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4 years ago

Solve. -7x=x^2+12 help

Mathematics

1 answer:

Nat2105 [25]4 years ago

3 0

Hey There!

The answer to your problem is $x=-3$ or $x=-4$ both answers are correct!

Step 1: Subtract x²+12 from both sides.

−7x−(x²+12)=x²+12−(x²+12)

−x²−7x−12=0

Step 2: Factor left side of equation.

$(-x-3)(x+4)=0$

Step 3: Set factors equal to 0.

$-x-3=0$ or $x+4=0$

Get your answer:

$x=-3$ or $x=-4$

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Carl is standing at the top of 35 Ft cliff looking down at a rock for motion in the sea. He estimates the angle of depression is

Liula [17]

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Data;

Angle = 30 degree
Opposite = 35
Adjacent = x

<h3>Trigonometric Ratio</h3>

Given the angle of depression from his point to the sea, we can use trigonometric ratio to calculate for the horizontal distance from his location to the bottom of the sea.

SOHCAHTOA

Since we have the value of angle and opposite and we need to calculate the adjacent side of the right-angle triangle, we can use the tangent of the angle to this effect.

$Tan\theta = \frac{opposite}{adjacent} \\tan 30 = \frac{35}{x}\\ x = \frac{35}{tan30}\\ x = 60.62ft$

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Learn more on trigonometric ratio here;

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2 years ago

Which order pair is the solution of the system of equations shown?ITS DUE TONIGHT HELP

kap26 [50]

Answer:

Step-by-step explanation:

-x + 5 = 5x - 6

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6 0

3 years ago

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Annie spent $20.02 at the post office. She bought 2 times as many 32-cent stamps as 13-cent stamps. How many of each did she buy

ivolga24 [154]

Answer:

52 32- cent stamps and 26 13-cent stamps

Step-by-step explanation:

Let x be the 32-cent stamps and y be the 13-cent stamps then...

x=2y

32x+13y=2002 (note that $20.02 is 2002 cents)

We can solve using substitution (substitute 2y for x)

32(2y)+13y=2002

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2 years ago

The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

NemiM [27]

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

$60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120$

Let's find h with the quadratic formula:

$\fbox {Quadratic formula:} \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}$

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation

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