Step-by-step explanation:
graphing.
substitution method.
elimination method.
We will use as an example the following system of inequalities:
3x +2y ≥ 5x -4
y < (1/2)x +3
For each inequality, do the following:
1. If it is not this way already, arrange the inequality so that each variable appears on only one side of the inequality. Putting the inequality into any of the standard forms will do this. It will be helpful later if you arrange the inequality so that at least one variable has a positive coefficient. (You may have to multiply by -1 (and change the sense of the inequality) to do this.)
Our example inequalities are now ...
-2x +2y ≥ -4 . . . . . or divide by 2 to get . . . . -x +y ≥ -2
y < (1/2)x +3
2. Notice the inequality symbol, and whether it includes the "or equal to" case.
the first inequality is ≥, so includes "or equal to"
the second inequality is <, so does not include "or equal to"
3. Replace the inequality symbol with an equal sign and graph the resulting equation. If the "or equal to" case is included, the line is graphed as a solid line. If it is not, then the line is graphed as a dashed line.
the first equation (-x +y = -2) is graphed with a solid line
the second equation (y = (1/2)x +3) is graphed with a dashed line
4. It is not necessary, but is less confusing, to choose a variable in the inequality (after step 1) that has a positive coefficient. Notice whether this variable is "less than" or "greater than" the stuff on the other side of the inequality.
y ≥ . . . . for the first inequality
y < . . . or . . . x > . . . . for the second inequality
If it is less than, shade the portion of the graph below (for y <) or to the left (for x <) of the line you graphed in step 3.
the second inequality has y < , so the graph will be shaded below the dashed line. It also has x > , so will be shaded to the right of the dashed line. (These are the same shading.)
If it is greater than, shade the portion of the graph above (for y >) or to the right (for x >) of the line you graphed in step 3.
the first inequality has y ≥ , so the graph will be shaded above the solid line.
5. The solution set is where the shaded areas overlap. Any point on a dashed line is not in the solution set.
_____
The graph for the example inequalities is attached. The first one is graphed and shaded in red; the second one is graphed and shaded in blue.
A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.
Three methods of solving inequalities are the graphing method, substitution method, and elimination method.
What is inequality in math?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
We will use as an example the following system of inequalities:
3x +2y ≥ 5x -4
y < (1/2)x +3
For each inequality, do the following:
If it isn't already set up this way, organize the inequality so that each variable only appears on one side. This can be accomplished by putting inequality into any of the accepted formats. If you set up the inequality so that at least one variable has a positive coefficient, it will be useful later. To accomplish this, you might need to multiply by -1 (and alter the inequality's sense).
Our example inequalities are now ...
-2x +2y ≥ -4 . . . . . or divide by 2 to get . . . . -x +y ≥ -2
y < (1/2)x +3
Take note of the inequality sign and whether the "or equal to" instance is present.
The first inequality is, so "or equal to" is included. The second inequality is, so "or equal to" is not included.
Create a graph of the equation that results from replacing the inequality symbol with the equal sign. The line is graphed as a solid line if the "or equal to" scenario is present. If not, a dashed line is used to represent the line on the graph.
Graphing the first equation (-x + y = -2) using a solid line
Graphing the second equation (y = (1/2)x + 3) uses a dashed line.
Choosing a variable in the inequality that has a positive coefficient after step one is not required, but it is less ambiguous. If there is an inequality, pay attention to whether this variable is "less than" or "greater than" the items on the other side.
For the initial inequality, y
In the case of the second inequality, y or x >
Shade the area of the graph below (for y) or to the left (for x) of the line you graphed in step 3 if it is smaller than.
The graph will be darkened below the dashed line since the second inequality has the value y. It will be tinted to the right of the dashed line because it also has x >. The shading here is the same.
Shade the area of the graph above (for y >) or to the right (for x >) of the line you graphed in step 3 if it is bigger than.
The graph will be shaded above the solid line because the first inequality has y.
The overlap of the colored areas is the solution set. The solution set does not include any points on a dashed line.
When the lines are parallel, a system cannot have a solution. If you get a false statement after solving the system (a number that is equal to a different number), there are no solutions.
Learn more about inequalities here:
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plz help me answer step by step 2+7/x=-12
Answer:
x = -1/2
Step-by-step explanation:
First, subtract 2 from both sides to get 7/x alone. Then muliply both sides by x to get rid of 7/x's denominator. Divide both sides by -14 to get rid of x's coefficient and to get x alone. You will then get -1/2 as your answer.
2 + 7/x = -12
-2 -2
7/x = -14
*x *x
7 = -14x
÷-14 ÷-14
- 1/2 =x
x = -1/2
I NEED HELP ASAP DUE IN 3 MINUTES WHOEVER ANSWERS IT RIGHT GETS BRIANIST
Answer:
It is D.
Step-by-step explanation:
what is decending order
Descending order is a list of numbers starting at the highest value going to the lowest. For example 10, 8, 5, 2, 1, -1, -4.
5(x+3)-3x^2 when x is -1.4
Answer:
The answer would be C.) 2.12
Examine the figure below.
B
(4x-16)
6756
(5x+7)
с
A
D
Determine which of the following angle measures are correct. Select all that apply.
OmZBAC = 72°
O
m2BCD = 68°
Om ACB = 112°
m2ABC = 68°
mzBCD=108°
*see attachment for diagram
Answer:
✔️m<BAC = 72°
✔️m<BCD = 108°
Step-by-step explanation:
Given:
m<ABC = (4x - 16)°
m<ACB = (5x + 7)°
Find the numerical value of m<ABC, m<ACB, m<BAC, and m<BCD.
First we need to determine the value of x.
The ∆ given is an isosceles triangle with two equal sides, therefore, the angles opposite the two equal sides would also be equal.
Therefore:
(4x - 16)° + 2(5x + 7)° = 180° (sum of ∆)
Solve for x
4x - 16 + 10x + 14 = 180
Add like terms
14x - 2 = 180
Add 2 to both sides
14x = 182
Divide both sides by 14
x = 13
Find the measure of each angle by plugging in the value of x where necessary:
✔️m<ABC = (4x - 16)° = 4(13) - 16
m<ABC = 36°
✔️m<ACB = (5x + 7)° = 5(13) + 7
m<ACB = 72°
✔️m<BAC = m<ACB (both are base angles of the isosceles ∆, so they are equal)
Therefore,
m<BAC = 72°
✔️m<BCD = m<ABC + m<ACB (exterior angle theorem of a triangle)
m<BCD = 36 + 72 (Substitution)
m<BCD = 108°
Therefore, the angle measures that are correct are:
✔️m<BAC = 72°
✔️m<BCD = 108°
please help!!
Find the slope of the line. Enter your answer as
a number, fraction, or undefined. Reduce to
lowest terms where necessary.
Answer:
m = undefined
General Formulas and Concepts:
Algebra I
Vertical Line Test - Tells us if a graph is a functionVertical Lines - slopes are undefinedStep-by-step explanation:
If the slope m was equal to 0, then it would be a horizontal line rather than a vertical line.
Using the Vertical Line Test, we also know that the graph is not a function.
Usually a vertical line has an undefined slope, as x equals a certain number, and m = unknown.
Answer: It's undefined, because it's vertical
A man left his waiter a $10 tip that was 20% of his bill. How much was the man's bill?
Answer:
50
Step-by-step explanation:
Answer:
The bills total was 50$
Step-by-step explanation:
So 20% is equal to 10 dollars.In order to find out the total you need to reach 100% so 5 mulitplied by 20 is 100 so 10 multiplied by 5 is 50 therefore the bill was 50.
$290.00 marked up 65%
PLEASE HELP WAS DUE YESTERDAY
Answer:
478.5
Step-by-step explanation:
Hope this helps. Have a great winter break!
Answer:
Revenue: 478.50$
profit: 188.50$
Step-by-step explanation:
profit
markup = ------------
cost * 100%
hope this helped plz give brainliest if it helped and have a great day ((((:
Please help! Me and my bestie are both stuck on this. . .
Use table to solve the inequality 2x<2
Answer:
x>1
Step-by-step explanation:
Answer:
-2, 0, 2, 4, 6 these are the answers for the boxes and they are in order. solution x<1
Step-by-step explanation:
if you look at the box you will see that it says x and 2x at the bottom. The x at the top is the same as the one at the bottom. So they want you to multiply the number in the row of x by the number below x I hope this helps
Find the cube root of the fraction 27/512.
A 3/8
B -3/8
C Cannot be done
Answer: can't be done
Step-by-step explanation:
Answer:
The principal, real, root of:
27−−√3
=3
All roots:
3
−1.5+2.59807621i
−1.5−2.59807621i
27 is a perfect cube
I’ll mark you brainlist I’ll mark you brainlist
Answer:
The rate of change is 0 because 0/1=0.
Step-by-step explanation:
hope this helps
What is the value of 3/8 x - 4.5 when x =0.4
HELP ME PLZ I NEED TO GET THIS RIGHT
Answer:QR = 54
Step-by-step explanation:
help please !
-3 + x/3 = 15
What is x?
Answer:
x = 54
Step-by-step explanation:
Simplify both sides of the equation. Add 3 to both sides.Multiply both sides by 3.Answer:
x = 5
the correct answer is perpendicular I have not received
yes is 54 the correct answer
The points (-2, 4) and (1,r) lie on a line with slope 3. Find the missing coordinate r.
Answer:
-9
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
(r - 11)/(4 - (-1)) = (r - 11)/5
So, (r - 11)/5 = -4
r - 11 = -20
r = -9
I dont know wht
way you are doing this but hope it helps
7th grade
HELP MEEEE!
due today
Answer:
A.
Step-by-step explanation: Because as you see the dot is past the 2 and is on the third line out of 4, the 4th line is the next number.
The angles of a triangle are in an extended ratio of 5:7:3. What is the measure of the
largest angle?
Answer:
84°
Step-by-step explanation:
Let the measures of the triangle be 5x, 7x, 3x.
By interior angle sum postulate of a triangle.
5x + 7x + 3x = 180°
15x = 180°
x = 180°/15
x = 12°
7x = 7*12°= 84°
Measure of the largest angle = 84°
x-y=11 2x+ y=19 solve using elimanation
Answer:
the answer is [tex]x=10,\:y=-1[/tex]
Step-by-step explanation:
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.
hope this helps :)
If 3 pens cost $2, then how many can can you buy with $20
Answer:
30
Step-by-step explanation:
help me plzzzzzzzzzzzzzzzzz
Answer:
717,051
seven hundred seventeen thousand, fifty-one
Step-by-step explanation:
try putting 717,051 into it starting at the hundred thousands place so basically you would put in 7 and then go down one and put in 1 and so on
what's 2+2???????????:]
Answer:
4
Step-by-step explanation:
Plz help I’m getting timed
Answer:
38
Step-by-step explanation:
Answer:
38
Step-by-step explanation:
1-4 round down 5-10 round up
1/2x + 3/4 x = 5 - 2.5x
Answer: I don't know if you wanted it to be solved or re-written but the answer is x=4/3 and re-written is 3x=4
Which Equation represents a Non-Proportional relationship between X and Y?
A. y=x
B. y=7x
C. y= 2/3x -1
D. y=3x + 0
Answer: C
Step-by-step explanation:
proportional relationship will have an equation that goes through the origin (0,0)
The equation for C will not go through the origin because it has a y-intercept of -1 and the line will be going through (0,-1) instead of (0,0).
All the other equations will be going through the origin because they have no y intercepts.
Which point in the coordinate plane represents the number 7+5i in the complex plane?
Answer:
Pythagoras:
ρ
=
√
7
2
+
(
−
5
)
2
=
√
49
+
25
=
8.6
ASAP pls help me with this
Answer:
x = 20
Step-by-step explanation:
If A || B, then ∠2 should equal to ∠3 (Alternate angles).
3x - 10 = x + 30
Isolate like terms.
3x - x = 30 + 10
Evaluate like terms.
2x = 40
Find x.
x = 40 ÷ 2
x = 20
Answer:
x = 20.
Angles 2 and 3 are measured as 50 degrees.
Step-by-step explanation:
Angles 2 and 3 are congruent, meaning that they are equal.
Set the two equations equal to each other and solve for x.
3x-10=x+30 (subtract x from the left side and add 10 to the right. This gets the x's and the plain numbers on the same side of the equation)
2x=40 (Divide by 2)
x = 20
Check your work by plugging in 20 for x in each expression. If the two expressions are equal when you do so, then you know you've worked out the problem correctly.
Angle 2:
3(20)-10
60 - 10 = 50
Angle 3:
20 + 30 = 50
Both expressions equal 50 when plugging in 20 for x, so this is the correct answer.
what is 149866.37636 rounded as a whole number
Answer:
149866
Step-by-step explanation:
Hope this helps.
Answer:
149866.
This is because the '.3' part means that you do not have to round the '6' up.
HELP PLSSSSSS
Examine the figure below.
Determine which of the following angle measures are correct. Select all that apply.
Answer:
I believe the answer is A, C
HELP PLEASE ITS MY LAST QUESTION!!
Jonathan and his band want to record and sell CDs. The recording studio charges an initial set-up fee of $250, and it charges $6.00 to burn each CD.
a) Define the variables:
Let n = _______
Let C = _______
Answer:
N=CD C=2-3 sentance
Step-by-step explanation:
Charlie bought 2 3/4 pounds of pears for $0.76 per pound and 2 3/4 pounds of grapes for $1.40 per pound. How much money in dollars and cents did charlie pay for the pears and grapes.
Answer
Charlie paid $5.94
Step-by-step explanation:
0.76x2 3/4=2.09
1.40x2.75=3.85
3.85+2.09=$5.94