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kherson [118]
3 years ago
11

7. Subtract the polynomials: 5x2 + 4x + 1 and x2 + 3x - 4

Mathematics
2 answers:
rodikova [14]3 years ago
5 0

Answer: 4x^​2+x+5

Step-by-step explanation:

5x2 + 4x + 1 - (x2 + 3x - 4)

5x^​2+4x+1−x^​2−3x+4

(5x^​2​​−x^​2​)+(4x−3x)+(1+4)

4x^​2+x+5

Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! As well as a great Superbowl Weekend! :-)

- Cutiepatutie ☺❀❤

Colt1911 [192]3 years ago
3 0

Answer:

4x²+x+5.

Step-by-step explanation:

5x²+4x+1-(X²+3x-4).

5x²+4x+1-x²-3x+4.

5x²-x²+4x-3x+1+4.

4x²+x+5.

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1. A buoy floats 19 yards from the eastern most point of a boat and 15 yards from the western most point of a second boat. The a
Black_prince [1.1K]

The laws of cosines and law of sines can be used given that two sides

and an included angle, or two angles a side are known.

Response:

1. The other angles in the triangle formed by the buoy are approximately;

  • <u>31.1° and 40.9°</u>

2. Distance of the helicopter from the first island is approximately;

  • <u>14.5 miles</u>

<h3>How is the Law of Sines and Cosines used?</h3>

Given parameters are;

Distance of the buoy from the easternmost point of a boat = 19 yards

Distance of the buoy from the westernmost point of the other boat = 15 yards

Angle formed from the buoy to the two boats = 108°

Distance between the two boats, <em>d</em>, is given by the law of cosines, as follows;

d² = 19² + 15² - 2 × 19 × 15 × cos(108°) = 586 - 570·cos(108°)

d = √(586 - 570·cos(108°))

By the law of Sines, we have;

\dfrac{d}{sin(108^{\circ})} = \mathbf{\dfrac{15}{sin(Angle \ formed \ from \ the \ boat \ on \ the \ West, \ \theta_1)}}

Which gives;

sin(\theta_1) = \mathbf{ \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} }}

The o

\theta_1 = arcsin \left( \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} } \right) \approx   \mathbf{31.1^{\circ}}

The other angles formed in the triangle containing the buoy are;

  • θ₁ ≈ <u>31.1</u>
  • θ₂ ≈ 180° - 108° - 31.1° ≈<u> 40.9°</u>

2. Distance between the two islands = 20 miles

Angle of elevation with one island = 15°

Angle of elevation with the second island = 35°

Required:

The mileage (distance travelled) of the helicopter.

Solution:

Let <em>A</em> represent the island that has an angle of elevation to the helicopter

of 15°, and let <em>B</em> represent the other island.

Angle formed by the helicopter and the two island, θ, is found as follows;

θ = 180° - (15° + 35°) = 130°

By the Law of Sines, we have;

\dfrac{20}{sin(130^{\circ})} = \mathbf{ \dfrac{Distance \ from \  island \ A }{sin(35^{\circ})}}

Which gives;

Distance \ of \ helicopter \ from \  island \ A = \mathbf{ \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ})}

Mileage \ from \ island \ A =  \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ}) \times cos(15^{\circ}) \approx 14.5

  • The mileage of the helicopter from the first island is approximately <u>14.5 miles</u>

Learn more about the Law of Sines and Cosines here:

brainly.com/question/8242520

brainly.com/question/2491835

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2 years ago
Solve for r in terms of q, s, t and u. <br> St= -ruq
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Answer:

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a full matchbox contains x matches. A man has three full matchboxes and a matchbox containing y matches. How many matches does h
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Answer:

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Step-by-step explanation:

hope it helps

6 0
3 years ago
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natali 33 [55]
Because December is really cold
5 0
2 years ago
,please help me solve these 2. problems I am having trouble
Harlamova29_29 [7]
Hi,

1) D

Working :
If the bell rings for 2 weeks straight that means it rings for 14 days.

The bell rings 48 times a day (2 * 24).

The answer is then: 48*14 = 672

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Working:

144 cookies * 8 batches = 864 cookies

864 divided into boxes of 8 = 864 / 8 = 108


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