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3 years ago

5

An earthquake wave travels 55 km of rock in 25

1 answer:

navik [9.2K]3 years ago

8 0

Answer:

The answer is D) 2.2km

Step-by-step explanation:

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Solve for x<br><br> THANK YOU

Anestetic [448]

Answer:

$x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}$

Step-by-step explanation:

$\textsf{Given equation}:$

$\dfrac{2}{3}x+\dfrac{3x}{x}=\dfrac{4x}{2}(3x+6)$

$\textsf{Cancel the common factor } x \textsf{ in }\dfrac{3x}{x}:$

$\implies \dfrac{2}{3}x+3=\dfrac{4x}{2}(3x+6)$

$\textsf{Simplify }\dfrac{4x}{2}\textsf{ by dividing the numbers}:$

$\implies \dfrac{2}{3}x+3=2x(3x+6)$

$\textsf{Apply the distributive law}\quad \:a\left(b+c\right)=ab+ac:$

$\implies \dfrac{2}{3}x+3=6x^2+12x$

$\textsf{Multiply both sides by 3 to cancel the denominator of }\dfrac{2}{3}:$

$\implies \dfrac{2}{3}x\cdot 3+3\cdot 3=6x^2\cdot 3+12x \cdot 3$

$\implies 2x+9=18x^2+36x$

$\textsf{Switch sides}:$

$\implies 18x^2+36x=2x+9$

$\textsf{Subtract }2x \textsf{ from both sides}:$

$\implies 18x^2+36x-2x=2x+9-2x$

$\implies 18x^2+34x=9$

$\textsf{Subtract 9 from both sides}:$

$\implies 18x^2+34x-9=9-9$

$\implies 18x^2+34x-9=0$

Solve using the <u>Quadratic Formula:</u>

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Define the variables:

$\implies a=18, \quad b=34, \quad c=-9$

Substitute the defined variables into the quadratic formula and solve for x:

$\implies x=\dfrac{-34 \pm \sqrt{34^2-4(18)(-9)} }{2(18)}$

$\implies x=\dfrac{-34 \pm \sqrt{1156+648} }{36}$

$\implies x=\dfrac{-34 \pm \sqrt{1804} }{36}$

$\implies x=\dfrac{-34 \pm \sqrt{4 \cdot 451} }{36}$

$\implies x=\dfrac{-34 \pm \sqrt{4}\sqrt{451} }{36}$

$\implies x=\dfrac{-34 \pm 2\sqrt{451} }{36}$

$\implies x=\dfrac{-17 \pm \sqrt{451} }{18}$

Therefore, the solutions to the given equation are:

$x=\dfrac{-17+ \sqrt{451} }{18}, \quad x=\dfrac{-17- \sqrt{451} }{18}$

Learn more about the Quadratic Formula here:

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3 0

2 years ago

Read 2 more answers

The length of a side of a square is 3x + 2. What is the area of the

MrMuchimi

Answer:

D. 9x^2 + 12x + 4

Step-by-step explanation:

3 0

3 years ago

The perimeter of a rectangle is 90 feet. The length is 27 feet. What is the width of the rectangle?

Alona [7]

2x + 2y = 90
2(27) + 2y = 90
54 + 2y = 90
2y = 36
y = 18

width = 18 feet

3 0

3 years ago

Read 2 more answers

anygoal [31]

Answer:

$43,799.50

Step-by-step explanation:

USing the formula:

A = P(1+r)ⁿ

n is the time = 5

1 + r = 1.04

P = 36,000

Substitute the values into the formula

A = 36000(1.04)⁵

A = 36,000(1.2166529024)

A = 43,799.50

Hence the value in the fifth year will e $43,799.50

7 0

3 years ago

Think about all the ways in which a line and a parabola can intersect select all the numbers of ways in which a line in a parabo

creativ13 [48]

Answer:

0, 1, 2

Step-by-step explanation:

There is a way for them to intersect at 0 points, for example y=x^2 and y = -1

The way to intersect at 1 point is for the linear function to be tangent to the parabola, like y = x^2 and y = 0

The way to intersect 2 points is just for the linear function to be a secant to the parabola, like y = x^2 and y = 1

4 0

3 years ago

Read 2 more answers