*******ASAP******The coordinate plane below represents a city. Points A through F are schools in the city.
graph of coordinate plane. Point A is at 1, 3. Point B is at 3, 1. Point C is at 3, negative 3. Point D is at negative 4, 2. Point E is at negative 1, 5. Point F is at negative 3, negative 3.
Part A: Using the graph above, create a system of inequalities that only contains points B and C in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.
Part B: Explain how to verify that the points B and C are solutions to the system of inequalities created in Part A.
Part C: Lisa can only attend a school in her designated zone. Lisa's zone is defined by y > 2x + 5. Explain how you can identify the schools that Lisa is allowed to attend.
Answers
Answer:
Part A: We have the points A = ( 1,3 ) , B = ( 3,1 ) and C = ( 3,-3 ).
We will first find the equation of line AB and AC.
Now, the slope of AB is .
So, substituting in y = mx + b along with the point ( 1,3 ) gives,
3 = -1 + b i.e. b = 4.
So, the equation of AB is y = -x + 4.
Further, slope of AC is .
Again, substituting in y = mx + b along with the point ( 1,3 ) gives,
3 = -3 + b i.e. b = 6
So, the equation of AC is y = -3x + 6.
Using 'zero test', we get that,
y = -x + 4 gives 0 = 4, which is not true.
y = -3x + 6 gives 0 = 6, which is not true.
Hence, the solution region will be away from the origin as shown in the figure 1 below.
Thus, we get the system y>-x+4 and y>-3x+6 containing point B and C.
Part B: We have the equations y = -x + 4 and y = -3x + 6.
Substitute the points B = ( 3,1 ) and C = ( 3,-3 ) into these equations respectively, we get,
y = -x + 4 gives y = -3 + 4 i.e. y = 1
y = -3x + 6 gives y = -3 × 3 + 6 i.e. y = -9 + 6 i.e. y = -3.
Hence, points B and C are the solutions of the system in Part A.
Part C: After plotting y>2x+5, we ca see from the second figure that the points included in the shaded region are D = ( -4,2 ) and E = (-1, 5).
So, Lisa is allowed to attend the schools D and E.
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Stamps = 100, Postcards = 40
100 x 0.41 cents + 40 x 0.26 cents = $41 + $10.4 = $51.4
------ Solution-----
$0.41 x STAMPS + $0.26 x POSTCARDS = $51.4
1 STAMP = 20 + 2 x POSTCARDS
$0.41 x (20 + 2 x POSTCARDS) + $0.26 POSTCARDS = $51.4
POSTCARDS = 40
STAMPS = 20 + 2 x 40 = 100
Answer:
Julie bought 40 postcards and 100 stamps.
Step-by-step explanation:
Write the equation by adding the total values of each item.
0.41 (2p+20)+0.26p = 51.40
We can solve this equation for p to find the number of postcards.
0.41(2p+20)+0.26p =51.40
0.82p+8.20+0.26p=51.40
1.08p=43.2
p=40
So, the number of postcards she bought is 40. Since the number of 41-cent stamps is 20 more than twice the number of postcards, the number of 41-cent stamps is 2(40)+20=100.
Answers
Explanation/Calculation:
You can clearly see that the white shapes are positive while the black shapes are negative. You can determine this because all (except F) claim that the 6 shapes are negative.
To make it easier, use elimination. It's definitely not J because you are not subtracting -6, but adding (as seen in the equation.) It is not F because 2(3)=6 when the equation needs -6.
So it is either G or H...
H claims that 12x+3+(-6) is what the model symbolizes; but this is incorrect. Unless x is a decimal, you can not have the large shape as the "purest" form (so to speak.) The "purest" state you can go in this model is a cube/square which=1.
Therefore, "G Jamey modeled 12 + 3x + (-6) and it is equivalent to 12x-3" is the correct answer.
Hope this helps you!
1. If we multiply by three the numerator of a fraction and add 12 to the denominator, the value of the fraction is three quarters, and if the numerator increases in 7 and the denominator trebles the value of the fraction is a way, finds the fraction.
Please I am grateful for them to him very much thank you for the given attention...:)
Answers
y - denominator
Answers
x equals negative four sevenths
x = −2
x = 2
Answers
An equation is formed of two equal expressions. The solution of the equation 6(3x + 4) = 4x − 4 is x=-2.
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for the equation is,
6(3x + 4) = 4x − 4
18x + 24 = 4x - 4
18x - 4x = -24 - 4
14x = -28
x = -2
Hence, the solution of the equation 6(3x + 4) = 4x − 4 is x=-2.
Learn more about Equation:
#SPJ2
Answer:
x = - 2
Step-by-step explanation:
Given
6(3x + 4) = 4x - 4 ← distribute parenthesis on left side
18x + 24 = 4x - 4 ( subtract 4x from both sides )
14x + 24 = - 4 ( subtract 24 from both sides )
14x = - 28 ( divide both sides by 14 )
x = - 2
Answers
If Thomas drew a rectangle with an area of 6 than the perimeter is 10.
Work
3 (length) * 2 (width)= 6 (area)
length- 3+3 and width 2+2=10
So, (3*2)+(2*2)= 10
In conclusion, the perimeter is 10.
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