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3 years ago

Solving an Inequality

Mathematics

1 answer:

Ganezh [65]3 years ago

4 0

Answer:

D. Multiply both sides by -7

Step-by-step explanation:

So solving would look like this

m/-7 < 14

m > -2

Remember when multiplying by a negative the sign flips, hope that helps :)

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A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic

Rainbow [258]

angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

$c^2 = a^2 + b^2 - 2ab (cosx)$

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ $c^2 = a^2 + b^2 - 2ab (cosx)$

⇒ $c^2 -a^2 - b^2 = -2ab (cosx)$

⇒ $(cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}$

⇒ $(cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}$

⇒ $(cosx) =0.18310$

⇒ $cos^{-1}(cosx) = cos^{-1}(0.18310)$

⇒ $x = 79.45$

The Law of Sines (or Sine Rule) is very useful for solving triangles:

$\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}$

We can now find another angle using the sine rule:

⇒ $\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}$

⇒ $sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}$

⇒ $Y = 59.02 degrees$

So, the third angle = $180 - 79.45 - 59.02 = 41.53 degrees.$

Therefore, angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

4 0

4 years ago

F(x)=4x+1 and g(x)=x2-5, find (f+g)(x)

yulyashka [42]

Answer:

$(f+g)(x) = x^{2} + 4x - 4$

Step-by-step explanation:

f(x) + g(x) = $(4x +1) + (x^{2} - 5)$

$x^{2} + 4x - 4$

5 0

4 years ago

Factor completely: 3x2 + 12x + 7

zepelin [54]

Answer:

Step-by-step explanation:

Eliminate answer 4 immediately, because (4)(3) is not 7.

Look at answer 2: 7x + 3x = 10x, which does not match the middle term 12x in the original polynomial. Eliminate answer 2.

Look at answer 1: 1x + 21x = 22x, which does not match the middle term of the original polynomial. Eliminate answer 1.

All quadratics have solutions. Let's apply the quadratic formula to 3x^2 + 12x + 7: Here a = 3, b = 12 and c = 7, so that the discriminant b²-4ac is

12²-4(3)(7), or 144 - 84, or 60. Being positive, this tells us that the given poly has two real, unequal roots:

-12 ± √60 -12 + 2√15 -12 - 2√15

x = ----------------- = ------------------- and x = --------------------

3 3 3

Normally, if c is a root, then x - c is a factor.

If we try this here, however, the resulting factors do not at all match any of your answer choices.

Don't be offended...but please ensure you have copied this problem down correctly.

3 0

4 years ago

Plsss help 6th grade plsssssssss

gulaghasi [49]

Answer:

that confusing

Step-by-step explanation:

6 0

3 years ago

The difference in the X coordinates of two points is three and the difference in the Y coordinate is two points is six what is t

charle [14.2K]

Answer: The slope is 2.

Step-by-step explanation: Slope is Rise/Run

The rise is the difference in y-values, given as 6.

The Run is the difference in x-values, given as 3

6/3 = 2

4 0

4 years ago