The sequences that would map the triangles so as to support both claims are explained below:
<em>Transformation</em> is a process in which the dimensions, size or orientation of a given shape is <em>adjusted</em>. The types are: translation, reflection, rotation and dilation.
Thus;
A. The sequence of transformations that will <u>support</u> Tim's thinking are:
i. <em>Reflection</em> of triangle A <em>about</em> the y-axis.
ii. <em>Reflection</em> of the triangle the <em>second</em> time now about x-axis.
iii. <em>Translation</em> of the triangle two units to the right (i.e towards the x-axis)
These steps would map triangle A unto triangle B supporting Tim's claim.
B. The sequence of transformations that will <u>support</u> Jennifer's claim are:
i. First <em>rotate</em> triangle A by using the origin of the axis as the reference point.
ii. Then <em>translate</em> triangle A two units to the right (i.e towards the x-axis).
Therefore, these steps will map triangle A unto B to support Jennifer's claim.
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Answer:
Part 1) The unit rate is
Part 2) A 56 ounce bag of pumpkin Seeds cost $14.00
Step-by-step explanation:
Part 1) What is the unit rate for the pumpkin seeds?
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or
Let
y ----> the cost of pumpkin seeds in dollars
x ---> the weight in ounces
we have
For x=24 ounces, y=$6
Find the value of the constant of proportionality k
substitute the values
The unit rate is the same that the constant of proportionality k
therefore
The unit rate is
Part 2) How much would 56.
ounce bag of pumpkin seeds cost?
we know that
The linear equation is equal to
For x=56 ounces
substitute in the linear equation and solve for y
5 1/5% of 99 quarts= 5.148 quarts
The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).
<h3>How to determine the characteristics of the roots of a quadratic equation by discriminant</h3>
Herein we have a <em>quadratic</em> equation of the form a · x² + b · x + c = 0, whose discriminant is:
d = b² - 4 · a · c (1)
There are three possibilities:
- d < 0 - <em>conjugated complex</em> roots.
- d = 0 - <em>equal real</em> roots (real and rational root).
- d > 0 - <em>different real</em> roots (real and irrational root).
If we know that a = 3, b = 7 and c = - 2, then the discriminant is:
d = 7² - 4 · (3) · (- 2)
d = 49 + 24
d = 73
The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).
To learn more on quadratic equations: brainly.com/question/2263981
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