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3 years ago

To solve the equation 2x−3=3x−7 , Esin graphs the functions f(x)=2x−3 and g(x)=3x−7 on the same set of coordinate axes.

Mathematics

1 answer:

Alecsey [184]3 years ago

8 0

We have that

f(x)=2x−3
g(x)=3x−7

2x-3=3x-7-------------> 3x-2x=-3+7-------> x=4
find the value of f(x) or g(x) for x=4
f(x)=2x−3 -------> f(4)=2*4-3------> f(4)=5
the solution is the point (4,5)

using a graph tool
see the attached figure

statement

case a) The solution of the equation cannot be found graphically. Esin should solve the equation algebraically.
this is not correct

case b) The solution of the equation is the y-intercept of the linear equations.
this is not correct

case c)The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.
this is correct

case d) The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect
this is not correct

the answer is
case c) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

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The bakery will bake 600 butterscotch bread, 550 chocolate bread, and 1,000 coconut bread

Step-by-step explanation:

In order to answer the word problem question, we list the parameters as follows;

The number of bread types the bakery takes = 3 types of bread

The monthly cost of the bakery for baking the bread, C = RM 6,850

The number of bread loaves baked = 2,150

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The sale price of a chocolate bread = Rm 4.50

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The amount of monthly profit the bakery makes, P = Rm 2,975

Therefore, the total revenue of the company, R = C + P

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Let 'x', 'y', and 'z', represent the number of loaves of butterscotch, chocolate, and coconut bread the company bakes respectively

Then we get;

x + y + z = 2,150...(1)

2·x + 3·y + 4·z = 6,850...(2)

3·x + 4.5·y + 5·z = 9,825...(3)

Multiplying equation (1) by 2 and subtracting from equation (2) gives;

2·x + 3·y + 4·z - 2×(x + y + z) = 6,850 - 2 × 2,150 = 2,550

2·x - 2·x + 3·y - 2·y + 4·z - 2·z = 2,550

∴ y + 2·z = 2,550...(4)

Adding equation (1) to (2) and subtracting from (3) gives;

3·x - 3·x + 4.5·y - 4·y + 5·z - 5·z = 9,825 - (6,850 + 2,150) = 825

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y = 825/1.5 = 550

The number of loaves of chocolate bread baked, y = 550

From equation (4), we get;

550 + 2·z = 2,550

2·z = 2,550 - 550 = 2,000

z = 2,000/2 = 1,000

The number of loaves of coconut bread baked, z = 1,000

∴ From equation (1) x = 2,150 - (550 + 1,000) = 600

The number of loaves of butterscotch bread baked, x = 600.

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