Six grapefruit cost as much as a dozen oranges. The cost of a dozen grapefruit and two dozen oranges

is $12. If Susan purchased one orange and one grapefruit, how much did she spend? Show your

thinking.


a.Write System of equations for the above problem.



b. Solve the system of equations


c.Explain the meaning of the solution in the context of the problem.

Answers

Answer 1

Answer:

$0.73

Step-by-step explanation:

Let's say an orange costs O dollars and a grapefuit costs G dollars.

We add G dollars for each grapefuit and O dollars for each orange, so, for example, 12 grapefuit = G added 12 times = 12 *G = 12G

a.

6G = 10O

12G + 24O = 12

6 grapefuit = 6G = 10 oranges = 10O

b.

6G = 10O

12G + 24O = 12

We can solve this using substitution. First, we can solve the first equation for G. After that, we can plug that into the second to find O and go from there.

6G = 10O

divide both sides by 6 to remove the coefficient for G

G = (10/6)O

plug that into the second equation

12*(10/6)O + 24O = 12

20O + 24O = 12

44O = 12

divide both sides by 44 to solve for O

O=12/44 = 6/22

6G = 10O

6G = 60/22

divide both sides by 6 to solve for G

10/22 = G

c.

These solutions mean that an orange (O) costs 6/22 dollars and a grapefuit (G) costs 10/22, so 1O + 1G = 16/22 dollars ≈ $0.73. Note that O and G are kept as fractions because they are not exact dollar amounts, e.g. 0.27 repreating


Related Questions

y=1.5x+8 which represents the equation when solved for x?

Answers

[tex]y=1.5x+8\\\\\implies 1.5x = y-8\\\\\implies x = \dfrac{y-8}{1.5}\\\\\implies x = \dfrac{y-8}{\tfrac 32}}\\\\\implies x = \dfrac{2(y-8)}{3}\\\\\implies x = \dfrac 23 y- \dfrac{16}3[/tex]

Which of the following represents the zeros of f(x) = 6x3 − 31x2 + 4x + 5? (1 point)

Answers

Answer: 5, -1/3 and 1/2

Did this question before and I have many study guide websites

How do i do 5√2 x 3√2? Please show a step by step explanation Thank you <3

Answers

Step-by-step explanation:

As it's a product, just multiply each number! We notice there are 2 identical square roots multiplied, and we know that: [tex]\sqrt{x} * \sqrt{x} = x\\[/tex].

So we'll remain with: 5 * 2 * 3 = 30.

:)

Answer:

30

Step-by-step explanation:

First multiply 2 square root with 2 square root and since they are identical the answer will be 2.

Now multiply 3 and 5:

3×5= 15

Now we have two numbers 15 and 2, we will multiply 15 with 2 and we get 30

I couldn't explain well but I hope you understand

The lines represented by the equations y=-2x-6 and 2y+x=-16 are

Answers

Answer:

Is that the entire question? I want to help but I don't see a full question it looks like half of one

Find the value of x.

Answers

Answer:

Step-by-step explanation:

The line which 3x represents is twice as big as the 48. That's because both sides other than the base are bisected.

3x = 2 * 48

3x = 96            Divide by 3

3x/3 = 96/3     Combine

x = 32

A culture of bacteria has an initial population of 74000 bacteria and doubles every 3 hours. Using the formula
P
t
=
P
0

2
t
d
P
t

=P
0

⋅2
d
t


, where
P
t
P
t

is the population after t hours,
P
0
P
0

is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?

Answers

Using an exponential function, it is found that the population of bacteria in the culture after 13 hours is of 1,491,747.

An exponential function, with a doubling time of d, after t hours, is given by:

[tex]A(t) = A(0)(2)^{\frac{t}{d}}[/tex]

In which A(0) is the initial amount.

In this problem:

The doubling time is of 3 hours, hence [tex]d = 3[/tex].The initial population is of 74000 bacteria, hence [tex]A(0) = 74000[/tex].

Then:

[tex]A(t) = A(0)(2)^{\frac{t}{d}}[/tex]

[tex]A(t) = 74000(2)^{\frac{t}{3}}[/tex]

After 13 hours:

[tex]A(13) = 74000(2)^{\frac{13}{3}} = 1491747[/tex]

The population of bacteria in the culture after 13 hours is of 1,491,747.

To learn more about exponential functions, you can take a look at https://brainly.com/question/25958656

The perimeter of the figure is given. Find the length of the indicated side. 4x -4 is one side what's the unknown slide the figure is a rectangle Perimeter = 12x + 4 The length of the indicated side is​

Answers

Answer:

2x+6

Step-by-step explanation:

Perimeter of a rectangle= 2(length + width)

12x+ 4= 2(length + 4x-4)

2(6x+2)= 2(length + 4x-4)

divide both sides by 2

6x+2= length+4x-4

length = 2x +6

Find 51% of the number 93.

Answers

Answer:

47.43

Step-by-step explanation:

To find 51% of the number 93, multiply the latter by 0.51:

0.51(93) = 47.43

Answer:

47.43

Step-by-step explanation:

51% of 93

[tex]\frac{51}{100}\times \frac{93}{1}[/tex]

[tex]=\frac{4743}{100\times \:1}[/tex]

[tex]=\frac{4743}{100}[/tex]

Find the missing parts of the triangle. Round to the
nearest tenth when necessary or to the nearest minute
as appropriate.
1) C = 105.8°
a = 4.7 km
b = 8.3 km



A) No triangle satisfies the given
conditions.
B) c = 16.4 km, A = 23.2°, B = 51°
C) c = 13.5 km, A = 27.2°, B = 47°
D) c = 10.6 km, A = 25.2°, B = 49°

Answers

Answer:

1) C = 105.8°

Step-by-step explanation:

The African elephant can weigh eight tons. A ton is two thousand
pounds. How many pounds can an African elephant weigh?

Answers

If
1 ton = 2,000 points

8 tons = (2,000) 8 pounds

= 16,000 pounds

Hope you find this helpful!
Brainliest and a like is much appreciated!

if you add two obtuse angles do they sometimes make supplamentary angles?

Answers

Answer:

No, they can NEVER make supplementary angles.

Step-by-step explanation:

Two angles are supplementary when they add to 180 degrees. Since two obtuse angles have their angles greater than 90 degrees, they can never be supplementary. Let's take the angles as 91 degrees (the lowest whole obtuse measure). 91 + 91 = 182, which is more than 180.

Therefore, the answer is no.

Answer:

Adding two obtuse angles can never make supplementary angles.

Step-by-step explanation:

An obtuse angle has a measure of greater than 90°, and less than 180°.  

Supplementary angles are two angles whose sum add up to 180°.

We must determine whether adding two obtuse angles can make them supplementary angles through the following example.

Example:

Suppose that we have two obtuse angles:

m ∠ 1 = 90.1°

m∠ 2 = 90.1°

Let us add these two obtuse angles together to determine whether their sum is at most 180°.

m ∠ 1 + m ∠ 2 = ?

90.1° + 90.1° = 180.2°

Since their sum is greater than 180°, then it means that they are not supplements.

Conclusion:

Adding two obtuse angles will have a sum of greater than 180°, thus making them invalid as supplementary angles.

What are the other steps?

Answers

Answer:

63 degrees

Step-by-step explanation:

Angle IGH is 40 degrees because it is vertical to angle BGD.

Angle HIG is 77 degrees because it is a linear pair with CIH.

Since 2 of the angles of triangle GHI are 40 and 77 degrees, and the 3 angles add to 180, angle IHG must be 63 degrees

2/3 of 12 3/8


this is easy but im dum.b

Answers

Answer: 17/2

Step-by-step explanation: 2/3 of 12 3/8 = 8.25

8.25 as a fraction= 17/2.

Answer:

17 divided by two

Step-by-step explanation:

Alisha has a five–year car loan of $15,000 with an interest rate of 6 percent. If the interest is compounded annually, how much will she pay in total for her car?

Answers

Answer:

$20,073.38

Step-by-step explanation: Step 1: Find the percentage. The formula for annual compound interest is A = P(1 + r)^t, where A = amount (total amount), P = principal (initial amount), r = rate (percentage), and t = time (in years). Our rate is 6%, which is 0.06 in decimal form. Add it to 1. 1 + 0.06 is 1.06.

Step 2: Raise 1.06 to the 5th power. Because we are finding the amount in 5 years, we do that step. 1.06^5 is 1.3382255776.

Step 3: Do not delete the decimal from the calculator. Multiply it by 15,000 to find the total amount. When you do, you get 20,073.383664 or 20,073.38 when rounded to the nearest hundredth.

Is there a relationship between deforestation and Global climate change

Answers

Answer:

There is a relationship between Deforestation and Global Climate Change.

Step-by-step explanation:

Deforestation is a cause of global climate change.

is 4.57691 rational?

Answers

Answer:

Possibly

Step-by-step explanation:

Depending on how the number is depicted, there are some easy tells. If the number is an integer, or a finite decimal, or decimal with an infinitely repeating portion (like ), or a fraction with integers, finite decimals, or repeating decimals

Which graph shows a dilation?

Answers

the 1st and 3rd one shows dilation. mark me brainlist

Need help with properties if dilations homework

Answers

With a dial action, although the dilated image may get smaller or larger the angles/ slope of lines would remain the same.

Slope = change I. Y over the change in X

Slope = (5-4) /(3-2) = 1/1 = 1

Slope = 1

For f(x) = 4 - x and g(x) = 3x² + x + 5, find the following functions.
a.
(fog)(x); b. (gof)(x); c. (fog)(3); d. (gof)(3)

Answers

Look at the attached photo for the answers.

Which number line model represents the expression -\dfrac23+\left(-\dfrac13\right)−

3

2



+(−

3

1



)minus, start fraction, 2, divided by, 3, end fraction, plus, left parenthesis, minus, start fraction, 1, divided by, 3, end fraction, right parenthesis?

Choose 1 answer:

Answers

Answer:

: If you cut it in 2 equal-sized pieces and eat one, you have eaten ... whole number - you will get a fraction equivalent to 1/ 2

Answer:

XD yall all ways doing this to me so yall somthings don't give me the Answer

Step-by-step explanation:

Greg is recording the changes in his bank account balance. In the morning, he records a deposit of $7. In the afternoon, he records a purchase of
$8
Create two expressions that each represent the total change in Greg's bank account balance after his deposit and purchase. Move numbers
to the lines to create the expressions.



Expression a: _-_
Expression b: _-_
Choices -8, -7, 7, 8

Answers

Answer:

Step-by-step explanation:

i think that it is either -7 - -8 or -7 + 8 or -7+-8.

Two expressions that each represent the total change in Greg's bank account balance after his deposit and purchase are

Expression a  = 7 - 8

Expression b = -8 - (-7)

What is expression?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

For example, x + y is an expression, where x and y are terms having an addition operator in between.

Given,

Greg records deposit of $7

He records purchase of $8 b

Total change = 7 + (-8)

Expression a  = 7 - 8

Expression b = -8 - (-7)

Hence, 7 - 8 and -8 - (-7) are the two expressions for total change in Greg's bank account after his deposit and purchase.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ2

3 friends share a cake in the ratio of 5:7:4. the cake costs Rs.96 how much does each share cost?

Answers

uh the three shares are 30, 42 and 24

Answer:

Cost of each share is [tex]6Rs[/tex]

Step-by-step explanation:

Let the cost be [tex]5x,7x,4x[/tex]

We have

[tex]5x+7x+4x=96\\\\16x=96\\\\x=6[/tex]

Cost of each share is [tex]6Rs[/tex]

13)The final grade on your math exam was determined by the function f(x) = 100 - 2x. Which statements are correct?
A) 100 is the maximum grade,
B) y equals your final grade..
C) This is an exponential function.
D) 2 is what each question is worth.
E) x is the number of correct problems

Answers

Answer:

A, B, D

Step-by-step explanation:

from this function, we can see that 2x is being subtracted from 100. x is the number of incorrect problems, so this can not be a negative value. therefore, the maximum score you can get is 100. y is equal to your final grade as calculating the right side of the equation results in the grade you receive based on the number of incorrect answers. this is a linear function since its highest power is 1. each question is worth 2 points as 2 is being multiplied by the number of incorrect questions (x).

A and B and D and that’s it

20 Points Please Help

Answers

1. 31, 37, 43, 49, 55

That’s all I know from this I apologize, I’m only a freshman in hs lol
Good luck and Merry Christmas, happy holidays

Solve for x. x^2+6x+9=0

Answers

Answer:

x=-3

Step-by-step explanation:

x^2+6x+9=0

Factor

(x+3)(x+3) =0

Using the zero product property

x+3 =0  x+3=0

x=-3   x=-3

Solution

x=-3

Find the greatest common factor. 54,81

Answers

27 is the greatest common factor

54: 1, 2, 3, 6, 9, 18, 27, and 54

81:  1, 3, 9, 27, and 81

The equation y + 6 = one-third (X minus 9) is written in point-slope form. What is the equation written in slope-intercept form?

A: y = 1/3 x - 3
B: y = 1/3 x + 9
C: y = 1/3 x - 9
D: y = 1/3 x + 3

Answers

Pretty sure it’s D yeah okay yes I’m sure now

-4+6p+18+3p=9(p+1)+5

What is the answer?

Answers

Answer:

Step-by-step explanation:

Expand

-4 + 6px + 18 + 3p = 9p + 9 + 5

Simplify

14 + 9p = 9p + 14

Solve

Take away 14 from both sides

9p = 9p

p = p

p = 0

Step-by-step explanation:

as shown in the photo

p equals to p

Plz help. Find the value of each variable. 1. 95° 120° 4120° 125° x + 840° ​.

Answers

Answer:

Step-by-step explanation:

1.
Which expression is equivalent to 5(3x + 1)(x − 2)(x – 3)?

Answers

Answer:

15x^3-70x^2+65x+30

Step-by-step explanation:

1) 5(3x+1)= (15x+5)

2) (15x+5)(x-2)=15x^2-25x-10

3) (15x^2-25x-10)(x-3)=15x^3-70x^2+65x+30

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