variable
THE SCENARIO IS REPRESENTED BY
A LINEAR FUNCTION, SINCE THE RATE OF CHANGE, IS CONSTANT - True
The rate of change is 53 cups per hour, hence the function is linear.
AS THE AMOUNT OF TIME CONTINUES, THERE ARE FEWER CUPS OF JUICE POURED PER HOUR - False
The rate of change is a positive value, hence the number of cups poured per hour will increase
FOR EVERY ADDITIONAL HOUR, 53 CUPS OF JUICED IS POURED - True
The difference between the number of cups poured hourly is a constant of 53
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Much a
5. The box plot represents the distribution of the
number of points scored by a cross country team
at 12 meets. (Lesson 1-2)
22 24 26-28 30 32 34 36 38 40-42-
Points
a. If possible, find the mean. If not possible, explain why not.
b. If possible, find the median. If not possible, explain why not.
34
c. Did the cross country team ever score 30 points at a meet?
Answers
a. Frequency is not displayed on a box plot, so it is impossible to find the mean.
b. The median = 34.
c. It is difficult to determine by looking at the box plot.
How to Determine the Median of a data Distribution From a Box Plot?A box plot is a graphical display of the five-number summary of a data which includes the upper and lower quartiles, the maximum and minimum data points, and the median which is at the point where the vertical line divides the box.
In a box plot, the measure of center that can easily be determined is the median value, which lies between the upper and lower quartiles. The box plot doesn't show the frequency of each data point which makes it difficult to calculate the mean of the data.
a. It is impossible to find the mean using a box plot as frequency for each data is not displayed.
b. The median = 34.
c. It is difficult to tell if the cross country team scored exactly 30 points at a meet by mere looking at the box plot.
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-2= 6/7x please help me
Answers
Here are two similar pentagons which make up a badge.
width - 3x cm & length - 27cm - large badge
width - x cm & length - (x+3)cm - small badge
Work out the width of the badge.
Answers
Answer: 6
Step-by-step explanation:
3x ÷ x = 3
27 ÷ 3 = 9
9 = x + 3
x = 6
I don't which one is the width so I just assume the smaller badge side x cm is the width
Can someone help me!?
Answers
Byron agrega una cantidad de 17 / 80 kilogramos por cada pimentero. (Opción correcta: D)
¿Cuánta pimienta pone Byron en cada pimentero?
En este problema debemos interpretar y emplear fracciones para encontrar una cantidad determinada, así como saber utilizar operaciones para obtener el resultado deseado y elegir la opción correcta entre las cuatro disponibles.
Byron tiene 17 / 10 kilogramos de pimienta negra y distribuye equitativamente siete octavas partes de esa pimienta en siete pimenteros. En consecuencia, la cantidad por pimentero es igual a siete octavas partes de la cantidad dispuesta por Byron y dividida a su vez por la cantidad de pimenteros:
x = [(7 / 8) × (17 / 10 kg)] / 7
x = (119 / 80 kg) / 7
x = 17 / 80 kg
Byron agrega una cantidad de 17 / 80 kilogramos por cada pimentero. (Opción correcta: D)
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0.5(3.34+10)9 how do I answear this?
Answers
30.06+90
120.06
0.5(120.06)
=60.06
Answer:
Step-by-step explanation:
1). You would add the numbers inside of the parenthesis first this would give you (13.34) inside of the parenthesis.
2). You equation should look like 0.5(13.34)9 now then you would multiply the 0.5 to the number inside of the parenthesis and you will have (6.67)9 now.
3). Lastly you will multiply the 6.67 to the 9 and you will get 60.03 as your final answer.
I need help with this please asap
Answers
Answer:
|Least percentage = |32% - 5%| = 27%
Greatest percentage = |32% + 5%| = 37%
Step-by-step explanation:
|Percentage who favor ± error
At a school recess, there needs to be a ratio of 2 adults for every 24 children on the playground. how many adults are needed if there are 72 children? *
Answers
Answer: 6
Step-by-step explanation: 2=24 4=48 6=72
11 m
The figure shows a diver diving from a platform. The diver reaches a depth of 4 meters. What is the change in elevation of the diver?
The change in the elevation of the diver is meter(s).
Sorry ik the pic is blurry
Answers
The diver's elevation changes by 15 meters.
The diver is initially stopped at a height of 11 meters.
After that, he leaps, falling 11 meters, causing an initial elevation drop of 11 meters.
Finally, he descends to a depth of 4 meters, or 4 meters below the surface of the water, adding 4 more meters to the elevation change (11 + 4 = 15).
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
You may calculate the angle of elevation, for instance, by standing on the ground and looking up at the peak of a mountain. For instance, you can determine the angle of elevation by standing on the ground and gazing up at a mountain's peak.
Therefore, making the diver's elevation change 15 meters.
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Question is down below, please answer only if you know :)
Answers
Answer: b:180
Step-by-step explanation: since it 100% cant be A:90 or d:360 it could be c: 270 but after i looked up that angle, no not at all. so the only one that makes since is b:180
What is a simpler form of 2/x -5 / 6/x - 3} ?
(A) 2-5 x / 6-3 x
(B) 2+5 x / 6-3 x
(C) 2x - 5 / 6 x+3
(D) 6 + 3x / 2 - 5 x
Answers
The simpler form of given fraction 2/x -5 / 6/x - 3 is (2 - 5x)/(6 - 3x)
The correct answer is an option (A)
In this question,
we have been given a rational function 2/x -5 / 6/x - 3
We need to simplify given fraction.
2/x -5 / 6/x - 3
= [(2/x) - 5] / [(6/x) - 3]
= [(2 - 5x) / x] / [(6 - 3x) / x]
= (2 - 5x) / (6 - 3x)
Therefore, the simpler form of given fraction 2/x -5 / 6/x - 3 is: (2 - 5x) / (6 - 3x)
The correct answer is an option (A)
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Choose the true statement.
-2/3 = -3/4
-2/3 > -3/4
-2/3 < -3/4
Answers
Out of these equations and inequalities, -2/3 > -3/4 is the true statement.
What is an mathematical statement?Briefly, A mathematical statement is a sentence that is either true or false. It may include words and symbols. "The square root of 4 is 5" is an example of a mathematical statement (which is, of course, false).
We use language in mathematics in a very precise way that is sometimes slightly different from everyday use. We'll start by talking about some common disagreements.
In everyday language, we say "either A or B" to mean that one of the two options is correct but not both.
And therefore out of these equations and inequalities
-2/3 = -3/4
-2/3 > -3/4
-2/3 < -3/4
The true statement is -2/3 > -3/4
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URGENTT, PLS PLS ANSWER QUICKLY!!!!!!!
In the first half football season, Marco ran 4 plays for a gain of 60 yards. During the second half of the season, Marco was responsible for 6 penalties resulting in a loss of 80 yards. What was his total yardage for his football season?
Answers
Marco ran 4 plays for a total of 60 yards throughout the first half of the football season. Marco committed 6 penalties that cost his team 80 yards in the second half of the season. His total 160 yardage for his football season.
Given that,
Marco ran 4 plays for a total of 60 yards throughout the first half of the football season.
Marco committed 6 penalties that cost his team 80 yards in the second half of the season.
We have to calculate his total season yardage in football.
In the 1st half of the football season, Marco ran 4 plays for a total of 60 yards.
4[tex]\times[/tex]60=240
In the 2nd half of football season, Marco committed 6 penalties that cost his team 80 yards.
That is.
240-80=160
Therefore, his total 160 yardage for his football season.
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Write a proof of the following.
Theorem 4.9 (Hint: Use the Pythagorean Theorem.)
Answers
There are above and beyond 371 Pythagorean Hypothesis confirmations, initially gathered and put into a book in 1927, which incorporates those by a 12-year-old Einstein (who utilizes the hypothesis twenty years after the fact for something about somewhat), Leonardo da Vinci and Leader of the US James A.
What is the definition of Pythagorean theorem?In science, the Pythagorean hypothesis, or Pythagoras' hypothesis, is a basic connection in Euclidean math among the three sides of a right triangle. It expresses that the region of the square whose side is the hypotenuse is equivalent to the amount of the region of the squares on the other different sides.
The Pythagorean equation be a² + b² = c²
a be the side of right triangle
b be the side of right triangle
c be the hypotenuse
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5. (a) A surveyor found that a rectangular playground is 20 m long and 13 m wide, corrected to the nearest metre. Suppose the actual length of the playground is x m and the breadth is y m. Write down an inequality for the range of the values of
(i)x
(ii) y
Answers
Length of the rectangular playground =(b+2)
Area of rectangular playground = Length × Breadth
⇒195=(b+2)×b
⇒195=b
2
+2b
⇒b
2
+2b−195=0
⇒b
2
+15b−13b−195=0
⇒b(b+15)−13(b+15)=0
⇒(b−13)(b+15)=0
⇒b=13 or b=−15
Value b of can't be negative. So b=13
Therefore, breadth of the rectangular playground =13 m
and length of the rectangular playground =15 m
Rosie ate 2 1/2 bananas on Saturday. On Sunday she ate 1/2 as many bananas as she ate on Saturday. How many bananas dod Rosie eat over the weekend?
Answers
Answer:
0.5
Step-by-step explanation:
because 1/2=0.5 jgxuydiyxiyxit ugxutx itxutx itxugx
2.5+1.25=3.75
Mark had been watching the calories he consumes each day. On the first day, he consumed 1500 calories, then 1450 calories the next day, and 1400 calories the day after that .
Answers
Answer:
His calories go down 50 calories every day. Hope it helps!
Step-by-step explanation:
Stella is using her compass and straightedge to complete a construction of a polygon inscribed in a circle. which polygon is she in the process of constructing? a circle is drawn with five arc markings that lie on the circle, with an additional point also marked on the circle. a regular octagon a square a regular pentagon a regular hexagon
Answers
The polygon is a regular hexagon.
Stella is using a compass and a straight edge to construct a polygon inscribed in a circle.
Also the circle is drawn with five arc markings that lie on the circle. Also there is an additional point marked on the circle.
So there are in total 6 points on the circle. Also the lines joining these five points will be equal. So we will get a regular hexagon through this construction.
The following is the process of construction.
First she starts at a point on the circle placing the compass there. Then she will measure the radius of the circle on compass. Fixing this distance, she will draw an arc on the circle. The process is repeated by placing the compass on the new point obtained on the circle.
So in total she will get the 6 vertexes of the regular hexagon. Joining the adjacent points, a regular hexagon is inscribed inside the circle.
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Answer: A regular hexagon
What is the equation?
Answers
Answer:
Slope-intercept form: y=3x-5
Step-by-step explanation:
The slope is 3 and the y-intercept is -5. We plug those in for m and b, respectively.
Some two-step equations can be written in the form ax + b = c, where a, b, and c are constants and x is the variable. a. Write the equation ax + b = cin terms of x. b. Use the formula to solve 3x + 7 = 19 and x-1=5.
Answers
a. the equation of the formula in terms of x is: x = (c - b)/a
b. x = 4 and x = 6
How to Solve an Equation?Where we have a, b, and c as constants of the equation, ax + b = c, and the variable is x, we can solve for the value of x as shown below:
ax + b = c
Subtract b from both sides
ax - b = c - b
ax = c - b
Divide both sides by a
ax/a = c/a - b/a
x = c/a - b/a
x = (c - b)/a
b. 3x + 7 = 19
a = 3, b = 7, and c = 19
Substitute a = 3, b = 7, and c = 19 into x = (c - b)/a
x = (19 - 7)/3
x = (12)/3
x = 4
x - 1 = 5
a = 1, b = -1, and c = 5
Substitute a = 1, b = -1, and c = 5 into x = (c - b)/a
x = (5 - (-1))/1
x = 6/1
x = 6
In summary, we have:
a. the equation of the formula in terms of x is: x = (c - b)/a
b. x = 4 and x = 6
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Evelyn has completed 5/12 of her ELA class essay. Evaluate this value as a decimal. SHOW YOUR WORK here using long division. please
Answers
Evaluating 5/12 a decimal gives 0.4166666666....≈ 0.4167
Given data
5/12 of her ELA class essay
How to rewrite to decimal using long division5 / 12 is same as 12 dividing 5
this is done as follows
12 | 5
we form the decimal in the answer column then add 0 to 5 to get 50
12 | 50 0.
12 | 50 0.4 50 - (12 * 4 )= 50 - 48 = 2
12 | 2 0.4
add 0 to 2 to get 20 and divide by 12
12 | 20 0.41 20 - ( 12 * 1 ) = 20 - 12 = 8
add 0 to 8 to get 80 and divide by 12
12 | 80 0.416 80 - ( 12 * 6 ) =80 - 72 = 8
add 0 to 8 to get 80 and divide by 12
12 | 80 0.4166 80 - ( 12 * 6 ) =80 - 72 = 8
The procedure is repeated to get 0.4166666666....≈ 0.4167
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