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3 years ago

For the equation --4y = 8x, what is the constant of variation?

Mathematics

1 answer:

larisa86 [58]3 years ago

6 0

Answer: 1) B is correct, constant of variation is -2.

Step-by-step explanation:

Direct variation states that a relationship between the two variables. we say y varies directly as x

i.e, or y =kx.................[1] ; where k is the constant of variation.

Given the equation:

Divide both sides by -4 we get;

Simplify:

.......[2]

On comparing equation [2] with [1] we get;

k = -2

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F (x )= 1/4 x for x = -5

Sholpan [36]

Answer:

-5/4

Step-by-step explanation:

f(x)=1/4x

f(-5)=1/4(-5)

f(-5)=-5/4

6 0

3 years ago

Read 2 more answers

What valur of x makes the equation below true? 9^5 * 9^7=9^x

klasskru [66]

Answer:

x=12

Step-by-step explanation:

(9^5)(9^7)=9^x

282429536481=9^x

<em>Step 1: Flip the equation.</em>

9^x=282429536481

<em>Step 2: Solve Exponent.</em>

9^x=282429536481

log(9^x)=log(282429536481)(Take log of both sides)

x*(log(9))=log(282429536481)

x=log(282429536481)/log(9)

x=12

8 0

2 years ago

Janine babysits for $14.50 per hour. She also works as a dishwasher at her family's restaurant for $9.50 per hour. Her family ne

FrozenT [24]

The system of inequalities are
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) 14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
3) 8 hours babysitting, 7 hours dishwashing
Step-by-step explanation:
The given parameters are;
The amount per hour Janine makes from babysits = $14.50
The amount per hour Janine makes from dishwashing = $9.50
The minimum number of hours Janine can spend dishwashing = 7 hours
The maximum number of hours Janine can spend dishwashing = 10 hours
The maximum number of hours Janine can work each week = 7 hours
The minimum amount she wants to make each week = $140
Let x represent the number of hours Janine spends babysitting and let y represent the number of hours Janine spends dishwashing
1) From the question, we have;
14.5·x + 9.5·y ≥ 140
7 ≤ y ≤ 10
x + y ≤ 15
2) Where
14.5·x + 9.5·y ≥ 140 represents the total amount of money Janine can earn
7 ≤ y ≤ 10 represents the range of values, Janine can spend dishwashing
x + y ≤ 15 represents the total number of hours Janine will like to work each week
Making, y, the subject of the formula of the above inequalities and plotting as functions is given as follows;
y ≥ 140/9.5 - (14.5/9.5)·x
y ≤ 15 - x
3) In order to earn as much money as possible given that the amount Janine earns from babysitting is more than the amount she earns from dishwashing, Janine should spend the least amount of time dishwashing, which is 7 hours, as given, and then spend the remaining 8 hours babysitting to receive $14.5 × 8 + $9.5×7 = $182.5

3 0

3 years ago

An object launched straight up at a speed of 29.4 meters per second has a height, h, in meters of h , t seconds after the object

Nostrana [21]

Answer:

h = 44.06 meters (maximum height)

the time the object takes to complete this whole path is 6 seconds, this is why the time at which the object reaches its maximum height will between 0 and 6 seconds

Step-by-step explanation:

To solve this question, we need to first recognize that this is a constant acceleration problem, specifically, it can be thought of as a projectile motion problem.

Recall, the equations of motion:

$1) v^2 - v_0^2 = 2a(s - s_0)\\2) s = v_0^2 + \frac{1}{2} at^2\\3) v = v_0 + at$

What do we already know?

$v_0 = 29.4 ms^-1$
The launch is straight up
$a = -9.81 ms^-2$ this is the gravitational acceleration $g$

$s_0 = 0 m$ , since our reference point is at s = 0, (the ground)

We can use use the Eq(1):

we know that when any object is launched up, at maximum height its velocity is going to be zero, $v = 0 ms^-2$

$v^2 - v_0^2 = 2a(s - s_0)\\0^2 - (29.4)^2 = 2(-9.81)(s- 0)\\s = 44.06 m$

this is the maximum height!

Why does t have to between zero and six?

We can answer this using a bit visualization, if you think about the second equation

$s = v_0 t - \frac{1}{2}at^2\\ s = 29.4t - 4.905t^2$

this is the equation of the whole trajectory that object makes.

and if you solve this by making $s = 0$ , you will get the times at which the object was at the ground. the times will be 0s and 5.99s.

so the amount of time the object takes to go through this whole path is 6 seconds and this why the object will only reach its maximum height in between this time interval.

hope this helps :)

5 0

3 years ago

Consider a collection of envelopes consisting of 1 red envelope, 2 blue envelopes, 2 green envelopes.and 3 yellow envelopes. If

katrin [286]

Answer:

C. 1/16

Step-by-step explanation:

The probability of picking a blue envelope is 2/8 = 1/4. You want to select a blue envelope twice with replacement so we multiply 1/4*1/4 which is 1/16.

5 0

3 years ago