This is a question for those of you interested in mathematics or are taking proof classes: when will you know when you are writing too much or too little in a proof? I'm taking a proof class right now, and my professor doesn't do a good job of explaining this to me and just shows/implies the right answer.

Answer:

Find the slope for each of the points in the table. If all the slopes equal each other, the table represents a linear function. If not, then it's the opposite.

Step-by-step explanation:

(You didn't post the full picture, but I'll try to make sense of your problem and answer anyways.)

A linear function, or a line, has a constant slope. This means that no matter where you are on the line, it was always be "rising" some y and "running" some x. It will never be fluctuating in slope or anything like that because it's a line, not a curve, not a zigzag, etc. Just a line.

How do we observe this in tables? Well, remember that the slope m can be found with the following formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where (x1, y1) and (x2, y2) are two points on a line.

So, we can show that all these points have equal slopes to see if they form a line. For example, let's look at the table shown in the picture. We have five points, so let's find the slope for two of them at a time.

First, let's find the slope between (1, 5) and (2, 20).

[tex]m=\frac{20-5}{2-1} \\m=\frac{15}{1} \\m=15[/tex]

The slope between these two points is 15.

Now, let's find the slope between (2, 20) and (3, 45).

[tex]m=\frac{45-20}{3-2} \\m=\frac{25}{1} \\m=25[/tex]

And the slope is ... 25? This can't be right!

Well, it is. This means that these three points can't all form a line, and therefore, all of these points can't form a line. So, the table shown in the picture does not represent a linear function. Do this for the other tables in the question, and you got yourself your answer.

Answers with Method:-

1) Multiply the length value by 100,000.

[tex]2.5 \: hm = 2.5 \times 100000[/tex]

[tex] = >2.5 \: hm = 250000 \: mm[/tex]

2) For this, divide the length value by 1000.

[tex] = > \frac{1800}{1000} [/tex]

[tex] = > 1.8 \: dam[/tex]

3) For finding the approximate value, just multiply the value of length by 1.609.

[tex] = >6450 \: m = (6450 \times 1.609) \: km[/tex]

[tex] = > 10380.27 \: km[/tex]

4) Multiply the given mass value by 100.

[tex] = > 1.2 \: kg = 1.2 \times 100 [/tex]

[tex] = > 1200 \: g[/tex]

5) Multiply the given value by 10,000.

[tex]4.37 \: dag = 4.37 \times 10000[/tex]

[tex] = > 43700 \: mg[/tex]

1- 27 apricots will cost R10.08.

2- 1 kg of polony will cost R71.71.

3- 7.2 kg of sugar cost R51.84.

4- It will use 4 liters of oil to travel a distance of 80km.

5- Peter can paint 8 square meters with 1 liter of paint.

To answer the questions made, the following calculations must be made:

1. If 15 apricots cost R5.60, how many apricots will cost R10.08?

2. How much will it cost for 1kg of polony if 0.35 kg of polony costs R25.10?

3. If 12.5 kg of sugar cost R90, how much will 7.2 kg of the sugar cost?

4. A scooter uses 6.5ℓ petrol to travel a distance of 130 km. How much petrol will it use to travel a distance of 80km?

5. Peter used 5ℓ of paint to paint a wall that is 8m long and 5m high. How many square meters can Peter paint with 1ℓ of paint?

Learn more about calculus in https://brainly.com/question/26453068

Answer:

3/2 is not a interger a interger is any number that does not have a decmil point if we convert 3/2 to a decmil point you get 1.5 which has a desmil point

no

Hope This Helps!!!

I don't know if there is supposed to be a picture, but 3/2 is not an integer, simplified it would be 1 and 1/2 which isn't a integer

Answer:

60/63, 60 : 63

Step-by-step explanation:

63 - 3 = 60

60 is left over. The total amount is 63

Therefore 60/63

Work Shown:

1/4 = 2/8

1/4 - 1/8 = 2/8 - 1/8 = (2-1)/8 = 1/8

She ran 1/8 of a mile further than she walked.

Answer:

P=13

Step-by-step explanation:

Solution:

P=2(l+w)=2·(2.5+4)=13

Answer:

You can solve it yourself

Step-by-step explanation:

By using demos graphing calculator

Applying the leg rule, the value of b in the triangles is: C. 3√13.

The leg rule states that where the altitude of a right triangle bisects its hypotenuse, then, hypotenuse/leg = leg/part, of the right triangle.

Given:

Hypotenuse = 4 + 9 = 13

Leg = b

part = 9

Thus:

13/b = b/9

Cross multiply

b² = 9 × 13

b = √(9 × 13)

b = 3√13

Thus, applying the leg rule, the value of b in the triangles is: C. 3√13.

Learn more about the leg rule on:

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Answer:

Tennessee

Step-by-step explanation:

First, let's find out how much tax he paid...

$695.49-$649.99=$45.50

We can use this to set up an equation...

x%(649.99)=45.50

We can convert x% to x/100 since any percentage is just that number over one hundred...

[tex]\frac{x}{100}*649.99=45.50\\\\\frac{649.99x}{100}=45.50[/tex]

Multiply 100 to both sides

[tex]649.99x=4550[/tex]

Divide both sides by 649.99

[tex]x$\approx$6.92[/tex]

This is closest to 7 (our answers is not exact since you can only have two decimal places in money), therefore he lives in D. Tennessee

Answer:

3.2

Step-by-step explanation:

3 1/5 = 3 + 1/5

Calculate 1/5:   1/5 * 20/20 = 20/100 = 0.2

3 + 0.2 = 3.2

Hope this helps :)

Have a great day!

Answer:

The answer is a.

Step-by-step explanation:

M < 7

Hope that helps!

Answer: 9

Step-by-step explanation:

Add 20, 12, and 32 together then divide by 7 because it says "One week" and a week is 7 days. So, it should be like 20 +12 + 32= 64

64 / (divided by) 7 = 9

The number of daily work hours, if in One week, Steph worked 20 hours, Marco worked 12 hours, and Destiny worked 32 hours, is 9.1 hours.

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

One week, Steph worked 20 hours, Marco worked 12 hours, and Destiny worked 32 hours,

Calculate the total time of work as shown below,

The total time = 20 + 12 + 32

The total time = 64 hours in a week

Calculate the daily work time as shown below,

Daily work time = 64 / 7

(1 week = 7 days)

Daily work time = 9.1 hours

To know more about division:

https://brainly.com/question/27566440

#SPJ2

The complete question is: One week, Steph worked 20 hours, Marco worked 12 hours, and Destiny worked 32 hours. Find the total work time in a day?

The two triangles are both right triangles and are both formed by the

intersection of the lines AS and BD and are therefore similar.

Response:

(a) Yes, ΔABC is similar to ΔSDC according AA similarity postulate

(b) The distance from the ship to the shore is approximately 282.6 feet

(a) Yes, Gilligan can conclude that ΔABC and ΔSDC are similar by

Angle-Angle, AA, similarity postulate.

Reason:

Angle ∠SCD in ΔSDC and ∠ACB in ΔABC are vertically opposite angles,

and they are therefore congruent by vertical angles theorem.

∠SDC = 90° and ∠ABC = 90° therefore ∠SDC ≅ ∠ABC because all 90°

are congruent.

Therefore, two angles in ΔABC are congruent to two angles in ΔSDC,

therefore, ΔABC is similar to ΔSDC according to AA similarity postulate

(b) The ratio of corresponding sides in similar triangles are equal,

therefore;

[tex]\dfrac{BC}{DC} = \mathbf{\dfrac{AB}{SD}}[/tex]

Which gives;

[tex]\dfrac{23}{130} = \dfrac{50}{SD}[/tex]

[tex]SD = \dfrac{130}{23} \times 50 \approx 282.6[/tex]

Learn more about triangle similarity postulates here:

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Answer:

67.307

Step-by-step explanation:

30×25=750

100×80=8000

750+8000=8750

8750/130=67.307... total hits divided by total games

Take two points

Equation of line in two points form

[tex]\\ \rm\hookrightarrow y-y_1=(y_2-y_1/x_2-x_1)(x-x_1)[/tex]

[tex]\\ \rm\hookrightarrow y-25=(\dfrac{165-25}{100-30})(x-30)[/tex]

[tex]\\ \rm\hookrightarrow y-25=(\dfrac{140}{70})(x-30)[/tex]

[tex]\\ \rm\hookrightarrow y-25=2(x-30)[/tex]

[tex]\\ \rm\hookrightarrow y-25=2x-60[/tex]

[tex]\\ \rm\hookrightarrow y=2x-35[/tex]

[tex]\\ \rm\hookrightarrow y=2(106)-35=177hits[/tex]

Answer:

(x + 45) - (1.5x - 12) = 17

Step-by-step explanation:

The number of waffles there were initially is; 80 waffles

Let the number of pancakes be x.

Let the number of waffles be y

Hence, after she baked 45 more waffles, and her grandchildren eat 12 pancakes, what she has is;

There were 17 more waffles than pancakes.

And initially, x = 1.5y

Hence, to determine y, we must substitute x = 1.5y into equation (1)

Therefore, we have;

Read more on simultaneous equations;

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Answer:

x > 15

Step-by-step explanation:

At least means that x will be greater than 15 so it is x > 15.

Answer:

lala i dont really know aaa

Step-by-step explanation:

Area of parallelogram:

Area of parallelogram:

8 is not an element of set A since all the elements must be greater than 8. 8 ∉ A is correct.

Given the following set of values

U = {x|x is a real number}

A = {x|x ∈ U and x + 2 > 10}

B = {x|x ∈ U and 2x > 10}

The equivalent elements of the sets are:

U = {real numbers}

A = {x > 8}
B = {x > 5}

From the set above, we can see that 8 is not an element of set A since all the elements must be greater than 8.

Learn more on sets here: https://brainly.com/question/13458417

It's C. 8 ∉ A; 8 ∈ B

Answer:

The angel of this elevation is 30.5°

Step-by-step explanation:

...

Answer:

Cosine rule formula

[tex]a^{2} = b^{2} + c^{2} - 2bc \times \cos( a) [/tex]

*the small a in cos represents the angle

Conditions

You can only do Cosine rule if the angle is in between the 2 lengths

a^2=22^2+27^2-2(22)(27)×cos(105)

a^2=1520.477026 * so sqaure root to find a

a=38.99329462 *to 2 d.p.

a=38.99ft

Answer:

the answer is 4

Step-by-step explanation:

if you multiply 2 x 1 = 2 then multiply 2 x 2 = 4 add two two times

Answer:

The next they will ring again is after 8 hours.

Step-by-step explanation:

Find the least common multiple of 3,6 and 8:

3,6,9,12,15,18,21,24

6,12,18,24

8,16,24

The least common multiple is 24 so all 3 bells will ring together every 24 minutes.

answer: 3:24

Answer:

Write inequality and for problem

equal to 10.

Check the picture below.