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nika2105 [10]
3 years ago
6

Question: A box of chocolates contains square chocolates, which weigh 10 g each, and round chocolates, which weigh 8 g each. The

combined weight of all the chocolates is 210 g. The number of round chocolates is 3 less than twice the number of square chocolates. Write a pair of linear equations to represent the information given above. Be sure to state what the variables represent. Solve the pair of equations to find the number of square chocolates. Show your work.
Mathematics
1 answer:
Viktor [21]3 years ago
3 0

Answer: the box contained 9 square chocolates and 15 round chocolates.

Step-by-step explanation:

Let x represent the number of square chocolates contained in the box.

Let y represent the number of round chocolates contained in the box.

The box of chocolates contains square chocolates, which weigh 10g each and round chocolates which weigh 8g each. The combined weight of all the chocolates is 210g. It means that

10x + 8y = 210- - - - - - - - - - -1

The number of round chocolates is 3 less than twice the number of square chocolates. It means that

y = 2x - 3

Substituting y = 2x - 3 into equation 1, it becomes

10x + 8(2x - 3) = 210

10x + 16x - 24 = 210

26x = 210 + 24

26x = 234

x = 234/26

x = 9

y = 2x - 3 = 2 × 9 - 3

y = 18 - 3

y = 15

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The population of rabbits on an island is growing exponentially. In the year 1991, the population of rabbits was 9100, and by 19
lisabon 2012 [21]

Answer:

39,223\ rabbits

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

y=a(1+r)^x

where

y is the population of rabbits

x is the number of years since 1991

a is the initial value

r is the rate of change

we have

a=9,100

substitute

y=9,100(1+r)^x

For the year 1998

the number of years is equal to

x=1998-1991=7 years

so

we have the ordered pair (7,18,000)

substitute in the exponential equation and solve for r

18,000=9,100(1+r)^7

(18,000/9,100)=(1+r)^7

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(1+r)=1.1023

r=0.1023

therefore

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y=9,100(1.1023)^x

Predict the population of rabbits in the year 2006

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y=9,100(1.1023)^{15}

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6 0
2 years ago
Consider the parabola given by the equation: f(x) = 2x2 + 14.0 – 4
Softa [21]

Answer:

Step-by-step explanation:

f(x)  = 2x² + 14x - 4

= 2(x² + 7x) - 4

= 2(x² +7x + 3.5²) - 2(3.5²) - 4

= 2(x+3.5)² - 28.5

vertex (3.5, -28.5) = (7/2, -57/2)

The vertical intercept is the y-intercept, i.e., f(0) = -4.

The x-intercepts are the values of x for which y=0.

2x² + 14x - 4  = 0

x = [-14±√(14²-4(2)(-4))]/[2(2)] = [-7±√57]/2 ≅ -7.27, 0.27

5 0
2 years ago
.Jim opened an account with $400. The account pays three percent quarterly. How much is in the account at the end of two years?
podryga [215]
We may have this planned like this:
two years is 8 quarters 
<span>Assuming simple interest, </span>
You will use the formula
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7 0
3 years ago
According to research, how does the public view children and teens with mental health disorders? Group of answer choices A stati
Liono4ka [1.6K]

According to research, the public views children and teens with mental health disorders as over 1,300 U.S. adults believe children with depression are prone to violence

Answer: Option B

<u>Explanation:</u>

Most Americans trust that the people count has increased with mental health disorders in the last 20 years (69 %) and that is a major health issue in the US (89 %) according to the results of survey. They believe that mental health disorders are caused by physical disorders (like brain’s chemical imbalance or due to environmental criteria (daily stress or alcoholism / abuse of drugs).

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7 0
3 years ago
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