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3 years ago

Based on the graph, what are the approximate solutions to the equation −3x + 8 = (0.25)x?

Mathematics

1 answer:

storchak [24]3 years ago

6 0

Let

$f(x)=3x+8$

$g(x)=0.25^{x}$

in this problem

f(x)=g(x)

$3x+8=0.25^{x}$

using a graph tool

the solution is the intersection of both graphs

see the attached figure

the solutions are

x=-1.89

x=2.66

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PLEASEEEEE HELPPPP MEEEEEEE BRAINLIEST TO THE FIRST ANSWER AND 30 POINTS

icang [17]

Answer:

CD ≠ EF

Step-by-step explanation:

Using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = C(- 2, 5) and (x₂, y₂ ) = D(- 1, 1)

CD = $\sqrt{(-1+2)^2+(1-5)^2}$

= $\sqrt{1^2+(-4)^2}$

= $\sqrt{1+16}$ = $\sqrt{17}$

Repeat using (x₁, y₁ ) = E(- 4, - 3) and (x₂, y₂ ) = F(- 1, - 1)

EF = $\sqrt{(- 1+4)^2+(-1+3)^2}$

= $\sqrt{3^2+2^2}$

= $\sqrt{9+4}$ = $\sqrt{13}$

Since $\sqrt{17}$ ≈ $\sqrt{13}$ , then CD and EF are not congruent

6 0

3 years ago

The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485. For each decrease in unit p

ANTONII [103]

Answer:

Demand Equation: q = 15125 - 25p.

Supply Equation: 80p - 24000 = 9q.

Equilibrium Price: $525.

Equilibrium Quantity: 2000 units.

Step-by-step explanation:

To solve this question, first, the demand equation has to be calculated. Let price be on the y-axis and quantity by on the x-axis. It is given that p = $485 when q = 3000 units. This can also be written as (q₁, p₁) = (3000, 485). It is also given that when the price goes down by $20, the quantity increases by 500 units. Therefore, (q₂, p₂) = (3500, 465). Due to the statement "For each decrease in unit price of $20 below $485, the quantity demanded increases by 500 units", the demand function will be linear i.e. a straight line. This is because the word "for each" has been used. Therefore, finding the equation of the demand function:

(p - p₁)/(q - q₁) = (q₂ - q₁)/(p₂ - p₁).

(p - 485)/(q - 3000) = (465 - 485)/(3500 - 3000).

(p - 485)/(q - 3000) = (-20)/(500).

(p - 485)/(q - 3000) = -1/25.

25*(p - 485) = -1*(q - 3000).

25p - 12125 = -q + 3000.

25p + q = 15125.

q = 15125 - 25p. (Demand Equation).

Second, find the supply equation. It is given that the suppliers will not sell the product below or at the price of $300. Therefore, (q₁, p₁) = (0, 300). Also, the suppliers will sell 2000 units if the price is $525. Therefore, (q₂, p₂) = (2000, 525). Since it is mentioned that supply equation is linear, therefore:

(p - p₁)/(q - q₁) = (q₂ - q₁)/(p₂ - p₁).

(p - 300)/(q - 0) = (525 - 300)/(2000 - 0).

(p - 300)/(q) = (225)/(2000).

(p - 300)/(q) = 9/80.

80*(p - 300) = 9*(q).

80p - 24000 = 9q. (Supply Equation).

Equilibrium exists when demand = supply. This means that the demand and the supply equations have to be solved simultaneously. Therefore, put demand equation in supply equation:

80p - 24000 = 9(15125 - 25p).

80p - 24000 = 136125 - 225p.

305p = 160125.

p = $525.

Put p = $525 in demand equation:

q = 15125 - 25p.

q = 15125 - 25(525).

q = 15125 - 13125.

q = 2000 units.

To summarize:

Demand Equation: q = 15125 - 25p!!!

Supply Equation: 80p - 24000 = 9q!!!