N 4. Select the correct answer. Function fis an increasing exponential function that is negative on the interval (-C, 2) and positive on the interval (2,). Which could graph of function f? O A. Х -2 -2 OB. All rights reserved

From the diagram given

1. Inscribed angle of the circle

2. AC is a tangent to the circle

3. HI is a chord of the circle

4. L is the center of the circle

5. GEH is a major arc

6. HL is the radius of the circle

7. central angle

8. central angle

9. BD is a secant

10. GHI is a semi-circle

To solve the linear system of equations given, let's substitute y = x - 2 to 2x + 4 = 7.

We get,

By applying the Inverse Property of Addition,

Let find the value of y by substituting x = -6 to y = x - 2.

Therefore, the answer is No. 3 - (-6,-8).

Answer:

h = -3/8

Step-by-step explanation:

-3/4 - h + 1/3h - 2 = -4/3h -3

combine like terms

-2 = -8/4

-3 = -12/4

-2/3h - 11/4 = -4/3h -12/4

2/3h - 11/4 = -12/4

2/3h = -1/4

8/12h = -3/12

8h = -3

h = -3/8

SOLUTION

The formula for an exponential growth is:

From the question:

a=26,237

r=2.4%

x=10

Substitute the values into the equation:

Calcualte the value of y:

This gives:

Therefore the population will be approximately 33259 people

we know that

Focus (0,-1)

Directrix is the line y=0

so

we have a vertical parabola open downward

Remember that

The distance from the vertex to the directrix must be the same that the distance from the vertex to the focus

which means

The vertex is the point (0,-0.5) ----> midpoint between the focus and the directrix

Find out the value of p (focal distance)

p=0.5

The equation of the parabola is given by

The vertex is (0,-0.5)

The value of p=0.5

So,

Given:

An (x,y) solution to this equation could be found just replacing any value of x to check out which value could "y" take.

For example,

When x=1:

Therefore, an (x,y) solution to this equation could be (1,3).

We can write the perimeter as the sum of both sides, multiplied by two.

If one side is 11 in. and the other is x in., we can write the perimeter as:

If the perimeter is 52 inches or more, then x can be calculated as:

The value of x is 15 inches or more.

The equatio of a circle with radius 3 would be: x^2 + y^2=9. If the radius is 9, then the equation would be:

x^2+ y^2 = 81. If a point is inside the circle then x^2+ y^2 <= 81

A. (-9)^2+ (3)^2 <= 81 (Replacing point A)

A. 81 +9 <= 81 (Raising both numbers to the power of 2)

A. 90 <=81 (As 90 is greater than 81, this point is not inside the circle)

The answer is the option A.

The answer is letter A. (x + 4)(x - 2)

The answers are the black circles, just we need to change the signs as i did.

Answer:

A

Step-by-step explanation:

The given piecewise-defined function is:

It is required to graph the function.

To do this, graph each piece with respect to the corresponding domain.

Graph g(x)=2 over x<-1:

Notice that an open circle is at x=-1 since it is not included in the interval x<-1.

Graph g(x)=3 for x=-1. This is just a point:

Finally, graph g(x)=-1 for x>-1:

There is an open circle at x=-1 since it is not included in the interval x>-1.

Thus, the required graph of the piecewise-defined function is shown below:

EXPLANATION

In order to order the real numbers from least to greatest we need to consider that we need to draw a number line.

The line scale marks are equally spaced and usually represent integers.

To plot a real number:

Draw and label a number line

Find where the number is on the number line and place a dot on the numbers.

Plotting Real numbers on the Number Line

Example: Graph the number 3/2 and -3.5 on a number line.

Comparing Real Numbers:

In order to compare the real numbers, we need to replace the blank with > , < or = to make a true sentence.

Example:

2/7 < 0.5

3/2 > 0.5

4/4 = 1

When we are asked to order numbers from least to greatest we can use the number line to help us to plotting the numbers and reordering them.

A strategy we can use here is to convert the numbers to decimals and then plot and/or order them as requested.

a)

x - intercepts: 2 and -1/2

Point = (3, -14)

quadratic formula:

y = a(x -2)(x + 1/2)

we need to solve for a.

-14 = a(3 - 2)(3 + 1/2)

-14 = a(7/2)

a = - 4

so:

y = -4(x -2)(x + 1/2)

y = -4x^2 + 6x + 4

b)

x - intercept = -2 = (-2, 0)

point: (-1, 4)

We can plug both points into two separated equations, as follows:

4 = a(-1)^2 + b(-1) + c (EQUATION 1.)

0 = a(-2)^2 + b(-2) + c (I'll multiply this equation by -1 in order to add the 2 equations together and get rid of c)

4 = a - b + c

0 = -4a + 2b - c

_____________

4 = -3a + b

a = 1/3b - 4/3**

Now we plug back in to the first equation to find c.

4 = 1/3b - 4/3 - b + c

c = 2/3b + 16/3 **

Now we plug one last time on the equation 1 with all b variables:

4 = 1/3b - 4/3 - b + 2/3b + 16/3

b =

Step-by-step explanation:

Think of absolute value as a distance. For example, |5| can be written as |5 - 0| = 5 since the distance between 5 and zero on the number line is 5. Also, |-5| which is the same as |-5 - 0| is also 5 since the distance between -5 and zero on the number line is 5.

Since you want an absolute value equation with solutions 8 and 18, think of which number is the same distance from both 8 and 18 on the number line? Find the average of 8 and 18, (8 + 18)/2 = 13. 13 is the same distance from both 8 and 18. 13 is 5 units away from both 8 and 18. Now you need an equation that is looking for the numbers x which are 5 units distance from 13.

Therefore,

Hence, the answer is

Given equation:

At

Put the value of x in the given equation

That implies

So,

Similarly when x=200

That implies

In the same way

when

That implies

Here x represents the number of computer desk and y represent the amount

Therefore plugging the value of y equals 2800 in the given equation we obtain

that implies

The number of computer desks is 30

From the drawing above :

• Sin (B) = opp/hyp = (b /c )= 55/73

• Cos (B) = adj / hyp =(a/c ) = 48 /73

• Tan(B) = opp/adj = (b/ a) = 55/48

Q.21:

We are asked what f(3) = 32 means?

In Q.20, we are given the following function

Where f(x) is the height (in feet) of the apple and x is the time in seconds.

If we substittute x = 3 seconds into the function, we get the corresponding height of the apple.

As you can see, the height of the apple is 32 feet at 3 seconds.

Therefore, the correct answer is the option (B)

The height of the apple at 3 seconds is 32 feet.

We will have the following:

2. The graph showing each account's balance are:

The one that increases at a constant rate is represented by the "triangles".

The one that doubles each time is represented by the "circles"

You will determine it as follows: First of all a constant increase represents a linear growth [In other words the graph would be a straigh line], and the values that double each time represent an exponential growth, so It will start "slow" and then it will "spike" in an instant.

3.If given the choise you should pick the one that doubles each time. Each time the money will double and after a few weeks will have more money than the one that increases by a constant rate.

To find the graph that represents an absolute value function with a coefficient of least value, we need to understand the following:

An absolute value function with a coefficient of 1 takes the form:

The graph of this function is shown below:

If the function is reflected across the x-axis, it becomes :

Its graph is shown below:

For any absolute value function:

If a > 1 , the function is stretched,

if a < 1 and a >0, the function is dilated

Using the information provided above:

The coefficient with the least value is D

The coefficient closest to zero is C

We know that

So, we can see that g(x) is f(x) reflected in the x-axis. But, it has another change which is a downward movement in 3 units.

So, we can deduce that

Sketch of the situation:

When you reflect f(x) in the x-axis, you obtain something like -f(x).

We can see that -f(x) intersect the y-axis in -1. But, g(x) intersect the y-axis in -4.

So, we need to move the function 3 units down. Whe we make the movement the graph will intersect the y-axis in -4 because -1-3=-4.

We are given three points, and told to find out if they are collinear. What collinear means is that the set of points lay on a line. So, based on this, the strategy to check if this points are collinear is that we are going to pick two points, find the equation of the line that passes through them and them find out if the third point belongs to the line by simply evaluating the equation at the especific value of x.

Let us take, for example the points (-1,11) and (2,23). We will find the line equation that passes through them. To do so, first recall that the line equation is of the form y=mx+b where m is the slope and b is the y-intercept.

First, we will find the slope. Recall that given points (a,b), (c,d) the slope m of the line that joins this two points is given by the equation

In our case, we take a=-1,b=11, c=2, d=23. Then

So, so far our equation looks like this

Now, we want the point (-1,11) to belong to this line. That is, that if we replace x by -1, we should also replace y by 11. Then we have

If we add 4 on both sides, we get

So the equation of the line is

Now, we want to check if (6,42) belongs to this equation. To do so, we replace by 6 and operate. If at the end we get a result of 42, it means that the point belongs to the line, and hence, is collinear to the other two points. We check that

Since we didn't get 42, this means that the point does not belong to the line. Then, the three points are not collinear

In order to find the volume, we will use the next formula

where l is the length, w is the width and h is the height.

In our case

l=28 ft

w=25 ft

h=12 ft

we substitute the data

The volume is 8400 cubic feet

To graph the equation, we would pick three values for x and determine the corresponding y values.

firstly, we would divide both sides of the equation by 2. It becomes

y = 3x/2 + 1

For x = 1,

y = 3*1/2 + 1 = 3/2 + 1 =5/2 = 2.5

For x = 2,

y = 3*2/2 + 1 = 6/2 + 1 = 3 + 1 = 4

For x = 3,

y = 3*3/2 + 1 = 9/2 + 1 = 4.5 + 1 = 5.5

We would plot the corresponding x and y values on the graph

You can see the line that appeared on the graph. It joined the 3 plotted points

Step 1: Write out the nth term of a geometric sequence

Step 2: Write out the sequence and calculate for a1 and r

Step 3: Write out the formula for the sixth term and substitute a1 and r

Hence the sixth term is 32

In order to solve this, we can use trigonometric ratios. The cosine ratio is given by the following formula:

Where ca is the adjacent leg to angle θ and hy is the length of the hypotenuse. In this case, θ=50°, ca = 6 and hy = x.

By replacing these values into the above formula, we get:

From this equation, we can solve for x to get:

Then, x = 9.3

We are given two figure, i) Cube, ii) rectangular box

The volume of any shape is calculated by multiplying height, width, length.

Volume = height x length x width

In the case of a cube, all the dimensions are the same. So volume would be = length x length x length

here, length = 6

So,

V(cube) = 6^3

For a rectangular box:

V(rect) = height x length x width

V(rect) = h x 12 x 6

As given, V(cube) = V(rect). Therefore,

6^3 = h x 12 x 6

Hence, the first option is correct.

1. Consider that the sum of the angles is equal to 90°, then, you have:

30° + 44° + x = 90° simplify left side

74° + x = 90° subtract 74° both sides

x = 90° - 74°

x = 16°

2. As in the previous excersice:

x + 74° = 90°

x = 90 - 74°

x = 16°

3. The sum of the angles is equal to 180°.

134° + x = 180°

x = 180° - 134°

x = 46°

4. The given angles are congruent because they are vertical, then:

x = 59°

We will determine the length and width of the patio as follows:

*First: We write the equations that we can derivate from the text, those are:

&

&

*Second: We will replace this last two equations in the first one and solve for x:

So, we have that the width of the patio is 14 feet long.

*Third: We determine the length:

So, we have that the lenght of the patio is of 35 feet long.

1) Gathering the data

P = 19,000

rate = 0.6% or 0.006

Period : 7 years

A =?

2) Let's plug into the formula below:

3) So the answer is:

We have a vector that which location is true bearing of 140°.

We have to express the quadrant bearing.

True bearing is a directional measurement where the angle is measured clockwise from North.

We can graph this vector as:

Then, as the vector is close to the South direction, we measure the angle of the vector from the South direction. in this case, the angle goes to the East.

The angle has to complete 180° between S and N, so the angle for the quadrant bearing is 180-140 = 40°.

We then can express the quadrant bearing as: S 40° E.

NOTE: if the vector was closest to the N, we should have used the N direction to measure the quadrant bearing, to the East or to the West depending on the vector.

Answer: S 40° E.

We can write the above expression as

Now we know that

And

Also for the piece

So we shall use

And

To fill the blanks so that this expression will be similar to the above.