In circle K with m/JKL = 30 and JK = 15 units, find the length of arc JL.
Round to the nearest hundredth.

Answer:

AB = 27.2

BC = 33.5

AC = 50.4

∠A = 38°

∠ABC = 112°

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\implies \sf \cos(30^{\circ})=\dfrac{29}{BC}[/tex]

[tex]\implies \sf BC=\dfrac{29}{\cos(30^{\circ})}[/tex]

[tex]\implies \sf BC=\dfrac{58\sqrt{3}}{3}=33.5\:(nearest\:tenth)[/tex]

[tex]\implies \sf \tan(30^{\circ})=\dfrac{BD}{29}[/tex]

[tex]\implies \sf BD=29\tan(30^{\circ})[/tex]

[tex]\implies \sf BD=\dfrac{29\sqrt{3}}{3}[/tex]

[tex]\implies \sf \sin(38^{\circ})=\dfrac{BD}{AB}[/tex]

[tex]\implies \sf AB=\dfrac{\dfrac{29\sqrt{3}}{3}}{\sin(38^{\circ})}[/tex]

[tex]\implies \sf AB=27.2\:(nearest\:tenth)[/tex]

[tex]\implies \sf \tan(38^{\circ})=\dfrac{BD}{AD}[/tex]

[tex]\implies \sf AD=\dfrac{\dfrac{29\sqrt{3}}{3}}{\tan(38^{\circ})}[/tex]

[tex]\implies \sf AD=21.4\:(nearest\:tenth)[/tex]

[tex]\implies \sf AC=AD+DC=21.4+29=50.4[/tex]

The interior angles of a triangle sum to 180°

⇒ ∠A + 52° + 90° = 180°

⇒ ∠A = 180° - 90° - 52°

⇒ ∠A = 38°

⇒ ∠ABC + 38° + 30° = 180°

⇒ ∠ABC = 180° - 38° - 30°

⇒ ∠ABC = 112°

**I have checked the measures using a graphing programme - see attached**

Answer:

log base(6) [tex]\frac{z^{2}y^{3} }{w^{10} }[/tex]

Step-by-step explanation:

log base(6) [tex]\frac{z^{2}y^{3} }{w^{10} }[/tex]

The expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).

Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.

The expression given in the problem is

f(x)=-4x³+x²-6x+8

The option given as,

From the given expression, if we take out x from the first three terms, it looks like option 2.

f(x)=-4x³+x²-6x+8

f(x)=x(-4x²+x-6)+8

From the given expression, if the last three terms factored, it looks like option 3.

f(x)=-4x³+x²-6x+8

f(x)=-4x³+x^2-4x-2x+8

f(x)=-4x³+x(x-4)-2(x-4)

f(x)=-4x³+(x-4)(x-2)

Rearrange the given expression, and make it looks like option 4.

f(x)=-4x³+x²-6x+8

f(x)=-4x²+8+x²-6x

f(x)=-4(x³-2)+x(x-6)

Thus, the expression which is not equivalent to the provided expression is expression number 1, x²(-4x+1)-2(3x-4).

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Answer:

369.5 ft²

Step-by-step explanation:

Area of figure :

Area (rectangle 1) + Area (rectangle 2) + Area (triangle 1) + Area (triangle 2)

Answer:

369.5 ft²

Step-by-step explanation:

Separate the figure into 2 rectangles and 2 triangles.

(see attached image)

Area 1

Area of a rectangle = width × length

                                 = 4 × 5

                                 = 20 ft²

Area 2

Area of a rectangle = width × length

                                 = 8 × (4 + 4 + 5)

                                 = 8 × 13

                                 = 104 ft²

Area 3

Area of a triangle = 1/2 × base × height

                             = 1/2 × (6 + 4 + 5 + 4 - 6) × 23

                             = 1/2 × 13 × 23

                             = 149.5 ft²

Area 4

Area of a triangle = 1/2 × base × height

                             = 1/2 × 8 × (21 + 8 - 5)

                             = 1/2 × 8 × 24

                             = 96 ft²

Total Area

Area 1 + Area 2 + Area 3 + Area 2 = 20 + 104 + 149.5 + 96

                                                        = 369.5 ft²

Answer:

Step-by-step explanation:

Discussion

This is a proportion question. A proportion is 2 ratios separated by an equal sign.

If you know three of the components you can solve for the fourth.

Givens

28.1 % are females

42000 are female doctors.

100% is what is required.

Equation

28.1% / 100% = 42000 / x                  Cross Multiply

28.1 * x = 42000 * 100                        Combine

28.1 * x = 4200000                             Divide by 28.1

28.1/28.1 x = 4200000/28.1

x  = 149466 is the total doctors

Answer

149366 is the total number of doctors.

El oh Elllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll

In the end, Fatima only has 0.395 kg of roses, because she used up a total of 0.115 kg of rose petals.

To calculate the amount of rose petals that Fatima has at the end, we must perform the following mathematical operations:

Subtract 0.02kg to 0.454kg

Add 0.056 kg to 0.434 kg

Subtract 0.095kg from 0.49kg

Based on the above, Fatima is wrong because she thinks she should have 0.413 kg of rose petals, but she has 0.395 kg.

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Answer:

  multiply them

Step-by-step explanation:

Units work in algebraic equations the same way that variables do. They can be multiplied and divided as though they were variables.

For units conversion, we want to change the units without changing the value of the quantity. We do that by multiplying by a unit conversion factor that has a numerator equal to its denominator.

__

We know ...

  1 cup = 8 fl oz

  2 cups = 1 pint

These relations can be written as the conversion factors ...

  (8 floz)/(1 cup)   and   (2 cups)/(1 pint)

Multiplying these together, the units of cups cancel, leaving fluid ounces per pint.

  [tex]\dfrac{8\text{ fl oz}}{1\text{ cup}}\times\dfrac{2\text{ cup}}{1\text{ pint}}=\dfrac{8\cdot2\text{ fl oz$\cdot$cup}}{1\cdot1\text{ pint$\cdot$cup}}=\boxed{\dfrac{16\text{ fl oz}}{1\text{ pint}}}[/tex]

_____

Additional comment

The concept of "like terms" applies to expressions involving units as well as expressions involving variables. Terms can only be added or subtracted if they have the same units.

Explanation:

If line r and line s are parallel, then the two angles marked must be congruent. Refer to the corresponding angles theorem for more details.

This means we'll set the angles equal to one another and solve for x.

angle1 = angle2

40-4x = 50-8x

-4x+8x = 50-40

4x = 10

x = 10/4

x = 2.5

Answer:

[tex]2.75[/tex]

Step-by-step explanation:

Step 1:  Determine the median

[tex]0.8, 1.0, 2.7, 2.8, 3.1, 13.3[/tex]

The median of a set is the middle of the set.  In this instance, we have 6 numbers so we don't have a number directly in the set representing the median.  Instead, we need to find the average or middle between the 3rd and 4th number.  So we take 2.7 and 2.8, add them together to get 5.5 and then we divide by 2 to get 2.75 which is our median.

Answer:  [tex]2.75[/tex]

Answer:

Step-by-step explanation:

Problem a

a is an isosceles triangle. It has 2 sides marked as equal. Therefore the two angles marked in red are also equal.  

The top angle = x

x + 70.5 + 70.5 = 180      All triangles have 180 degrees.

x + 141 = 180                    Subtract 141 from both sides

x + 141-141 =180 - 141       Combine

x = 39

c + 39 + 87.2 =180           Combine the left

c + 126.2 = 180                 Subtract 126.2 from both sides

c+126.2-126.2 = 180-126.2

c = 53.45

Answer: 53.45

Problem B

Comment

Problem b can only be found by taking the supplements of the two given angles. After that is done, the vertically opposite angle to d can be found because d is opposite the third angle.

Supplement of 115.6

Call the supplement = y

y + 115.6 = 180                         Supplementary angles = 180 degrees

y +115.6-115.6 = 180 - 115.6     Combine

y = 64.2

Now we need the supplement of 99.9

Call the supplement = z

z + 99.9 = 180                           Supplementary angles = 180

z+99.9-99.9 = 180-99.9

z = 80.1

Now subtract y + z from 180

180 - 64.2 - 80.1 = x

x = 35.7

x is opposite d

d = x

d = 35.7 degrees.

Answer

d = 35.7

Answer:

0.0000000673

Step-by-step explanation:

7.4*10^-8=0.000000074

6.7*10^-9=0.0000000067

0.000000074-0.0000000067

=0.0000000673=673*10^-10

Answer:

6.73 × [tex]10^{-8}[/tex]

Step-by-step explanation:

7.4 × [tex]10^{-8}[/tex]

6.7 × [tex]10^{-9}[/tex] = 0.67 × [tex]10^{-8}[/tex]

7.4 × [tex]10^{-8}[/tex] - 0.67 × [tex]10^{-8}[/tex] = ( 7.4 - 0.67 ) × [tex]10^{-8}[/tex] = 6.73 × [tex]10^{-8}[/tex]

In the first circle, x is the radius and also the hypotenuse of a right triangle with legs measuring 9 and 12. So by the Pythagorean theorem,

x² = 9² + 12² = 225 = 15²  ⇒   x = 15

In the second circle, the chords AB and CD have the same length, and each of AP, BP, CP, and DP are radii of the circle and also have the same length. This means ∆ABP and ∆CDP are congruent, so the two labeled angles are also congruent, so x = 54.

Answer:

2/9 or 9/2

Step-by-step explanation:

The original figure is 2/9 of the size of the rescaled version, as each measurement is 2/9 of the rescaled version (eg 10/45 = 2/9)

If they want you to tell them how much bigger the rescaled version is, the answer would be 9/2 for the same reason, I'm just not sure which way they want you to go.

Hope this helps! :)

Answer:

36 different combinations

Answer: 16

Here are the steps to solve for x:

3(x+4) + 2 = 2+5(x-4)

1. Distribute to get rid of the parentheses

3x+12+2 = 2+5x-20

2. Combine like terms

3x+14 = 5x -18

3. Get like terms on the same side

3x+14 = 5x -18

-14            -14

3x = 5x -32

-5      -5

-2x = -32

4. Divide by -2 to isolate x

-2/2 x = -32/2

x=16

Apply Pythagorean theorem

Answer:

30240

Step-by-step explanation:

3x7x36x40 I hope this helps

Answer:

brainly please

Step-by-step explanation:

yes because 5 is less than 8

Answer:

No, the correct solution is q < 8 because 5 can not be equal to 8 but rather less than 8 (only)

Answer:

1:1

Step-by-step explanation:

Answer:

3.5 m/hr  

Step-by-step explanation:

2 + c   =   5 -c           c = speed of current

2 c = 3      c = current speed = 1.5 m/hr

                         your speed =   5 - 1.5    (or  2 + 1.5)  =  3.5 m/hr

Answer:

y: -2 x: -1

Step-by-step explanation:

because if m turns 1/4 of a way clockwise it basically turns upside down 180 would be flipped, so it would be y:2 x:-1.

comment if you need help.

Answer:

v=2143.57

Step-by-step explanation:

4/3 x 3.14 x 8³

3.14 x 512 x 4/3

3.14 x 512=1607.68

1607.68 x 4/3=2143.57333333

round to nearest hundreth

v=2143.57

Answer:

V ≈ 2143.57= 2144

Step-by-step explanation:

[tex]v=\frac{4}{3} *3.14*8^3[/tex]

=2143.57333333

you dont need to round, so!

=2144 (if you want)

sorry for the confusion

Answer:

Angles around a point sum to 360°

⇒ ∠SPT + ∠TPU + 86° + 60° + 154° = 360°

⇒ ∠SPT + ∠TPU = 60°

Therefore:

∠SPQ clockwise = ∠SPT + ∠TPU + 86°

                            = 60° + 86°

                            = 146°

∠SPQ anticlockwise = 60° + 154°

                                  = 214°

Answer:

See below ~

Step-by-step explanation:

The total internal measure is 360°.

Finding ∠SPQ (clockwise):

Finding ∠SPQ (counterclockwise) :

The 15 years it will take its population to reach 5,000 if  initial population of 20 organisms.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

Let's assume the exponential growth is:

[tex]\rm y = Ae^{rt}[/tex]

From the problem:

[tex]\rm 130 = 20e^{5r}[/tex]

[tex]\rm e^{5r}= 6.5[/tex]

Taking ln both side:

We get:

r = 0.374

[tex]\rm 5000 = 20e^{0.374t}[/tex]

After solving, we get:

t = 14.76 ≈ 15 years

Thus, the 15 years it will take its population to reach 5,000 if  initial population of 20 organisms.

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Answer:

106500

Step-by-step explanation: