A pot of soup, currently 16°C above room temperature, is left out to cool. If that temperature
difference decreases by 6% per minute, then what will the difference be in 16 minutes?
If necessary, round your answer to the nearest tenth.

°C

Step-by-step explanation:

2 things to remember :

1. the sum of all angles in a triangle is always 180°.

2. the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

triangle 1 :

angle B = 180 - 62.2 - 43.8 = 74°.

a/sin(62.2) = 15.8/sin(74)

a = 15.8 × sin(62.2)/sin(74) = 14.53961961... in

c/sin(43.8) = 15.8/sin(74)

c = 15.8 × sin(43.8)/sin(74) = 11.37657122... in

triangle 2 :

14.9/sin(49) = 11.6/sin(A)

sin(A) = 11.6 × sin(49)/14.9 = 0.587559136...

angle A = 35.98398776...° ≈ 36°

angle C = 180 - 49 - 35.98398776... = 95.01601224...° ≈

≈ 95°

c/sin(95) = 14.9/sin(49)

c = 14.9 × sin(95)/sin(49) = 19.66708505...

newly weds triangle :

let's call the 2 sides a and b (25 m and 30 m).

the angle between them is 60°.

here we should use the extended Pythagoras for general triangles :

c² = a² + b² - 2×a×b×cos(C)

with c being the side opposite to the angle C.

so, we have in our case

c² = 25² + 30² - 2×25×30×cos(60) = 625 + 900 - 750 =

= 775

c = sqrt(775) = sqrt(25×31) = 5×sqrt(31) = 27.83882181... m

the area of the triangle we get via Heron's formula :

s = (a+b+c)/2 = (25+30+c)/2 = 41.41941091...

area = sqrt(s(s-a)(s-b)(s-c)) = sqrt(s(s-25)(s-30)(s-c)) =

= sqrt(105,468.75) = 324.7595264... m²

with Php 2000 per m² this would cost

324.7595264... × 2000 = Php 649,519.0528...

By using the information given on the graph, we can see that a = 3.

Here we have an exponential of the form:

[tex]y = p*a^x[/tex]

And by looking at the graph, it passes through (0, 4) and (2, 36), so we can write:

[tex]4 = p*a^0\\\\36 = p*a^2[/tex]

From the first equation we get that p = 4, replacing that on the second one we get:

[tex]36 = 4*a^2\\\\36/4 = 9 = a^2\\\\\sqrt{9} = 3 = a[/tex]

So we conclude that a = 3.

If you want to learn more about exponential equations:

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Answer:

6 units

Step-by-step explanation:

The distance between two points can be calculated with the formula

[tex]\boxed{\textcolor{steelblue}{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

However, since (0, 2) and (0, 8) have the same x coordinate of 0, the distance between them is the difference in their y-coordinates.

Distance between (0, 2) and (0, 8)

= 8 -2

= 6 units

Answers:

8/12

2/3

4/6

============================================================

Explanation:

There are 8 pizza slices shaded out of 12 total.

One fraction we can form is 8/12

Divide each part by the GCF 4

This means 8/12 is the same as 2/3

Check out the image below to see how 8/12 and 2/3 are the same. Refer to figure 1. We have 2 slices shaded out of 3 total.

Then check out figure 2 to see how 2/3 and 4/6 are the same. By extension, this means that 8/12 and 4/6 are the same. Figure 2 shows 4 shaded slices out of 6 total.

There are infinitely many ways we can split up this pie, so there are infinitely many fractions to write as the answers.

Answer:

Jesse would need to wash four cars.

Step-by-step explanation:

9 times 4 is 36, so Jesse would need to wash 4 cars, and if he washed only 3 cars, you would do 9 times 3 which would get you to 27, which is too little for the game he wishes to buy.

Answer:

Step-by-step explanation

the answer is A.

Answer:

1 out of 3 people vote for junior

Step-by-step explanation:

Using the Empirical Rule, it is found that 95% of the employees will have a travel time within the following range:

B. 8 minutes to 28 minutes.

It states that, for a normally distributed random variable:

Considering that the mean time is 18 minutes and the standard deviation is 5 minutes, the the bounds of the 95% range are given by:

Hence option B is correct.

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Answer:

  B)  192 pi

Step-by-step explanation:

The volume of a cylinder is found from the formula ...

  V = πr²h

where the radius is r and the height is h. The radius is half the diameter.

__

  V = π(8/2)²(12) = 192π . . . . . . using the given values

Answer:

x        y                                 ordered pair

-2      3(-2) + 2 = -4             (-2, -4)

-1       3(-1) + 2 = -1                (-1, -1)  

0       3(0) + 2 = 2                 (0, 2)

1        3(1) + 2 = 5                  (1, 5)

2       3(2) + 2 = 8                 (2, 8)

Answer:

x>-9

Step-by-step explanation:

1. bring x over to the other side to make it a positive (4+x>-5)

2. bring 4 to the other side (x>-5-4)

3. simplify (x>-9)

Answer:

252

Step-by-step explanation:

Hope this helped you, and have a good day! (Please tell me if the answer is incorrect and I will try and correct it as soon as possible)

Answer:

20°

Step-by-step explanation:

Solution,

Here,

→(x+20°)+160°=180°[Sum of a straight line is 180°]

→x=180°-180°

→x=0°

Again,

→x+20°

→0°+20°

→20°

Answer:

I have the same problem as you and it told me that it’s 40

Step-by-step explanation:

Step-by-step explanation:

The father is presently 25 years old.

And his daughter is presently 5 years old.

Therefore, the father is 5 times older than his so. Currently.

In 5 years, the father will be 30 years old and the son will be 10 years old. So the father will be 3 times the daughters age.

Answer:

Yes

Step-by-step explanation:

Use synthetic division

2 | 1 -8  14 -4

____2 -12_4__

    1 -6   2 | 0

Thus, [tex](x^3-8x^2+14x-4)\div(x-2)=x^2-6x+2\:\text{R}0[/tex], so [tex](x-2)[/tex] is indeed a factor of f(x) since there's no remainder.

Put y 's value in second equation

And

Solution is (1,-3)

Verification

Verified

Answer:

A≈32[tex]\frac{3}{10}[/tex]ft²

--

To find the surface area of a right rectangular prism you must use this formula A=2(wl+hl+hw)

Then plug in your variebles

A=2( 1.33*1.5+5+1.5+5+1.33)

This comes out to be A≈32 [tex]\frac{3}{10}[/tex]

Answer:

32 1/3 ft² for K12

Answer:

A, Yes because each t value is paired with exactly one number of gallons.

Step-by-step explanation:

Simply perform the vertical line test. On a graph, draw a vertical line, and if the line crosses the graph exactly once, it is a function. See the diagram below. Hope it helps, have a fantastic day.

Answer:

a

Step-by-step explanation:

because i am built diffrent thats why

Answer:

y = 5x

Step-by-step explanation:

y = 5x

Where, y = amount of money library receives and x  = number of books sold.

So if 1 book is sold, y = 5 (1) = 5, which means y =5 (this matches answer on row 1 which says 1 book sold makes 5 bucks.)

If the triangle ABC is enlarged using the point P as a center, then the point of the dilated triangle will be A'(-3, 2), B'(1, 2), and C'(-1, -2).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The coordinate of point P will be (5, 4).

Let shift the origin at P, then the coordinate of ABC will be

A(-4, -1), B(-2, -1), and C(-3, -3)

If the scale factor is 2. Then the coordinate of the triangle A'B'C' will be

A'(-8, -2), B'(-4, -2), and C'(-6, -6)

Then shift the origin at (0, 0), then the coordinate of A'B'C' will be

A'(-3, 2), B'(1, 2), and C'(-1, -2)

The graph is shown below.

More about the dilation link is given below.

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Answer:

See below ~

Step-by-step explanation:

Q2

Q3

Q4

The power of a number says how many times to use the number in a multiplication.

--

For instance 6 to the power of 2

This means

Which is also equal to 36

Answer: 27

Step-by-step explanation:

6 is the 1st

13 is the 2nd

20 is the 3rd

27 is the 4th

34 is the 5th

Answer:

1. Volume of the cube = width * length * height = 25 * 25 * 25 = 15,625 m³

2. Volume of the cube = width * length * height = 24 * 24 * 24 = 13,824 m³

3. Volume of the cube = width * length * height = 7 * 7 * 7 = 343 m³

4. Combined volume = volume cube 2 + volume cube 3 = 13,824 + 343 = 14,167 m³

5. 15, 625 - 14,167 = 1,458 more m³

—-

Have a nice day!!

Answer:

1. Volume of a cube = l³

therefore: Volume of first cube = 25³

= 15625

2. Same formula as number 1. = l³

= 24³

= 13824

3. 7³ = 343

4. Combined volume Multiplication = 15625 × 13824

or addition = 15625 + 13824

if according to question

5. Don't get paraphrase

Answer:

Ꮎ = 72.123°

Step-by-step explanation:

AC² = BC²+ AB² - 2BC AB x cos (ABC) 4.52 4.12 +3.52 - 2 x 4.1 x 3.5 x cos (8) =

Answer:

See below ~

Step-by-step explanation:

3. coordinate proof

4. exterior

5. included angle

Answer:

coordinate proof

exterior

included angle

Answer:

this gives 36/100 that is the fraction for the decimal

Answer:

9/25

Step-by-step explanation:

Step 1. Multiply by 100 :

Step 2. Divide by 100 and leave in fractional form :

Step 3. Simplify by dividing throughout 4 :