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3 years ago

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You are selling pizzas to raise money for a school field trip. Cheese pizza cost $8 and pepperoni pizza cost $9. You need to sel

l at least two of each kind of pizza, and you want to sell at least $180 worth of pizza. Write an inequality.

1 answer:

Snowcat [4.5K]3 years ago

6 0

Answer: $180 ≤ 8c + 9p

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In triangle $ABC$, let angle bisectors $BD$ and $CE$ intersect at $I$. The line through $I$ parallel to $BC$ intersects $AB$ and

Umnica [9.8K]

Answer:

41

Step-by-step explanation:

If you work through a series of obscure calculations involving area and the radius of the incircle, they boil down to a simple fact:

... For MN║BC, perimeter ΔAMN = perimeter ΔABC - BC = AB+AC

.. = 17+24 = 41

_____

Wow! Thank you for an interesting question with a not-so-obvious answer.

_____

<em>A little more detail</em>

The point I that you have defined is the incenter—the center of an inscribed circle in the triangle. Its radius is the distance from I to any side, such as BC, for example.

If we use "Δ" to represent the area of the triangle and "s" to represent the semi-perimeter, (AB+BC+AC)/2, then the incircle has radius Δ/s. The area Δ can be computed from Heron's formula by ...

... Δ = √(s(s-a)(s-b)(s-c)) . . . . where a, b, c are the side lengths

For this triangle, the area is Δ = √38480 ≈ 196.1632 units². That turns out to be irrelevant.

The altitude to BC will be 2Δ/(BC), so the altitude of ΔAMN = (2Δ/(BC) -Δ/s). Dividing this by the altitude to BC gives the ratio of the perimeter of ΔAMN to the perimeter of ΔABC, which is 2s.

Putting these ratios and perimeters together, we get ...

... perimeter ΔAMN = (2Δ/(BC) -Δ/s)/(2Δ/(BC)) × 2s

... = (2/(BC) -1/s) × BC × s = 2s -BC

... perimeter ΔAMN = AB +AC

8 0

3 years ago

Eight more then seventimes a number (x) is atleast twenty nine

Mademuasel [1]

Answer:A number increased by seventeen is equal to seventy-three. x + 17 = 73

Some number decreased by seven is thirty-three. x - 7 = 33

A number increased by twelve is forty. x + 12 = 40

A number increased by fifteen is sixty-two. x + 15 = 62

Eight less than a number is nine. x - 8 = 9

A number divided by 11 is 4. x/11 = 4

Seven more than three times a number is 19. 3x + 7 = 19

Four more than five times a number is thirty-six. 5x + 4 = 35

Eight less than nine times a number is eleven. 9x - 8 = 11

Twelve more than four times a number is seven. 4x + 12 = 7

Seven more than triple a number is fifteen. 3x + 7 = 15

Seven times a number increased by eight equals twenty-three. 7x + 8 = 23

Eight more than six times a numbers is eleven. 6x + 8 = 11

Nine times a number increased by thirteen is twelve. 9x + 13 = 12

The quotient of a number and four is seventeen. x/4 = 17

A number increased by seven is twenty-five. x + 7 = 25

Fifty-five is the sum of a number and sixteen. x + 16 = 55

The product of a number and eleven is seventy-five. 11x = 75

Eight times a number increased by eleven is thirty-seven. 8x + 11 = 37

The difference of a number and twelve is thirty-four. x - 12 = 34

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

What is the name of an account managed by a third party who makes

Andrej [43]

D the Escrow Account

6 0

3 years ago

Read 2 more answers

What number comes after 12 24 72 to 288

BARSIC [14]

What number comes after 12 24 72 to 288 first please explain that again and second 11 comes after 12 and 23 comes after 24 and 71 comes after 72 hope this helps

8 0

3 years ago

Of the 48 oranges in a carton 1/3 of them were rotten Ben and David took the remaining good oranges it's been took eat my orange

Burka [1]

Answer:

David took 16 oranges.

Step-by-step explanation:

We are given the following in the question:

Total number of oranges = 48

Oranges rotten =

$\dfrac{1}{3}$

Number of oranges rotten =

$\dfrac{1}{3}\times 48\\\\=16$

There were 16 rotten oranges.

Number of good oranges left =

$= 48-16\\=32$

These are equally divided among Ben and David.

Number of oranges each Ben and David get =

$\dfrac{32}{2} = 16$

Thus, David took 16 oranges.

8 0

3 years ago