The velocity of a drone relative to the air is modeled by v = 13i + 3j. The drone encounters wind with velocity modeled by w = −7i − 2j. Which is the true velocity vector of the drone?

Let us assume that the number of classes is x and the total fee is y

In the Fitness works, there is a monthly fee of $20 and $5 per class, then

The total fee y = 20 + 5(x), then

y = 20 + 5x ------ (1)

In the Gym-tastic, there is a monthly fee of $100 for unlimited classes, then

y = 100 ------- (2)

Equate (1) and (2)

20 + 5x = 100

Subtract 20 from both sides

20 - 20 + 5x = 100 - 20

5x = 80

Divide both sides by 5 to find x

x = 16

The number of the classes is 16

Answer:

29.7

Step-by-step explanation:

To calculate this we need to convert the percentage to a decimal and then multiply.  345% is 3.45, so our math problem is 8.6 x 3.45.  If you put that into a calculator you will get 29.67, but since the least precise number is to one decimal place (8.6), I put my answer to one decimal place as well - I rounded 29.67 to the nearest tenth.

For the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.

It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (a circle is a special type of ellipse).

The given equations are,

P(x)=(x+5)(x-5)

q(x)=(x+3)(x-3)

Parabola is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

The given equation represents a parabola as the equation is graphed we see that the graph of the two never intersects each other.

Thus,for the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.

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Explanation:

First we can see that there's a minus sign in both sides of the equation, so we can take it out:

Now we have to multiply both sides by 15:

Answer:

t = 45

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

With a being a positive real, a > 0, and different from 1, a ≠ 1.

When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.

For example: the function

Since a = 2 > 1, the function is increasing. We have the graph below:

And the function

Since a = 0.5 < 1, the function is decreasing. Then, the graph is:

Given:

Car uses 1.6 gallons to go 32 miles

Let's find the amount of gallons of gas the car needs to travel 420 miles.

Here, the relationship between the miles driven and the amount of gas needed is direct variation.

Since it is a direct variation, we have the variation equation when y varies directly with x:

y = kx

Where k is the constant of variation.

Hence, we have:

32 = 1.6k

Let's solve for k.

Divide both sides by 1.6:

The constant of variation is 20.

The equation that represents this situation is:

y = 20x

Therefore, to find the amount of gallons of gas needed if the car travels 420 miles, substitute 420 for y and solve for x.

420 = 20x

Divide both sides by 20:

Therefore, the car needs 21 gallons of gas

Answer:

y = 12

Step-by-step explanation:

Consider the triangles in the diagram. Triangle QRS (the smaller one on the left) and Triangle PRO (the whole shape)

These two triangles are similar. It helps to write them separately. See image.

You can use a proportion (two ratios equal to each other) to solve this.

There are two good ways to set up an equation.

EITHER:

bottomLeg/sideLeg=bottomLeg/sideLeg

OR

smallbottom/bigbottom=smallside/bigside

see image.

Either way you set it up the answer comes out the same. Pretty much all the work is the same after you crossmultiply.

Solve 9/y = 12/16

OR 9/12 = y/16

see image.

658 text messages

Explanation:

. Since you already know that for 7$ she gets 550 text messages, we can remove the 7$ from the 39.40$ she spent for the month, which leaves 39.40 - 7 = 32.40$

. Now since we know that for each extra 30 cents she gets to send one addition text,

=> we need to figure out first how many cents there is in the amount of money left she had to pay 32.40 * 100 = 3240 cents { since 1 $ = 100 cents }

=> then we need to figure out how many text does 3,240 cents represent, since 1 text is equivalent to 30 cent it means that in 3,240 / 30 = 108 texts messages is the amount of text she got to send with 32.40$

So in total she sent 550 + 108 = 658 texts messages for 39.40$

The measure of angle m∠CGE is 83°

Given,

∠AGF = 62°

∠DGB = 35°

Since, ∠DGB is vertically opposite angle of ∠CGA

Then, ∠CGA = 35°

And also,

             ∠AGF is vertically opposite angle of ∠EGB

Then, ∠EGB = 62°

Now, we know that  CD is straight line

Using angle - sum property,

Then,

      ∠CGE + ∠EGB + ∠CGA = 180°

Putting the values we get

      ∠CGE + 62° + 35° = 180°

       ∠CGE + 97° =  180°

            ∠CGE = 180° - 97°  

           ∠CGE = 83°

Hence,  ∠CGE = 83°

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The number of minutes Bob has used his phone in a month is 1024 minutes.

For the given question;

Monthly phone service paid by Bob = $29.

Additional charges = $0.06 per minute of use.

Total last month charge = $90.44.

Let number of minutes he used be 'm'.

The, the inequality forms is-

90.44 ≤ 29 + 0.06m

Simplifying,

0.06m ≥ 61.44

m ≥ 1024

Thus, the number of minutes Bob has used his phone in a month is 1024 minutes.

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The consecutive integers that are odd numbers are 17, 19 and 21.

In this problem we need to find the values of three consecutive integers that odd integers such that the following equation is satisfied:

x₁ + x₂ = 3 · x₃ - 27

Please notice that two odd numbers are consecutive when their difference is 2.

x₁ + (x₁ + 2) = 3 · (x₁ + 4) - 27

2 · x₁ + 2 = 3 · x₁ + 12 - 27

2 · x₁ + 2 = 3 · x₁ - 15

17 = x₁

x₁ = 17

Thus, the three odd integers that are consecutive are 17, 19 and 21, respectively.

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Recall that a fraction is of the form

where a is the numerator and b is the denominator. The GCF of two numbers is the biggest number that is less than both numbers and that it divides them without any remainder. When the GCF of the numerator and the denominator is 1. This means that we cannot find a common factor for both numbers, so we cannot cancel any more factors. This leads to the fact that the fraction is irreducible or that it is in its simplest form.

We are given the following inequation:

To find the solution we need to subtract 7 to both sides, like this:

Therefore, the solution is the values of "k" smalled than 28.

In this problem we can see that the intercept with the y axis is positive one, so we know that the answer is A) or D), now we can see that the slope is positie so the term with the x has to be positive so the correct function is:

Given:

The length of the arc is (1/12) x circumference of unit circle.

The objective is to find the area of the sector.

Since it is given as a unit cirle, the radius of the circle will be 1 unit.

The circumference of the circle will be,

Then, the length of the arc will be,

Now, the formula to find the area of the sector is,

On plugging the values in the above relation,

Hence, the area of the sector is 0.262 square units.

The control group is the group C, since they take sugar pills.

The dependent variable is the percentage of people that got fewer headaches.

The independent variables is the type of pills they gave to each of the groups.

Notice that:

Answer:

1) y = 1 2) y =3 3) x = -3 4) y= -7 and y = 1

We are to answer the questions stated using the graph:

1) From the graph, when x = 0:

To understand this, check the point on the line that only lies on y

y = 1

2) f(-4) is the same as what is the value of y when x = -4

This is because f(x) = y

From the graph, when x = -4

y = 3

3) From the graph, when y =4

Trace the value of y=4 on the line to get corresponding x value:

x= -3

4) When f(x) = 0

This means what is the value of x when y = 0. This is because f(x) = y.

From the graph, we have two values of x when y = 0

y = -7

y = 1

To fill the blank spaces starting with the smaller number:

-7 and 1

Answer:Q(2,-3)

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

We have to complete a table with some points (x,y) from the line that is represented in the graph.

To do that we choose a value of x and wee which value of y corresponds to that value of x in the line.

For example, we can do it for x = 1 as:

Then, we have one point for the table: when x = 1, y = -9.

We can repeat this process for some points of x:

x | y

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

-4 | 1

-3 | -1

-2 | -3

-1 | -5

0 | -7

1 | -9

2 | -11

We can see that for each unit increase in x, the value of y decreases by 2. This indicates that the slope is m = -2.

Also, for x = 0, y = -7. Then b = -7 is the y-intercept.

Given

0.216

Find

Cube root of the given number

Explanation

Cube root is the value which when multiplying by itself thrice or three times produces the original number

0.216 can be written as the product of

prime factorization of 216 and 1000

prime factorization of 216 =

1000 -

we have to find the cube root so , we make pair of three

so

hence

so , the cube root of 0.216 is 0.6

Final Answer

Therefore , The cube root of 0.216 is 0.6

Answer:

289.8.

Explanation:

Let the number = x

Then, it implies that:

Next, solve for x:

The number is 289.8 to the nearest tenth.

In Equilateral triangle all sides are equal.

So,

We want to find the value in the box such that:

I wrote x instead the box.

To solve this equation, the first thing we need to do is to let the "x term" alone.

For this, we could start by multiplying both sides of the equation by 4:

Now, we could substract 1 to both sides:

And then multiply by 6:

Now, substract 2:

Therefore, the value in the box should be 1.

According to the problem, the function f(x) represents the height of the airplane, and x is the time in seconds since the airplane was thrown.

The graph shows the zeros x = -1 and x = 4, however, the positive zero is the only one that makes sense to the problem because time can't be negative. So, the zero x = 4 means that the paper airplane will reach the water level after 4 seconds.

As we said, just the positive zero has meaning to this situation because, in real life, time is not negative.

Therefore, just one zero (x=4) has real-world meaning.

According to the zero x = 4, the paper airplane will hit the water after 4 seconds.

Answer:

y+6=(3/2)(x-6)

Step-by-step explanation:

Point slope form is:  y-y1=m(x-x1)

We know:

x1= 6

y1= -6

m=3/2

We have the event E defined as:

E: The sum of two rolled dice is greater than or equal to 3

The event E^c is the negation of the event E. Then:

E^c: The sum of two rolled dice is smaller than 3

For two dice, the minimum sum is 2, so this is equal to the event "the sum of two rolled dice is 2". There is only one outcome:

Dice 1: 1

Dice 2: 1

Sum: 2

Then, the only possible outcome for E^c is {1, 1}

John rode his bike 65616.8 feet on Monday which is determined by converting 20 kilometers into feet.

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

John rode his bike 20 kilometers on Monday which is given in the question.

To determine the number of feet John rides.

We have to convert  20 kilometers into feets

We know that

one kilometer = 3280.84 feet

Here 20 kilometers into feet will be:

⇒ 20 × 3280.84

Apply the multiplication operation, and we get

⇒ 65616.8 feet

Therefore, John rode his bike 65616.8 feet on Monday

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The domain and range for the relation is [-∞, ∞]  and [0,-3], and both  of them can be described by interval notation .

Since the graph given to us present a relation or a function, The domain and range of a function are the set of all the inputs and yield a function that can grant separately. The domain and range are vital viewpoints of a function. The domain takes all the conceivable input values from the set of real numbers and the range takes all the yield values of the function. In simple words, the domain is the set of all "x" values and the range is the set of all "y" values in a set of ordered sets and the requested sets are composed as in the form (x, y) or [x,y]

For the given the points are : (0,-3),(1,-3),(2,-3),(3,-3),(4,-3),(5,-3),(-1,-3)(-2,-3),(-3,-3),(-4,-3),(-5,-3)

so the domain set is ={-5,-4,-3,-2,-1,0,1,2,3,4,5}

and the range set is ={0,-3,-4,-5,-6,-7,-8}

so the domain and range is [-∞, ∞] and [0,-3]

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