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givi [52]
3 years ago
6

In Figure 1, the area of square A is 9 square units, the area of square B is 16 square units, and the area of square C is 25 squ

are units. In Figure 2, the area of square D is 36 square units and the area of square E is 64 square units, and the area of square F is 100 square units. In Figure 3, the area of square G is 25 square units and the area of square H is 144 square units, and the area of square I is 169 square units. What can be concluded about the areas of the squares? A. The sum of the areas of the two smaller squares is less than the area of the larger square. B. The sum of the areas of the two smaller squares is greater than the area of the larger square. C. The sum of the areas of the two smaller squares is equal to the area of the larger square. D. The sum of the areas of the two smaller squares is equal to the area of the triangle.
Mathematics
2 answers:
weqwewe [10]3 years ago
7 0

Answer:

C. The sum of the areas of the two smaller squares is equal to the area of the larger square.

Step-by-step explanation:

9 + 16 = 25

36 + 64 = 100

25 + 144 = 169

The relations "less than" and "greater than" can be ruled out. These observations are consistent with selection C.

The triangle area is half the product of the square roots of the squares on the legs, so the areas of the triangles are (respectively) 6, 24, 30. These are not related to the sum of the smaller squares, so the last selection can also be ruled out.

gtnhenbr [62]3 years ago
7 0

Answer:

A. The sum of the areas of the two smaller squares is equal to the area of the larger square.

Step-by-step explanation:

In Figure 1, a, b, and c form the sides of PQR. They also form the sides of square A, square B, and square C respectively.

For a right triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Applying the Pythagorean theorem to PQR, it can be seen that a2 + b2 = c2.

Similarly, the following statements will be true for XYZ and STU.

For XYZ, d2 + e2 = f2.

For STU, g2 + h2 = i2.  

By observation, along with the Pythagorean theorem, the sum of the areas of the two smaller squares is equal to the area of the larger square.

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Find the value of the term in the arithmetic sequence using an = a^1+ (n-1)d. 3,5,7,9,11, (8th term)
saveliy_v [14]
<h3>Answer:  17</h3>

=========================================================

Work Shown:

a1 = 3 = first term

d = 2 = common difference (since we add 2 to each term to get the next one)

Let's compute the nth term.

an = a1 + (n-1)*d

an = 3 + (n-1)*2

an = 3 + 2n-2

an = 2n+1

-----------------------

To check things so far, we can plug in something like n = 2

an = 2n+1

a2 = 2*2+1

a2 = 5

Showing that the 2nd term is 5, which matches with the sequence given to us

Let's check n = 3

an = 2n+1

a3 = 2*3+1

a3 = 7

That matches as well. I'll let you check the others.

-----------------------

Plug in n = 8 to find the 8th term

an = 2n+1

a8 = 2*8+1

a8 = 17

The eighth term is 17, which is the final answer.

-----------------------

You could extend out the given sequence by adding 2 each time until you reach the 8th term

3,5,7,9,11,13,15,17

Though this method is slow if you need to find say the 38th term

8 0
2 years ago
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luda_lava [24]

Answer:

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Step-by-step explanation:

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Stels [109]

Answer:  2 1/4 more flour for 9 servings

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3 years ago
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2 years ago
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Using the triangle inequality theorem, we can figure this out.

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