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Tom [10]
3 years ago
9

Use substitution to solve each system of equations. y = 5x -2 3 x- 5y =4

Mathematics
2 answers:
Nezavi [6.7K]3 years ago
7 0
  • x = 3/11
  • y = -7/11

Step-by-step explanation:

y = 5x - 2…Equation 1

3x - 5y = 4…Equation 2

Subtitute value of y to Equation 2 :

3x - 5(5x - 2) = 4

3x - 25x + 10 = 4

-22x + 10 = 4

10 - 4 = 22x

6 = 22x

6/22 = x

<u>3/11 = </u><u>x</u>

Subtitute value of x to one of Equation :

for example Equation 2…

3x - 5y = 4

3(3/11) - 5y = 4

9/11 - 5y = 4

9/11 - 4 = 5y

(9 - 44)/11 = 5y

(-35)/11 = 5y

(-35)/11 × 1/5 = y

<u>-7/11 = y</u>

Mrrafil [7]3 years ago
3 0
3x - 5(5x - 2) = 4

3x - 25x + 10 = 4
-22x = 4 - 10
-22x = -6 ➗ -22
X = 3/11
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A necklace regularly sells for $18.00. the store advertises a 15% discount. what is the sale price of the necklace in dollars
SSSSS [86.1K]
I can solve with 2 methods:

I. Because the discount is 15 % of 18 $ , the price will be (100-15=85) 85 % of 18 $
18*85/100= 15,3 $ ( the sale price)

II. The discount is 15 % of 18$
15*18/100= 2,7$  ( the discount)
then I decrease it from the regularly price
18$-2,7$=15,3 $ (the sale price)

Personally I believe the first is an easier method.
I hope you understand and you can apply this in every similary problem.



6 0
3 years ago
Fiona invested $1000 at 7% compounded continuously. At the same time, Maria invested $1100 at 7% compounded daily. How long will
Natali [406]

9514 1404 393

Answer:

  14,201 years

Step-by-step explanation:

The two compound interest formulas are ...

  A = P·e^(rt) . . . . . continuous compounding at rate r for t years

  A = P·(1 +r/365)^(365t) . . . . . daily compounding at rate r for t years

We went the amounts to be equal:

  1000·e^(0.07t) = 1100·(1+0.07/365)^(365t)

Dividing by 1000(1 +0.07/365)^(365t), we have ...

  ((e^0.07)/(1+0.07/365)^365)^t = 1.1

The base of the exponential on the left is ...

 ( e^0.07)/(1+0.07/365)^365 ≈ 1.00000671149321522

Taking logs, we have ...

  t×ln(1.00000671149321522) = ln(1.1)

  t = ln(1.1)/ln(1.00000671149321522) ≈ 0.09531018/(6.7114704·10^-6)

  t ≈ 14,201.09 . . . . . years

It will take about 14,201 years for the investments to be equal.

_____

<em>Additional comment</em>

The investment value at that time will be about $5.269·10^434. (That's a larger number than <em>anything</em> countable in the known universe, including energy quanta.)

These calculations are beyond the ability of many calculators, so might need to be carefully rewritten if the calculator only keeps 10 significant digits, or only manages exponents less than 100.

This shows that daily compounding is very close in effect to continuous compounding. It would take almost 150 years to make a difference of 0.1% in value.

4 0
3 years ago
What is the equation of the line through (-6, -5) and (-4, -4)?
Norma-Jean [14]

Answer:

  y = 1/2x -2

Step-by-step explanation:

The 2-point form of the equation for a line is useful for answering questions like this.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . equation of a line through (x1, y1) and (x2, y2)

Filling in the given points, the equation becomes ...

  y = (-4 -(-5))/(-4 -(-6))/(x -(-6)) -5

  y = 1/2(x +6) -5

  y = 1/2x -2

3 0
3 years ago
Write 631.8 as a mixed number.​
docker41 [41]

Answer:

631 4/5

Step-by-step explanation:

5 0
2 years ago
Is to be constructed for use on padre island beaches. it is to have a back, two square sides, and a top. if 96 square feet of ca
ss7ja [257]
Area of the canvas: 96 = 2 · W² + 2 · W L,
where W is the width and L is the length of a back and a top side. Two square sides have area W².
2 W L = 96 - 2 W² /:2
W L = 48 - W²
L = ( 48 - W² ) / W.
The inside volume of the shelter:
V = L · W · W = L · W²
V = W² · ( 48 - W² ) / W ;
V = 48 W - W³
We have to find the derivative:
V ` = 48 - 3 W²
48 - 3 W² = 0 ( for V max. )
3 W² = 48
W² = 48 : 3
W² = 16;  W = √16;  W = 4 ft.
L = ( 48 - 16 ) / 4 = 32 / 4 = 8 ft.
Answer: The length of the shelter for which the volume inside is maximized is  8 ft.
8 0
3 years ago
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