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2 years ago

Using a graphical method, solve the simultaneous equations x+y =4 and y=2x+1

Mathematics

1 answer:

adoni [48]2 years ago

7 0

Answer:

(1, 3)

Step-by-step explanation:

Given the expression

x+y = 4 ... 1

y = 2x+1 ....2

Substitute equation 2 into 1

x + (2x+1) = 4

3x + 1 = 4

3x = 4-1

x = 3/3

x = 1

Since y = 2x + 1

y = 2(1) + 1

y = 3

Hence the solution to the equation is (1,3). This means that the coordinate point on the graph where both lines intersect will be at (1, 3)

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35. V112 + V63<br> How do I solve this please

konstantin123 [22]

Answer: 175V

Step-by-step explanation:

V112+V63=112v+63V

Add them together because the terms are like terms. Therfore, 112V+63V=175V

4 0

3 years ago

What is the area of the composite figure in problem 3?

suter [353]

Answer:

trapazoid

Step-by-step explanation:

5 0

3 years ago

Lisa set her watch 20 seconds behind, and it falls behind another 1 second every day. How many days has it been since Lisa last

DENIUS [597]

Answer:

Step-by-step explanation:

46-20

7 0

3 years ago

The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a

Bond [772]

Answer:

Step-by-step explanation:

A) Demand per month= 40 cars

Annual Demand (D)= 12*40 = 480

Fixed Cost per order (K)= 15

Holding Cost= 20% of cost= 60 *0.2 = 12

a. Economic Order Quantity=

Q^{*}={\sqrt {{\frac {2DK}{h}}}}

= √(2*480*15)/12

=34.64 ~ 35

Total Cost =P*D+K(D/EOQ)+h(EOQ/2) P= Cost per unit

= 60*480+ 15(480/35) + 12(35/2)

= 28800+ 205.71+ 210

=$29215.71

B). Backorder Cost (b)= $45

Qbo= Q* × √( b+h/ h)

= 35*√(12+45/ 45)

= 35* 1.12

=39.28 ~ 39

Shortage (S)= Qbo * (K/K+b)

= 39* (15/15+45)

= 39* 0.25

= 9.75

Total Cost Minimum=( bS2/ 2Qbo) + P (Qbo- S)2/2Qbo + K(D/Qbo)

=45* 9.752 / 2* 392 + 60 (39-9.75)2/ 2* 392 + 15 ( 480/39)

= 1.40+ 21.9.+ 184.61

=$207.91

C)Length of backorder days (d) = Demand ÷ amount of working days

d = 480 ÷ 300

d = 1.6

Calculate the backorders as the maximum number of backorders divided by the demand per day

s/d = 9.75/1.6 = 6.09 days (answer)

D) Calculate the difference in total between not using backorder:

$207.85 + $207.85 - 207.91 = $207.79

The saving in using backorder is $207.79.

Therefore I would recommend using a backorder

6 0

2 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

maxonik [38]

Answer:

Total weight of the wheat placed on 45th square will be = $1.26\times 10^{6}tons$

Step-by-step explanation:

King rewarded the inventor of chess by giving grain of wheat on every square of the chess board. He places one grain of wheat on first square, 2 on second, 4 on 3rd, 8 on 4th and so on.

In fact he places grains of wheat in a progression S = 1, 2, 4, 8, 16.........n terms where value of n is 64.

We can rewrite the progression as S = 2°, 2, 2², 2³,.........n terms (n = 64)

In a geometric progression we know the nth term = $a(r^{n-1})$

where a = first term of the series, r = common ratio, n = number of terms

Now we have to calculate the weight of all wheat placed on 45th square.

So we will put the values in the given formula 45th term =

$1\times (2^{45-1})$ = $2^{44}$ = $1.76\times 10^{13}$

Then the weight of wheat will be = $2.51\times 10^{9}pounds$ = $1.26\times 10^{6}tons$

7 0

3 years ago