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2 years ago

Please help me please! I’m stuck, and I can’t figure this out. Please include the form in your answer! No phony answers pls!

Mathematics

1 answer:

nevsk [136]2 years ago

6 0

Answer:

x ≈ - 6.74, 0.74

Step-by-step explanation:

x² + 6x - 5 = 0 ( add 5 to both sides )

x² + 6x = 5

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 5 + 9

(x + 3)² = 14 ( take square root of both sides )

x + 3 = ± $\sqrt{14}$ ( subtract 3 from both sides )

x = - 3 ± $\sqrt{14}$

Then

x = - 3 - $\sqrt{14}$ ≈ - 6.74 ( to the nearest hundredth )

x = - 3 + $\sqrt{14}$ ≈ 0.74 ( to the nearest hundredth )

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Solve and check SOLVE: 2x + 5 – 3 (2x - 7) = 2 (3x – 5) – 4

vlada-n [284]

Good morning ☕️

______

Answer:

x=4

___________________

Step-by-step explanation:

-Solving:

2x + 5 – 3 (2x - 7) = 2 (3x – 5) – 4

2x + 5 – 6x + 21 = 6x – 10 – 4

-4x + 26 = 6x - 14

10x= 26+14

10x=40

x=4

-Checking:

x=4

2(4) + 5 – 3 (2(4) - 7) = 8+5-3(8-7) = 13-3(1) =13-3=10

2 (3(4) – 5) – 4 = 2(12-5)-4 = 2(7)-4=14-4=10.

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3 years ago

The circumference of a circle is 20π cm. What is the DIAMETER of the circle?

marshall27 [118]

D≈6.37

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5 0

3 years ago

Read 2 more answers

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago

Please help me someone

nlexa [21]

Base = 5 * 12 = 60 in^2

Height = 4 in

Perimeter is the sum of all straight

Perimeter = 20 + 16 + 48

Perimeter = 84 in

Perimeter of base = 12 * 2 + 5 * 2 = 34

4 0

2 years ago

PLSSS C= <img src="https://tex.z-dn.net/?f=%5Cfrac%7B12%5E%7B3%7D%20.%206%5E%7B5%7D%20%7D%7B9%5E%7B4%7D%20.%202%5E%7B10%

Rudiy27

Answer:

Step-by-step explanation:

The trick here is to reduce each of the bases to lowest form first

$12 = 3.4 = 3 .2.2 = 3.2^{2}\\12^{3} = (3.2^{2} )^{3} = 3^{3}2^{6} \\6 = 3.2\\6^{5} = (3.2)^{5} = 3^{5} .2^{5} \\\\Numerator = 3^32^63^52^5 = 3^82^{11}\\Denominator computation\\9 = 3^2\\9^{4} = (3^{2} )^4 = 3^{8} \\Denominator = 3^82^{10} \\\\\frac{Numerator}{Denominator } =\frac{{3^8}{2^{11} }}{3^82^{10}} = \frac{2^{11}} {2^{10}} = 2^1 = 2$

7 0

1 year ago