Answer:
<h2>
y = ²/₃x + ⁴/₃</h2>
Step-by-step explanation:
The point-slope form of the equation of line: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.
y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂
{Two lines are parallel if their slopes are equal}
y = 2/3x + 1 ⇒ m₁ = 2/3 ⇒ m₂ = 2/3
(-5, -2) ⇒ x₁ = -5, y₁ = -2
point-slope form:
y - (-2) = 2/3(x - (-5))
y + 2 = 2/3(x + 5)
y + 2 = 2/3x + 10/3 {subtact 2 from both sides}
y = 2/3x + 4/3 ← slope-intercept form
Cardi B
Step-by-step explanation:
It is decreasing in the time interval 0 < x < 2 hours.
Answer:
<em>Henson: 3x + y = 163</em>
<em>Garcia: 2x + 3y = 174</em>
<em>adult ticket price: $45</em>
<em>child ticket price: $28</em>
Step-by-step explanation:
Henson Family:
3 adults + 1 child; total $163
3x + y = 163
Garcia Family:
2 adults + 3 children; total $174
2x + 3y = 174
Now we solve the system of equations.
Solve the first equation (Henson Family) for y.
y = 163 - 3x
Substitute 163 - 3x for y in the second equation (Garcia Family).
2x + 3<em>y</em> = 174
2x + 3(<em>163 - 3x</em>) = 174
2x + 489 - 9x = 174
-7x + 489 = 174
-7x = -315
x = 45
Now substitute 45 for x in the first original equation and solve for y.
3x + y = 163
3(45) + y = 163
135 + y = 163
y = 28
adult ticket price: $45
child ticket price: $28
Answer:
From the attached graphic we see that
rhombus side = Sqr Root [(Long Diagonal / 2) ^ 2 + (Short Diagonal / 2) ^ 2]
rhombus side = Sqr Root [(24/2)^2 + (18/2)^2]
rhombus side = Sqr Root [144 + 81]
rhombus side = Sqr Root (225)
rhombus side = 15 feet
Step-by-step explanation:
Answer:
14/45
Step-by-step explanation:
So we have the fraction:
We can do this algebraically. Follow to following steps:
Let's let this number equal to n. Thus:
Since there is only 1 digit repeating, let's multiply everything by 10. So:
Now, subtract n from both sides:
On the left, substitute the number for n. On the right, combine like terms:
All of the 1s will cancel. So:
Subtract:
Divide both sides by 9:
Remove the decimal by multiplying both sides by 10:
Reduce:
And we're done!
Use a calculator to check:
