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3 years ago

11. What values of a, b, and c make this equation true?

Mathematics

1 answer:

borishaifa [10]3 years ago

4 0

9514 1404 393

Answer:

A, a = 4, b = -3, c = 3

Step-by-step explanation:

Expanding the left side gives ...

2x^2 -x -10 +ax^2 +bx +c

= (2 +a)x^2 +(b -1)x +(c -10)

Equating coefficients with terms on the right side gives ...

x^2: (2 +a) = 6 ⇒ a = 4 . . . . . . eliminates choice C

x: (b -1) = -4 ⇒ b = -3 . . . . . . . . eliminates choices B, D

constant: c -10 = -7 ⇒ c = 3 . . . confirms choice A

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B = { α , β , γ } Is the following statement True? B 2 ⊆ B 3

Verdich [7]

Answer:

Step-by-step explanation:

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3 years ago

Which radical expression is equivalent to y^1/7 ?

yaroslaw [1]

Answer:

$\sqrt[7]{y}$

Step-by-step explanation:

The rule for a fraction as an exponet is:

$a^{\frac{b}{c}}=\sqrt[c]{x^b}$

Apply the rule to the expression given:

$y^{\frac{1}{7}}=\boxed{\sqrt[7]{y}}$

Hope this helps you.

7 0

3 years ago

A ship sails 250km due North qnd then 150km on a bearing of 075°.1)How far North is the ship now? 2)How far East is the ship now

olga_2 [115]

Answer:

1) 288.8 km due North

2) 144.9 km due East

3) 323.1 km

4) 207°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Cosine rule

$c^2=a^2+b^2-2ab \cos C$

where a, b and c are the sides and C is the angle opposite side c

-----------------------------------------------------------------------------------------------

Draw a diagram using the given information (see attached).

Create a right triangle (blue on attached diagram).

This right triangle can be used to calculate the additional vertical and horizontal distance the ship sailed after sailing north for 250 km.

Question 1

To find how far North the ship is now, find the measure of the short leg of the right triangle (labelled y on the attached diagram):

$\implies \sf \cos(75^{\circ})=\dfrac{y}{150}$

$\implies \sf y=150\cos(75^{\circ})$

$\implies \sf y=38.92285677$

Then add it to the first portion of the journey:

⇒ 250 + 38.92285677... = 288.8 km

Therefore, the ship is now 288.8 km due North.

Question 2

To find how far East the ship is now, find the measure of the long leg of the right triangle (labelled x on the attached diagram):

$\implies \sf \sin(75^{\circ})=\dfrac{x}{150}$

$\implies \sf x=150\sin(75^{\circ})$

$\implies \sf x=144.8888739$

Therefore, the ship is now 144.9 km due East.

Question 3

To find how far the ship is from its starting point (labelled in red as d on the attached diagram), use the cosine rule:

$\sf \implies d^2=250^2+150^2-2(250)(150) \cos (180-75)$

$\implies \sf d=\sqrt{250^2+150^2-2(250)(150) \cos (180-75)}$

$\implies \sf d=323.1275729$

Therefore, the ship is 323.1 km from its starting point.

Question 4

To find the bearing that the ship is now from its original position, find the angle labelled green on the attached diagram.

Use the answers from part 1 and 2 to find the angle that needs to be added to 180°:

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{Total\:Eastern\:distance}{Total\:Northern\:distance}\right)$

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{150\sin(75^{\circ})}{250+150\cos(75^{\circ})}\right)$

$\implies \sf Bearing=180^{\circ}+26.64077...^{\circ}$

$\implies \sf Bearing=207^{\circ}$

Therefore, as bearings are usually given as a three-figure bearings, the bearing of the ship from its original position is 207°

8 0

2 years ago

Read 2 more answers

How do I do this 16-3p=34 because i get the wrong answer

RUDIKE [14]

16-3p =34. First you need to get the numbers and letters on different sides.
-16 -16
- 3p = 18 then divide by -3
__ __
-3 -3

p = -6 Hope that helps

6 0

3 years ago

Read 2 more answers

Fourteen less than eight times a number is three more than four times the number. What is the number?

wel

Answer:

8n - 14 = 4n + 3 is the equation

and

n = 4.25

Step-by-step explanation:

hope this helped a little bit :))

7 0

3 years ago