Partial product for 7*43

To calculate the total surface area of a three-tier wedding cake and determine the number of frosting cans needed, we use the formula for the surface area of a square prism. The total surface area of the cake is 1848 square inches. As each can covers 250 square inches, we would need to buy 8 cans.

In this task, we are asked to calculate the total surface area of a three-tiered wedding cake made of square prisms to determine how many cans of frosting are needed. Each tier has a different length but they all share the same height. The surface area of a square prism is calculated by using the formula 2(a² + 4ah), where 'a' is the length of a side and 'h' is the height.

The total surface area for each tier becomes:

1. Bottom Tier: 2*(20^2 + 4*20*6) = 880 square inches
2. Middle Tier: 2*(14^2 + 4*14*6) = 616 square inches
3. Top Tier: 2*(8^2 + 4*8*6) = 352 square inches

Add these together to get the total surface area for the whole cake, which is 1848 square inches. As each can of frosting can cover 250 square inches, you will need to divide 1848 by 250. This gives approximately 7.4, so you would need to buy 8 cans of frosting to fully cover the cake (as we can't buy partial cans).

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Used Area from bottom box (green)= All 4 vertical faces +EFGH-IJKL
=(20*6+6*6+20*6+6*6)+20*6-14*6= 348 Square inches ...(i)

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Used Area from middle box (Blue)= All 4 vertical faces +MNOP-QRST
=(14*6+6*6+14*6+6*6)+14*6-8*6=276 square inches...(ii)

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Used Area from top box (Brown)= All 4 vertical faces +UVWX
=(8*6+6*6+8*6+6*6)+8*6=216 square inches...(iii)

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so the surface area of the cake to be covered= 348+276+216=840 square inches.

given that 1 can covers 250 square inches

so number of cans needed = 840/250=3.36

which means 4 cans needed.

Answer: Sales tax would be $5.40

Step-by-step explanation: The sales value itself of the dress (that is, without tax) is $65.49.

The amount charged as sales tax in Pearland is given as 8.25% (or 0.0825).

Hence if she is shopping in Pearland, the AMOUNT OF SALES TAX she would pay can be calculated as,

Sales tax = Sales price x 0.0825

Sales tax = 65.49 x 0.0825

Sales tax = 5.402925

Approximately to two decimal places, the sales tax becomes $5.40

Answer:

A'(1, 1); B'(3, 2); C'(1, 2)

Step-by-step explanation:

The original points are A(1,1 ), B(2, 3) and C(2, 1).

Reflecting the triangle across the x-axis will negate every y-coordinate; this maps

(1, 1)→(1, -1); (2, 3)→(2, -3); (2, 1)→(2, -1)

Rotating the figure 90° clockwise about the origin switches the x- and y-coordinates and negates the x-coordinate; this maps

(1, -1)→(-1 -1); (2, -3)→(-3, -2); (2, -1)→(-1, -2)

Reflecting across the line y=x will negate both the x- and y-coordinates; this maps

(-1, -1)→(1, 1); (-3, -2)→(3, 2); (-1, -2)→(1, 2)

Final answer:

To find the coordinates of ∆ABC after reflection across the x-axis, rotation by 90°, and reflection across y = x, we would apply these transformations to each point. Initially reflected across x-axis results in (x, -y), the 90° rotation gives (-y, x), and final reflection over y = x gives (x, -y). To find A′B′C′ we would need original coordinates, but general rule follows this pattern.

Explanation:

In this mathematics problem, we will find the coordinates for vertex A′, B′, and C′ of ∆A′B′C′. Given a triangle ∆ABC reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the line y = x, we need the original coordinates of A, B, and C to find A′B′C′. However, if we take a generic point (x, y), we can assume the following:

1. The reflection about the x-axis would turn it into (x, -y).
2. The 90° clockwise rotation about the origin would give the new coordinates (-y, x).
3. Finally, the reflection over the line y = x would change (-y, x) to (x, -y).

Assuming these transformations, we can find the final coordinates for A′, B′, and C′.

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Answer:

15 is the correct answer

Step-by-step explanation:

because if you divide 90 by 6 its 15