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3 years ago

Find −315÷134. Write your answer as a mixed number in simplest form.

Mathematics

1 answer:

kipiarov [429]3 years ago

3 0

Answer:

$-2\frac{47}{134}$

Step-by-step explanation:

$-2\frac{47}{134} = -\frac{315}{134}$

$134$ can go into $-315$ twice at the most, so doubling $134$ will give us $268$ , which leaves us with $47$ left over to reach 315, which is why $47$ is the numerator. The remainder is ALWAYS the numerator.

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The total points by Washington High School = 162 points

The total points by Johnson High School = 159 points

The total points by Roosevelt High School = 108 points

The total points by Lewis High School = 196 points

Washington High School has WON the meet.

Johnson High School came second.

The difference in the points= 2 points

Step-by-step explanation:

Points awarded for first place = 10 points

Points awarded for second place = 8 points

Points awarded for third place = 7 points

About Washington High School

10 first places = 10 x ( 10) = 100 points

6 second places = 6 x ( 8) = 48 points

2 first places = 2 x ( 7) = 14 points

So, the total points by Washington High School = Sum of all points

= 100 + 48 + 14 = 162 points .............. (1)

About Johnson High School

8 first places = 8 x ( 10) = 80 points

9 second places = 9 x ( 8) = 72 points

1 first places = 1 x ( 7) = 7 points

So, the total points by Johnson High School = Sum of all points

= 80 + 72 + 7 = 159 points .............. (2)

About Roosevelt High School

4 first places = 4 x ( 10) = 40 points

5 second places = 5 x ( 8) = 40 points

4 first places = 4 x ( 7) = 28 points

So, the total points by Roosevelt High School = Sum of all points

= 40 + 40 + 28 = 108 points .............. (3)

About Lewis High School

3 first places = 3 x ( 10) = 30 points

3 second places = 3 x ( 8) = 24 points

6 first places = 6 x ( 7) = 42 points

So, the total points by Lewis High School = Sum of all points

= 30 + 42 + 24 = 96 points .............. (4)

Now, comparing all four equation, we get that:

Washington High School has WON the meet.

Johnson High School came second.

The difference in the points = 162 - 159 = 2 points

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3 years ago

PLEASE HELP ME WITH THIS THANKS

kotykmax [81]

Answer:

SA = 1244.64 square centimeters

Step-by-step explanation:

From the attached figure

The formula of the surface area of the prism is SA = 2B + PH, where

B is the area of its base
P is the perimeter of its base
H is the distance between its bases

The base of the prism is a regular hexagon with side 8 cm

If you join each vertex of the hexagon with its center you will form 6 congruent triangles with base 8 cm and height 6.93 cm

The area of the hexagon = 6 × area of a triangle

∵ The base of the triangle = 8 cm

∵ Its height = 6.93 cm

- The formula of the area of a triangle is A = $\frac{1}{2}$ × base × height

∴ Area of the triangle = $\frac{1}{2}$ × 8 × 6.93 = 27.72 cm²

- Lets find the area of the hexagon

∴ The area of the hexagon = 6 × 27 .72 = 166.32 cm²

∴ B = 166.32 cm²

The formula of the perimeter of the regular hexagon is P = 6 × s, where s is the length of its side

∵ The side of the hexagon is 8 cm

∴ P = 6 × 8

∴ P = 48 cm

∵ The distance between the two bases is 19 cm

∴ H = 19 cm

Substitute the values of B, P and H in the formula of the surface area above

∵ SA = 2(166.32) + (48)(19)

∴ SA = 332.64 + 912

∴ SA = 1244.64 square centimeters

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3 years ago