Answer:
i think its 6c+240=1200
Step-by-step explanation:
6 = amount of nights
240=tax
c = total cost a night
1200 = budget
For the first expression
15 + 2d
A possible word problem would be this:
A person saves $2 per day of money. Before he started saving, he had $15 dollars set aside. Look for the expression that expresses the total amount of money saved in terms of the number of days passed
The second expression is
200 - 2m
A possible word problem would be this:
The distance from school to the park is 200m. A kid riding a bike is traveling at a speed of 2m/s from the school to the park. Write an expression for the distance remaining between the park and the kid.<span />
Answer:
(x + 1)² = 7
Step-by-step explanation:
Given:
-2x = x² - 6
We'll start by rearranging it to solve for zero:
x² + 2x - 6 = 0
The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.
Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:
x² + 2x + 1 - 1 - 6 = 0
Now can group our perfect square on the left and our constants on the right:
x² + 2x + 1 - 7= 0
x² + 2x + 1 = 7
(x + 1)² = 7
To check our answer, we can solve for x:
x + 1 = ± √7
x = -1 ± √7
x ≈ 1.65, -3.65
Let's try one of those in the original equation:
-2x = x² - 6
-2(1.65) = 1.65² - 6
- 3.3 = 2.72 - 6
-3.3 = -3.28
Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.
The solution to the linear expressions are:
- a. $36.26
- b. -$19.35
- c. $70.38
<h3>Solving linear expressions:</h3>
The solution to linear expression is determined by taking into consideration the arithmetic operations used in each linear expression.
From the information given:
a. $18.79 + $2.11 + ‐$1.92 + $17.28
By rearrangement:
= $18.79 + $2.11 + $17.28 ‐$1.92
= $36.26
b. $7.45 + ‐$24.45 + $74.17 + ‐$76.52
By rearrangement:
= $7.45 + $74.17 ‐ $24.45 ‐ $76.52
= -$19.35
c. $98.45 − $10.63 + $2.82 − $20.26
By rearrangement:
= $98.45 + $2.82 − $10.63 − $20.26
= $70.38
Learn more about solving linear expressions here:
brainly.com/question/2030026
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Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
