Factor out the greatest common factor

Given:

A figure of a circle. [tex]KJ=6,KL=x-2,ML=4[/tex].

To find:

The length of KJ.

Solution:

From the given figure it is clear that the number 6 is marked between K and J it means the number 6 represents the distance between the points K and j.

Therefore, the length of KJ is 6 units.

Note: In the given question we need to find KL instead of KJ because KJ is already given.

According to the tangent secant theorem:

[tex]a^2=bc[/tex]

Where,

Using the tangent secant theorem, we get

[tex]ML^2=KL\times JL[/tex]

[tex](4)^2=(x-2)\times (6+x-2)[/tex]

[tex]16=(x-2)\times (4+x)[/tex]

[tex]16=4x+x^2-8-2x[/tex]

On further simplification, we get

[tex]16=x^2+2x-8[/tex]

[tex]0=x^2+2x-8-16[/tex]

[tex]0=x^2+2x-24[/tex]

Splitting the middle term, we get

[tex]x^2+6x-4x-24=0[/tex]

[tex]x(x+6)-4(x+6)=0[/tex]

[tex](x+6)(x-4)=0[/tex]

[tex]x=-6,4[/tex]

For [tex]x=-6[/tex],

[tex]KJ=-6-2[/tex]

[tex]KJ=-8[/tex], which is not possible because side cannot be negative.

For [tex]x=4[/tex],

[tex]KJ=4-2[/tex]

[tex]KJ=2[/tex]

Therefore, the measure of KL is 2 units.

Answer:

a rooster can't lay eggs

Step-by-step explanation:

a rooster is a male-

Answer:

0, A rooster is a male, it does not lay eggs. Hens lay eggs

Step-by-step explanation:

Answer:

284.625

Step-by-step explanation:

Arrange the numbers highest to lowest.

Find the middle value in the arrangement.

Given that y₁(x) = x is a solution to the given second-order ODE, assume a second solution of the form

y₂(x) = y₁(x) v(x) = x v(x)

Take the first two derivatives and substitute this solution into the ODE:

y₂ = x v

y₂' = x v' + v

y₂'' = (x v'' + v' ) + v' = x v'' + 2 v'

→   (1 - x ²) y₂'' - 2 x y₂' + 2 y₂ = 0

→   (1 - x ²) (x v'' + 2 v' ) - 2 x (x v' + v) + 2 x v = 0

→   (x - x ³) v'' + (2 - 4 x ²) v' = 0

Next, reduce the order by substituting w(x) = v'(x) and w'(x) = v''(x) :

→   (x - x ³) w' + (2 - 4 x ²) w = 0

and now you have a linear equation in w. Solve for w(x) however you like; I'll just separate variables.

Write w'(x) = dw/dx, then separate variables as

(x - x ³) dw/dx + (2 - 4 x ²) w = 0

(x - x ³) dw/dx = (4x ² - 2) w

dw/w = (4x ² - 2) / (x - x ³) dx

Integrate both sides:

∫ dw/w = (4x ² - 2) / (x - x ³) dx

ln|w| = ∫ (4x ² - 2) / (x - x ³) dx

For the remaining integral, expand the integrand into partial fractions.

x - x ³ = x (1 - x ²) = x (1 - x) (1 + x)

→   (4x ² - 2) / (x - x ³) = a /x + b / (1 - x) + c / (1 + x)

→   4x ² - 2 = a (1 - x ²) + b x (1 + x) + c x (1 - x)

→   4x ² - 2 = (-a + b - c) x ² + (b + c) x + a

→   -a + b - c = 4, b + c = 0, a = -2

→   a = -2, b = 1, c = -1

→   (4x ² - 2) / (x - x ³) = -2/x + 1 / (1 - x) - 1 / (1 + x)

Then

ln|w| = ∫ (-2/x + 1 / (1 - x) - 1 / (1 + x)) dx

ln|w| = -2 ln|x| - ln|1 - x| - ln|1 + x| + C

ln|w| = -ln|x ² (1 - x ²)| + C

exp(ln|w|) = exp(-ln|x ² (1 - x ²)| + C )

w = C / (x ² (1 - x ²))

v' = C / (x ² (1 - x ²))

Solve for v(x) by integrating both sides, expanding the right side into partial fractions again:

x ² (1 - x ²) = x ² (1 - x) (1 + x)

→   1 / (x ² (1 - x ²)) = a / x + b / x ² + c / (1 - x) + d / (1 + x)

→   1 = a x (1 - x ²) + b (1 - x ²) + c x ² (1 + x) + d x ² (1 - x)

→   1 = (-a + c - d) x ³ + (-b + c + d) x ² + a x + b

→   -a + c - d = 0, -b + c + d = 0, a = 0, b = 1

→   a = 0, b = 1, c = 1/2, d = 1/2

→   1 / (x ² (1 - x ²)) = 1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))

dv/dx = C (1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x)))

dv = C (1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))) dx

Integrate both sides:

∫ dv = ∫ C (1 / x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))) dx

v = C₁ (-1/x - 1/2 ln|1 - x| + 1/2 ln|1 + x|) + C₂

v = C₁ (1/2 ln|(1 + x) / (1 - x)| - 1/x) + C₂

Solve for y₂(x) by multiplying both sides by x :

y₂ = C₁ (1/2 x ln|(1 + x) / (1 - x)| - 1) + C₂ x

Now, y₁(x) = x, so we can omit the last term from the second solution, giving us

y₂(x) = C (1/2 x ln|(1 + x) / (1 - x)| - 1)

Answer:

The value of x is 28°

Step-by-step explanation:

Here, In a given figure

4x + 3° ...(1)

2x + 9° ...(2)

Now, we know that the sum of all angle is 180° on a straight line

So,

4x + 3° + 2x + 9° = 180°

6x + 12° = 180°

6x = 180° - 12°

6x = 168°

x = 168° ÷ 6

x = 28°

Thus, The value of x is 28°

4x + 3° + 2x + 9° = 180°

4(28) + 3° + 2(28) + 9° = 180°

112° + 3° + 56° + 9° = 180°

180° = 180°

Hence, L.H.S = R.H.S

-TheUnknownScientist

Answer:

Look at the answers bolded below

Step-by-step explanation:

To get the reference angle, just subtract 115° from 180°

180 - 115 = 65

So the reference angle is 65°

I'm not sure how many coterminal angles you need, but to get them you could just add or subtract 360°.

For example, a positive coterminal angle could be:

115 + 360 = 475°

a negative coterminal angle could be:

115 - 360  = -245°

Hope this helped :)

Answer:

140 degrees i think

Step-by-step explanation:

Answer:

Henry has $19, Dan has $57, and Melissa has $11

Step-by-step explanation:

Let x represent how much money Henry has

Since Dan has 3 times what Henry has, his amount is 3x

Since Melissa has $8 less than Henry, her amount is x - 8

Create an equation that sets these 3 values equal to 87, then solve for x

(x) + (3x) + (x - 8) = 87

5x - 8 = 87

5x = 95

x = 19

So, Henry has $19

Find how much Dan has by multiplying 19 by 3

19(3)

= 57

Find how much Melissa has by subtracting 8 from 19

19 - 8

= 11

So, Henry has $19, Dan has $57, and Melissa has $11

Answer:

Dan has $261 and Melissa has $79

Answer:

Step-by-step explanation:

that implies a simple multiplication:

snow = (3/4)(6) = 4.5 inch

and note the units elimination in the operation as well:

= [inch/hour][hour] = inch

My fault if im wrong :(

Answer:

32

Step-by-step explanation:

5 + 6 * (5 - 2) + 9

5 + 6 * 3 + 9

5 + 18 + 9

23 + 9

32

Answer:

21134 bacteria

Step-by-step explanation:

The given parametrs can be interpreted as:

[tex]y = 8(2.4)^t[/tex]

Required

Find y when t = 9

Substitute [tex]t = 9[/tex]

So:

[tex]y = 8(2.4)^9[/tex]

[tex]y = 8 * 2.4^9[/tex]

[tex]y = 8 * 2641.81[/tex]

[tex]y = 21134.48[/tex]

[tex]y = 21134[/tex] --- approximated

Hence, there are 21134 bacteria

Answer:

b and d

Step-by-step explanation:

The equations have at least one integer solution are equation B: √(3x) = 75 and equation D:√x = x - 12.

The value of x is known as the solution.

A.  √(4x) = 5

On squaring, we have

4x = 25

 x = 6.25

The value is not an integer.

B.  √(3x) = 75

On squaring, we have

3x = 5625

 x = 1875

The value is an integer.

C.  8√x = √16

On squaring, we have

64x = 16

    x = 0.25

The value is not an integer.

D.  √x = x - 12

On squaring, we have

          (x - 12)² = x

x² - 24x + 144 = x

x² - 25x + 144 = 0

  (x - 16)(x - 9) = 0

                    x = 9, 16

The value is an integer.

E.  √(10 - x) = x - 2

On squaring, we have

                (x - 2)² = 10 - x

          x² - 4x + 4 = 10 - x

           x² - 3x - 6 = 0

(x - 4.37)(x + 1.37) = 0

                          x = -1.37, 4.37

The value is not an integer.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

She rated 32% percent of the movies very good

Answer:

y= x⁴ -21x²-100

combine x's I think

x⁴= 1x? cuz if it's 1x⁴ that's 1x*1x*1x*1x = 1x

1x * -21x²

-21x * -21x = 441x

+1x = 442x

y= 442x -100

I'm not sure if I did that right

Answer:

Hypotenuse = 85 cm

Hypotenuse = 89 cm

Hypotenuse = 103.08 cm (Approx.)

Hypotenuse = 54.71 cm (Approx.)

Step-by-step explanation:

Shape 1

Hypotenuse = √Perpendicular² + Base²

Hypotenuse = √36² + 77²

Hypotenuse = √1,296 + 5,929

Hypotenuse = √7,225

Hypotenuse = 85 cm

Shape 2

Hypotenuse = √Perpendicular² + Base²

Hypotenuse = √39² + 80²

Hypotenuse = √1,521 + 6,400

Hypotenuse = √7,921

Hypotenuse = 89 cm

Shape 3

Hypotenuse = √Perpendicular² + Base²

Hypotenuse = √25² + 100²

Hypotenuse = √625 + 10,000

Hypotenuse = √10,625

Hypotenuse = 103.08 cm (Approx.)

Shape 4

Hypotenuse = √Perpendicular² + Base²

Hypotenuse = √17² + 52²

Hypotenuse = √289 + 2,704

Hypotenuse = √2,993

Hypotenuse = 54.71 cm (Approx.)

Answer:

The answer is A

Step-by-step explanation:

Yep im so smart. You defininetly need this answer a month later ;)

Answer:

it would be 145

Step-by-step explanation:

the two angles make a straight line, 180-35 is 145

Answer: 145

Step-by-step explanation:

supplementary angle rule: on a straight line, all angles add up to 180

180 = 35 + x

180 - 35 = x

145 = x

Answer:

x = 45°

Step-by-step explanation:

x = 90° - 45° = 45°

Answer: 14

Step-by-step explanation:

VW corresponds to BA. VW is twice the length of BA, so VU must be twice the length of BC

Answer:

2.5 times 60 equals 150. 150-78 equals 72. So the answer is 72.

Step-by-step explanation:

Hope this helps.

Answer:

D.

Step-by-step explanation:

divide 45 by 3

Answer:

The value of g(2.7) is 31.49.

Step-by-step explanation:

Translations of a function:

Suppose that we have a function f(x).

The translation of f(x) a units to the left is given by g(x) = f(x+a).

The translation of f(x) a units to the right is given by g(x) = f(x-a).

The translation of f(x) a units up is given by g(x) = f(x) + a.

The translation of f(x) a units down is given by g(x) = f(x) - a.

Suppose the graph of f(x)=x^2 is translated 3 units right and 1 unit down.

Three units right:

[tex]g(x) = f(x+3) = (x+3)^2[/tex]

One unit down:

[tex]g(x) = f(x+3) - 1 = (x+3)^2 - 1[/tex]

What is the value of g(2.7)?

This is g when [tex]x = 2.7[/tex]. So

[tex]g(2.7) = (2.7+3)^2 - 1 = (5.7)^2 - 1 = 31.49[/tex]

The value of g(2.7) is 31.49.

Answer:

b the area

Step-by-step explanation:

you will need to see if you have enough area for the microwave to fit

9514 1404 393

Answer:

  b.  255.5 to 499.5

Step-by-step explanation:

The middle 50% is the range between the first and third quartiles. In this group of 9 numbers, the first quartile is the average of numbers 2 and 3 when the numbers are listed from smallest to largest.

  first quartile = (230 +281)/2 = 255.5 . . . . . . matches answer choice B

The third quartile is the average of numbers 7 and 8:

  third quartile = (468 +531)/2 = 499.5 . . . . .  also matches answer choice B

The middle 50% is 255.5 to 499.5.

_____

When I put the numbers in order, I get ...

  198 230 ^ 281 246 376 426 468 ^ 531 540

^ indicates that the quartile here is the average of the adjacent numbers

bold indicates the median (2nd quartile)

Answer:

70

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

If probablikty is 5/12 then, not picking is 7/12

Answer:

41.81

Step-by-step explanation:

∠B = arcsin(b·sin(A)a)

= 0.72973 rad = 41.81° = 41°48'37"

∠C = 180° - A - B = 0.84107 rad = 48.19° = 48°11'23"

c = a·sin(C)sin(A)=4.47214 = 2√5

Answer:

The height is 13.3 in

Step-by-step explanation:

Pythagorean Theorem

23.5²+b²=27²

552.25+b²=729

b²=729-552.25

b²=176.75

b=√176.75

13.2947

Answer:

128 seats

Step-by-step explanation:

7/11 = 224 seats

11/11 = ?

(11/11 × 224) ÷ 7/11

224 ÷ 7/11 =

224 × 11/7 = 352 seats(total number of seats)

352 - 224 = 128 seats