Solve each equation by using the square roots property round to the nearest hundredth if necessary

Please Help Me On These Math Questions!!!!! Solve Each System By Elimination

nekit [7.7K]

11) -x + y = -1 ; 2x - y = 0
y = -1 + x ; 2x - (-1+x) = 0 ⇒ 2x + 1 - x = 0 ⇒x = -1
y = -1 + (-1) ⇒ y = -2

12) -2x + y = -20 ; 2x + y = 48
y = -20 + 2x ; 2x + (-20 + 2x) = 48 ⇒ 2x -20 + 2x = 48 ⇒ 4x = 48 + 20
4x = 68 ⇒ x = 68/4 ⇒ x = 17
y = -20 + 2(17) ⇒ y = -20 + 34 ⇒ y = 14

13) 3x -y = -2 ; -2x + y = 3
y = 3 + 2x ; 3x - (3 + 2x) = -2 ⇒ 3x - 3 - 2x = -2 ⇒ x = -2 + 3 ⇒ x = 1
y = 3 + 2(1) ⇒ y = 3 + 2 ⇒ y = 5

14) x - y = 4 ; x - 2y = 10
x = 4 + y ; (4 + y) - 2y = 10 ⇒ 4 + y - 2y = 10 ⇒ 4 - y = 10
⇒ -y = 10 - 4 ⇒ -y = 6 ⇒ y = -6
x = 4 + (-6) ⇒ x = 4 - 6 ⇒ x = -2

15) x + 2y = 5 ; 3x + 2y = 17
x = 5 - 2y ; 3(5-2y) + 2y = 17 ⇒ 15 - 6y + 2y = 17 ⇒ -4y = 17 - 15
⇒ -4y = 2 ⇒ y = -2/4 ⇒ y = -1/2
x = 5 - 2(-1/2) ⇒ x = 5 + 2/2 ⇒ x = 5 + 1 ⇒ x = 6

5 0

3 years ago

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The Fruitz fruit and vegetable shop is selling grapes at a price which is 10% cheaper than the Happy Fruiterer fruit and vegetab

sdas [7]

Answer:

(a) It costs $55 at Happy Fruiterer

(b) It will cost $49.64

(c) It is cheaper at Happy Fruiterer the second week

Step-by-step explanation:

Since Fruitz shop sells as 10% less than Happy Fruiterer at $50

10% more of $50 = 50 × 10/100 + 50

= $5 + $50 = $55

(a) n Kg of grapes will cost $55 at Happy Fruiterer

(b) if Happy Fruits discounts $55 by 5%, we will have

55 × 5/100 = 2.75

that is $55 - $2.75 = $52.25

If it is discounted further at 5% more the following week, we will have

$52.25 × 5/100 = $2.6125

≈ $2.61

Then the new price for the 2nd week is $52.25 - $2.61

= $49.64

(c) at the second wee of discounting, Fruitz shop still sells at $50 will Happy Fruiterer now see at $49.64. Therefore, it is cheaper at Happy Fruiterer

8 0

3 years ago

Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1).

Vesna [10]

Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way: $y'= \frac{x(0)-3(1)}{x^2}$ so $y'=- \frac{3}{x^2}$ . The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is: $y'=- \frac{3}{3^2}=- \frac{3}{9}=- \frac{1}{3}$ . So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b. $1=- \frac{1}{3}(3)+b$ so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is $y=- \frac{1}{3}x+2$