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Genrish500 [490]
2 years ago
13

Which of the following has a constant of proportionality of 2?

Mathematics
2 answers:
uysha [10]2 years ago
8 0

Answer : y= 2x

When y is directly proportional to x then

y = kx where k is the constant of proportionality.

y = 2x , the value of k is 2. so 2 is the constant of proportionality.

y = x + 2, the equation is not in the form of y=kx

2y = x , y= \frac{x}{2} so constant of proportionality k is \frac{1}{2}

y + 2 = 2x , y = 2x -2 is not in the form of y=kx


denis-greek [22]2 years ago
6 0
Linear fonction's equation : y = ax

So only in y = 2x
2 is the constant of <span>proportionality</span>
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If Florist B increases the cost per rose to $5.20,for what number of roses is it less expensive to order from Florist A? From Fl
Alenkinab [10]

Answer:

For<em> </em>38 roses at <em>$5.15</em> per rose, Florist A is Less Expensive then Florist B

For<em> </em>34 roses at <em>$5.20</em> per rose, Florist A is Less Expensive then Florist B

Step-by-step explanation:

The Full Question Reads:

<u><em>Derek wants to order some roses online.  Florist A charges $4.75 per blue rose plus $40 delivery charge.  Florist B charges $5.15 per red rose plus $25 delivery charge.  If Florist B increases the cost per rose to $5.20, for what number of roses is it less expensive to order from Florist A?  From Florist B?</em></u>

To begin we need to understand our given information and what we are actually looking for.

<u>Given Information</u>

Florist A:

charges $4.75 per blue rose

charges $40 per delivery

Florist B:

charges $5.15 per red rose

charges $25 per delivery

Note: in this problem we ignore the colour of the rose (red or blue) as it does not affect our solution or contributes to it. Therefore we shall call our first variable representing the number of roses as x.

The next step is to construct a system of equations representing our problem and our given information. Here we are looking at linear relationships so a linear function of the form:

y=ax+b   Eqn(1).

<em>will suffice where</em>

y: represents the total cost from the Florists (i.e. number of roses and delivery charges). Dependent Variable

x: represents the number of roses purchased from the Florists. Independent Variable

a: is our relationship factor between y and x

b: is our constant which in this problem is the <em>delivery charge</em> value for each florist.  

Since we have two Florists, we will construct two equations, one for each florist, by employing Eqn(1).  and our given information as follow:

Florist A:  y=4.75x+40   Eqn(2).

Florist B:  y=5.15x+25   Eqn(3).

By employing both equations above and writing them as an inequality <em>since we are looking for which value of </em>x<em> (i.e. number of roses) will the less expensive Florist be and then solving for </em>x<em> we have: </em>

<em>4.75x+40</em>

<em>4.75x-5.15x       Gathering all similar terms together</em>

<em>-0.4x                       Simplifying</em>

<em>x>\frac{-15}{-0.4}\\                             Solving for x </em>

<em>x>37.5</em>

<em>(note how < changes to > since any multiplication/devision process of negative sign in an Inequality will change the order of < to > and vice versa). </em>

Since a rose has to be sold as a whole and not half we will say that <em>x>38</em> So we can then plug in the value of x in Eqn(2) and Eqn(3) and find the cost of buying more than 38 roses from each:

Eqn(2):  Florist A:  y(x>38)=4.75*38+40=220.5  

Eqn(3):  Florist B:  y(x>38)=5.15*38+25=220.7

Which tells us that Florist A is less expensive than Florist B by $0.20 for a purchase of more than 38 roses.

Next the question tells us that Florist B increases the cost from $5.15 to $5.20 per rose, which in Eqn(3) denotes our a value and thus Eqn(3). now becomes:

Florist B:  y=5.20x+25   Eqn(3).

Applying the same method like before and solving for the value of x<em> we have: </em>

<em>4.75x+40</em>

<em>4.75x-5.20x       Gathering all similar terms together</em>

<em>-0.45x                       Simplifying</em>

<em>x>\frac{-15}{-0.45}\\                           Solving for x </em>

<em>x>33.3</em>

Similarly as a rose has to be sold as a whole and not half we will say that <em>x>34</em> So we can then plug in the value of x in Eqn(2) and Eqn(3) and find the cost of buying more than 34 roses from each:

Eqn(2):  Florist A:  y(x>34)=4.75*34+40=201.5  

Eqn(3):  Florist B:  y(x>34)=5.15*34+25=201.8

Which tells us that Florist A is again less expensive than Florist B by $0.30 for a purchase of more than 34 roses. It was also shown that as the cost of the rose increased by $0.05 the number of roses for purchase decreased.

4 0
3 years ago
15 points please help!! :)<br> Find the value of x.
andriy [413]

Answer:

Question 4: -11

Question 5: -7

Step-by-step explanation:

Four

Every triangle has 180 degrees.

So all three angles add to 180

<em><u>Equation</u></em>

60 + 80 + x + 51 = 180

<em><u>Solution</u></em>

Combine the like terms on the left. This is the first time I've seen x be a negative value. Almost all of the time it isn't, which should make you wonder.

191 + x = 180    

Subtract 191 from both sides.

191 - 191 + x = 180 - 191

x = - 11

Five

If a triangle is a right triangle and one of the angles is 45, then so is the other one.

<em><u>Proof</u></em>

a + 45 + 90 = 180         Combine like terms on the left

a + 135 = 180                Subtract 135 on both sides.

a + 135-135=180-135    Combine the like terms

a = 45

<em><u>Statement</u></em>

That means 52 + x = 45 and here is another negative answer. Subtract 52 from both sides

52 - 52 + x = 45 - 52    Combine like terms.

x  = - 7

6 0
3 years ago
Read 2 more answers
Of every 5 CDs produced in a
Anestetic [448]

Answer:

880

Step-by-step explanation:

2/5 times 2200

4 0
2 years ago
Read 2 more answers
Simplify the expression:z2-z(z+3)+3z
n200080 [17]
z^2-z(z+3)+3z=z^2-z\cdot z-z\cdot3+3z=z^2-z^2-3z+3z=0
8 0
3 years ago
Write a mathematical sentence that expresses the information given below. Use t as your variable name. If necessary:Susanne chec
Feliz [49]

Answer:

t+8>82^{\circ}

Explanation:

We were given that:

Let "temperature" be represented by "t"

Suzan checks the temperature at 11:00. If the temperature rises by 8 more degrees, it will break the record high temperature for the day which is 82 degrees

This information is mathematically represented as:

t+8>82^{\circ}

7 0
1 year ago
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