A 12 m ladder propped against a wall forms an angle of 60° with the ground. Determine
how far the top of the ladder is from the ground. Include a diagram.

Answer:

  (smallest, largest) = (B, C), (D, E), (G, J)

Step-by-step explanation:

Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

__

The shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.

The shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.

The shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.

_____

Additional comment

Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there cannot be two angles in a triangle such that the smaller angle has the larger sine.

The approximate solution to the given equation is x ≅ 148.4. The correct option is C. x ≈ 148.4

From the question, we are to determine the approximate solution to the given equation,

The given equation is

[tex]4lnx -8 =12[/tex]

First, add 8 to both sides

[tex]4lnx -8+8 =12+8[/tex]

[tex]4lnx =20[/tex]

Now, divide both sides by 4

[tex]ln x =\frac{20}{4}[/tex]

[tex]ln x = 5[/tex]

Take the exponents of both sides

[tex]e^{lnx} = e^{5}[/tex]

x = 148.413

x ≅ 148.4

Hence, the approximate solution to the given equation is x ≅ 148.4. The correct option is C. x ≈ 148.4

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The 62.5% of residences in the country that are rentals if the total number of residence in the country is 144,000.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We are assuming:

Total number of residence in the country = 144,000

In which 900,00 residences are rentals.

Percentage of residences in the country that are rentals:

= (90000/144000)×100

= 0.625×100

= 62.5%

Thus, the 62.5% of residences in the country that are rentals if the total number of residence in the country is 144,000.

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The probability of drawing three queens from a standard deck of cards is 0.000162.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Total cards = 54

No. queens in a deck = 4

Probability of drawing a queen card = 4/54

Now that 1 queen has been taken, the no. of cards becomes = 53

and

no. of queens = 3

Probability of getting a queen again = (3/53)(4/54)

Two queens have already been removed.

No. of cards in the deck = 52

No. of queens in the deck = 2

Probability of drawing three queens

= (2/52)(3/53)(4/54)

= 0.000162 approximately

The probability of drawing three queens from a standard deck of cards is 0.000162.

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Answer:

[tex]the \: probability \: is \: \frac{5}{60} \\ when \: simplified \: becomes \: \frac{1}{12} [/tex]

Step-by-step explanation:

The solution is in the image

Answer: 432

Step-by-step explanation:

  12

x 36

--------

    72

+ 36

-------

432

The amount paid for the computer including sales tax is 0.918p

The price paid is given as:

Price = p

A 15% off means that he pays 85%.

So, we have:

Amount = 85% * p = 0.85p

A sales tax of 8% means:

Total = 0.85p * (1 + 8%)

Evaluate the product

Total = 0.918p

Hence, the amount paid is 0.918p

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The correct answer is A. y - 3 = -6(x + 1) of the  linear equation in point-slope form for the line that goes through (-1,3) and (1, -9).

To write the linear equation in point-slope form, we need to use the formula:

[tex]y - y_1 = m(x - x_1),[/tex]

where [tex](x_1, y_1)[/tex] represents one of the given points, and m represents the slope of the line.

Step 1: Find the slope (m):

[tex]m = \frac {(y_2 - y_1) }{(x_2 - x_1)}\\= \frac {(-9 - 3)} { (1 - (-1))}\=\frac {-12 } {2}= -6.[/tex]

Step 2: Choose one of the given points (-1, 3), and substitute its coordinates into the point-slope form:

[tex]y - 3 = -6(x - (-1)).[/tex]

Step 3: Simplify and rearrange the equation:

[tex]y - 3 = -6(x + 1)\\y - 3 = -6x - 6.[/tex]

Therefore, the correct equation is A. y - 3 = -6(x + 1).

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This are function used to determine the term of a sequence. The second and the third term of the sequence is 6 and 18

This are function used to determine the term of a sequence. Given the following functions

an+1 = 3an

Given that a1 = 2

a2 = 3a1

a2 = 3(2)

a2 = 6

For the third term a3

a3 =3a2

a3 = 3(6)

a3 = 18

Hence the second and the third term of the sequence is 6 and 18

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Answer:

84.8

Step-by-step explanation:

Begin by finding the total area of the circle. You have been given the radius.

A = πr²

A = π(6)²

A = 36π

A = 113

If there is only 3/4 of the circle, then multiply the entire area by 3/4 to find the final answer.

113 x 3/4 = 84.8

Answer:

-2c-16

Step-by-step explanation:

do 7-9 because it's the only thing you can solve.
--> -2c-16

Step-by-step explanation:

1. So first you have to cross multiple the two terms

2.Solve the algebraic equation

By dividing with 12 on both sides

(Note :That's a 32 in the picture sometimes i really write bad)

Since the limit of f(x) is non-zero, the limit distributes over the quotient and

[tex]\displaystyle \lim_{x\to c} \frac{g(x)}{f(x)} = \frac{\displaystyle \lim_{x\to c}g(x)}{\displaystyle \lim_{x\to c}f(x)} = \frac{\dfrac15}{-4} = \boxed{-\frac1{20}}[/tex]

Answer:

i think its 4.7

Step-by-step explanation:

Answer:

AC is an enlargement of AE

scale factor = 11.7 ÷ 5.2 = 2.25

CD is an enlargement of AB

10.5 ÷ 2.25 = 4.666666...

= 4.7 (rounded to nearest tenth)

Answer:because it’s like a quarter

Step-by-step explanation:

A quarter is 25c, 25•3=75

Answer: y=2x+7

(this is a rearranged version of y-2x=7 from question)

Step-by-step explanation:

4x=5-2y

y-2x=7

i would rearrange the 2nd value into y intercept form y=mx+b

so move the -2x to the other side of the = sign by doing the opposite, +2x on both sides to isolate the y

y=2x+7

you didn't give any options for "correct answer" so i can't give

you A B C or D answers

Answer:

The answer is option A

Step-by-step explanation:

The solution is in the image

Answer:

It is the third option

Step-by-step explanation:

Trust me

Answer:

3 < x < 6

Step-by-step explanation:

1) Subtract 2 from the whole equation.

- 13 - 2 > -5x > -28 - 2

2) Simplify.

-15 > -5x > -30

3) Divide the whole equation by -5.

-15/-5 < x < -30/-5

4) Simplify.

3 < x < 6

Answer:

x is 92 degrees

The lines x and a are parallel and congruent, meaning they are evenly proportioned and have the same length.

Answer:

f(x)=11.1035−0.920848x

Step-by-step explanation:

Answer:

D. 2<=x<=6

Step-by-step explanation:

domain: all possible x-values

Answer:

3

Step-by-step explanation:

The total value of Daniel's large assets is $59,600

From the question, we are to determine the total value of Daniel's assets

From the given information,

Daniel has $600 in a checking account and he has $12,000 in a savings account.

He also owns a $12,000 car and a $35,000 house

Then,

The total value of his assets = $600 + $12,000 + $12,000 + $35,000

The total value of his assets = $59,600

Hence, the total value of Daniel's large assets is $59,600

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Answer: 47,000

Step-by-step explanation:

large assets: House+car

12,000+35,000=47,000

The balloon's vertical distance above the ground is 430 feet.

You look straight parallel to the ground. But when you have to watch something down, then you take your sight down by moving your head up.

The angle from horizontal to the point where you stopped your head is called the angle of depression.

From a hot-air balloon, Brody measures a 39° angle of depression to a landmark that's 532 feet away, measuring horizontally.

The angle of depression = 39°

The base = 532

We need to find the vertical distance consider perpendicular.

[tex]\rm Tan \theta = \dfrac{perpendicular}{base } \\\\\rm Tan 39 = \dfrac{perpendicular}{532} \\\\\rm Tan 39 \times 532 =perpendicular\\\\0.80 \times 532\\\\P = 430.80[/tex]

Therefore, the balloon's vertical distance above the ground is 430.80 feet.

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Answer:

430.81

Step-by-step explanation:

hard way

Answer:

[tex]C= 62.8m[/tex]

Step-by-step explanation:

Let's round [tex]\pi = 3.14[/tex]. Area of a circle if [tex]\pi r^2[/tex]. In our case, we can easily find out the radius[tex]\pi r^2 = 100\pi \rightarrow r=10m^[/tex]. At this point, it's easy to find the length of the circumference by doubling it and multiplying again by [tex]\pi[/tex]:

[tex]C= 2\pi r = 62.8 m[/tex]

So we replace "x" with the necessary value (3):

[tex]f(3) \: = \: 2 \: \times \: 3[/tex]

[tex]f(3) \: = \: \boxed{ \bold{6}}[/tex]

[tex]\text{Opción A. } \boxed{ \bold{55}}[/tex]