Solve the right triangle. State the side lengths to the nearest tenth and the angle measures to the nearest degree.

Answer:

  83 25/27 yd³

Step-by-step explanation:

Assuming a 4 ft depth of fill, the cut volume is ...

  (2 ft)(33 ft)(65 ft) = 4290 ft³

The fill volume is ...

  (23 ft)(22 ft)(4 ft) = 2024 ft³

The left over dirt occupies a volume of ...

  4290 ft³ -2024 ft³ = 2266 ft³ = (2266 ft³)(1 yd³)/(27 ft³) = 83 25/27 yd³

Answer:

A) (2, -1/2)

Step-by-step explanation:

Start with one equation and isolate a variable:

4x - 4y = 10

4x - 4x - 4y = 10 - 4x

-4y = 10 - 4x

-4y/-4 = 10/-4 - 4x/-4

y = -2 1/2 + x

Now plug this in for y in the other equation:

3x + 2(-2 1/2 + x) = 5

3x - 5 + 2x = 5

5x - 5 = 5

5x - 5 + 5 = 5 + 5

5x = 10

5x/5 = 10/5

x = 2

Right here we can tell your answer is A since it is the only one with 2 as the x-value

Answer:

c

Step-by-step explanation:

It would be c because you would add subtract 30 - x which equals 30x then you would divided 5 / 6 which equals 0.12 then you would add y plus some number which equals 12y then you would add 12y+12=24y=24y / 2=12 thenyou have 30x,12y.

Answer:

D

Step-by-step explanation:

A might be right for the wrong linear equation type. It could be describing a y intercept slope line. So even if it is right, it is not the answer. Actually the answer to A should be y = (5/6)x - 13

The general formula for the answer you want is

Givens

y -y1 = m(x - x1)

x1 = 30

y1 = 12

m = 5/6

Solution

y - 12 = (5/6)(x - 30)

That makes the answer D

Answer:

142.4 cubic units

Step-by-step explanation:

Formula: π * r²

Radius = 4

Height = 8.5

Volume = 1/3 x 3.14 x (4)^2 x 8.5 =

The volume of an oblique cone is given in cubic units. The two options presented as cubic units are 142.4 and 196.0. Without additional measurements, we cannot calculate the exact volume, but we know that the volume must be one of these two options.

The question is asking to determine which of the provided values represents the volume of an oblique cone. Volume is the measure of space occupied by a three-dimensional object and is expressed in cubic units. In general, the volume of a cone can be calculated using the formula V = (1/3)πr²h, where 'r' is the radius of the base, 'h' is the height, and π is Pi, approximately 3.14159. Since an oblique cone has a circular base but is tilted, the formula for its volume is the same as that of a right cone.

Looking at the options provided, we need to determine which value most likely represents the volume of a cone. Since volume is expressed in cubic units, the correct answer will be in cubic units, not square units. Therefore, we can immediately eliminate the options with 'square units' as they represent an area measure instead of volume.

Thus the potential answers could either be 142.4 cubic units or 196.0 cubic units. Without additional information, such as the dimensions of the base and the height, we cannot perform the calculation to further refine the answer. However, the question might be simplifying the process by providing the answer directly, and it is up to the student to choose between the given cubic unit options based on an understanding of volumes rounding procedures, if applicable.

Using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution

Let the quadratic equation given be of the form [tex]ax^2 + bx + c = 0[/tex], then

The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

There are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.

For this case, the given equation is:

[tex]x^2 - x = -1/4[/tex]

Converting this to the form [tex]ax^2 + bx + c = 0[/tex], we get:

[tex]x^2 - x + 1/4= 0\\or\\4x^2 -4x + 1 = 0[/tex]

Thus, we get:

a = 4, b = -4, c = 1

Putting these values in the expression for discriminant, we get:

[tex]D = b^2 - 4ac =(-4)^2 - 4(4)(1) = 16 - 16 = 0[/tex]

The discriminant is 0, so the considered quadratic equation is going to have both roots real and equal. Or in terms of distinct solutions, it is going to have one real solution (distinct).

Thus, using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution

Learn more about discriminant of a quadratic equation here:

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Answer:

Radius of the Earth is 3978.8 Miles

Circumference of the Earth is 25000 Miles

Step-by-step explanation:

The angle of the sun shone at an angle of 7.2° to the zenith

This means that the angle of the sector of the circle is 7.2° (θ)

S = Length of the sector of the circle = 500 miles

r = radius of earth

Converting 7.2° to radians

[tex]\theta =7.2\frac{\pi}{180}[/tex]

[tex]S=r\theta\\\Rightarrow r=\frac{S}{\theta}\\\Rightarrow r=\frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow r=3978.8\ Miles[/tex]

∴ Radius of the Earth is 3978.8 Miles

[tex]C=2\pi r\\\Rightarrow C=2\times \pi \frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow C=25000\ Miles[/tex]

∴ Circumference of the Earth is 25000 Miles

The radius and circumference are respectively; r = 3978.86 miles and C = 25000 miles

We are told that the angle of the sun shone at an angle of 7.2° to the zenith. Thus, we can liken this to the angle of a sector and so;

Angle of the sector of the circle; θ = 7.2° = 0.125664 rad

Length of the sector of the circle; S = 500 miles

Formula for length of arc is;

S = rθ

where;

S is length of arc

r is radius

θ is angle of sector in radians

Thus;

r = S/θ = 500/0.125664

r = 3978.86 miles

Formula for circumference is;

C = 2πr

C = 2 * π * 3978.86

C = 25000 miles

Read more about Circumference at; https://brainly.com/question/14283575

Answer:

See below in bold.

Step-by-step explanation:

The ratio of oil to vinegar is 5 : 1. That means that 5/6 of the mixture is oil and 1/6 is vinegar.

So to make 57 oz of the polish,  57/ 6 = 9 1/2 oz is vinegar and 5/6 * 57 =

47 1/2 oz is olive oil.

Answer:

AC, CE, AB, and AS

I belive those are your answers

Answer:

chords: CE and AB; secant: CE; tangent:t; diameter AB; radii: AS and SB

Step-by-step explanation:

Finding the slope using two points:

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =7\\y_{1} =6\\x_{2} =8\\x_{1} =4[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{7 - 6}{8 - 4}[/tex]

C) [tex]\frac{1}{4}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

400,000,000 tons

Step-by-step explanation:

You could reword this sentence to ask the question, "100,000,000 is 25% of how much?"

The word "is" means equals, the percent will be .25 in decimal form, the word "of" means to multiply, and "how much" is x, our unknown.  In equation form, then, this looks like

100,000,000 = .25 × x

We will divide both sides by .25 to get that

x = 400,000,000

That's how much grain was grown in 2008

Answer: 400 million tons

Step-by-step explanation:

100 millions is 1/4 of 400 million

Answer:

5.779 x 10^-8 =0.00000005779

Step-by-step explanation:

The E-8 at the end means the number is multiplied by 10^-8.

So 5.779E-8=5.779 x 10^-8

A negative power means move the decimal place that many places to the left

So 5.779 x 10^-8 =0.00000005779

Answer:

Sample response: The E indicates scientific notation. The first number is the coefficient of the number in scientific notation. This number is multiplied by a power of 10. The number following the E, which is –8, is the exponent, and the base is 10.

Step-by-step explanation:

2020

Answer:

Widow's Share = Rs 500.05

Son's share = Rs 1400.14

Step-by-step explanation:

Property = 4000.40

Widow get share = 0.125

So, Share of Widow = 0.125 * 4000.40

Widow's Share = Rs 500.05

Remaining Property = 4000.40 - 500.05

Remaining Property = 3500.35

Son's share = 0.4 * 3500.35

Son's share = Rs 1400.14

To solve this problem, we will follow these steps:
1. Calculate the widow's share of the property.
2. Determine the remainder of the property after the widow has received her share.
3. Calculate the son's share of the remainder of the property.
Step 1: Calculate the widow's share.
The widow gets 0.125 (or 12.5%) of the total property. The total property is valued at 4000.40 units (where the unit could be in rupees, dollars, etc.).
Widow's share = Total property * Widow's share percentage
              = 4000.40 * 0.125
Let's calculate that:
Widow's share = 4000.40 * 0.125
              = 500.05
So, the widow gets 500.05 units.
Step 2: Determine the remainder of the property.
Now, subtract the widow's share from the total property to find out how much is left for the son to receive his share from.
Remainder of property = Total property - Widow's share
                      = 4000.40 - 500.05
Let's calculate that:
Remainder of property = 4000.40 - 500.05
                      = 3500.35
Now we have 3500.35 units remaining after the widow has received her share.
Step 3: Calculate the son's share.
The son gets 0.4 (or 40%) of the remainder of the property.
Son's share = Remainder of property * Son's share percentage
            = 3500.35 * 0.4
Let's calculate that:
Son's share = 3500.35 * 0.4
            = 1400.14
So, the son gets 1400.14 units.
To summarize, the widow receives 500.05 units of the property, and the son receives 1400.14 units of the property after the widow has received her share.

Answer:

Explanation:

1) Set the algebraigic expression that represents the combinations of sofa and pillow orders:

2) Predict the graph of the inequality x + 2y ≥ 4

        x = 0 ⇒ 2y = 4 ⇒ y =4/2 ⇒ y = 2 ⇒ point (0,2)

        y = 0 ⇒ x = 4 ⇒ point (4,0)

        Then the lines goes through (0,2) and (4,0) ... [the four graphs meet this]

3) Conclusion:

That means that the correct graph is the last one: solid line, shaded area over the line y = 2 - x/2.

Note: a more detailed graph would include the fact that the items cannot be negative, i.e. x ≥ 0 and y ≥ 0, which would result in that the shaded area would be on the first quadrant.

Answer: D

Step-by-step explanation:

Answer:

x = 5.34

Step-by-step explanation:

The reference angle is 24 degrees.  I'm sure you are aware from the square at the other base angle that is a right triangle.  Right triangles have ratios by which we can determine missing side and angle measures.  The sin of a reference angle has a ratio that is side opposite/hypotenuse.  The cos of a reference angle has a ratio that is side adjacent/hypotenyse.  The tan of a reference angle has a ratio that is side opposite/side adjacent.

We need to decide which of these fits our needs according to the angle and sides we are given and need to find.  We have the reference angle as 24 degrees, we have the side adjacent to this angle as 12.  We are looking for x, which is the side opposite the reference angle.  Looking to what our definitions are for each ratio, the sides opposite and adjacent are defining the tan of the reference angle.  Setting up the ratio then looks like this:

[tex]tan(24)=\frac{x}{12}[/tex]

Multiply both sides by 12 to get

12 tan(24) = x

Do this on your calculator in DEGREE mode to get that

x = 5.342744224

Not sure what your teacher has you round to, but I usually have my students give me 2 decimal places

Answer:

t = 4.06 sec

Step-by-step explanation:

First of all, if the initial velocity is 64 feet per second, then the parabola should actually look like this:

[tex]h(t)=-16t^2+64t+4[/tex]

The initial velocity is in the place of our linear term, so it should be 64 not just 4.

Anyways, the h(t) value represents the height of the object after a certain number of seconds, t, it was launched from the initial height. We are looking for the length of time it takes the object to hit the ground.  The height of something on the ground is 0.  So we replace h(t) with a 0 and factor to solve for the values of t:

[tex]0=-16t^2+64t+4[/tex]

If you plug that into the quadratic formula to factor it, you will get that the values of t are

t = -.06 seconds and

t = 4.06 seconds

We all know that the 2 things in math that will never EVER be negative are time and distance/measures, so we can safely disregard the negative value of time.  

It takes the ball 4.06 seconds to hit the ground when it is launched from an initial height of 4 feet.

Answer:

Step-by-step explanation:

The product of two identical binomial factors will be a perfect square trinomial. The appropriate answer choices are those having both factors the same.

Answer:

Step-by-step explanation:

(xy + x)(xy + x)

(16 x2)(x2 16)

(4y2 + 25)(25 + 4y2)

The base is a right triangle with side lengths of 6 and 8 ft.

The area of a triangle is 1/2 x base x height = 1/2 x 6 x 8 = 24 square feet.

Now to find the volume, multiply the area by the height:

24 square ft x 12 ft = 288 ft^3

Answer:

i think it is 288 ft^3

Step-by-step explanation:

Answer:

(0.78,0)

Step-by-step explanation:

I would use the quadratic formula.

[tex]a=3[/tex]

[tex]b=-8[/tex]

[tex]c=5[/tex]

[tex]\text{ The quadratic formula is } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{ Let's find } b^2-4ac \text{ first}\\(-8)^2-4(2)(5)\\64-8(5)\\64-40\\24\\\\\text{ Now let's find } -b\\-b=8\\\text{ And } 2a\\2(2)=4\\\\\text{ Let's plug in this information }\\x=\frac{8 \pm \sqrt{24}}{4}\\\\\text{ We are now going to simplify }\\x=\frac{8}{4} \pm \frac{\sqrt{24}}{4} \\x=2 \pm \frac{\sqrt{4 \cdot 6}}{4}\\x=2 \pm \frac{\sqrt{4} \sqrt{6}}{4} \\x=2 \pm \frac{2 \sqrt{6}}{4}\\[/tex]

[tex] x=2 \pm \frac{\sqrt{6}}{2}[/tex]

So let's put both of these into out calculator

2 + sqrt(6)/2                  and             2-sqrt(6)/2

One of them should be approximately 3.22 as the question suggests.

3.22                                                        0.78

So the other x-intercept is approximately (0.78,0)

Answer:

  84 child tickets were sold

Step-by-step explanation:

Had they all been adult tickets, revenue would have been ...

  $9.80 × 147 = $1440.60

It was less by ...

  $1440.60 -1054.20 = $386.40

The child's ticket costs less by ...

  $9.80 -5.20 = $4.60

so there must have been $386.40/$4.60 = 84 child tickets sold.

__

Replacing an adult ticket with a child ticket reduces the revenue by $4.60 without changing the number of tickets sold.

_____

You can let c represent the number of child tickets sold. Then (147 -c) is the number of adult tickets sold, and total revenue is ...

  5.20c + 9.80(147 -c) = 1054.20

  -4.60c +1440.60 = 1054.20 . . . . simplify

  -4.60c = -386.40 . . . . . . . . . . . . . subtract 1440.60

  c = 386.40/4.60 = 84

Answer:

r = +2√3

Step-by-step explanation:

The equation of a circle with center at (0, 0) and radius r is

x^2 + y^2 = r^2.

Here we have

x^2 + y^2 = 12,

and so we can deduce that r^2 = 12.  Then r = +2√3.

Answer:

The radius is: [tex]2\sqrt{3}[/tex]

Step-by-step explanation:

The equation of a circle in center-radius form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

So, given the equation of the circle:

[tex]x^2+y^2=12[/tex]

You can identify that:

[tex]r^2=12[/tex]

Then, solving for "r", you get that the radius of this circle is:

[tex]r=\sqrt{12}\\\\r=2\sqrt{3}[/tex]

Answer:

Option B A rectangular prism in which BA=30 and h=5 has a volume of 150 units³, therefore, Shannon is correct

Step-by-step explanation:

step 1

Find the area of the base of the rectangular pyramid

The volume of the rectangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base and H is the height of the pyramid

we have

[tex]V=50\ units^{3}[/tex]

[tex]H=5\ units[/tex]

substitute and solve for B

[tex]50=\frac{1}{3}B(5)[/tex]

[tex]B=30\ units^{2}[/tex]

step 2

Find the volume of the rectangular prism with the same base area and height than the rectangular pyramid

The volume of the rectangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base and H is the height of the pyramid

we have

[tex]B=30\ units^{2}[/tex]

[tex]H=5\ units[/tex]

substitute

[tex]V=(30)(5)=150\ units^{3}[/tex]

step 3

Compare the volumes

Volume of the rectangular pyramid -------> [tex]50\ units^{3}[/tex]

Volume of the rectangular prism -------> [tex]150\ units^{3}[/tex]

therefore

The volume of the rectangular prism is three times the volume of the rectangular pyramid

Shannon is correct

Answer:

b. 9/5

Step-by-step explanation:

Cotangent is the inverse of tangent.

tan θ = y/x

cot θ = x/y

cot θ = (-9)/(-5)

cot θ = 9/5

just to add to that great reply by @MathPhys above

[tex]\bf (\stackrel{adjacent}{-9},\stackrel{opposite}{-5})~\hfill cot(\theta )=\cfrac{\stackrel{adjacent}{-9}}{\stackrel{opposite}{-5}}\implies cot(\theta )=\cfrac{9}{5}[/tex]

bear in mind that, the value coordinate pairs we get is the (x,y) coordinates, and x = adjacent side of the triangle whilst y = opposite side of it.

Answer:

The probability that the card drawn is a club is 0.25.

The probability that card drawn is a club, when it is given that the card is black is 0.5.

Step-by-step explanation:

In a standard​ deck of cards:

Total number of cards = 52

Total number of cards of each suit (club, spade,heart, diamond) = 13

The probability that the card drawn is a club is

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]P=\frac{^{13}C_1}{^{52}C_1}=\frac{13}{52}=0.25[/tex]

Therefore the probability that the card drawn is a club is 0.25.

Let A and B represents the following events:

A : Card is black

B : Card is a club

Total number of black cards = 26

[tex]P(A)=\frac{26}{52}=\frac{1}{2}=0.5[/tex]

From the above parts

[tex]P(B)=0.25[/tex]

Total number of black club cards = 13

[tex]P(A\cap B)=\frac{13}{52}=\frac{1}{4}=0.25[/tex]

We need to find the probability that card drawn is a club, when it is given that the card is black.

[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]

[tex]P(\frac{B}{A})=\frac{0.25}{0.5}=0.5[/tex]

Therefore the probability that card drawn is a club, when it is given that the card is black is 0.5.

Answer with explanation:

For a Lopsided coin ,probability of getting Head is equal to [tex]\frac{1}{3}[/tex] For a Lopsided coin ,probability of getting Tail  is equal to [tex]\frac{1}{3}[/tex].

→Probability of getting Tail > Probability of getting Head

→Coin is heavier from tail side and lighter from Head side.

→→We have to Calculate number of flips of coin that is needed to have both heads and tails appear at least once.

[tex]\rightarrow P(\text{Head})=\frac{1}{3}\\\\ \frac{1}{3} \times x=1\\\\x=3\\\\\rightarrow P(\text{Tail})=\frac{2}{3}\\\\ \frac{2}{3} \times y=1\\\\y=\frac{3}{2}[/tex]

→We need to find common multiple of 3 and [tex]\frac{3}{2}[/tex].

Least common multiple of 3 and [tex]\frac{3}{2}[/tex] is 6.

→So,on Average number of flips of this coin are needed to have both heads and tails appear at least once=6 tosses

Answer:

0 and 1

Step-by-step explanation:

binary

Answer:

quarters = 6+x

dimes = x

Total value = 325

Dime value = 10

Quarter value = 25

Step-by-step explanation:

25x+150+10x=325 (simplify)

35x=175

x=5  

6+5 = 11  

Hence Zoe has 5 dimes and 11 quarters.

Hope this helps!!❤

Answer:

210 is the only choice I see listed that works.

Step-by-step explanation:

I don't know if you know this but you can apply a co-function identity here giving you the equation:

[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].

If you are unsure of the identity sin(90-x)=cos(x) then I can show you another identity that leads to this one.

The difference identity for sine is sin(a-b)=sin(a)cos(b)-sin(b)cos(a).

Applying this to sin(90-x) gives you sin(90)cos(x)-sin(x)cos(90).

Let's simplify that using that sin(90)=1 while cos(90)=0:

sin(90-x)=sin(90)cos(x)-sin(x)cos(90)

sin(90-x)=1cos(x)-sin(x)(0)

sin(90-x)=cos(x)

You can also prove this identity using a right triangle like the one in this picture:  

That missing angle is 90-x since we need the angles in this triangle to add up to 180 which it does:

(x)+(90)+(90-x)

x+90+90-x

x-x+90+90

0+180

180

Anyways you should see that sin(90-x)=b/c while cos(x)=b/c.

Since they are equal to the same ratio, then you can say sin(90-x)=cos(x).

There are other co-function identities you can get from using this idea.

Anyways back to the problem.

We are solving:

[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].

It looks like you have a drop-down menu with answers ranging from 0 to 360.

So I'm going to answer in degrees using the unit circle.

cosine value refers to the x-coordinate.

We are looking for when the x-coordinate is [tex]-\frac{\sqrt{3}}{2}[/tex] which is at [tex]\theta=150^\circ , 210^\circ[/tex].

Amount of expenditure to be shown on the income statement = 0 and Income from the reversal of additional balance = $200

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Given that the Allowance for Uncollected Accounts is at 2% based on the percentage of sales method, the closing amount for the current year must be 2% of credit sales.

Current year credit sales = $140,000

Allowance for Uncollected Accounts = $140,000 × 2% = $2,800

the current amount of Allowance for Uncollected Accounts is $3,000, it is already $200 in excess of the threshold ($3000 - $2800), hence it must be reversed by $200.

Amount of expenditure to be shown on the income statement = 0.

Income from the reversal of additional balance = $200

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Final answer:

To calculate the expense for uncollectibles using the percent-of-sales method, multiply the net credit sales by the estimated percentage of uncollectibles. For Millford Company, this calculation is $140,000 * 2%, resulting in an expense of $2,800, ignoring the existing allowance balance.

Explanation:

The student has asked how to calculate the expense to report on the income statement for uncollectibles using the percent-of-sales method. Millford Company estimates that 2% of their net credit sales of $140,000 will be uncollectible. To find the uncollectible expense, you multiply the total net credit sales by the estimated percentage, which is $140,000 * 2% = $2,800. Since the Allowance for Uncollectible Accounts has a prior credit balance of $3,000, the current period's expense recognized in the income statement is calculated by adjusting for this existing balance. However, if the question simply asks for the expense amount based on current sales, it ignores the pre-adjustment balance and focuses solely on the estimated uncollectibles from current sales, which is $2,800.

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let [tex]\text{Opposite}[/tex] denotes the length of the side opposite to the [tex]30^{\circ}[/tex] acute angle, and [tex]\text{Adjacent}[/tex] be the length of the side next to this [tex]30^{\circ}[/tex] acute angle.

[tex]\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}[/tex].

Similarly,

[tex]\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}[/tex].

The longer leg in this case is the one adjacent to the [tex]30^{\circ}[/tex] acute angle. The answer will be [tex]3[/tex].

There's a shortcut to the answer. Notice that [tex]\sin{30^{\circ}} < \cos{30^{\circ}}[/tex]. The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the [tex]30^{\circ}[/tex] angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship [tex]\sin{\theta} < \cos{\theta}[/tex] holds for all acute angles? (That is, [tex]0^{\circ} < \theta <90^{\circ}[/tex]?) It turns out that:

Answer:

A

Step-by-step explanation:

Since the triangle is right use the cosine ratio

cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex], so

[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex]

Multiply both sides by 2[tex]\sqrt{3}[/tex]

adj = [tex]\frac{\sqrt{3} }{2}[/tex] × 2[tex]\sqrt{3}[/tex] = 3

Answer:

  45 = (one third)x + 15

Step-by-step explanation:

If x represents the number of minutes Tom commutes, then (1/3)x is "one-third as many minutes as Tom's commute." 15 minutes more than that is ...

  (1/3)x + 15

We are told this is the length of Paul's commute, and that it is 45 minutes. So, the appropriate equation is ...

  45 = (1/3)x +15

Answer: 45 = (one third)x + 15

Step-by-step explanation: