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Travka [436]
3 years ago
11

What is the value of y in this system of equations: 3x + y = 9 y = –4x + 10 ?

Mathematics
1 answer:
Ahat [919]3 years ago
6 0
<span>3x + y = 9 (I)
</span><span>y = –4x + 10 (II)
------------------------
</span>\left \{ {{3x + y = 9 } \atop {y = -4x + 10 }} \right.

Pass the incognito "4x" to the first term, changing the signal when changing sides.
<span>-------------------------
simplify by (-1)
</span>\left \{ {{3x + y = 9.(-1)} \atop {4x + y = 10 }} \right.<span>

-------------------------
</span>\left \{ {{- 3x - \diagup\!\!\!\!y =-9} \atop {4x + \diagup\!\!\!\!y = 10}} \right.     &#10;
<span>
-------------------------
</span>\left \{ {{- 3x = - 9} \atop {4x = 10}} \right.<span>

-----------
</span>\boxed{x = 1}<span><span>

</span></span><span>Substitute in equation (I) to find the value of "Y".

</span>3x + y = 9 (I)
3*(1) + y = 9
3 + y = 9
y = 9 - 3
\boxed{y = 6}

Answer:
\boxed{\boxed{ \left \ {{x=1} \atop {y=6}} \right. }}

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Need help on this problem
faust18 [17]

Using an exponential function, it is found that:

  • For Country A, the doubling time is of 43 years.
  • For Country B, the growth rate is of 1.9% per year.

<h3>What is the exponential function for population growth?</h3>

The exponential function for population growth is given as follows:

P(t) = P(0)e^{kt}

In which:

  • P(t) is the population after t years.
  • P(0) is the initial population.
  • k is the exponential growth rate, as a decimal.
  • t is the time in years.

For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:

P(t) = P(0)e^{kt}

2P(0) = P(0)e^{0.016t}

e^{0.016t} = 2

\ln{e^{0.016t}} = \ln{2}

0.016t = \ln{2}

t = \frac{\ln{2}}{0.016}

t = 43 years.

For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.

P(t) = P(0)e^{kt}

2P(0) = P(0)e^{36k}

e^{36k} = 2

\ln{e^{36k}} = \ln{2}

36k = \ln{2}

k = \frac{\ln{2}}{36}

k = 0.019.

For Country B, the growth rate is of 1.9% per year.

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

3 0
1 year ago
Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.
Natali [406]
The answer to what the length of the leg would be is 15.

You would do this problem by first writing down your Pythagorean Theorem, which is a^2 + b^2 = c^2.

Since we have our hypotenuse which is c^2 in our equation, we would write or insert the number we have.

So our equation could be that a or b leg equals 20, it doesn’t matter which one.

So we could write, 20^2 + b^2 = 25^2. So we don’t know what b leg is.

First we should figure out what 20^2 is and what 25^2 is.

20^2 is 400 and 25^2 is 625.

Our equation now comes to 400 + b^2 = 625.

Now we take 400 and subtract it from
625 -> 400 + b^2 = 625
-400.

So 625 - 400 comes out to be 225.

Lastly instead of squaring or putting 225 to the second power, we do the opposite.

So instead of squaring 225 we must square root 225. √ 225 .

The square root of √ 225 comes out to be 15.

3 0
3 years ago
Tina and her friend are picking apples at Newberry Orchard. The apples cost $1.40 per pound. If they pick 2.5 pounds of apples,
sp2606 [1]

Answer:

$3.50

Step-by-step explanation:

the apples cost $1.40 per pound, so if we have 2.5 pounds, we would need to do this:

1.40 × 2.5

3.5

I hope this helps!

8 0
3 years ago
Dany has a business selling bracelets for 7.50 each. She only has enough material to make 5 bracelets. If x represents the numbe
ziro4ka [17]

Answer:

The range is [0,37.5]

Step-by-step explanation:

We start by writing the equation that links x and y

From the question;

y = 7.5x

Now, she has enough material to make 5 only

When we talk of range, we are referring to the values on the y-axis

So the lowest y value is 0

and since the highest number of bracelets is 5;

The total cost of the 5 is 7.5(5) = 37.5

So the range is [0,37.5]

6 0
2 years ago
A bicycle wheel has a radius of 13 inches.
mario62 [17]

Step-by-step explanation:

the circumference of a wheel is one revolution

so

formula: circumference=π*diameter

D=26cm (13*2 to find the whole length from one end to other)

so you'll do 3.14*26 equals 81.64

one revolution=81.64

30 revolutions=2,448.3 inches (times by 30 with 81.64)

3 0
3 years ago
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