The cost of creating a software program is $5000. Every extra feature added to the software costs $100. Thetotal charge of the software with x extra features is given by the function f(x) = 100x + 5000. How will the graphof this function change if the basic cost is raised to $5200 and the cost of each extra feature is increased to$120?

We have to find the equation of the line, in point-slope form, that is perpendicular to y - 25 = 2(x - 10) and passes through (-3,7).

The line y - 25 = 2(x - 10) has a slope m = 2.

Perpendicular lines have slopes that are negative reciprocals, so our line will have a slope that is:

Then, we have the slope m = -1/2 and the point (-3,7), so we can write the point-slope form of the equation as:

Answer: y - 7 = -1/2 * (x + 3) [Option C]

Remember that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

In this problem

Figure A and Figure B are similar

so

step 1

Find out the scale factor

scale factor^2=18/98

scale factor=√(18/98)

step 2

To find out the corresponding side length of Figure A, multiply the side length of figure B by the scale factor

so

14*√(18/98)=6

In Equilateral triangle all sides are equal.

Recall that the surface area of the cylinder is

Given the following

radius of 8 cm, and height of 24 cm (3 times the radius), then the surface area of the cylinder is

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

Learn more about the units of measurement here:

brainly.com/question/15402847

#SPJ1

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]

To know more about the range and domain refer to the linkhttps://brainly.com/question/28135761?referrer=searchResults.

#SPJ1

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.

Let's graph the function and find the positive intervals, as follows:

Therefore, the interval is : (-∞ , +-∞)

Answer:

Explanation:

Here is what we know;

Both Kathy and Cheryl cover the same distance ( one course).

Kathy completes the course in 3.6 hours.

Kathy's speed is 2 miles/hour faster than Cheryl's

Cheryl completes the course in 6 hours

Cheryl's speed is yet unkown.

Now, the speed v is defined as

where D is the distance covered and t is the time taken.

Now, let us say D = distance of one course. Then in Kathy's case, we have

since Kathy's speed is 2 miles per hour faster than Cheryl's, we have

For Cheryl, we know that

or simply

Putting this into the equation for Kathy's speed gives

We have to solve for D, the distance of a course.

Subtracting D/6 from both sides gives

Hence, the distance of a course is 18 miles.

With the value of D in hand, we can now find the velocity of Kathy and Cheryl.

Hence, Cheryl's speed is 3 miles/hr.

Next, we find Kathy's speed.

Hence, Kathy's speed is 5 miles/hr.

Therefore, to summerise,

Kathy's speed = 5 miles/hr

Cheryl's speed = 3 miles/hr

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}

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.

If we have the equation:

We can solve it as follows:

1. Add 16 to both sides of the equation (addition property of equality):

Then, we have:

Therefore, the value for x is equal to 46 (x = 46). We can check this as follows:

We substituted the value, x = 46, in the original equation. This is always TRUE. Therefore, the value for x = 46.

Answer:

G. 30 ÷ (x+3)

Explanation:

Given the expression:

From the given options, note that:

Therefore, an equivalent expression is:

The correct choice is G.

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.

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

The red function has the form of:

In order to obtain the green function, we need to do a reflection over y-axis, then a translation one unit to the right, a translation 1 unit down, and finally a reflection over the x-axis, so:

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.

Learn more about the conic section here:

brainly.com/question/8412465

#SPJ1

Answer:

[tex]2.0806 * 10^{2}[/tex]

Step-by-step explanation:

Standard notation, also known as scientific notation, is when the whole number can only be [tex]1\leq 0 < 10[/tex]. The rest of the number is behind the decimal point.

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$

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.

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

2/5 of bulbs were not shining. It is equal to 4 bulbs.

Step-by-step explanation:

10/10 bulbs equals all 10 bulbs. 3/5 were shining, that is equal to 6/10 of all ten bulbs. (or 60%). 60% of ten is 6 bulbs shining.The number of bulbs that werent shining is 10 - 6=4.

Given the following question:

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.

To know more about the inequality, here

https://brainly.com/question/24372553

#SPJ1

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

Okay, here we have this:

Considering the provided expression, we are going to analize which exponential expression is equivalent, so we obtain the following:

As the property of the exponent of a multiplication says that it is equal to the product of each number raised to that power. We have this:

Finally we obtain that the correct answer is the option D.

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.

Notice that:

Answer:

Answer:

Thats nice

Step-by-step explanation: