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3 years ago

Water freezes at 0 ° Celsius and 32° Fahrenheit. Water boils at 100° Celsius

Mathematics

1 answer:

Schach [20]3 years ago

5 0

Answer:

See below.

Step-by-step explanation:

We need degrees C as a function of degrees F.

Just like when we have y as a function of x, we have (x, y) ordered pairs, here we will have (F, C) ordered pairs.

We are given two ordered pairs: (32, 0) and (212, 100).

We can find the slope of the line.

m = (100 - 0)/(212 - 32) = 100/180 = 5/9

y = mx + b

C = mF + b

C = (5/9)F + b

Use point (32, 0) for F and C to solve for b.

0 = (5/9)(32) + b

b = -(5/9)(32)

C = (5/9)F - 5/9(32)

C = (5/9)F - 160/9

The slope is 5/9. The slope is the rate of change of degrees F to degrees C. For each change of 9 degrees F, the corresponding change in degrees C is 5.

The y-intercept is -160/9.

It means that a temperature of 0 degrees F equals -160/9 degrees C.

You might be interested in

<1 and <2 form a linear pair. If m<1= 4m<2, find the measure of each of the two angles.

ozzi

Answer:

The angle ∠1 = x = 36°

The angle ∠2 = 4x = 4(36°) = 144°

Step-by-step explanation:

We know that when two lines meet or intersect, we get a linear pair of angles.

Linear pairs are basically two adjacent angles that form a line.

The measure of two adjacent angles forming a straight line is 180, meaning they are supplementary.

We are given that <1 and <2 forms a linear pair, and

m∠1 = 4m∠2

It means the angle ∠1 is 4 times the measure of angle ∠2.

Let the angle ∠1 be = x

As the angle 1 is 4 times the measure of angle ∠2, so

The angle 2 will be = 4x

As <1 and <2 forms a linear pair, thus the measure of the sum of <1 and <2 will be 180°, so

x + 4x = 180

5x = 180

divide both sides by 5

5x/5 = 180/5

x = 36°

Therefore,

The angle ∠1 = x = 36°

The angle ∠2 = 4x = 4(36°) = 144°

8 0

3 years ago

(15 POINTS!) The graph shows the distance a ghost crab can run over time the D equals the distance in meters and the t equal the

Maru [420]

Answer:

B. d = 5/3t

Step-by-step explanation:

The complete question is shown in the figure attached with.

We need to find the equation of direct variation using the graph. The general equation for a direction variation is:

y = kx

In this case, the variable along x axis is time in seconds i.e. "t" and the variable along y axis is distance in meters i.e. "d". So, the equation for this case would be:

d = kt

We need to find the value of "k" to complete this equation. For this we can use any point from the graph and substitute it in the above equation. From the graph we can see that the distance covered for time = 3 seconds is 5 meters. Substituting t =3 and d = 5 in above equation, we get:

5 = 3k

k = 5/3

Using the value of k in the above equation, we get:

$d=\frac{5}{3}t$

Therefore, option B gives the correct answer

7 0

3 years ago

PLEASE HELP MY FUTURE DEPENDS ON THIS QUESTION 6

oksano4ka [1.4K]

Answer:

Five more than a number

Step-by-step explanation:

7 0

3 years ago

Help with 12!! ASAP will gove brainliest!! How to find the surface area!!

Shkiper50 [21]

Answer: 659 13/18 yd^2 or 659.7yd^2 ^ =squared

Step-by-step explanation:

This is the answer because you have 6 sides of this prism. That means 3 sides are parallel to the sides across from them. So, 12 1/2 yd by 8 1/3 yd is 104 1/6, then multiply by 2. That equals 208 1/3. Then, 10 5/6 yd by 8 1/3 yd is 90 5/18. then times by 2. That equals 180 5/9. Next, 10 5/6yd by 12 1/2 is 135 and 5/12. then times by 2 and that is 270 5/6yd.

add 208 1/3 + 180 5/9 + 270 5/6

659 13/18 yd^2

3 0

4 years ago

If ABCD is an A4 sheet and BCPO is the square, prove that △OCD is an isosceles triangle. And find the angles marked as 1 to 8 wi

Dmitry [639]

Answer:

The diagram for the question is missing, but I found an appropriate diagram fo the question:

Proof:

since OC = CD = 297mm Therefore, Δ OCD is an isoscless triangle

∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

∠DOP = 22.5°

∠PDO = 67.5°

∠ADO = 22.5°

∠AOD = 67.5°

Step-by-step explanation:

Given:

AB = CD = 297 mm

AD = BC = 210 mm

BCPO is a square

∴ BC = OP = CP = OB = 210mm

Solving for OC

OCB is a right anlgled triangle

using Pythagoras theorem

(Hypotenuse)² = Sum of square of the other two sides

(OC)² = (OB)² + (BC)²

(OC)² = 210² + 210²

(OC)² = 44100 + 44100

OC = √(88200

OC = 296.98 = 297

OC = 297mm

An isosceless tringle is a triangle that has two equal sides

Therefore for △OCD

CD = OC = 297mm; Hence, △OCD is an isosceless triangle.

The marked angles are not given in the diagram, but I am assuming it is all the angles other than the 90° angles

Since BC = OB = 210mm

∠BCO = ∠BOC

since sum of angles in a triangle = 180°

∠BCO + ∠BOC + 90 = 180

(∠BCO + ∠BOC) = 180 - 90

(∠BCO + ∠BOC) = 90°

since ∠BCO = ∠BOC

∴ ∠BCO = ∠BOC = 90/2 = 45

∴ ∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

For ΔOPD

$Tan\ \theta = \frac{opposite}{adjacent}\\ Tan\ (\angle DOP) = \frac{87}{210} \\(\angle DOP) = Tan^-1(0.414)\\(\angle DOP) = 22.5 ^{\circ}$

Note that DP = 297 - 210 = 87mm

∠PDO + ∠DOP + 90 = 180

∠PDO + 22.5 + 90 = 180

∠PDO = 180 - 90 - 22.5

∠PDO = 67.5°

∠ADO = 22.5° (alternate to ∠DOP)

∠AOD = 67.5° (Alternate to ∠PDO)

3 0

3 years ago