The area of the rectangular painting is

Explain how you decide wether to multiply or divide by 3 if you need to convert yards to feet.

Valentin [98]

Answer:

Step-by-step explanation:

Converting yards to feet means that we want the label of yards to cancel, leaving feet as our label. Use the factor-label method taught in chemistry.

$???yds *\frac{3feet}{1yd}$

The yards label cancels out, leaving feet as our label. So to answer the question, in order to convert from yards to feet you are multiplying by 3.

6 0

3 years ago

21. Tom buys a DVD player on 12 monthly payments. The cash price is $600. He pays

slamgirl [31]

Answer:

Each monthly payment is $ 49.05, and in total Tom paid $ 648.60.

Step-by-step explanation:

Given that Tom buys a DVD player on 12 monthly payments, whose cash price is $ 600, and he pays a 10% deposit and the store charges 9% interest, to determine how much is each payment and the total amount Tom pays for the DVD player the following calculations must be performed:

600 - 600 x 0.1 = 540

540 x 1.09 = 588.6

588.6 / 12 = 49.05

Thus, each monthly payment is $ 49.05, and in total Tom paid $ 648.60.

8 0

3 years ago

- Which is greater?<br> 5 2<br> a) or<br> 16 9

azamat

Answer:

5/2

Step-by-step explanation:

5/2= 2 1/2

while 16/9=1 7/9

6 0

3 years ago

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago

Figure A

Amiraneli [1.4K]

<h2>Answer:</h2>

Figure B

<h2>Step-by-step explanation:</h2>

The Pythagorean Theorem is $a^2 + b^2 = c^2$ , where c is the longest side of the triangle (the hypotenuse).

To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.

In Figure A, if the triangle is right-angled, the equation $3^2 + 6^2 = 8^2$ must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.

In Figure B, if the triangle is right-angled, the equation $5^2 + 12 ^2 = 13^2$ must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.

Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.

8 0

2 years ago

Read 2 more answers