All categories

3 years ago

PLZ HELP ASAP!! 100 points!!! Are these examples of direct variation? Please explain

Mathematics

2 answers:

Grace [21]3 years ago

5 0

Answer:

mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.

8 - direct variation Since the equation can be written in the form y=kx. , y varies directly with x and k. The constant of variation, k, is 3.25

9 - When solving for y, y=5x-9 so y doesn't vary directly with x.

y doesn't vary directly with x

10 - direct variation Since the equation can be written in the form y=kx, y varies directly with x and k. The constant of variation, k, is -2.4

Ulleksa [173]3 years ago

5 0

Answer:

8 and 10 - yes, 9 - no

Step-by-step explanation:

<u>Direct variation formula:</u>

y = kx, where k- variation coefficient

16.25 = 5*3.25, yes, same format as above

y = 5x - 9, no, not same format as above

y = -2.4x, yes, same format as above

You might be interested in

The coordinates of triangle GBW are G (20, 10) B (-35, 20), and W (5,-10). Is GBW a right triangle? Justify your answer.

Artist 52 [7]

We know from Pythagoras' Theorem, a right angle triangle can be identified by the relationship:

$a^2+b^2=c^2$

Thus, we know if the side lengths of the triangle in question abide by this relation, the triangle is right.

First, we must find the greatest side length.

We know, using the distance formula.

$GB= \sqrt{(-35-20)^2 +(20-10)^2} =\sqrt{3125}$
$BW= \sqrt{(5+35)^2 +(-10-20)^2} =\sqrt{2500}$
$WG= \sqrt{(20-5)^2 +(10+10)^2} =\sqrt{625}$

From this, we know that:
$GB\ \textgreater \ BW\ \textgreater \ WG$
Therefore, GB would be the hypotenuse of the triangle.
Now we substitute the values for the two shorter lengths and the greater length into the pythagorean theorem:
$a^2+b^2=2500+625=3125$
$c^2=3125$
$\therefore LHS=RHS$
Therefore, this triangle is a right angled triangle

6 0

3 years ago

I need help with this

boyakko [2]

9514 1404 393

Answer:

vertical shrink by a factor of 1/3
shift right 2 units
shift down 4 units

Step-by-step explanation:

The transformations of interest here are ...

g(x) = k·f(x) . . . . . vertically scale f(x) by a factor of k

g(x) = f(x -h) . . . . shift f(x) right by h units

g(x) = f(x) +k . . . . shift f(x) up by k units

Working left to right, the first factor we encounter is 1/3, multiplying the value that is cubed. This means the vertical scale factor of f(x) = x^3 is 1/3. A scale factor less than 1 represents a shrink, so ...

transformation #1 = shrink by a factor of 1/3

The next number we encounter is -2 in the factor (x -2)^3. This means h=2 in f(x -h) = (x -2)^3. The horizontal shift right is 2 units:

transformation #2 = right shift 2 units

Finally, we encounter the number -4. This means k=-4 in g(x)=f(x)+k. The up-shift is negative, so ...

transformation #3 = shift down 4 units

The right- and down-shifts can be done in either order. Here, we have done them as we see them when scanning the equation left-to-right. The vertical scaling must be done before the down-shift, so that it does not affect the amount of down-shift.

4 0

3 years ago

A triangle has side lengths measuring 2x + 2 ft, x + 3 ft, and n ft. Which expression represents the possible values of n, in fe

cluponka [151]

Answer:

$x-1$

Step-by-step explanation:

If a, b and c are the lengths of the triangle's sides, then

$a+b>c,\\ \\a+c>b,\\ \\b+c>a.$

Since

$a=2x+2,\\ \\b=x+3,\\ \\z=n,$

then

$2x+2+x+3>n\Rightarrow nx+3\Rightarrow n>1-x,\\ \\x+3+n>2x+2\Rightarrow n>x-1.$

Thus,

$x-1$

3 0

3 years ago

Read 2 more answers

What's the difference between a independent variable and dependent variable

Travka [436]

Answer:

The dependent variable depends on the independent variable.

Step-by-step explanation:

The variable whose values are deliberately changed by the researcher in order to obtain the desired outcome is called independent variable...
The values of the independent variable can be changed as per requirement, by the researcher...
Manipulation can be done in the values of independent variable, but the researcher observes the value of a dependent variable during an experiment.
An independent variable is a presumed cause whereas dependent variable is a measured effect.
In a simple linear regression, ‘y’ denotes dependent variable while ‘x’ denotes independent variable, which means y depends on x

8 0

3 years ago

16. Mum went shopping at the vegetable stand.

kondaur [170]

Good evening

Answer:

<em>a) the cost of one apple is €</em><em>0.9</em>

<em>b) the cost of one pineapple is €</em><em>5.4</em>

<em>c) the cost of two pineapples and six apples is €</em><em>16.2</em>

Step-by-step explanation:

Consider P the price of a pineapple

A the price of an apple

A pineapple costs six times as much as an apple means P = 6A

Mum paid €7.20 for one pineapple and two apples means P + 2A = 7.20

then

6A + 2A = 7.20

then

8A = 7.20

then

A = €0.9

Since P = 6A then P = 6×(0.9) = €5.4

the cost of two pineapples and six apples

= 2P + 6A

= 2P + P

= 3P

= 3×(5.4)

= €16.2

7 0

4 years ago