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3 years ago

What is the solution to the system of equations? Use the substitution method. {y=−2x+53x−4y=2 Enter your answer in the boxes.

1 answer:

6 0

We have the following system:
y = -2x + 5
3x-4y = 2
Substituting y in equation 2 we have:
3x-4 (-2x + 5) = 2
We clear x:
3x + 8x - 20 = 2
11x = 2 + 20
x = 22/11
x = 2
Then, we substitute x = 2 in equation 1:
y = -2 (2) +5
y = -4 + 5
y = 1
Answer:
The solution to the system of equations is:
x = 2
y = 1

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Find the product <br> -1/2y(2y^3-8)

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Answer:

-y^4+4y

Step-by-step explanation:

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2 years ago

An arithmetic sequence "a" starts with 84, 77 define "a" recursively

sweet [91]

Answer:

First, let's define an arithmetic sequence:

In an arithmetic sequence, the difference between any two consecutive terms is always the same.

Then we can write it in a general way as:

aₙ = a₁ + (n - 1)*d

where:

aₙ is the n-th term of the sequence.

d is the constant difference between two consecutive terms.

a₁ is the initial term of our sequence.

Now in this case we know that the first terms of our sequence are:

84, 77, ...

Then we know the initial term of our sequence:

a₁ = 84.

And the value of d can be calculated as:

d = a₂ - a₁ = 77 - 84 = -7

Then the general way of writing this sequence is:

aₙ = 84 + (n - 1)*(-7)

And the recursion relation is:

aₙ = aₙ₋₁ - 7

So for the n-th term, we must subtract 7 of the previous term.

4 0

3 years ago

What is the equation of the line with an x-intercept of -2 and a y-intercept of 1?

vaieri [72.5K]

Answer:

the desired line is y = (1/2)x + 1

Step-by-step explanation:

Write these two points as (0, 1) and (-2, 0).

Now, as we go from (-2, 0) to (0, 1), x increases by 2 and y increases by 1. Thus, the slope, m, of the desired line is m = rise / run = 1 / 2.

Then the desired line is y = (1/2)x + 1 (since b is already given as (0, 1) )

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3 years ago

What is the length of the diagonal of the square shown below?

Tatiana [17]

Answer:

sqrt(50)

Step-by-step explanation:

Since it is a right triangle, we can apply the Pythagorem Theorem.

a^2 + b^2 = c^2

25 + 25 = c^2

50 = c^2

c = sqrt(50)

6 0

3 years ago

Read 2 more answers

A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential gr

Rufina [12.5K]

The answer is 138 million.

Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.

We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time

Step 1:
A = 120 million = 120 000 000
P = 114 million = 114 000 000
n = ?
x = 1997 - 1991 = 6
Therefore:
$120 000 000 = 114 000 000 * e ^{n*6} \\ e ^{n*6} =120 000 000 /114000000 \\ e ^{n*6} =1.05 \\$
Logarithm both sides of the equation:
$ln(e ^{n*6})=ln(1.05) \\ n*6*ln(e) = ln(1.05) \\ 6n=ln(1.05) \\ n = \frac{ln(1.05)}{6} \\ n = \frac{0.05}{6} \\ n = 0.0083$

Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2014
A = ?
P = 120 000 000
n = 0.0083
t = 2014 - 1997 = 17
$A = 120 000 000 * e ^{0.0083*17} \\ 
A = 120 000 000 * e^{0.1411} \\ 
A = 120 000 000 * 1.15 \\ 
A = 138 000 000
$
Thus, the population will be 138 million in 2014

8 0

3 years ago