[tex]\sqrt{3} sinx+cosx=2[/tex]

Answer:

Step-by-step explanation:

If the roots of p(x) are a, b, c, then it factors as ...

  p(x) = (x -a)(x -b)(x -c)

and the expanded form is ...

  p(x) = x^3 -(a+b+c)x^2 +(ac +b(a+c))x -abc

The requirement that the coefficients match the roots means we have three equations in three unknowns:

  a = -(a+b+c)

  b = ac +b(a+c)

  c = -abc

The attachment shows the solutions to these equations. The solutions are found by making the substitutions ...

This leaves us with two equations in two unknowns that can be graphed on a Cartesian plane. The graph of the second equation is a circle:

  x(1 -a -y) -ay = 0   ⇒   (x +1)^2 +y^2 = 1

The graph of the first equation is the union of the line y=0 and two hyperbolas. The points of intersection between this graph and the circle are ...

  (x, y) = (-2, 0), (-1, -1), (0, 0)   ⇒   (a, b, c) = (1, -2, 0), (1, -1, -1), (0, 0, 0)

The three polynomials that correspond to these values are shown above and in the attachment.

_____

Additional comment

There is an irrational fourth solution to the requirement that the roots match the coefficients.

Answer:

- (b - 9)(b + 8)

Step-by-step explanation:

72 + b - b² ← factor out - 1 from each term and rearrange into standard form

= - (b² - b - 72) ← factor the quadratic

Consider the factors of the constant term (- 72) which sum to give the coefficient of the b- term (- 1)

The factors are - 9 and + 8

Use these factors to split the b- term

b² - 9b + 8b - 72 ( factor the first/second and third/fourth terms )

b(b - 9) + 8(b - 9) ← factor out (b - 9) from each term

(b - 9)(b + 8)

Then

72 + b - b² = - (b - 9)(b + 8)

The steps to construct a parallelogram using a ruler and a compass are;

1. Draw a starting line segment l linger than 8 cm.

2. Mark point K on the line segment.

3. Widen the compass to a radius of 8 cm using the ruler.

4. Place the compass at point K and with the 8 cm radius mark point L on the line l.

5. At point L construct a 45° angle as follows;

The above steps bisects the 90° angle of the perpendicular lines.

6. Adjust the radius of the compass to give an opening of 6 cm and from point L draw an arc to intersect XL at M.

7. At point M construct a line YM at 45° angle to the line l.

8. From point M draw an arc to intersect YM and label the point as point N.

9. Join point M and N to complete the construction of the parallelogram KLMN.

Learn more about construction using a compass and a ruler here:

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Answer:

f(x) =x2 3x 5?

c = 5

therefore the solpe = 5

Answer:

You can't really determine anything here, as we'd need to know also the value of F(x)! Check again if there misses anything in this question.

Answer:

1)x=1.5

2) p=0.7

Step-by-step explanation:

You should do 585 × 0.50 to find the markdown. Then subtract the markdown from the selling price to find the sale price.

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

If we find the average for both companies, it is 72, therefore there are two rows each with 72 cadets

Answer:

the answer is 16 please make me brainliest :> thx uuu

Answer:

A. 9

Step-by-step explanation:

Multiply 3x with x+2

3x(x+2)

Which is 3x^2+6x

Now substitute x with 1

1^2 is 1

3 times 1 is 3

6 times 1 is 6

3+6 is 9

Thus A.

Hope this helps!

The vertical asymptotes of the function are 3 and 6

Given the function

[tex]\frac{x+6}{x^2-9x+18}[/tex]

The vertical asymptotes of the function occur at the point where the denominator is zero.

Equate the denominator to zero.

x^2 - 9x + 18 = 0

Factorize the quadratic expression:

x^2 - 3x - 6x + 18 =0

x(x-3)-6(x-3) = 0

(x-3)(x-6) = 0

x - 3 = 0 and x - 6 = 0

x = 3 and 6

Hence the vertical asymptotes of the function are 3 and 6

Learn more on vertical asymptotes here: https://brainly.com/question/21678319

Answer:

Step-by-step explanation:

The median is the line segment connecting the vertex with the midpoint of the opposite side.

The midpoint has coordinates:

Use the distance formula to find the distance between points (2, 7) and (1, 2):

Step-by-step explanation:

the formula for the length of a median based on the 3 side lengths is

m = sqrt(2AB² + 2AC² - BC²)/2

where BC is the side opposite of the indicated vertex.

let's say

A = (2, 7)

B = (-3, 3)

C = (5, 1)

AB² = (2 - -3)² + (7 - 3)² = 5² + 4² = 25 + 16 = 41

AC² = (2 - 5)² + (7 - 1)² = (-3)² + 6² = 9 + 36 = 45

BC² = (-3 - 5)² + (3 - 1)² = (-8)² + 2² = 64 + 4 = 68

m = sqrt(2×41 + 2×45 - 68)/2 = sqrt(82+90-68)/2 =

= sqrt(104)/2 = sqrt(104/4) = sqrt(26) =

= 5.099019514...

We are given –

Now put the values –

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf x - 9y - 3x + 6y -13[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 9 -(9 \times -3) -(3 \times 9) +(6 \times -3) -13 [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 9 + 27 -27 -18 -13 [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf 9 +\pink{\cancel{27}}-\pink{\cancel{27}} -31[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\bf-22[/tex]

________________________________________

Answer:

Step-by-step explanation:

In the question we have given an expression and values of x and y that is 9 and -3 respectively and ,

We have asked to find the value of x - 9y - 3x + 6y -13 by substituting values of x and y .

[tex] \longmapsto \:x - 9y - 3x + 6y -13[/tex]

So , Substituting the values of x and y ,

[tex] \longmapsto \: 9 - 9 \bold{( - 3)} - 3\bold{(9)} + 6\bold{( - 3)} - 13[/tex]

Now , calculating the values ,

[tex] \longmapsto \: 9 + 27 - 27 - 18 - 13[/tex]

[tex] \longmapsto \: 9 + \cancel{ \red{27}} - \cancel{ \red{27 }}- 18 - 13 [/tex]

[tex] \longmapsto \: 9 - 31[/tex]

[tex] \longmapsto \: \pink{\boxed{- 22}}[/tex]

Answer:

This is not possible with 2 equal symbols

Answer:

Step-by-step explanation:

y = 5x is the reference line (as best as I can interpret " y = 5* - .").

We want a line, y=mx+b, where m is the slope and b is the y-intercept, that is parallel to y=5x.

Parallel lines will have the same slope as the reference line, in this case m=5.  Our new line will take the form of y=5x+b.  An important difference is that the new line must go through (2,6).  We need to find a value of b that will make that work.

Use y=5x + b with point (2,6) and solve for b:

6 = 5*(2) + b

b = -4

The line that is parallel to y=5x and goes through the point (2,6) is thus:

y = 5x - 4

See the attachment.

The equation of line [d] in the slope intercept form can be written as -

y = 5x - 4

The general equation of a straight line is of the form -

y = mx + b

where -

[m] is slope of line

[b] is y - intercept

Given is the equation of line [c] is y = 5x and Line [d] is parallel to line [c] and passes through (2, 6).

The equation of line [d] in the slope intercept form can be derived as follows -

Slope of line [c] = Slope of line [d]  (parallel lines)

m[d] = 5

Assume the equation of line [d] as -

y = m[d]x + b

6 = 5 x 2 + b

b = 6 - 10

b = - 4

The equation will be -

y = 5x - 4

Therefore, the equation of line [d] in the slope intercept form can be written as -

y = 5x - 4

To solve more questions on straight lines, visit the link below-

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Answer:

hi

Step-by-step explanation:

Two forces X = 50N and Y = 60 N are acting on a wooden block and it moves to the left as

shown below in figure.

The force which causes motion is ?

Answer:

(x+3)(x^2+2x-2)

Step-by-step explanation:

rewrote the expression

then factor out common numbers, variables, and exponents

Answer:

Area = 867 meters

Step-by-step explanation:

You have a rectangle. This means opposite sides are equal. If you set these expressions equal to each other, you will get two equations with two unknowns, x and y. Next, solve the system of equations to find x and y. Then, use the values to find the length and width of the rectangle. Last, multiply length × width to find the area.

The answer is 17, Volume = h × π×r^2

Divide by known height from both sides

Divide by pi

square root

Answer:

D

Step-by-step explanation:

Answer:

20m

Step-by-step explanation:

let the length be x and the width be y

x = 4y

2x + 2y = 50

2(4y) + 2y = 50 ( since x = 4y )

8y + 2y = 50

10y = 50

y = 5m

x = 4y

x = 4(5)

x = 20

pls mark me the brainliest

Answer:

k = -3/4

Step-by-step explanation:

The lines will be parallel if their slopes are equal.  To find the slope of each line, write its equation in slope-intercept form (y = mx + b).  In other words, solve each equation for y and look at the coefficient of x.

2x + 3y = 4k

3y = -2x + 4k

y = (-2/3)x + 4k/3

The slope of the first line is -2/3.

x - 2ky = 7

-2ky = -x + 7

y = [1/(2k)]x - 7/(2k)

The slope of the second line is 1/(2k).

If the slopes are equal, then

1/(2k) = -2/3

Multiply by 2k.

1 = (-2/3)(2k) = (-4/3)k

1 = (-4/3)k

k = -3/4

Step-by-step explanation:

let's ignore the question, if the statue can cast an isolated shadow based on its location ...

2 objects and their shadows create 2 similar right-angled triangles.

that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.

so,

48 × f = 9

f = 9/48 = 3/16

therefore, the height of the statue is

70 × f = 70 × 3/16 = 210/16 = 13.125 ft

Answer:

a) 1 04.

b) 160 * 0.94.

Step-by-step explanation:

b) We multiply by 1 - 0.06 = 0.94.

Answer:

where is the question like background info

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

180/15 = 276/x

12 = 276/x

12x = 276

x = 23

Answer:

$37,396

Step-by-step explanation:

take 2388.5x4 since there are 4 weeks = $9554

then you subtrct since the portfolio fell.

So $46,950-9554 = $37,396

B) Juan Victor gave a 25% gratuity of $12 on a bill that was $48.

hope this is helpful!