Hi! I need some help with my precalculus homework question, please. Thank you for your time.

Using the sine formula;

sin 60 / x = sin 90 / 16

cross-multiply

x sin 90 = 16 sin 60

Divide both-side of the equation by sin 90

x = 16 sin 60 /sin 90

x= 13.86

To find y, we can simply use the Pythagoras theorem

opp² + adj² = hyp²

13.86² + y² = 16²

192.0996 + y² =256

subtract 192.0996 from both-side of the equation

y² = 256 - 192.0996

y² = 63.9004

Take the square root of both-side

y = 7.99

Using the vector form of velocity, it is possible to calculate the airspeed and bearing, which are 165.33 mph and 0.7 degrees respectively.

Given:

A plane may go 360 miles straight north in 2.0 hours if the wind is blowing at 15 mph and 331 degrees from the north.

You can use the following formula to calculate airspeed.

[tex]V^{2} =V_{x} ^{2} + V_{y} ^{2}- 2v_{x} v_{y}cos\beta \\[/tex] ...........equation (1)

[tex]v_{x}[/tex] is the velocity of the wind and [tex]v_{y}[/tex] is the velocity of the plane.

[tex]\beta = 331-180 = 151 degree[/tex]

Putting [tex]v_{x}, v_{y} , \beta[/tex] in equation (1)

[tex]V^{2}= 15^{2} +180^{2} -2*15*180*cos151\\ V^{2} = 225 + 32400 - 5400*cos151\\V^{2} = 27336.49\\V = 165.33[/tex]

Hence, The airspeed of the plane is 165.33 mph

Now,

[tex]\frac{sin\alpha }{v_{x} } =\frac{sin\beta }{V} \\\frac{sin\alpha }{15 } =\frac{sin151 }{165.33} \\\\sin\alpha = 10*0.00122\\\alpha = 0.7[/tex]

Hence bearing required is 0.7 degrees.

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Given:

A graph

To determine if the given function is continuous, we first note that the given function has gaps or holes. As we can see, the function has two holes.

We must also remember that a function that has any hole or break in its graph is known as a discontinuous function.

Therefore, the answer is:

To divide the 1/4 of a pound into two equal parts, it is necessary to divide 1/4 by 2, as follow:

(1/4)/2

if 2 is written as 2/1, the previous quotient can be written as a product:

(1/4) (1/2) = 1/8

Now, to write a general expression that takes into account the number of siblings, you name the number of siblings as x. Thus, you have:

(1/4)/(x) = 1/(4x)

see the figure below to better understand the problem

cos(F)=EF/DF --------> by CAH

substitute given values

cos(F)=72/78

simplify

We get from the question the following equation:

S = d/t

We have the following informations:

Speed(S) = 75 miles /h

Distance(d) = 187.5 miles

If you plug those informations into the formula, you'll get the following:

75 miles/h = 185.5 miles/ t

Now, you just have to solve for "t". If you invert the equation, you'll get(I'm going to omit the units, to make it clearer, but don't forget about them!)

1/75 = t / 185.5

If you multiply both sides by 185.5, you'll get

185.5/75 = t

Solving this calculation, we get the final solution!

t = 185.5/75 hours = 2.47 hours

In order to find the number of ways, we must simply calculate:

4! = 4*3*2*1 = 24

24 possible ways.

Answer:

Step-by-step explanation:

statement:

1 = 2

reason:

since 1 and 4 are equal to each other and because lines AB and CD are parallel, any line crossing both lines will create the same angles in the same areas, thus connecting 4 and 2 together. And since 4 is equal to 1, it is also equal to 2.

I hope this helps!

Answer:

statement is 1=2

reason: since 1 and 4 are eqaul to eachothers and beacause lines AB CD are parelle, any line crossing both lines will create the same angels and same area

The vehicle speed is 53 units if s = 24d and d = 245ft

Given the formula for speed is  =  √24 d

s denotes the vehicle's speed.

d = the length of the skid marks

We need to find the speed of the vehicle.

We know that the displacement d is 117 ft

d = 117 ft

And also it is mentioned in the question to use the below-given formula.

s = √24d

Now substituting the value of displacement in the formula we get

=> s = √24 x 117

=> s = √2808

=> s = 52.99

Now approximating to the nearest value of the decimal, we get.

=> s = 53

Therefore the speed of the vehicle is 53 units.

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The decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25

The given mixed fraction = [tex]14\frac{25}{100}[/tex]

The mixed fraction is the fraction that consist of one whole number and the simple fraction.

The simple fraction is the fraction that consist of numerator and denominator as whole number. The top term of the simple fraction is called numerator and bottom term is called denominator

The decimal number is a number that consist of one whole number and the fractional part. The fractional parts are separated by a decimal point.

The number is [tex]14\frac{25}{100}[/tex]

Convert the mixed fraction to simple fraction

[tex]14\frac{25}{100}[/tex] = (100×14+25)/100

= 57/4

Convert the simple fraction to decimal number

57/4 = 14.25

Hence, the decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25

The complete question is:

Rewrite the decimal fraction as a decimal number.

[tex]14\frac{25}{100}[/tex]

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You have to perform two transformations the first one is a 180º rotation with respect to the origin r(180º,O) and the second one is a translation of one unit left and 5 units up T(-1,5)

Given point A(8,-6)

To make a 180º rotation you have to invert the signs of both coordinates, following the rule:

For point A, the rotation is the following:

Once you rotate the point, you have to perform the translation T(-1,5). The rule for the translation can be expressed as follows

So, the translation of point (-8,6) is:

We illustrate the division of fractions by taking the example below.

The first step is to change the division sign to multiplication by changing the fraction after the division sign.

Next, we multiply the numerators together and the denominators together.

You then simplify by dividing common factors.

9 is the greatest number of plants in one row.

The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.

To find the greatest number of plants she can put in one row  , need to find

HCF of 45 , 81 and 63

45 = 3× 3 × 5 = 3² ×5¹

63 = 3 ×3 × 7  = 3² × 7¹

HCF Highest common factor of given numbers is the largest factors which divides all the given numbers perfectly.

HCF = product of common factors of least power

HCF = 3² = 9

Hence greatest number of plants she can put in one row  is 9

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Area of square = L x L

12sq feet =L x L

INFORMATION:

We have the graph of a function that has the form y = ( x - h)² and we must find the value of h.

STEP BY STEP EXPLANATION:

we can see that the graph is a parabola which its vertex is at the point (2, 0)

Now, having this point we can replace the values of its components in the formula of the function

Since the point is (2, 0), then x = 2 and y = 0

Finally, we must solve the equation for h

ANSWER:

C) 2

As we can se from the graph, the maximum value of the function is almost 15 meters, it is reached between t=1s and t=2s, and the height is 0 again when the time is approximately 3 seconds.

We can find the exact values by using the equation.

First, find the zeroes of the function by setting h(t)=0 and solving the quadratic equation for t:

Then, the projectile hits the ground at t=3s.

To find the time at which the projectile reaches its maximum height, find the average between both zeroes:

To find the maximum height, evaluate h at t=1.3s:

Therefore, to the nearest tenth, the projectile reached a maximum height of 14.5 meters in 1.3 seconds and it took 3.0 seconds for it to hit the ground.

The correct option is the second one.

Answer:

C. 64 units squared

Step-by-step explanation:

do 4•4•4 so 4 • 4 = 16 then 16 • 4 = 64 and since its surface area square it. so the answer would actually be 4096 units

a)  Amount of paint needed for 200 km road = 6250 litres

b)  Length of road that can be painted by using 4000 litres of paint = 128 km

Amount of paint used for painting white lines on road= 250 litres

Length which was painted = 8 km

By using unitary method;

Thus for 1 km amount of paint required = 250/8

= 31.25 litres

a) Amount of paint needed for 200 km road = 31.25 × 200

= 6250 litres.

therefore, Amount of paint needed for 200 km road = 6250 litres

b) Since for 1 km 31.25 liters paint is required this implies with 1 liter = 1/ 31.25 =  0.032 km can be covered.

Length of road that can be painted by using 4000 litres of paint = 4000× 0.032

= 128 km

Thus, Length of road that can be painted by using 4000 litres of paint = 128 km

A single or unique unit is referred to as unitary. Determining values in relation to a single unit is the goal of this strategy. For instance, we can use the unitary technique to determine how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

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Given that,

base salary = b = 5000$

Comission rate = 6% = 0.06

Let's say, the sales are = x

As given in the question, he receives 6% commission on all sales over $8000.

Hence, the commissionable amount is (x - 8000) '.' x - 8000 shows the amount greater than 8000, which receives a commission.

hence, gross income will be

base salary + commission * (commisonable amount)

=> 5000 + 0.06 * (x - 8000)

Answer:

g=30

Step-by-step explanation:

Answer:

g = 28

Step-by-step explanation:

( n - 2 ) × 180

( 30 - 2 ) × 180

( 28 ) × 180 = 5040

6g × 30 = 180g

5040 = 180g

÷180     ÷180

--------------------

28 = g

I hope this helps!

Answer:

25 more cups

Step-by-step explanation:

1. You need more than $636.00, but you already have $492.00. To find the needed amount of cups needed to sell, you need to find the difference of the two prices first. In other words, you need to subtract the total needed by the amount already raised.

2. You can get the equation, 636 - 492 = 144

3. Now that you have the amount needed, you can divide the number that you got (144) by 6. You divide it by 6 because that is the amount each cup costs.

4. After dividing 144 by 6, you should get 24. This gives your answer for getting EXACTLY 636. However, in this case, you need more to reach your goal. Since you cannot sell fractions of a cup, just raising it by one can reach your goal. We can add one to 24, making it 25.

In conclusion, you need to sell 25 more cups to reach your goal.

Answer:

The axis of symmetry is -4 because the axis of symmetry is equal to h, in the vertex form!

Given:

Required:

To find the solution of the given equation.

Explanation:

From the given equation,

Now

Therefore,

Final Answer:

The solutions are

To solve the following calculation

You have to keep in mind the order of operations. Which states that multiplications and divisions are to be solved before additions or subtractions.

So the first step is to solve the multiplication "4*2" and the division "10÷2"

Now all that is left is to add the numbers when you have to perform the same operation several times, you have to solve them from lef

Given:

To Determine: The square root of the given number

Solution

Step 1: Express 225 as the product pf its prime factors of 225

Step 2: Separate the factors into their own square root

Step 3: Solve the individual's squares

Hence, the square root of 225 is 15

The equation of the line woth slope 0 and passing through (-9,7) in slope-intercept form is y = 7.

If a line L has a slope M and it has the intercept c, then the equation of the line L can be written in the point slope form as,

L : y = Mx + c

This above equation of line is known as slope-intercept form of line.

Here, we have to find the equation of line which has slope m equal to zero and passing through (-9,7).

putting the known values in y = mx+c

y = (0)x+ c

y = c

Putting the value of y = 7

c = 7

Here, we have,

y = 7

So, the equation of the required line is y=7.

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Given:

The slopr of line is m = -7.

The line passes through point (-6,8).

Explanation:

The equation of line in slope-intercept form is,

Substitute the valus in the equation to determine the value of c.

So equation of line is y = -7x - 34.

Based on the amount you paid for the shares and the selling price as well as the number of years, the total return would be -51.9%

The annual return would be -16.7%

The total return on the stock can be found by finding the difference in stock prices for the 4 years and dividing by the buying price:

= (1,300 - 2,700) / 2,700 x 100%

= -1,400 / 2,700 x 100%

= 0.51851851851851851851851851851852  x 100%

= -51.9%

The annual return can be found as:

= ((1,300 / 2,700) ^ 1/4  - 1) x 100%

= -16.7%

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