Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > −4x − 1
y is less than 3 over 2 times x minus 1
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (−1, −1) included in the solution area for the system? Justify your answer mathematically. (4 points)
Answers
Answer:
Part A: The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.
Part B: No, the point (-4,6) is not included in the solution area for the system.
Step-by-step explanation:
System of inequalities:
(1) y > 2x + 3
(2) y < -(3/2)x - 4
Part A
1) The first inequality represents the region over the line:
y=2x+3
This is a linear equation and its graph is a right line. We must graph the right line, and then shadow the area above this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:
x=0→y=2(0)+3→y=0+3→y=3; Point=(x,y)→Point=(0,3)
x=1→y=2(1)+3→y=2+3→y=5; Point=(x,y)→Point=(1,5)
1) The second inequality represents the region below the line:
y= -(3/2)x - 4
This is a linear equation and its graph isaright line. We must graph the right line, and then shadow the area below this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:
x=0→y=-(3/2)(0)-4→y=0-4→y=-4; Point=(x,y)→Point=(0,-4)
x=2→y=-(3/2)(2)-4→y=-3-4→y=-7; Point=(x,y)→Point=(2,-7)
The two lines intersect at the point (-2,-1). The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.
Part B
No, the point (-4,6) is not included in the solution area for the system, because this point is not below the right line y=-(3/2)x-4
Part A: The purple region in the graph attached below is the solution to the given inequalities.
Part B: (-1,-1) is not included in the solution area for the system of inequalities.
In mathematics, inequalities specify the connection between two non-equal expressions.
Given the following information:
1) y > −4x − 1
2) y is less than 3 over 2 times x minus 1, this can be expressed in inequality as follows:
[tex]y < \dfrac{3}{2}x-1[/tex]
Part A:
Attaching image to describe the graph of the system with shaded area.
The red colored region corresponds to the solution of inequality of line 1)
The blue colored region corresponds to the solution of inequality of line 2)
Thus, purple colored region corresponds to the common region due to the 2 lines.
Part B:
To check whether (-1,-1) is included in the solution area for the system:
Plot the point(-1,-1) of it falls in the purple shaded region then it wll be the solution. From the graph, it is clear that point lie outside the shaded region. Thus, (-1,-1) is not the solution.Mathematical justification:
Substituting (-1,-1) in eq1)
-1>-4(-1)-1
-1>3
This is false as -1 is less than 3.
Substituting (-1,-1) in eq2)
-1<3(-1)/2-1
-1<-3/2-1
-1<-5/2
-1<-2.5
This is also false as -1 is greater than -2.5
Thus, it is justified that (-1,-1) is not included in the solution.
Learn more about inequalities, here:
https://brainly.com/question/32788654
#SPJ4
Related Questions
use the subtraction property of equality to complete the following statement if RS + St = RT then RS =
Answers
RS = RT - ST
Just you know one value you so make a problem with subtraction equal it.
a sporting goods manufacturer requires 3/8yd of fabric to make a pair of soccer shorts. how many shorts can be made from 9yds of fabric
Answers
State whether each percent of change is a percent increase or a percent decrease. Then find the percent of increase or decrease . Round to the nearest whole percent
Original : $100
New : $59
Answers
percent change= (new-old)/old *100
= -41 % the negative means decreasing
Tia kayaked 2400 meters at a constant rate in 1.5 hours on Saturday. On Sunday, she kayaked 200 meters per hour faster. What was Tia’s average rate on Sunday? A. 1600 meters per hour B. 1800 meters per hour C. 2000 meters per hour D. 2200 meters per hour
A.
3
B.
5
C.
15
D.
30
Answers
Sunday rate =1800
Answer:
1800
Step-by-step explanation:
What's the distributive property for 16+48
Answers
so with 16 + 48, to show the distributive property, you could divide by any common factor of 16 and 48. some correct ways to do this are:
16 + 48 = 2(8 + 24)
16 + 48 = 4(4 + 12)
16 + 48 = 8(2 + 6)
16 + 48 = 16(1 + 3)
you're just dividing 16 and 48 by the outside term to get the 2 numbers in the ( )
what is the measure of jl
Answers
A. 64
32 is the measure of JKL. By multiplying 32 by 2 you will get 64 which is the measure of JL
After m months, the height of a plant is 10+3m millimeters. How tall is the plant after 8 months? 3 years?
Answers
After 8 months, the plant is 34 millimeters tall, and after 3 years (36 months), it's 118 millimeters tall.
To find the height of the plant after 8 months and 3 years, let's first understand the pattern. The height is given by the equation ( 10 + 3m ), where ( m ) represents the number of months.
Height after 8 months:
Substituting ( m = 8 ) into the equation:
[tex]\( \text{Height} = 10 + 3(8) \)[/tex]
[tex]\( \text{Height} = 10 + 24 \)[/tex]
[tex]\( \text{Height} = 34 \)[/tex] millimeters.
Height after 3 years (36 months):
Substituting ( m = 36 ) into the equation:
[tex]\( \text{Height} = 10 + 3(36) \)[/tex]
[tex]\( \text{Height} = 10 + 108 \)[/tex]
[tex]\( \text{Height} = 118 \)[/tex] millimeters.
So, after 8 months, the plant is 34 millimeters tall, and after 3 years (36 months), it's 118 millimeters tall.
4. An angle of 200° is a/an _______ angle.
Answers
Angles under 90° are called acute angles
Angles that are 90° are called right angles
Angles that are between 90° and 180° are called obtuse angles
Angles that are 180° are called straight angles
Angles that are between 180° and 360° are called reflex angles.
An angle of 200° is a/an reflex angle.
Hope This Helps You!
Good Luck :)
- Hannah ❤
thanks hope this helps
Eleanor can drive an average of 374 miles on one tank of gas. How many miles can she drive on 15 tanks of gas?
Answers
Help me please I need better grades
Answers
_______________________________________________________
Question 1: The answer is: " [tex] \frac{1}{6}[/tex] " .
_______________________________________________________
Question 2: The answer is: " -12.8 ".
_______________________________________________________
Question 3: The answer is: " 12.3 " .
_______________________________________________________
Explanation:
_______________________________________________________
Question 1:
_______________________________________________________
(-4/3) − (-3/2) = [tex] \frac{-4}{ 3} [/tex] + [tex] \frac{3}{2}[/tex] ;
→ The least common multiple (LCM) of the numbers "2" and "3" (which are the numbers in the denominators) is: "6" ; so we can convert each fraction value to the equivalent fraction with a denominator of "6" ;
→ [tex] \frac{-4}{3} [/tex] = [tex] \frac{?}{6} [/tex] ;
→ What value is the "?" ? ; → Look at the denominators.
→ (3 * ? = 6); → (6÷3 = 2).
→So; [tex] \frac{-4}{3} [/tex] = [tex] \frac{-4*2}{3*2} [/tex] ;
= [tex] \frac{-8}{ 6} [/tex] ;
_______________________________________________________
→ Now; → [tex] \frac{3}{2} [/tex] = [tex] \frac{?}{6} [/tex] ;
→ What value is the "?" ? ; → Look at the denominators.
→ (2 * ? = 6); → (6÷2 = 3).
→So; [tex] \frac{3}{2} [/tex] = [tex] \frac{3*3}{ 2*3} [/tex] ;
= [tex] \frac{9}{6} [/tex] ;
_______________________________________________________
Now, we can rewrite the problem:
________________________________
→ [tex] \frac{-8}{ 6} [/tex] + [tex] \frac{9}{ 6} [/tex] ;
= [tex] \frac{-8+9}{6}[/tex] ;
= [tex]\frac{1}{6} [/tex] .
_______________________________________________________
Question 2:
_______________________________________________________
" -3.9 − 8.9 " = - (3.9 + 8.9) = - 12.8 .
_______________________________________________________
Question 3:
_______________________________________________________
" 2.9 − (-9.4) " = 2.9 + 9.4 = 12.3 .
Note: Subtracting a negative number is "adding a positive number".
_______________________________________________________
The ratio of boys to girls in the school chorus is 3:2. If there are 39 boys in the chorus, how many girls are in the chorus?
A) 36 girls
B) 26 girls
C) 24 girls
D)58 girls
Answers
Answer:
The answer is 36 girls because 3:2 is 13x3 which equals 39 and 12x3=36. The ratio is 39 boys to 36 girls.
Not 26 girls.
What is 45.99 pounds rounded to the nearest tenth of a pound
Answers
What is −12÷23 ?
−36
−24
−18
−8
Answers
-12 / 23 = -0.52
so none of those are the correct answer.
if the 23 is suppose to be the fraction 2/3
then you have -12 / 2/3 which = -12 * 3/2 = -36/2 = -18
Answer:
hello your answer is -36
Step-by-step explanation:
1. 12 = 12/1 so we keep the first number then2. we change the division sign to times 3. flip the second number 2/3 is turned to 3/2 then multiply so 12/1 x 3/2 is 36/2 hope this helps have a nice day !
the parabola y=x^2 is shifted up by 4 units
Answers
[tex]f(x) = x ^{2} + 4[/tex]
By rigid transformations, the image of the parabola y = x² is equal to parabola y = x² + 4.
How to determine the image of a parabola
In this problem, we need to determine the image of a parabola by means of a rigid transformation known as vertical translation:
y = f(x) → y = f(x) + k, where k represents a translation upwards and f(x) is the original function.
If we know that f(x) = x² and k = 4, then the image of the function is:
f(x) = x² + 4
To learn more on rigid transformations: https://brainly.com/question/28004150
#SPJ3
Justine draws a square with an area of 150 square centimeters. What is the approximate length, in centimeters, of one side of the square? -2 cm -11 cm -12 cm -13 cm
Answers
This comes to s = 12.247 cm. Round that off to 12.2 cm or even 12 cm.
The approximate length is 12 centimeters, of one side of the square which is the correct answer would be an option (C).
What is the square?A square is a closed two-dimensional object with four equal-length sides and all interior angles of exactly 90 degrees.
The diagonal of the square is the distance between two vertices on opposing sides. A square has two diagonals of equal length.
We have been given that Justine draws a square with an area of 150 square centimeters.
The area of the square = (length of the side)²
150 square centimeters = (length of the side)²
Length of the side = √(150)
Length of the side = 12.24744
Rounded the nearest hundredth and we get
Length of the side = 12.24 centimeters
Therefore, the approximate length is 12 centimeters, of one side of the square.
Learn more about the area of the square here:
brainly.com/question/15287805
#SPJ5
4/9x+1/5x=87 what is x
Answers
20/45x + 9/45x = 87
Combine like terms.
29/ 45x = 87
Multiply both sides by 45/29
x = 3,915 / 29
x = 135
Hope this helps!
Answer:
The value of x is 135.
Step-by-step explanation:
Given : Expression [tex]\frac{4}{9}x+\frac{1}{5}x=87[/tex]
To find : What is the value of x?
Solution :
Expression [tex]\frac{4}{9}x+\frac{1}{5}x=87[/tex]
Take LCM,
[tex]\frac{4x\times 5+x\times 9}{9\times 5}=87[/tex]
[tex]\frac{20x+9x}{45}=87[/tex]
[tex]\frac{29x}{45}=87[/tex]
[tex]x=\frac{87\times 45}{29}[/tex]
[tex]x=135[/tex]
Therefore, The value of x is 135.
A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?
Answers
Find the GCF of 22ab 2 c 2 and 40a 3 c 2.
4a 3b 2c 2
2ab 2c 2
4ac 2
2ac 2
Answers
The Greatest Common Factor of 22ab2c2 and 40a3c2 is 2ac2, found by identifying the highest power of each variable and number that divides the coefficients 22 and 40.
Explanation:When finding the Greatest Common Factor (GCF) we need to look for the highest power of each variable and number that appears in all the terms. In the terms 22ab2c2 and 40a3c2, the GCF will consists of the highest power of each variable found in both terms, and the highest number that divides both 22 and 40.
To find the GCF you need to divide both 22 and 40 by common factor. The highest number that divides 22 and 40 is 2. For the variables, the lowest power of 'a' and 'c' in both terms is a and c2, respectively. 'b' is not in both terms, so we omit it. So, the GCF of 22ab2c2 and 40a3c2 is 2ac2.
Learn more about Greatest Common Factor here:https://brainly.com/question/29584814
#SPJ12
In the year 2005, a total of 750 fish were introduced into a manmade lake. The fish population was expected to grow at a rate of 8.3% each year. What will the fish population be in 2050? Round to the nearest whole number. Enter your answer in the box.
Answers
Let t be the number of years after 2005.
Let F be the fish population.
F = 750(1.083)^t
In this case, t = 45 (2050 - 2005 = 45)
F = 750(1.083)^(45)
= 27123.255...
Round to the nearest whole number.
F = 27123
That's the expected population in 2050.
Have an awesome day! :)
8.3% = 0.083, the growth rate
Let n = the number of years, counted from 2005.
Let a(n) = the number of fish after n years.
When n=1, a(1) = 750*1.083
When n=2, a(2) = 750*1.083²
When n=3, a(3) = 750*1.083³
Therefore, after n years, a(n) = 750*1.083ⁿ
The number of years between 2005 and 2050 is 2050-2005 = 45
Therefore in the year 2050, the number of fish will be
a(45) = 750*1.083⁴⁵ = 27123.26
We cannot have fractional fish, so a(45) =27123.
Answer: 27123
How many 4-digit numbers can you write if you cannot use any other digits except 0, 1, and 2?
Answers
There are 54 possible 4-digit numbers that can be created using only the digits 0, 1, and 2, considering that the first digit cannot be 0 and each position has a limited selection of digits.
Explanation:To determine the number of 4-digit numbers that can be written using only the digits 0, 1, and 2, we must take into account that a 4-digit number cannot start with 0, which leaves us two choices for the first digit (either 1 or 2). For the subsequent three digits, we have three choices each (0, 1, or 2). Therefore, the total number of 4-digit combinations is obtained by multiplying the number of choices for each digit's position.
The explanation you provided is correct, and the calculation is accurate. There are indeed 54 possible 4-digit numbers that can be created using only the digits 0, 1, and 2, considering the given conditions.
To summarize:
- The first digit has 2 possible choices (1 or 2).
- Each of the next three digits has 3 choices (0, 1, or 2).
So, the total number of 4-digit combinations is obtained by multiplying the number of choices for each digit's position:
\[2 \times 3 \times 3 \times 3 = 54.\]
Therefore, there are 54 possible 4-digit numbers that can be created following the given conditions.
The first digit has 2 possible choices, and each of the other three positions has 3 choices, which gives us a total of:
2 × 3 × 3 × 3 = 54 possible 4-digit numbers using the digits 0, 1, and 2.
What could be the intersection of plane PRS and plane QRS?
A.
RS
←
→
B.
PR
←
→
C.
QS
←
→
D.
The planes need not intersect.
Answers
plz help!
The line segment is reflected about the y-axis to form A'B'. Which statement describes A'B'?
A'B' is half the length of AB.
A'B' and AB are equal in length.
A'B' is greater than twice the length of AB.
A'B' and AB are perpendicular.
Answers
A $1, $5, $10, $20, $50, or $100 bill is mapped to all the sets of coins that are the same as the total value of the bill.
IS THIS SITUATION A FUNCTION OR NOT???
Answers
Please help, need as soon as possible
Answers
(-3.1-(-6.2))=3.1, but -1.55-3.1 is not 3.1, showing that that is not arithmetic. For the last one, 3-(-3)=6, 9-3=6, etc. proving that you add 6 every time and the sequence is therefore arithmetic.
How do you write 81/50 as a percentage?
Answers
1.62x100=162
=162%
hope this helps
si tenemos que tenemos una escala de 1 a 100%
A pronghorn antelope can travel 105 miles in 3 hours if it continues traveling at the same speed, how far could it travel in 11 hours?
Answers
you find average speed with distance/time
average speed is 35 mph
if you multiply is by 11 you get your answer which is 385 miles
during a football game, kevin gained 5 yards on the first play. then he lost 7 yards on the second play. how many yard does kevin need on the next play to get the team back to where when they started? show your work.
Answers
So to get back to 5 you need to first make the number positive so you will need to gain 2 points first making it equal . So then you need to get 5 more points to make it 5 .
So to sum it up I made the number positive when doing that your making it zero so then all you have to do is add the option Reginald number back in so here's my work
5-7= -2 -2 + 2= 0 0+5=5
Ps please rate me if u can
Mr. Venn knows that 60% of his students will score no more than 5 points above or below the class average,75% on the test.
Write an inequality that represents the test scores of 60% of his students?
Answers
Answer:
[tex]70\leq x\leq 80[/tex]
Step-by-step explanation:
Let x represent the test scores of 60% of his students.
We have been given that Mr. Venn knows that 60% of his students will score no more than 5 points above or below the class average,75% on the test.
We will use tolerance formula to solve our given problem.
[tex]|\text{Actual}-\text{Ideal}|\leq\text{Tolerance}[/tex]
[tex]|x-75|\leq5[/tex]
Using rule [tex]|u|\leq a[/tex], then [tex]-a\leq u\leq a[/tex], we will get:
[tex]-5\leq x-75\leq5[/tex]
[tex]-5+75\leq x-75+75\leq5+75[/tex]
[tex]70\leq x\leq 80[/tex]
Therefore, the inequality [tex]70\leq x\leq 80[/tex] represents the test scores of 60% of Mr. Venn's students.
SIMPLE QUESTION PLEASE HELP :(
Solve for all roots of the equation. Show all work for full credit. x3 + 216 = 0
Answers
1.1 Factoring: x3-216
Theory:
A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check: 216 is the cube of 6
Check: x3 is the cube of x1
The solution to the equation x³ + 216 = 0 is x = -6, by subtracting 216 from both sides and taking the cube root.
Explanation:To solve the equation x³ + 216 = 0, you must first isolate the variable on one side of the equation. To do this, we can subtract 216 from both sides, giving us the equation x³ = -216.
Next, to solve for x, we need to take the cube root of -216. The cube root of -216 is -6, so x = -6 is the root of the equation.
In conclusion, the solution to the equation x³ + 216 = 0 is x = -6.
Learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ2
John is calculating 6 % tax on an item in a store. He means to multiply the price of the item by 0.06, but he accidentally divides by 0.06. His answer is
a) correct
b) too small
c) too large
d) undefined
Please help me i need the answer!!