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3 years ago

What is the value of b in the equation 3b + 2(b - 1) =8

Mathematics

2 answers:

WARRIOR [948]3 years ago

6 0

Answer:

b = 2

Step-by-step explanation:

In order to find the value of b, we have to isolate b on one side of equation first

So,

$3b+2(b-1)=8$

Multiplying 2 with b-1

$3b+2b-2=8\\5b-2=8$

Adding 2 on both sides

$5b-2+2=8+2\\5b=10$

Dividing by 5 on both sides

$\frac{5b}{5}=\frac{10}{5} \\b=2$

So the value of b is 2 ..

Burka [1]3 years ago

3 0

ANSWER

The value of b is 2

EXPLANATION

The given linear equation in b is

$3b + 2(b - 1) = 8$

We expand to get:

$3b + 2b - 2= 8$

We now group similar terms to obtain:

$3b + 2b = 8 + 2$

Combine the similar terms now to obtain:

$5b = 10$

Divide both sides by 5 to get:

$b = \frac{10}{5}$

This simplifies to:

$b = 2$

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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 38 roses at $5.15 per rose, Florist A is Less Expensive then Florist B

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

Step-by-step explanation:

The Full Question Reads:

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?

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

Given Information

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).

will suffice where

$y$ : 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 delivery charge 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 since we are looking for which value of $x$ (i.e. number of roses) will the less expensive Florist be and then solving for $x$ we have:

$4.75x+40$

$4.75x-5.15x$ Gathering all similar terms together

$-0.4x$ Simplifying

$x>\frac{-15}{-0.4}\\$ Solving for x

$x>37.5$

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

Since a rose has to be sold as a whole and not half we will say that $x>38$ 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 $x$ we have:

$4.75x+40$

$4.75x-5.20x$ Gathering all similar terms together

$-0.45x$ Simplifying

$x>\frac{-15}{-0.45}\\$ Solving for x

$x>33.3$

Similarly as a rose has to be sold as a whole and not half we will say that $x>34$ 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

A set of bivariate data was used to create a least squares regression line. Which of the following is minimized by the line

77julia77 [94]

Answer:

B) The sum of the squared residuals

Step-by-step explanation:

Least Square Regression Line is drawn through a bivariate data(Data in two variables) plotted on a graph to explain the relation between the explanatory variable(x) and the response variable(y).

Not all the points will lie on the Least Square Regression Line in all cases. Some points will be above line and some points will be below the line. The vertical distance between the points and the line is known as residual. Since, some points are above the line and some are below, the sum of residuals is always zero for a Least Square Regression Line.

Since, we want to minimize the overall error(residual) so that our line is as close to the points as possible, considering the sum of residuals wont be helpful as it will always be zero. So we square the residuals first and them sum them. This always gives a positive value. The Least Square Regression Line minimizes this sum of residuals and the result is a line of Best Fit for the bivariate data.

Therefore, option B gives the correct answer.

5 0

3 years ago

Read 2 more answers

If you need to know the other options I'll tell you just ask :)

vazorg [7]

Answer:

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