Answer:
The first term of the sequence is:
Step-by-step explanation:
Given the sequence
aₙ = (-1)ⁿ · 3n²
substituting n = 1 to determine the first term
a₁ = (-1)¹ · 3(1)²
a₁ = (-1)¹ · 3(1)²
Applying the exponent rule: ![a^1=a](https://tex.z-dn.net/?f=a%5E1%3Da)
a₁ = -1 · 3(1)
a₁ = -1 · 3
a₁ = -3
substituting n = 2 to determine the 2nd term
a₂ = (-1)² · 3(2)²
a₂ = 1 · 3(4)
a₂ = 12
substituting n = 3 to determine the 3rd term
a₃ = (-1)³ · 3(3)²
a₃ = -1 · 3(9)
a₃ = -1 · 27
a₃ = -27
substituting n = 4 to determine the 4th term
a₄ = (-1)⁴ · 3(4)²
a₄ = 1 · 3(16)
a₄ = 1 · 48
a₄ = 48
Therefore, the first term of the sequence is:
Answer: a. 450
b. 7950
Step-by-step explanation:
If Cheryl earns 6% interest during the 6 years she will have
(7500*6)/100=450
450 is the interest that she received
her new balance will be
7500+450=7950
Answer: slope m=-1
Step-by-step explanation:
Answer:
y = 2/3x - 5 or in standard form 3y = 2x - 5
Step-by-step explanation:
Remember this fact: Parallel lines have the same slope
Step 1 Solve for y so that the equation is in the slope- intersect form
2x - 3y = 6
-3y = -2x + 6
-3y/-3 = -2x/-3 + 6/-3
y = 2/3 x -2
now we know the slope is 2/3 or
when the equation is in Standard form Ax + By = C you can use this fact: slope = - A/B so the slope = -2/-3 = 2/3
Remember the Parallel lines have the same slope
Find the y-intersect "b" use the slope = 2/3 and point (6, -1)
y = mx + b
-1 = 2/3(6) + b
-1 = 4 + b
-5 = b
Now write the equation of line that is parallel to the given line and passes through point (6, -1)
y = 2/3x - 5 or in standard form 3y = 2x - 5
Answer:
x = 133°
Step-by-step explanation:
Straight-line pair - A pair of angles that lie on a straight line.
<em>*</em><u><em>Property</em><em>*</em></u>
The sum of two angles of a straight-line pair is equal to <u>180°</u>.
The given angles – x and y – form a <u>straight-line pair.</u>
==> x + y = 180
<em>{</em><em>y</em><em> </em><em>=</em><em> </em><em>4</em><em>7</em><em>°</em><em> </em><em>(</em><em>given</em><em> </em><em>in</em><em> </em><em>t</em><em>he</em><em> </em><em>question</em><em>)</em><em>}</em>
<em>Substituting</em><em> </em><em>4</em><em>7</em><em> </em><em>for</em><em> </em><em>y</em><em>:</em>
==> x + 47 = 180
<em>Subtracting</em><em> </em><em>4</em><em>7</em><em> </em><em>from</em><em> </em><em>both</em><em> </em><em>sides</em><em>:</em>
==> x = 47 - 47 = 180 - 47
==><u> x = 133</u>