All categories

14 days ago

Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

2 answers:

4 0

The solution is x = 6 + √21. The standard equation of a quadratic function is ax2 + bx + c = 0. Thus, the equation x2 = 12x – 15 can be rearranged to x2 - 12x + 15 = 0. Next, we move the constant term to the right side: x2 - 12x = -15. Here, b = 12, so (b/2)² = (12/2)² = (6)² = 36. We add this value to both sides: x2 - 12x + 36 = -15 + 36. Consequently, (x-6)² = 21. Taking the square root on both sides results in x - 6 = √21. Solving for x reveals that x = 6 + √21.

tester [8.8K]14 days ago

3 0

We are presented with the following polynomial: The initial step is to move the variables to one side of the equation. After doing this, we have: We complete the square by adding (b / 2) ^ 2 to both sides of the equation. After doing so, we obtain: Rewriting this gives us: Therefore, the solutions are: The solution set of the equation is:

You might be interested in

What is a31 of the arithmetic sequence for which a5=3.2 and a9=12.0?

zzz [9093]

The formula for an arithmetic sequence:

$a_n=a_1+(n-1)d$

We are given:

$a_5=3.2,\ a_9=12.0$

Determine d (the common difference)

$a_9-a_5=4d\\\\4d=12.0-3.2\\\\4d=8.8\ \ \ |:4\\\\d=2.2$

Calculate a31:

$a_{31}=a_5+26d\\\\a_{31}=3.2+26\cdot2.2=60.4$

7 0

27 days ago

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

lawyer [9240]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Details: The cardiac output is assessed using the dye dilution technique with 3 mg of dye.

Goal: To determine the cardiac output value.

Solution:

Cardiac output formula: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Utilize integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Insert the value into 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Consequently, Cardiac output: $F=0.055 L\s$

4 0

18 days ago

At a hot air ballon festival, Erica spots a red ballon due east at an angle of elevation of 36 degrees. She turns due west and s

Zina [9179]

Answer:

Step-by-step explanation:

Information provided

The eastern balloon makes an elevation angle of $36^{\circ}$ and is positioned at a height of 461 m.

The western balloon creates an elevation angle of $51^{\circ}$ and is positioned at a height of 296 m.

Considering that Erica is 1.6 m tall, the effective height of the Red balloon becomes 459.4 m,

while the effective height of the Blue balloon ends up at 294.4 m.

Utilizing trigonometric principles,

$\tan 36=\frac{459.4}{d_1}$

$\tan 51=\frac{294.4}{d_2}$

$d_1=632.30 m$

$d_2=238.4 m$

Now calculating the distance separating the two Balloons,

$d=d_1+d_2$

$d=870.70 m$

7 0

20 days ago

Given f(x) = x3 – 2x2 – x + 2, the roots of f(x) are

PIT_PIT [9121]

The expression in question is:

f(x) = x³ – 2x² – x + 2

To determine the roots, follow these steps:

1. Set the equation to zero:

0 = x³ – 2x² – x + 2

2. Factor the equation to get:

(x-2)(x-1)(x+1) = 0

3. The roots can be identified as follows:

x1 = -1
x2 = 1
x3 = 2

3 0

27 days ago

Read 2 more answers

Students have organized

tester [8842]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed