In an arithmetic sequence:
Tn=t₁+(n-1)d
t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d
t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d
Therefore:
3t₁+12d=300 (1)
t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d
t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d
Therefore:
3t₁+45d=201 (2)
With the equations (1) and (2) we make an system of equations:
3t₁+12d=300
3t₁+45d=201
we can solve this system of equations by reduction method.
3t₁+12d=300
-(3t₁+45d=201)
-----------------------------
-33d=99 ⇒d=99/-33=-3
3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112
Threfore:
Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n
Now, we calculate T₁₈:
T₁₈=115-3(18)=115-54=61
Answer: T₁₈=61
<h2>Answer:</h2>
Number of biology textbooks sold: 257 textbooks
Number of psychology textbooks sold: 181 textbooks
<h2>Explanations:</h2>
Let the total number of biology textbook sold be "a"
Let the total number of psychology textbook sold be "b"
If a textbook store sold a combined total of 438 biology and psychology textbooks in a week, then:
a + b = 438 ................... 1
If the number of psychology textbooks sold was 76 less than the number of biology textbooks sold, then;
b = a - 76 ...................... 2
Substitute equation 2 into 1
a + (a-76) = 438
a + a - 76 = 438
2a = 438 + 76
2a = 514
a = 514/2
a = 257 biology textbooks
From equation 2;
b = a - 76
b = 257 - 76
b = 181 psychology textbooks
Number of biology textbooks sold: 257 textbooks
Number of psychology textbooks sold: 181 textbooks
Sub in 4 as x
3(4) - 29
= -17
Add all them up. 5+8+2 = 15
How many yellows? 8/15 = 0.533 ~~ 53%
Answer:
78 sqr units
Step-by-step explanation:
Use the Pythagorean Theorem to help find the base opposite the two.
The base of the second parallel line is sqrt( (15^2) - (12^2) ) = sqrt(81) = 9
The second base = 9 + 2 = 11
Area = (b1 + b2)*h/2
h = 12
b1 = 2
b2 = 11
h = 12
Area = (11 + 2)*12/2
Area = 13 * 12/2
Area = 78 square units
