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Vladimir79 [104]
2 years ago
14

During their last game, the Miami Dolphins scored ͸ times for a total score of ͵Ͳ points. They scored ͹ points for each touchdow

n and ͵ points for each field goal. Write and solve the systems of equations to find the total touchdowns and field goals scored.
Mathematics
1 answer:
Karolina [17]2 years ago
4 0

Answer:

The Miami Dolphins had 3 touchdowns and 3 field goals.

Step-by-step explanation:

It is given that During their last game, the Miami Dolphins scored 6 times, for a total score of 30 points. They scored 7 points for each touchdown and 3 points for each field goal.

We need to write and solve the system of equations to find the total touchdowns and field goals scored.

Let x represents the number of touchdowns.

Let y be the number of field goals.

It is given that the Miami Dolphins scored 6 times

x+y=6

x=6-y....(1)

They scored 7 points for each touchdown and 3 points for each field goal.

The total score is 30 points:

7x+3y=30 ...(2)

Put the value of x from equation (1) into equation (2).

7( 6-y)+3y=30

42-7y+3y=30

-4y=30-42

-4y=-12

y=3

Put y = 3 in equation 1.

x=6-3

x=3

Hence, the Miami Dolphins had 3 touchdowns and 3 field goals.

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In an insect colony there are 270 insects after 9 days. If there were initially 80 insects how long will it take the population
Semenov [28]

Answer:

The time it will take the population to grow to 800 insects is 17 days.

Step-by-step explanation:

The growth function of the insects is exponential.

The exponential growth function is:

y=a(1+r)^{t}

Here,

<em>y</em> = final value

<em>a</em> = initial value

<em>r</em> = growth rate

<em>t</em> = time taken

It is provided that there were 270 insects after 9 days and initially there were 80 insects.

Compute the value of <em>r</em> as follows:

y=a(1+r)^{t}\\\\270=80(1+r)^{9}\\\\3.375=(1+r)^{9}\\\\\ln(3.375)=9\cdot \ln(1+r)\\\\0.135155=\ln(1+r)\\\\1+r=1.14471\\\\r=0.145

Now, compute the time it will take the population to grow to 800 insects as follows:

800=80(1+0.145)^{t}\\\\10=(1.145)^{t}\\\\\ln(10)=t\cdot \ln(1.145)\\\\t=17.00522\\\\t\approx 17

Thus, the time it will take the population to grow to 800 insects is 17 days.

7 0
3 years ago
Is the polynomial t^4-7 in standard form?
slavikrds [6]

Answer:

no

Step-by-step explanation:

no,

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its c

Step-by-step explanation:

because 6 divided by 2 is three

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Simplify. Express your answer as a single fraction in simplest form.<br> x x<br> 5
lbvjy [14]

Answer:

\frac{x}{20}

Step-by-step explanation:

Given

\frac{x}{4} - \frac{x}{5}

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Three more than the quotient of a number and 6 is 8.
meriva

Answer:

x/6 + 3 = 8

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Step-by-step explanation:

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