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2 years ago

Solve the following quadratic equation:x/x+3 = 5/2x+6

Mathematics

1 answer:

Leni [432]2 years ago

7 0

Answer:

$x=5/2, x=-3\\$

Step-by-step explanation:

$x(2x+6)=5(x+3)\\2x^2+6x=5x+15\\2x^2+6x-5x-15=0\\2x^2+x-15=0\\2x^2+6x-5x-15=0\\2x(x+3)-5(x+3)=0\\(2x-5)(x+3)=0\\2x-5=0, x+3=0\\x=5/2, x=-3\\$

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kotykmax [81]

Answer:

4096π / 5

Step-by-step explanation:

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E is the range 0 ≤ r ≤ 4, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π.

∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r²) (r² sin φ dr dθ dφ)

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Evaluate the first integral.

∫₀ᵖⁱ∫₀²ᵖⁱ (⅕ r⁵ sin φ)|₀⁴ dθ dφ

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Evaluate the second integral.

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5 0

2 years ago

The altitude of a triangle is increasing at a rate of 1.5 1.5 centimeters/minute while the area of the triangle is increasing at

seraphim [82]

Answer:

The base reduces at 3.75cm/min

Step-by-step explanation:

Given

Let

$h \to altitude$

$b \to base$

$A \to Area$

So:

$\frac{dh}{dt} = 1.5cm/min$

$\frac{dA}{dt} = 1.5^2cm/min$

The area of a triangle is:

$A = \frac{1}{2}bh$

Calculate b when $A =88cm^2; h =8cm$

$A = \frac{1}{2}bh$

$88=\frac{1}{2} * b * 8$

$88 =b * 4$

Solve for b

$b = 88/4$

$b = 22$

We have:

$A = \frac{1}{2}bh$

Differentiate with respect to time

$\frac{dA}{dt} =\frac{1}{2}(h\frac{db}{dt} + b\frac{dh}{dt})$

Substitute the following values in the above equation

$\frac{dh}{dt} = 1.5cm/min$ $\frac{dA}{dt} = 1.5^2cm/min$ $b = 22$ $h = 8$

$1.5 = \frac{1}{2}(8 * \frac{db}{dt} + 22 * 1.5)$

Multiply both sides by 2

$3 = 8 * \frac{db}{dt} + 22 * 1.5$

$3 = 8 * \frac{db}{dt} + 33$

Collect like terms

$8 * \frac{db}{dt} = 3 -33$

$8 * \frac{db}{dt} = -30$

Divide both sides by 8

$\frac{db}{dt} = -\frac{30}{8}$

$\frac{db}{dt} = -3.75$

4 0

3 years ago

8 2/3 divided by 4 1/8=2 1/10

Serggg [28]

Answer:

8 2/3 divided by 4 1/8=2 1/10 is Correct

exactly 2 10/99

3 0

2 years ago

One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is

lianna [129]

Answer:

Step-by-step explanation:

Let the smaller integer be x.

The other integer is 1 greater than 3 times x, or 3x + 1.

The product is 154.

x(3x + 1) = 154

3x^2 + x - 154 = 0

157 = 2 * 7 * 11

14 * 11 = 154

22 * 7 = 154

(3x + 22)(x - 7) = 0

3x + 22 = 0 or x - 7 = 0

3x = -22 or x = 7

x = -22/3 or x = 7

-22/3 is not a positive integer, so we discard that solution.

The smaller integer is 7.

3x + 1 = 3(7) + 1 = 22

The greater integer is 22.

The sum of the integers is 7 + 22 = 29

5 0

3 years ago

Read 2 more answers

Solve the following quadratic equation using the quadratic formula.

valentina_108 [34]

The quadratic formula tells you the solution to
ax² +bx +c = 0
is
$x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$
Plugging in the values a=5, b=-8, c=5, you get
$x=\frac{8 \pm \sqrt{(-8)^{2}-4\cdot 5\cdot 5}}{2\cdot 5} = \frac{8 \pm \sqrt{-36}}{10} = \frac{4 \pm 3i}{5}$

Your solution is
$x=\frac{4-3i}{5},x=\frac{4+3i}{5}$

8 0

3 years ago

Solve the following quadratic equation:x/x+3 = 5/2x+6​

Solve the following quadratic equation:x/x+3 = 5/2x+6