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xenn [34]
2 years ago
15

Hi. I need help with these See image for question Answer no 8 ,9 and 10

Mathematics
1 answer:
Nezavi [6.7K]2 years ago
4 0

Answer:

  • 8) 4 + 2q²/p² - 4r/p + r²/p²
  • 9) (3/4, -9/4)
  • 10) (3/8, 41/16)

Step-by-step explanation:

8. ============

Given

  • α and β are roots of px² + qx + r = 0

The sum of the roots is α + β = -q/p, the product of then roots αβ = r/p

  • (2 + α²)(2 + β²) =  
  • 4 + 2(α² + β²) + (αβ)² =
  • 4 + 2((α + β)² -2αβ) + (αβ)² =
  • 4 + 2((-q/p)² - 2r/p) + (r/p)² =
  • 4 + 2q²/p² - 4r/p + r²/p²

------------------------------

9. ============

<u>Given function</u>

  • y = 2x² - 3x - 1

The minimum point is reached at vertex

<u>The vertex is:</u>

  • x = -b/2a
  • x = -(-3)/2*2 = 3/4

<u>The corresponding y-coordinate is:</u>

  • y = 2(3/4)² - 3(3/4) - 1 = 9/8 - 9/4 - 1 = 1/8(9 - 18 - 9) = - 18/8 = - 9/4

<u>So the point is: </u>

  • (3/4, -9/4)

---------------

10. ============

<u>Given function</u>

  • y = 2 - 3x - 4x²

The maximum is reached at vertex

<u>The vertex is:</u>

  • x = -b/2a
  • x = -(-3)/2(-4) = -3/8

<u>The corresponding y-coordinate is:</u>

  • y = 2 - 3(-3/8) -4(-3/8)² = 2 + 9/8 - 9/16 = 1/16(32 + 18 - 9) = 41/16

<u>So the maximum point is:</u>

  • (3/8, 41/16)

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Answer:

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Step-by-step explanation:

5 0
2 years ago
What are the domain and range of g of x equals the square root of the quantity x plus 4?
Vadim26 [7]

It is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).

<h3>What are the domain and range of a function?</h3>
  • The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x).
  • A function's range is the set of values that the function can take.
  • This is the set of values that the function returns after we enter an x value.

To find the domain and range:

  • The given function in the problem is: g(x)=\sqrt{x+4}
  • Because the square root function does not exist for negative numbers, the domain is denoted by: x+4 ≥ 0 → x ≥ -4
  • Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).
  • The range of the square root function is x ≥ 0, which remains the same as there are no vertical translations.

Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).

Know more about the range here:

brainly.com/question/26098895

#SPJ4

The complete question is given below:

What are the domain and range of g of x equals the square root of the quantity x plus 4?

(A) D: [4, ∞) and R: [0, ∞)

(B) D: (–4, ∞) and R: (–∞, 0)

(C) D: [–4, ∞) and R: [0, ∞)

(D) D: (4, ∞) and R: (–∞, 0)

3 0
11 months ago
EXPLAIN ANSWER PLZ!
Dmitriy789 [7]

height,h = 3"

base, b = length, l = 2

area of triangle, t = bxh/2...eqn 1

area of square, s = l^2...eqn 2

area of pyramid, p =4t + s...eqn 3

subst h = 3 and b = 2 in eqn 1

t = 3x2/2 = 3

subst l =2 in eqn 2

s = 2^2 = 4

subst t = 3 & s = 4 in eqn 3

p = 4(3) + 4 = 16sq inch

6 0
3 years ago
Which equation represents this sentence?
Oduvanchick [21]
It should be n+4=3n. Hope this helps
3 0
2 years ago
1. <br> Simplify: 5 + p &gt; 3<br> p -2<br> p &gt; 8
OlgaM077 [116]

Answer:

p > -2.

Step-by-step explanation:

5 + p > 3

5 - 5 + p > 3 - 5

p > -2.

7 0
2 years ago
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