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Neporo4naja [7]
2 years ago
13

Please help?????????????????????

Mathematics
1 answer:
iren [92.7K]2 years ago
5 0

Answer:

The answer is option (B)

Here is the explanation...

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If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁?<br>PLEASE HELP ME​
katen-ka-za [31]

\text{nth term of  an arithmetic sequence,}\\\\a_n = a_1 + (n-1)d\\\\a_4 = a_1 +3d=107~~~......(i)\\ \\a_8=a_1+7d = 191~~~......(ii)\\\\\\\text{(ii) -(i):}\\\\~~~~~~a_1+7d-a_1-3d = 191 -107\\\\\implies 4d = 84\\\\\implies d = \dfrac{84}4\\\\\implies d= 21\\\\\text{Substitute d= 21  in eq~(i):}\\ \\~~~~~ a_1 +3(21) =  107\\\\\implies a_1 + 63 = 107\\\\\implies a_1 = 107-63\\\\\implies a_1 =44

3 0
2 years ago
Can someone please answer. There is one problem. There's a picture. Thank you!
GrogVix [38]
The answer is B, 15,504.
The reasoning is 20C15.
      20!
---------------
(20-15)!15!

The answer to that is 15,504.
Hope I helped, boom!
7 0
2 years ago
The sum of two numbers is 45 . the smaller number is 9 less than the larger number. what are the numbers?
Cerrena [4.2K]
Larger Number: L
Smaller Number: L-9
Larger Number + Smaller Number = 45

L + L - 9 = 45
2L = 54
L = 54/2
L = 27

Smaller Number = L - 9
27 - 9 = 18

Check. .. 27 + 18 = 45. CORRECT!

Larger Number is 27
Smaller Number is 18
7 0
3 years ago
Ethan installs tiles on the floor of a room with a length of 14 feet and a width of 12 feet. It takes 9 hours to install the til
Stels [109]
Find total area
area=14 ties 12=168 ft^2
9 hours

168/9=56/3=18.6666666 ft^2 per hour

round
18.7 ft^2 per hour
6 0
3 years ago
Question 2 -of 15 Step 1 of 1No Time LimitA company manufactures two products. One requires 5 hours of labor, 3 poundsof raw mat
elena-14-01-66 [18.8K]

the cost of labour per hour is $7.20

the cost of raw materials per pound is $11.60

Explanation:

For product one:

time = 5 hours of labour

let the cost labour per hour = x

Amount = 3 pounds of raw amterials

let the cost of one pound raw material = y

Cost to produce each product = $70.8

The equation:

time (cost per hour) + amount (cost of one pound of raw material) = Cost to produce each product

5(x) + 3(y) = 70.80

5x+3y=70.8....\mleft(1\mright)

For product 2:

time = 3.5 hours of labour

let the cost of labour per hour = x

Amount = 13 pounds of raw amterials

let the cost of one pound raw material = y

Cost to produce each product = $176.00

The equation:

time (cost per hour) + amount (cost of one pound of raw material) = Cost to produce each product

3.5(x) + 13(y) = 176

3.5x+13y=176\text{   .... (2)}

combining both equations:

5x + 3y = 70.8 ...(1)

3.5x + 13y = 176 ....(2)

Using elimination method:

To eliminate y, we will multiply equation (1) by 13 and equation (2) by 3 so that both coefficient of y become the same

65x + 39y = 920.4 ...(*1)

10.5x + 39y = 528 ...(2*)

subtract equation (2*) from (1*):

65x - 10.5x + 39y - 39y = 920.4 - 528

54.5x + 0 = 392.4

54.5x = 392.4

divide both sides by 54.5:

x = 392.4/54.5

x = 7.2

substitute for x in any of the equations

Using equation 1: 5x + 3y = 70.8

\begin{gathered} 5\mleft(7.2\mright)+3y=\text{ 70.8} \\ 36\text{ + 3y = 70.8} \\ 3y\text{ = 70.8 - 36} \\ 3y\text{ = 34.8} \\  \\ \text{divide both sides by 3:} \\ \frac{3y}{3}=\frac{34.8}{3} \\ y\text{ = }11.6 \end{gathered}

Hence, the cost of labour per hour is $7.20 and the cost of raw materials per pound is $11.60

6 0
1 year ago
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