Amad was curious if triangles \triangle ABC△ABCtriangle, A, B, C, and \triangle EDF△EDFtriangle, E, D, F were congruent. He was
able to map one figure onto the other using a reflection and a rotation. Amad concluded: "I was able to map \triangle ABC△ABCtriangle, A, B, C onto \triangle EDF△EDFtriangle, E, D, F using a sequence of rigid transformations, so the figures are congruent."
1 answer:
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A function 
from a set A to a set B is defined as a relation that assings to each element 
in the set A exactly one element 
in the set B. The set A is called the domain of the function while the set B is the range. So we have five statements and need to find some functions. Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. If each side of the tomato patch is feet, then we have a square patch as shown in the Figure below.
1.a) Write the function Wa(x) representing the width of the bell pepper patch.
We know that she wants its width to be half the width of the tomato patch. Let be the width of the tomato patch, then the function that matches this statement is:
1.b) Write the function La(x) representing the length of the bell pepper patch.
In this case Melissa wants <span>its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:
</span>
<span>
2. Ar</span>ea of the bell pepper patch in terms of x.
Given that the bell pepper patch is a rectangle, then t<span>he area of a rectangle is the product of the length and width. So:
</span>
<span>
3. C</span><span>ombined area of the tomato patch and the bell pepper patch.
This function is the sum of both the area of the tomato patch and the bell pepper patch. So:
</span>
<span>
4. W</span>rite the function Aa(x) for the remaining planting area in the garden.
The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:<span>
</span>
5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.
Given that <span>Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:
</span>
<span>
Therefore the area of the remaining space is:
</span>
1.a) Write the function Wa(x) representing the width of the bell pepper patch.
We know that she wants its width to be half the width of the tomato patch. Let
1.b) Write the function La(x) representing the length of the bell pepper patch.
In this case Melissa wants <span>its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:
</span>
<span>
2. Ar</span>ea of the bell pepper patch in terms of x.
Given that the bell pepper patch is a rectangle, then t<span>he area of a rectangle is the product of the length and width. So:
</span>
<span>
3. C</span><span>ombined area of the tomato patch and the bell pepper patch.
This function is the sum of both the area of the tomato patch and the bell pepper patch. So:
</span>
<span>
4. W</span>rite the function Aa(x) for the remaining planting area in the garden.
The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:<span>
</span>
5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.
Given that <span>Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:
</span>
<span>
Therefore the area of the remaining space is:
</span>
Answer:
This represent an exponential function, because his savings increase by a constant factor of 2.
Step-by-step explanation:
It is given that,
Luis has saved $6 and he doubles the amount each week.
So, the amount saved in the next week = 6×2 = 12
This gives the amount saved in the third week = 12×2 = 24
So, we get the sequence 6, 12, 24, 48,.....
It can be written as, 6×2⁰, 6×2¹, 6×2², 6×2³,.....
So, the sequence in the exponential form , where 'n' is a natural number.
Also, 6, 12, 24, 48,.....
The numbers are increasing by the factor =
Hence, we get,
This represent an exponential function, because his savings increase by a constant factor of 2.
Answer:
Yes, 10.5 cm, 8.0 cm and 4.0 cm can be the side lengths of a triangle.
Step-by-step explanation:
We have been given three lengths as 10.5 cm, 8.0 cm and 4.0 cm. We are asked to determine whether these side can be the side lengths of a triangle.
We will use triangle inequality theorem to solve our given problem.
Triangle inequality theorem states that sum of two sides of a triangle must be greater than 3rd side. Using triangle inequality theorem we will get 3 inequalities as:
True
True
True
Since all the three side lengths satisfy triangle inequality theorem, therefore, 10.5 cm, 8.0 cm and 4.0 cm can be the side lengths of a triangle.