Solve for X using cosine law along with with written explanation.

Claire who took part in a cross-country race ran 21 km in 1 hour and 12 minutes.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Claire took part in a cross-country race and completed the course in 1 hour and 12 minutes which is (1 + 12/60) = (1 + 1/5) = 6/5 = 1.2 hours.

Her average speed for the race was 17.5 km per hour.

∴ The total distance she ran is,

= (17.5×1.2) km.

= 21 km.

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We will have that the equation with no real solution is:

Because:

y-intercept is the point in the y-axis that the graph intersects.

From the figure, the graph intersects at point (0, 3)

The y- intercept is (0, 3)

x-intercept is the point in the x-axis that the graph intersects.

Since the graph does not intersects the x-axis, the x-intercept does not exist

Vertex is a point on the graph that is a maximum or a minimum.

The vertex of the graph which is the lowest point as shown in the figure is at point (1, 2)

And this is a minima, since it is the lowest point.

Domain is the set of x-values that exist in the graph, the graph is going infinitely to the left and to the right, therefore the domain is (-∞, ∞)

Range is the set of y-values that exist in the graph, the y values starts from the vertex which is the lowest point at (1, 2) going upward.

So the range is all real numbers greater than or equal to 2. [2, ∞)

End behavior is the behavior of the function at large positive and negative values of x.

when x goes positive infinity, f(x) goes to positive infinity

As x ⇒ ∞, f(x) ⇒ ∞

when x goes negative infinity, f(x) goes to negative infinity

As x ⇒ -∞, f(x) ⇒ -∞

Decreasing interval occurs when the graph is going down, and increasing interval occurs when the graph is going up.

Decreasing interval will be (-∞, 1]

Increasing interval will be [1, ∞)

The expression would be:

Where x are the meters climbed.

For 2,000 m we'll have:

A 20°C decrease in temperature.

The numerator of the left hand side can be rewritten as:

Then, the given equation can be written as:

Since

we have

We can to can cancel out one term x+3 and get

which gives

Finally, in order to check that this value corresponds to a real answer, we need to subsitute this value into the equation and compute the limit when x approaches to -3, that is,

which gives

Since the limit has the form 0/0 we can to apply L'Hopital rule, that is,

which gives

Since the limit exists and is equal to zero then the solution of the equation is: x= -3

The population of one country changed from 23 million to 54 million. Use the information to find the unknown values in the bar diagrams a = L.347 b

y

​

Explanation:

The difference is:

To solve this we need the exponent of 10 be the same for both terms of the substraction. It is better is we change the exponent of the area of Texas, by moving the decimal point two places to the right:

Now we can substract the numbers and leave the 10³ out:

Scientific notation has always only one place with a number before the decimal point. Therefore 267.79x10³ is not in scientific notation, we have to move the decimal point two places to the left and add 2 to the exponent of 10:

Answer:

The difference is 2.6779 x 10⁵ square miles

[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]

Notice that both numbers 26 and 29 are divisible by 13:

thus, we can write the sum 26 + 39 like this:

Okay, here we have this:

Considering the provided measures, we are going to calculate the requested surface area, so we obtain the following:

So to calculate the surface area we will use the following formula:

A = a(a + √(a^2 + 4h^2))

A = 8 cm(8cm + √((8 cm)^2 + 4(3 cm)^2))

A = 8 cm(8cm + √(64 cm^2 + 4*9 cm^2))

A = 8 cm(8cm + √(64 cm^2 + 36 cm^2))

A = 8 cm(8cm + √(100 cm^2))

A = 8 cm(8cm + 10 cm)

A = 8 cm(18 cm)

total surface areaA = 144 m^2

Finally we obtain that the total surface area is equal to 144 m^2

Answer:

$1200 would be raised if 60 cars were washed.

Step-by-step explanation:

This question can be solved using a rule of three.

The total after 9 cars was of $180. How much would be raised with 60 cars washed?

9 cars - $180

60 cars - $x

Applying cross multiplication

9x = 180*60

9x = 10800

x = 10800/9

x = 1200

$1200 would be raised if 60 cars were washed.

Fractions

Ivanna has to drive 12 miles. She has already driven 1/4 so far.

The distance she has driven is:

Ivanna has driven 3 miles so far

You have the following expression:

it means that the number 3 is multipled by itself five times (because of the exponent), then, the previous expression can be written as follow:

The formula for equation of line pasing through point (x_1,y_1) with slope m is,

Substitute point and slope in the equation to obtain the equation of line.

So equation of line is y=5x+4.

The formula of compound interest is,

I) We have to convert the temperature from Celsius to Farenheit, using the formula:

The temperature in the Poconos is 15 °C, so we have C = 15. We can then calculate the temperature as:

The temperature in Canada is 5 °C, so we can calculate the temperature in Farenheit as:

II) We have to find the expression for the cost for each hotel in function of "n", the number of nights.

Holiday inn costs $80 per night plus $10 for parking.

We can express the total cost in function of n as:

SOLUTION

Write out the given information

Let the time at which both of them work be

Then

The individual rate will be

Then

Simplifying fraction, we have

Hence

Therefore

It will take both of them 3.53 minutes to solve it together

We can find the slope using the following formula:

Let:

Therefore:

Answer:

Recall that:

Therefore:

Then:

Now, notice that:

Then:

Therefore:

Then:

Therefore:

Since:

we get that:

Answer:

Suppose that the sides of the rectangle have lengths x and y, and that the measure of the side parallel to the creek is y, as shown in the drawing below

The total length of the fence, according to the drawing, is:

Since there is 120 feet of fencing available, then:

On the other hand, the area A of the pasture, is equal to the base 120-2x times the height x:

Find the maximum value of the 2nd degree polynomial for A. Since A has roots at x=0 and x=60, the maximum value is found at x=(60+0)/2=30.

Then, the maximum possible area of the pasture can be found by plugging in x

The question given is to convert

From a conversion calculator,

Therefore,

Therefore,

2250 watts will be

Hence,

The final answer = 3.017 horse power

Apply ln to both sides:

Ln e^-t = ln 125

Ln e (125) = -t

First, let's find the area circular sector:

Where:

r = radius = 7cm

θ = angle (in radians) = 5/6 π

so:

Now, let's find the area of the triangle, that triangle is an isosceles triangle, so, we can use the following formula in order to find its area:

where:

s = one of the equal sides = 7

θ = angle = 150

so:

Therefore, the area of the white region will be, the area of the circular sector minus the area of the isosceles triangle, so:

6=a/4+2

Subtract 2 from both sides of the equation:

6-2 = a/4+2-2

4 = a/4

Multiply both sides by 4

4 (4) = a/4 (4)

16 = a

a= 16

506.78 meters per min

distance = 400 m

time = 47.36 seconds

The result is meant to be in meters/min

We need to convert the seconds to minute:

60 seconds = 1 min

47.36 seconds = 47.36/60 = 0.7893

The average rate will be distance divided by time

Given:

Thesis about question is given

Required:

To select which option is correct

Explanation:

assumption S1 is the distance to the grocery store

assumption S2 is the distance to the south post office

assumption S3 is the distance to the north bank

assumption S is the total distance

according to the question

S1= 10 miles S2=6 miles S3=8 miles

S=S1+S2+S3=10+6+8=24 miles

Required answer:

option D

We have a rectangle of base 6 and height 4. We have a rectangle like this:

Now, we have a scale factor of 3. We need to multiply each side by 3:

Now the rectangle has a height of 12 and a base of 18.

The area of a rectangle is h*b. Then, the area of the scaled copy is:

Therefore, the scaled copy has an area of 216 square units.

Calculate the area of the square (A1), and then subtract the area of the circle (A2).

Square area = side length ^2

A1 = 12^2 = 144 ft2

Area of a circle = π r^2

where:

r= radius = diameter /2 = 12/2 = 6

Replacing:

A2 = π 6^2 = 113.09 ft^2

Area of the shaded region = A1- A2 = 144-113.09 = 30.92 ft2

Each term is 6 greater than the previous term.

First term is "7".

So,

a = 7

d = 6

Let's find the formula for the series,

We can immediately eliminate the firsst and third choice.

The variable is "t", so the general formula will be:

How many terms are there?

The series starts from t = 1,

since 6(1) + 1 = 6 + 1 = 7

and 6(2) + 1 = 12 + 1 = 13

The terms match!

So, 2nd answer choice is correct!!

The farmer would like to eclose a rectangle

First we know that the perimeter of the rectangle is

We also know that we have 36 ft of fence, that is we only can enclose a rectangle of 36 ft of perimeter. Then

From this we can find y

The area of the rectangle is

But we know the value of y, plugging this value into the last equation we have that

To find three possible values for the area we only have to give values to x. This values have to be positive (since we can't have a negative lenght). We also notice that the value can't exceed 18 since that would mean a zero area. With those point in consideration we choose three values between zero and 18.

If x=3, then the area is

If x=9, then the area is

if x=15, then the area is

Then we have three possible areas for the rectangle.

The maximum value for the area is 81, and we see that because the equation for the area is a parabola that opens down with vertex in the point (9,81)