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vazorg [7]
2 years ago
14

Tania has 56 liters of milk. She uses the milk to make muffins and cakes. Each batch of muffin requires 7 liters of milk and eac

h batch of cakes require 4 liters of milk. Let x be the number of batches of muffins and y be the number of batches of cakes that Tania can make. Which of the following graphs best shows all the possible number of batches of muffins and cakes that Tania can make? Line joining ordered pairs 0, 8 and 6, 3.5. Shade the portion of the graph below this line which lies within the first quadrant Line joining ordered pairs 0, 8 and 6, 3.5. Shade the portion of the graph above this line which lies within the first quadrant Line joining ordered pairs 0, 14 and 8, 0. Shade the portion of the graph above this line which lies within the first quadrant Line joining ordered pairs 0, 14 and 8, 0. Shade the portion of the graph below this line which lies within the first quadrant
Mathematics
1 answer:
mihalych1998 [28]2 years ago
4 0
Write the inequalities that are given by the :

<span>x: the number of batches of muffins

y: the number of batches of cakes

</span>Each batch of muffin requires 7 liters of milk and each batch of cakes require 4 liters of milk.

=> liters of milk use = 7x  + 4y

<span>Tania has 56 liters of milk.=> 7x + 4y ≤ 56

Which means that the amount of muffins and cakes made are limited by the availability of 56 liter of milk.

The inequality 7x + 4y ≤ 56 is graphed by drawing the line 7x + 4y = 56 and shading the region below that line.

The line 7x + 4y = 56 has these x and y intercepts:

y-intercept: x =0 => 4y = 56 => y = 56/4 => 14 => point (0,14)

x-intercept => y = 0 => 7x = 56 => x = 56/7= 8  => point (8,0)

So, the line passes through the poins (0,8) and (14,0) and the solution region is below that line.

Also, you know that x and y are restricted to be positive or zero =>

x ≥ 0

y ≥ 0.

So, the solution region is restricted to the first quadrant.

That implies that the answer is:
</span><span>
Line joining ordered pairs 0, 14 and 8, 0. Shade the portion of the graph below this line which lies within the first quadrant
</span>


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Second) You need to multiply 1/3 and 1/4 to have a denominator of 12. The equivalent fractions for them are 4/12 and 3/12.

Last) You just add the numerators together and you get 7/12 ( you don't need to simplify since it already is in simplest form)

Hope this Helps!

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<span>0 is a natural number, which is part of the rational numbers.</span>
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7 pages

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Triangle ABC was dilated and translated to form similar triangle A'B'C'.
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Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.

On this exercise is asked to find the scale factor by which the triangle ABC was 
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Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.

As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.

Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)

Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)

As said at the beginning of the question the triangle was not only dilated.
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