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My name is Ann [436]
3 years ago
7

There are ten pieces of pizza. Anthony ate 1 16 of the pizza for dinner. He ate 7 20 of the pizza for a bedtime snack. How much

of the pizza has he eaten in all?
Mathematics
1 answer:
DedPeter [7]3 years ago
8 0

Answer:4 ⅛ pieces of pizza

Step-by-step explanation:

Get lcm of 16 and 20 which is 80

5/80+28/80=33/80

80/80=10

33/80

33/80×10÷80/80=4⅛

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Find the area of the triangle with sides 40, 50, and 60.
Katyanochek1 [597]

Answer:

B. 992.2

Step-by-step explanation:

Area of Triangle Knowing All Sides:

Sides: 50.000, 60.000, 40.000

Area  : 992.1567

Area of Triangle given by its 3 Sides:

I will show two ways to find the area. One way is very short - The 2000 years old Heron's Formula. The other method may be longer but it's more "educational" as it teaches us important analytic geometry lessons.

But before we even start, we have to verify that the Basic Triangle Inequality is satisfied.

The Basic Triangle Inequality:

The Basic Triangle Inequality states that for a triangle with side lengths a,b,c , the following is true:

    a < b + c,    b < a + c,    c < a + c

What this means, in plain English, is that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Let us now check:

     60.000 < 40.000 + 50.000   true

     40.000 < 60.000 + 50.000   true

     50.000 < 60.000 + 40.000   true

Now that the basic inequalities are satisfied, we know that these three side lengths can make a triangle, so we can move on to calculating the area of said triangle

Heron's Formula for the area of a triangle:

The 2000 year old Heron's Formula states that the area of a triangle whose sides have lengths  a, b,  and  c  is

     SQRT (s(s-a)(s-b)(s-c))

where  s  is the semiperimeter of the triangle; that is,

     s = ( a + b + c ) / 2

Let us calculate

Area =  SQRT ( 75.000 • 15.000 • 35.000 • 25.000 ) =

           SQRT ( 984375.000 ) =

           992.1567  

Find area using the Base Height formula:

Let  B  (for base) denote the length of the longest side of the triangle

Let  h  (for height) denote the length of a perpendicular line, from the vertex opposite that side, to the side itself.

Note that  h  splits our triangle into two right-angled triangles, both having  h  as height, the base of the left triangle is denoted by  X  and the base of the right triangle is denoted by  40.000 - X

To find the area of a triangle, multiply the base by the height, and then divide by 2. In algebraic notation, Area  = 0.5 • 40.000 • h   To be able to find the Area, using this formula, we must know the value of  h

Using the Pythagorean theorem to find the Height:

Applying the Pythagorean theorem to the left right-angled triangle we get:

     h2 = (50.000)2- X2  

While the right right-angled triangle is "telling" us that:

     h2 = (60.000)2- (40.000 - X)2  

Two things which are equal to  h2 , are also equal to one another (It is a property of "Equation" that   if z=p and z=q then p=q ):

     (50.000)2- X2 = (60.000)2- (40.000 - X)2  

Expand the above and simplify :

     (40.000)2 + (50.000)2 - (60.000)2 = 80.000 • X

     500.000 = 80.000 • X

     X = 6.250

Plug this for X in:  h2 = (50.000)2- X2  

     h2 = (50.000)2- ( 6.250)2  

     h2 = (2460.938)

h = sqrt (2460.938) = 49.6078  

Put the Triangle Area Formula to use:

Finally put the formula  Area = Base * Height * 0.5   to use:

    Area  = 40.000 • 49.608 • 0.5

    Area  = 992.1567  

Note that this result is identical to the one we got using Heron's Formula !

Area of Triangle Knowing all Sides :

    Sides: 50.000, 60.000, 40.000      Area  : 992.1567

4 0
3 years ago
Read 2 more answers
Determine which of the following expressions can be factored to (x+ 2)(x +2)
inna [77]

(x+2)(x+2)

x^2+2x+2x+4

x^2+4x+4

Answer : C ( x^2+4x+4)

6 0
3 years ago
Read 2 more answers
I don’t know how to solve this
sleet_krkn [62]

9514 1404 393

Answer:

  x ∈ (-∞, 9) U (-1, ∞)

Step-by-step explanation:

Get the absolute value by itself. Do that by multiplying by 4.

  |3x +15| > 12

This resolves to two cases:

<u>3x +15 > 12</u>

  x +5 > 4 . . . . divide by 3

  x > -1 . . . . . . .subtract 5

<u>-(3x +15) > 12</u>

  x +5 < -4 . . . . divide by -3

  x < -9 . . . . . . . subtract 5

Then the solution in interval notation is ...

  x ∈ (-∞, 9) U (-1, ∞)

6 0
3 years ago
S
zzz [600]

Answer:

x = 4

Step-by-step explanation:

A trapezium is a quadrilateral (has four sides and four angles) with one pair of parallel sides. A trapezium is said to be isosceles if the bases are parallel, the two other sides known as the legs are equal and diagonals of the trapezium are equal to each other.

In trapezoid ABCD, BC and AD are the diagonals.

Hence BC = AD (property of isosceles trapezoid)

9x + 1 = 12x - 11

Simplifying:

12x - 9x = 1 + 11

3x = 12

Dividing both sides by 2:

x = 4

8 0
2 years ago
A pan of warm water (46∘ Celsius) was put in a refrigerator. After 15 minutes, the water's temperature was 27∘ C; 15 minutes aft
Cloud [144]

Answer:

The refrigerator was at around 13 ∘C

Step-by-step explanation:

Newton's Law of Cooling:

The rate of change of a body temperature  (amount of heat loss/time of loss) is directly proportional to the difference between its own temperature and the surroundings.

\frac{T(t2)-T(t1)}{t2-t1} = -h (T(t2) - Tenv)

T ⇒ temperature

t ⇒ time

Tenv ⇒refrigerator temperature

\frac{T(t2)-T(t1)}{t2-t1} ⇒ rate of change of he temperature

-h ⇒ constant of proportionality (negative because the temperature is decreasing inside the refrigerator)

We have 3 points:

time (minutes) - Temperature (∘ C)

0 (when the pan was put in the refrigerator) - 46

15 (after 15 minutes) - 27

30 (15 minutes after the first 15 minutes) - 19

\frac{27 - 46}{15 - 0} = -h (27 - Tenv)

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)

Now we have a system of two equations and two variables

\frac{-19}{15} = -h (27 - Tenv)\\ \frac{19}{15} = h (27 - Tenv)\\ \frac{19}{15(27 - Tenv)} = h

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)\\\frac{-8}{15} = -h (19 - Tenv)\\\frac{8}{15} = h (19 - Tenv)\\\frac{8}{15} = \frac{19}{15(27 - Tenv)} (19 - Tenv)\\8(27 - Tenv) = 19 (19 - Tenv)\\216 - 8 Tenv = 361 - 19 Tenv\\19 Tenv - 8 Tenv = 361 - 216\\11 Tenv = 145 \\Tenv = 145/ 11\\Tenv = 13. 18

The refrigerator was at around 13 ∘C

6 0
3 years ago
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