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Black_prince [1.1K]
3 years ago
13

Which table shows y as DIRECTLY PROPORTIONAL to x?

Mathematics
1 answer:
klemol [59]3 years ago
7 0

Answer:

Option B gives the directly proportional relation.  

Step-by-step explanation:

If a function can be written as in the form y = kx ........... (1), where x is the independent variable, y is the dependent variable and k is the proportionality constant.

Now, from the given four tables in options, the table in option B only satisfies this relation between x and y.

The ordered pairs in the option B are (1,0.5), (2,1), (3,1.5) and (4,2).

Now, take any two pairs of coordinates and find the equation of the function that satisfies all four points.

Taking (1,0.5) and (2,1) points, the equation of the straight line will be  

\frac{y - 1}{1 - 0.5} = \frac{x - 2}{2 - 1}

⇒ 2(y - 1) = x - 2

⇒ 2y = x

⇒ y = \frac{1}{2} x ............. (2)

Therefore, this equation (2) is similar to equation (1) and hence this table is directly proportional relationship. (Answer)

You might be interested in
(a) Find the three-digit number that increases by 30% when each of its
Elden [556K]

Step-by-step explanation:

So a three digit number can be expressed as: 100a + 10b + c where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:

100(a+1) + 10(b+1) + 1(c+1) = 1.30(100a+10b+c)

Distribute the multiplication on the left side:

100a+100+10b+10+c+1=1.30(100a+10b+c)

Distribute the multiplication on the right side:

100a+100+10b+10+c+1=130a+13b+1.3c

Add like terms on the left side:

100a+10b+c+111=130a+13b+1.3c

Subtract 100a, 10b, and c from both sides

111=30a+3b+0.3c

So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.

So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value

111 = 30(3) + 3b + 0.3c

111 = 90 + 3b + 0.3c

Now subtract the 90 from both sides

21=3b+0.3c

Well 3 can fit into 21, 7 times!

21 = 3(7) + 0.3c

21 = 21 + 0.3c

subtract 21 from both sides

0 = 0.3c

and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant

c = 0

This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!

part b:

So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.

So let's start with the same equation except this time instead of 1.3 it's 1.4

100(a+1) + 10(b+1) + 1(c+1) = 1.40(100a+10b+c)

Distribute on the left side;

100a+100+10b+10+c+1=1.40(100a+10b+c)

Distribute on the right side:

100a+100+10b+10+c+1=140a + 14b + 1.4c

Add like terms on left side:

100a + 10b + c + 111 = 140a + 14b + 1.4c

Subtract 100a, 10b, and c from both sides:

111 = 40a + 4b + 0.4c

Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.

So only 2 40's can fit in 111 without going over the value

111 = 40(2) + 4b + 0.4c

Subtract 80 from both sides

31=4b+0.4c

4 can fit into 31, 7 times

31 = 4(7) + 0.4c

31 = 28 + 0.4c

subtract 28 from both sides

3 = 0.4c

divide both sides by 0.4

7.5 = c.

Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.

7 0
2 years ago
In triangle A B D , the measure of angle A is 10 degree less than the measure of angle B . The measure of angle D is 20 degree m
elixir [45]

Answer:

<u><em>Measure of angle A is 27 7/9 degrees.</em></u>

Step-by-step explanation:

Lets call measure of angle A is <em><u>X-10</u></em>

Lets call measure of angle B is X

Lets call measure of angle D is 2.5X+20

We know that the sum of triangles add up to 180 degrees

X+X-10+2.5X+20=180

X=37 7/9

So measure of angle A is 27 7/9 degrees.

I hope this is right. :)

8 0
3 years ago
A chemist has two alloys, one of which is 5% gold and 20% lead and the other which is 30% gold and 50% lead. How many grams of e
dmitriy555 [2]

The amount of the first alloy is 450 grams and the amount of the second alloy is 30 grams.

<h3>What is a linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

A chemist has two alloys, one of which is 5% gold and 20% lead and the other which is 30% gold and 50% lead.

Let's suppose the x is the amount of the first alloy and y is the amount of the second alloy:

We can make two linear equation in two variables:

0.05x + 0.3y = 31.5  ...(1)

0.2x + 0.5y = 105  ...(2)

After solving the above two linear equations by substitution method, we get:

x = 450 grams

y = 30 grams

Thus, the amount of the first alloy is 450 grams and the amount of the second alloy is 30 grams.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

3 0
2 years ago
Can someone please help me with this question
zlopas [31]

Answer:

15 kilometers

Step-by-step explanation:

So we know:

For 4 days she runs 1500 meters each day.

For 3 days she runs 3 kilometers each day.

First off, lets convert 1500 meters into kilometers.

There are 1000 meters in a kilometer, so pluggin in 1500 meters:

1500/1000 = 1.5

So for 4 days she runs 1.5 kilometers each day.

Now, to find the total kilometers, we must find multiply the 1.5 kilometers by the 4 days, the 3 kilometers by the 3 days, then add those two together.

So lets do this:

1.5*4 = 6

So she ran 6 kilometers in the first 4 days.

Next we have:

3*3 = 9

So she ran 9 kilometers in the last 3 days.

Now finally add them together:

6 + 9 = 15

So she ran a total of 15 kilometers.

Hope this helps!

7 0
3 years ago
Convert: 6 cubic centimeters to fluid Ounces.<br> O 0.203<br> O 0.000203<br> 02.03<br> 0.00203
ladessa [460]

I think the correct answer is A because 6 cubic centimeters to fluid ounces equals 0.202884, but if you round it you get 0.203

Mark Brainliest if correct

6 0
3 years ago
Read 2 more answers
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