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2 years ago

9

Is the sum of the areas of two smaller squares equal to the area of a large square if the sides lengths of the squares are 8 fee

t, 5 feet, and 3 feet?

1 answer:

77julia77 [94]2 years ago

5 0

No.
The sum of the areas of the two smaller squares is 5^2 + 3^2 = 34
The area of the larger square is 8^2=64
34 does not = 64

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A four-sided die is rolled repeatedly, until the first time (if ever) that an even number is obtained. What is the sample space

Andrew [12]

Answer:

Sample space by its definition is termed as the list of all the possible outcomes of an experiment.

Therefore, the sample space for this experiment rolling a four-sided die will be: {1, 2, 3, 4}

Step-by-step explanation:

When you roll a a four-sided die, number of dots on uppermost face is said to be an outcome.

For example, whenever a four-sided die is rolled we can get either 1, 2,3 or 4 dots on the upper most face as an outcome.

As we know that rolling a four-sided die will bring the following possible outcomes: {1, 2, 3, 4}

Possibilities of the number being even (2 and 4) = 2

Probability of the number being even = 2/4 = 1/2

Sample space by its definition is termed as the list of all the possible outcomes of an experiment.

As we have already determined that rolling a four-sided die will bring the following possible outcomes: {1, 2, 3, 4}

Therefore, the sample space for this experiment will be: {1, 2, 3, 4}

Keywords: sample space, 4-sided dice

Learn more about sample space from brainly.com/question/2140973

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2 years ago

In a West Texas school district the school year began on August 1 and lasted until May 31. On August 1 a Soft Drink company inst

WINSTONCH [101]

Answer:

$95.78

Step-by-step explanation:

f(t) = 300t / (2t² + 8)

t = 0 corresponds to the beginning of August. t = 1 corresponds to the end of August. t = 2 corresponds to the end of September. So on and so forth. So the second semester is from t = 5 to t = 10.

$T₂ = ∫₅¹⁰ 300t / (2t² + 8) dt

$T₂ = ∫₅¹⁰ 150t / (t² + 4) dt

$T₂ = 75 ∫₅¹⁰ 2t / (t² + 4) dt

$T₂ = 75 ln(t² + 4) |₅¹⁰

$T₂ = 75 ln(104) − 75 ln(29)

$T₂ ≈ 95.78

3 0

2 years ago

Triangle XYZ with vertices X(0, 0), Y(0, –2), and Z(–2, –2) is rotated to create the image triangle X'(0, 0), Y'(2, 0), and Z'(2

Marina86 [1]

Answer: The correct options are

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.

Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.

The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).

And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).

<u>Option (A) Rotation 90°:</u>

We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.

So, rotation of 90° anticlockwise is a correct option.

<u>Option (B) Rotation 180°:</u>

If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.

So, rotation of 180° is NOT a correct option.

<u>Option (C) Rotation 270°:</u>

If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.

So, rotation of 270° clockwise is also a correct option.

<u>Option (D) (x, y) → (–y, x):</u>

We see that the co-ordinates of both the triangle follow the transformation

X(0, 0) ⇒ X'(0, 0)

Y(0, -2) ⇒ Y'(2, 0)

Z(-2, -2) ⇒ Z'(2, -2).

So, the transformation is (x, y) ⇒ (-y, x).

Therefore, the transformation (x, y) → (–y, x) is a correct option.

<u>Option (E) (x, y) → (y, -x):</u>

We see that the co-ordinates of both the triangle does NOT follow this transformation

For example, suppose this transformation is correct. Then, we have

Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.

Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.

Thus, the correct options are:

(A) Rotation 90° anticlockwise.

(D) (x, y) → (–y, x).

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2 years ago

Read 2 more answers

The diagram shows JKL. Which term describes point M?

laiz [17]

Answer:

A; Orthocenter

Step-by-step explanation:

6 0

1 year ago

Read 2 more answers

charmaine and tesha each have a number of cards, in the ratio 2:3. tesha and holly have a number of cards in the ratio 2:1. if t

Sav [38]

C:t=2:3
t:h=2:1

multiply first equation by 2 and 2nd by 3
c:t=4:6
t:h=6:3
so
c:t:h=4:6:3

if t is 4 more than c
t is 6 units and c is 4
6-4=2
so 4=2 units
2=1 unit

hollly is 3 units
3*2=6
holly has 6 cards

3 0

2 years ago