Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = -1

Answers

Answer 1

Answer: Substitute each variable for the coefficient. Remember PEMDAS.

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Algebraically solve the system of equations shown below. Note that you can use either factoring or the quadratic formula to find the X – coordinates, but the quadratic formula is probably easier.

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$6x^2+19x-15=-12x+15\n6x^2+31x-30=0\n6x^2+36x-5x-30=0\n6x(x+6)-5(x+6)=0\n(6x-5)(x+6)=0\nx=(5)/(6) \vee x=-6\n\ny=-12\cdot(5)/(6) +15\vee y=-12\cdot(-6)+15\ny=-10 +15\vee y=72+15\ny=5 \vee y=87\n\nx=(5)/(6) \wedge y=5\nx=-6 \wedge y=87$

$y=6x^2+19x-15 \ny=-12x+15 \n \n6x^2+19x-15=-12x+15 \n6x^2+19x+12x-15-15=0 \n6x^2+31x-30=0 \n \n a=6 \n b=31 \n c=-30 \n \n x=(-b \pm √(b^2-4ac))/(2a)=(-31 \pm √(31^2-4 \cdot 6 \cdot (-30)))/(2 \cdot 6)=(-31 \pm √(1681))/(12)=(-31 \pm 41)/(12) \n x=(-31 -41)/(12) \ \hbox{or} \ x=(-31+41)/(12) \nx=-6 \ \hbox{or} \ x=(5)/(6)$

$y=-12 \cdot (-6)+15 \ \hbox{or} \ y=-12 \cdot (5)/(6)+15 \ny=87 \ \hbox{or} \ y=5 \n \n \hbox{the answer:} \n \boxed{x=-6, \ y=87} \ \hbox{or} \ \boxed{x=(5)/(6), \ y=5}$

If a function f ( x ) has values f ( 4 ) = 6 and f ( 8 ) = 18, use what you have learned about function patterns to find f ( 16 ) = if f ( x ) is: a.) Linear function: f ( 16 ) = b.) Power function: f ( 16 ) = c.) Exponential function: f ( 16 ) = d.) Logarithmic function: f ( 16 ) =

Answers

Answer:

a) f(16) = 42

b) f(16) = 54

c) f(16) = 162

d) f(16) = 30

Step-by-step explanation:

a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3

b = y - mx = 6 - 3(4) = 6 - 12 = - 6

f(16) = 3(16) - 6 = 42

b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ

n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3

f(16) = 2/3 × 16ⁿ = 54

c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ

b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2

f(16) = 2eᵇ¹⁶ = 162

d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)

⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)

f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4

f(16) = a㏑(b16) = 30

4. Which of the following is an arithmetic sequence?
A. 4, 1, -2,-5, -8 B.4,-12, 36, -108

Answers

A is an arithmetic sequence since the common difference is -3 while B is a geometric sequence and depends on multiples

A is the answer :) it goes my increments of -3

Find 1st 2nd 3rd 4th and 10th nTH term. rule is 4n-5

Answers

Answer:

When n is 1

4n-5

=4*1-5

=4-5

= -1

When n is 2

4n-5

=4*2-5

=8-5

When n is 3

4n-5

=4*3-5

=12-5

When n is 4

4n-5

=4*4-5

=16-5

=11

When n is 10

4n-5

=4*10-5

=40-5

=35

Will all parallelograms have diagonals that are line of symmetry

Answers

A parallelogram will always have diagonal lines of symmetry. As if you have a look at a picture of a parallelogram, there are clearly diagonal lines of symmetry.

No, not all, but overall, most of them have diagonal lines of symmetry.

Which statement is true regarding the graphed functions? A. f(4) = g(4)
B. f(4) = g(-2)
C. f(2) = g(-2)
D. f(-2) = g(-2)

Answers

Answer:c. F(2)=g(-2)

Step-by-step explanation:

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