One loaf of bread and six rolls cost $1.80. At the same prices, two loaves of bread and four rolls cost $2.40. How much does one loaf of bread cost. I have go the answer which is 90 cents and one roll costs 15 cents but the math Olympiad book solution does not explain it well can someone explain it better?

Answers

Answer 1

9514 1404 393

Answer:

  loaf: $0.90; roll: $0.15

Step-by-step explanation:

Let b and r represent the cost of a loaf of bread and a roll, respectively.

The two purchases can be written in equation form as ...

  b +6r = 1.80

  2b +4r = 2.40

__

The usual ways to work problems like this are "substitution" or "elimination". The latter is sometimes called "addition."

Substitution

The way these equations are written, we can see that it is relatively easy to write an expression for b from the first equation:

  b = 1.80 -6r

Substituting that into the second equation, we get ...

  2(1.80 -6r) +4r = 2.40

  3.60 -8r = 2.40 . . . . . . . collect terms

  1.20 = 8r . . . . . . . . . . add 8r-2.40

  0.15 = r . . . . . . . . . divide by 8

Then substituting this into the expression for b, we have ...

  b = 1.80 -6r = 1.80 -6(0.15) = 0.90

One loaf costs $0.90; one roll costs $0.15.

__

Elimination

The idea with "elimination" is to combine the equations in such a way that one of the variables is eliminated in the process. Here, there are several ways that can be done.

We recognize that the b-coefficient in the second equation is double that in the first equation. So, we can subtract the second equation from double the first equation to make the b-terms disappear.

  2(b +6r) -(2b +4r) = 2(1.80) -(2.40)

  8r = 1.20 . . . . . . . simplify

  r = 0.15 . . . . . . . divide by 8

Using the first equation, we can find b:

  b + 6(0.15) = 1.80

  b = 0.90 . . . . . . . . . subtract 0.90

One loaf costs $0.90; one roll costs $0.15.

__

Another way we can eliminate one of the variables is to rewrite the second equation without its excess factor of 2:

  b +2r = 1.20

Then subtracting the first equation from 3 times this will eliminate the r variable:

  3(b +2r) -(b +6r) = 3(1.20) -(1.80)

  2b = 1.80 . . . . . . . . . simplify

  b = 0.90

Then, using the above version of the second equation, we have ...

  0.90 +2r = 1.20

  2r = 0.30

  r = 0.15

One loaf costs $0.90; one roll costs $0.15.


Related Questions

in the given circle the radius is 9 cm what is its diameter?​

Answers

Answer:

18

Step-by-step explanation:

The diameter is equal to twice the length of the radius

So if the radius is 9 then the diameter is 9 * 2 = 18

Multiply (2x-5)(x+3)

Answers

Answer:

2x^2+x-15

Step-by-step explanation:

foil

Answer:

2x^2 + x - 15

Step-by-step explanation:

using FOIL

(2x - 5)(x + 3)

[(2x ⋅ x) + (2x ⋅ 3) + (-5 ⋅ x) + (-5 ⋅ 3)]

[2x^2 + 6x - 5x - 15]

2x^2 + x - 15

Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly, and each person arrives at a different time.

a. In how many ways can they arrive?

b. In how many ways can Martha arrive first and Armando last?

c. Find the probability that Martha will arrive first and Armando last.

Show your work

Answers

Answer:

a) 120

b) 6

c) 1/20

Step-by-step explanation:

a) 5! = 120

b) (5 - 2)! = 6

c) 6/120 = 1/20

Which expression is equivalent to the given expression?

Answers

Answer:

a³b

Step-by-step explanation:

(ab²)³/b⁵

= a³b⁶/b⁵

= a³b

John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?

Answers

This question is incomplete , l can’t answer it . You have to say how much minutes or hours they work to get paid $40 ,if you just say that John’s work one hour and Mike work 1.5 hours then I don’t know what to solve ,this question is a complete

Find the missing segment in the image below

Answers

Answer:

The missing segment length is 20.

Step-by-step explanation:

2 is multiplied by 4 to get to 8, so 5 must be multiplied by 4 to get to 20.

slope of (30, 600) (75, 1050)

Answers

Answer:

y2-y1/x2-x1

y2: 1050

y1:600

x2:75

x1:30

1050-600=450

75-30=45

450/45=10

slope is 10

Answer:

let:

A(30, 600)=(x1,y1)

B((75, 1050)=(x2,y2)

now,

[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex] = \frac{1050 - 600}{75 - 30} [/tex]

[tex] = \frac{450}{ 45} [/tex]

[tex] = \frac{10}{1} [/tex]

An ice cream truck started the day with 454545 ice cream sandwiches. During a stop at a busy park they sold sss ice cream sandwiches. After the stop, the truck had 212121 ice cream sandwiches remaining.
Write an equation to describe this situation.
How many ice cream sandwiches did the truck sell at the park?

Answers

Answer:

45- s= 21

s= 45- 21

=24

so the answer is 24

The population model given dP/dt â P or dP dt = kP (1)

fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net rate that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t > 0.

Answers

Answer:

.

Step-by-step explanation:

help, please!
find x

Answers

This shape consists of two primary special triangles, 30-60-90 and 45-45-90.

the side with the 60° will be half of the hypotenuse because 30° is across from it.

the side with the 30° will be 5.5√3 because 60° is across from it, and any sides that has 60° across from it is associated with a √3.

x is 5.5√6 because any sides that is "below" the 45° angles are associated with a √2 times the side that's above the 45°

help whats the volume of this

Answers

Answer:

93.6

Step-by-step explanation:

The easiest way for me to complete this was to break it up into parts. I Separated the small triangle and the big triangle. I turned them both into squares and multiplied the dimensions. I then divided those by two and added them together.

If two numbers differ by 9 the same of their squares is 653. What are the numbers?

Answers

Answer:

Two numbers differ by 9 and the sum of their square is 653. What are the numbers?

Well,that's a mathematical question from algebra and it's quite difficult to answer such questions by writing through the circumstances offered by apps like quora.

However,I have tried to answer your question in an understandable way.Hope you may not find it difficult to analyze.

Let the numbers be x and (9+x)

Therefore,according to given,

x^2 + (9+x)^2 =653

=>x^2 + (9)^2 + x^2 + 2×(9)×(x)=653 (Applying the formula of (a+b)^2)

=>x^2 + 81 + x^2 + 18x =653

=>2x^2 + 18x + (81-653)=0

=>2x^2 + 18x - 572=0

=>2x^2 + (44x - 26x) - 572=0

=>2x^2 + 44x - 26x - 572=0

=>2x(x + 22) - 26(x + 22)=0

=>(x + 22)(2x - 26)=0

But since the number can't be negative

Therefore, x=13

Hence,the required numbers are 13 and 22.

Step-by-step explanation:

in first hope you like it

PLEASE HELP 40 POINTS
Express each logarithm in terms of ln 3 and ln 5.
ln 81 / 125

Answers

I’ll recommend b or c so choose answer c

The solution is 4ln3 - 3ln5, which is correct option(C).

What are the properties of logarithms?

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmatic operation are called arithmatic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

According to the problem, we will use some of the basic logarithmic properties,

Given expression,

⇒ ln81/125

⇒ ln81 - ln125   [used property : logₐ(x/y) = logₐx - logₐy]

⇒ ln3⁴ - ln5³    [ 81 =3⁴ and 125 = 5³ ]

⇒ 4ln3 - 3ln5   [used property : logₐ(xⁿ) = nlogₐx]

Hence, the solution is 4ln3 - 3ln5

Learn more logarithmic properties here:

brainly.com/question/24211708

#SPJ2

which of the following equations has both 1 and -3 as a solution?
A). x^2-2x-3=0
B). x^2+2x-3=0
C). x^2-4x+3=0
D). x^2+4x+3=0

Answers

i believe the answer is b

In which direction does the parabola x=2y2+1 open?

A up
B down
C Right
D left

Answers

Answer and Step-by-step explanation:

First, we need to set this equation equal to y, which means we need to get y by itself, and all other terms equal to y.

x = [tex]2y^2 + 1[/tex]

Subtract 1, then divide by 2 on both sides.

[tex]x - 1 = 2y^2\\\\\frac{x-1}{2} = y^2[/tex]

Now, take the square root of both sides.

[tex]y=\sqrt{\frac{x-1}{2}}[/tex]

We see that the value with the x (1) is positive, and that we have a square root function, which means the parabola would open to the right.

(If the x value was negative, the square root function's parabola would open to the left)

So, C (Right) is the correct answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

find the range of values of a for which 11- 2a>1 is ____

Answers

Answer:

a<5

Step-by-step explanation:

11-2a>1

-2a>1-11

-2a>-10

a<5

The values of y when x2 - 3 y2 = 1 are not only found among its terms, but the numbers x and y are.
74 pages·4 MB

What fraction is equivalent to eight tentHs

Answers

8/10 is equivalent to 4/5. just divide both 8 and 10 by 2

Oh Brian~
I need help again

Answers

Answer:

18c^3d^9

Step-by-step explanation:

2c^3 d^2 * 9d^7

We know that  we add the exponents when the base is the same

2*9  c^3 d^(2+7)

18c^3d^9

the product of two rational number is _______ number
give answers this question​

Answers

Answer:

rational number

Step-by-step explanation:

multiplying two rationals is the same as

multiplying two such fractions, which will

result in another fraction of this same form

since integers are closed under

multiplication. Thus, multiplying two rational numbers produces another rational number.

"The product of two rational number is rational" So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication.Sep 5, 2020

Find the average rate of change of g(x) = 2x^3 - 5 from x= -4 to x= 2

Answers

Step-by-step explanation:

the average change rate is the change of the functional values from the beginning to the end of the interval, and then that divided by the length of the interval.

like with every average or mean value calculation.

g(-4) = 2×(-4)³ - 5 = -128 - 5 = -133

g(2) = 2×2³ - 5 = 16 - 5 = 11

so, on an interval of x values of 2- -4 = 6 units the function changes its values by 11 - -133 = 144 units.

the average charge rate for this x interval is therefore

144 / 6 = 24 = 24/1

for 1 unit change of x, g(x) changes in the average by 24 units.

What is the domain of the function in the graph?

Answers

Answer:

7≤r≤12

Step-by-step explanation:

The domain is the values that the input takes

The input goes from 7 to 12

7≤r≤12

Answer: Choice B) [tex]7 \le r \le 12[/tex]

=============================================================

Explanation:

The domain is the set of allowed x inputs of a function.

How far to the left can we go on this red line? That would be x = 7.

How far to the right? That would be x = 12.

We can have x equal anything between 7 and 12, including both endpoints. We include the endpoints because they are filled in circles (as opposed to open holes).

So the domain is [tex]7 \le x \le 12[/tex]. If we replace x with r, then we update that inequality into [tex]7 \le r \le 12[/tex]. This replacement happens because r is along the horizontal x axis.

The LARGEST angle has a measure of ______degrees

Answers

Answer:

90 i think

Step-by-step explanation:

Julie wanted to find out the approximate percentage of non-traditional female college students at public universities. She decided to randomly select 25 females from each university in her state and collect and analyze the data.

Select the statement that is TRUE.


The 25 females that Julie interviews are the sample, and the females that Julie does not interview are the population.


The 25 females that Julie interviews are the sample, and all female college students at state universities are the population.


All female college students at state universities are the sample, and the 25 females that Julie interviews are the population.


The female college students at state universities are the sample, and the female college students at all universities in the United States are the population.

Answers

To solve this question, we need to understand sample and population concepts.

From this, the answer is:

The 25 females that Julie interviews are the sample, and all female college students at state universities are the population.

Example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents, which is the population of the study.

The sample will be: 1000 randomly selected New York state residents

The population will be: All New York state residents

In this question:

Sample: 25 females from each university in her state.

Population: All female college students in her student.

Thus, the correct statement is:

The 25 females that Julie interviews are the sample, and all female college students at state universities are the population.

For a similar example, you can check https://brainly.com/question/24331410

(5.5 X10^6 + 6.3 X10^6)2

Answers

Answer:

(5.5×10⁶+6.3×10⁶)×2

= (5.5+6.3)×10⁶×2

= 11.8×10⁶×2

= 23,600,000

If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.

Answers

Answer:

A) area decreases

Step-by-step explanation:

Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.

HOPE THIS HELPS

HAVE A GOOD DAY :)

ITS RASPUTIN002

(-72)(-15)= explain

Answers

1080 is the answer
Multiplying two negatives equals a positive.
72 multiplied by 15 is 1080.

DVD Video Rentals (Refer to Example 3.) The func-
tion V computes the percent share of disc DVD rentals
accounted for by various companies. This function is
defined by V(R) = 37, V(N) = 30, and V(S) = 17,
where R is Redbox, N is Netflix, and S is rental stores.
(Source: Business Insider.)
(a) Write V as a set of ordered pairs.
(b) Give the domain and range of V.
T

Answers

Answer:

[tex](a)\ V = \{(N,30),(R,37),(S,17)\}[/tex]

[tex](b)[/tex]

[tex]Domain = \{N,R,S\}[/tex]

[tex]Range = \{37,30,17\}[/tex]

Step-by-step explanation:

Given

[tex]V(R) = 37,\ V(N) = 30,\ V(S) = 17[/tex]

Solving (a): Set of ordered pair

A function y = f(x) is represented as (x,y)

So, the ordered pair of V is:

[tex]V = \{(R,37),(N,30),(S,17)\}[/tex]

Order the alphabets in increasing order

[tex]V = \{(N,30),(R,37),(S,17)\}[/tex]

Solving (b): The domain and the range

In a function [tex]\{(x_1,y_1),...,(x_n,y_n)\}[/tex]

The domain and the range are represented as:

[tex]Domain = \{x_1,x_2....x_n\}[/tex]

[tex]Range = \{y_1,y_2....y_n\}[/tex]

So, we have:

[tex]Domain = \{N,R,S\}[/tex]

[tex]Range = \{37,30,17\}[/tex]

Using the formula D = s:t where D equals distance traveled, r equals the average rate of
speed, and t equals the time traveled, choose the expression or equation that correctly
represents this information.
Mary drove 150 miles in three hours. What was her average rate of speed?
=
150 = 3
r = 3 = 150
O p + 150 · 3

Answers

Answer: r = 50 miles/h

Step-by-step explanation:

Let r be the rate of average speed.

Then

r = D/t

r = 150/3

r = 50 miles/h

please click thanks and mark brainliest if you like :)

The dotplot below displays the difference in scores for 18 games between a high school soccer team and its opponent.

A dotplot titled difference in Score. A number line going from negative 2 to 4 is labeled Team score minus opponent score. Negative 2, 1; negative 1, 2; 0, 2; 1, 3; 2, 6; 3, 3; 4, 1.

Which of the following is the best explanation for the dots at –1?

In one game, the team beat the opponent by 1 goal.
In two games, the team beat the opponent by 1 goal.
In one game, the team lost to the opponent by 1 goal.
In two games, the team lost to the opponent by 1 goal.

Answers

Answer: Choice D

In two games, the team lost to the opponent by 1 goal.

========================================================

Explanation:

Negative scores indicate the team lost, and the absolute value of those values represent how much of a loss.

So a difference of -1 means the team lost by 1 point.

We have 2 dots over this value, so there are 2 occasions where the team lost  to the opponent by 1 goal.

An example would be that say the team scored 3 goals and the opponent scored 4 goals. So we have a differential of 3-4 = -1. The order is important because we would not say 4-3 = 1.

Answer:

d

Step-by-step explanation:

took the test

2012
Descriptive Answer Questions
Attempt FIVE questions.
11.
Show the Fisher's ideal index number satisfies both time reversal test and factor
reversal test from the following information
Commodities
2010
Price Expenditure
Price
Expenditure
5
4
32
72
х
6
50
5
28
Y
4
3
18
40
Z
8
40
50
3 XN
10

Answers

im gonna 36 I’m not sure or 27 maybe
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