Answer:
77 is the ninth term.
Step-by-step explanation:
You start out with adding 3 and every time you add a new number you add the last number you added to it and add 2.
Answer:
a) 820
b)450
c) -540
d) -294
e) 1440
f) 1425
Step-by-step explanation:
a) it is an arithmetic progression with ratio=4
a1=3,
a2=3+r=3+4=7.....
a20=a1+19r
so a20=3+19*4=3+76=79
S=(a1+an)*n/2 where n=20
so S=(3+79)*20/2=820
b) a15=a1+14*r=2+14*4=2+56=58
S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450
It is the same formula for all the exercises
S=(a1+an)*n/2 , where n is the number of terms
c) a40=30+39*(-3)=30-87=-57
So S=(30-57)*40/2=-540
d) a14=5+13*(-4)=5-52=-47
S=(5-47)*14/2=-42*14/2=-42*7=-294
e) it is 5+7+9+......+75
nr of terms = (an-a1) :r+1=(75-5):2+1=36
S=(5+75)*36/2=36*40=1440
f) ratio=7-4=3
the same formula for n= (91-4):3+1=87:3+1=29+1=30
S=(4+91)*30/2=95*30/2=2850/2=1425
Answer:
Step-by-step explanation:
Let x represent the length of the shorter base in inches. Then the longer base has length x+6. The area of the trapezoid is given by the formula ...
A = (1/2)(b1 +b2)h
Filling in the values we know, we have ...
48 = (1/2)(x +(x+6))(6)
16 = 2x +6 . . . . . divide by 3
10 = 2x . . . . . . . . subtract 6
5 = x . . . . . . . . . . divide by 2
(x+6) = 11 . . . . . . find the longer base
The lengths of the bases are 5 inches and 11 inches. We found them by solving an equation relating area to base length.
I don’t understand I’m not sure
The function 1.5x + 0.5y = 12 represents the number of hardcover books x and softcover books y you can buy at a used book sale.
(a) solve for y
We need to isolate y
1.5x + 0.5y = 12
Subtract 1.5x on both sides
0.5y = 12 - 1.5x
Divide by 0.5 on both sides
![y = \frac{12}{0.5} - \frac{1.5}{0.5}](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7B12%7D%7B0.5%7D%20-%20%5Cfrac%7B1.5%7D%7B0.5%7D%20%20)
y= 24 - 3x
(b) Table for y= 24 -3x
x -----> y
0 -----> 24
1 ------> 21
2-------> 18
The ordered pairs are (0,24) (1,21)(2,18)
(c) Graph is attached below