What are the factors of x2 − 49? (x − 1)(x + 49) (x − 7)(x − 7) (x − 7)(x + 7) Prime

Step-by-step explanation:

First we have to find percent change by doing change/original

To find change: 45000-18000=27000

Now divide by original. 27000/18000=1.5

The change was 150 percent. Now we multiply 45000 by 150 percent to get the projected population for 2015.

45000*1.5=67500 people

Brainliest? :)

Projected population for 2015 using exponential growth model is 112,500, calculated with initial population of 18,000 and growth rate.

To determine the projected population for 2015 using an exponential growth model, we need to identify the growth rate and use it to extrapolate the population.

The exponential growth model can be represented as:

[tex]\[ P(t) = P_0 \times e^{rt} \][/tex]

Where:

- [tex]\( P(t) \)[/tex] is the population at time [tex]\( t \)[/tex]

- [tex]\( P_0 \)[/tex] is the initial population (in 2005)

- [tex]\( r \)[/tex] is the growth rate

- [tex]\( t \)[/tex] is the time in years since the initial population was measured

First, we need to find the growth rate [tex](\( r \))[/tex]. We can use the data provided from 2005 to 2010:

[tex]\[ P_0 = 18000 \][/tex]

[tex]\[ P(5) = 45000 \][/tex]

Using these values in the formula:

[tex]\[ 45000 = 18000 \times e^{5r} \][/tex]

Now, let's solve for [tex]\( r \)[/tex]:

[tex]\[ \frac{45000}{18000} = e^{5r} \][/tex]

[tex]\[ 2.5 = e^{5r} \][/tex]

Taking the natural logarithm of both sides:

[tex]\[ \ln(2.5) = 5r \][/tex]

Now, divide by 5:

[tex]\[ r = \frac{\ln(2.5)}{5} \][/tex]

Now, we have the growth rate [tex]\( r \)[/tex]. We can use this rate to project the population for 2015 [tex](\( t = 10 \) years)[/tex]:

[tex]\[ P(10) = 18000 \times e^{\frac{\ln(2.5)}{5} \times 10} \][/tex]

Now, calculate this:

[tex]\[ P(10) = 18000 \times e^{\ln(2.5) \times 2} \][/tex]

[tex]\[ P(10) = 18000 \times e^{\ln(2.5^2)} \][/tex]

[tex]\[ P(10) = 18000 \times e^{\ln(6.25)} \][/tex]

[tex]\[ P(10) = 18000 \times 6.25 \][/tex]

[tex]\[ P(10) = 112500 \][/tex]

So, the projected population for 2015 is 112,500.

Answer:

C. Graph the first equation, which has slope = −2 and y-intercept = 3, graph the second equation, which has slope = −4 and y-intercept = −1, and find the point of intersection of the two lines.

Step-by-step explanation:

The two equations are in slope intercept form which is y = mx + b where m is the slope and b is the y-intercept.

In the first equation (y = -2x + 3), -2 is the slope since it is the coefficient. "b" is 3 since it is the constant of the equation.

In the second equation (y = -4x -1), -4 is the slope is the coefficient, and the y-intercept is -1 since it is the constant.

To solve the equations graphically, graph them and find the point where they intersect.

The required explanation that is best for the solution of the given equation is given by option c. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given a system of equations,
y = −2x + 3                 (1)
y = −4x − 1                   (2)

The slope of equation 1
m = -2 and y-intercept  = 3
The slope of equation 2
m = -4 and the y-intercept = -1
So, From option that matched the calculation is

Graph the first equation, which has slope = −2 and y-intercept = 3, graph the second equation, which has slope = −4 and y-intercept = −1, and find the point of intersection of the two lines.

Thus, the required explanation that is best for the solution of the given equation is given by option c. Option C is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ3

Answer:

y-7 = 4(x+9)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is the point

y-7 = 4(x--9)

y-7 = 4(x+9)

8 times because you take 4 times 2 and get 8

Reasoning:

There are 2 outcomes if you flip only one coin (H or T).

There are 2^2 = 2*2 = 4 outcomes if you flip two coins (HH, HT, TH, TT).

There are 2^3 = 2*2*2 = 8 outcomes if you flip three coins.

There are 2^4 = 2*2*2*2 = 16 outcomes if you flip four coins.

Answer:

[tex]40 +20 = 72 -12\\\\60 = 60[/tex]

Step-by-step explanation:

If we have an expression in the following way:

[tex]c(a + b)[/tex]

So the distributive property says that:

[tex]c(a + b) = ca + cb[/tex]

In this case we have the expression:

[tex]4(10 + 5) = 6(12-2)[/tex]

Therefore we can rewrite it as:

[tex]4 * 10 + 4 * 5 = 6 * 12 -2 * 6[/tex]

Then we have left:

[tex]40 +20 = 72 -12\\\\60 = 60[/tex]

4*10+4*5=6*12-6*2

40+20=72-12

60=60

Answer: 60=60

Answer:

1.5(x)

Step-by-step explanation:

find out how many hours are in 90 minutes

1.5

x miles

I think the answer is most likely 80

Answer: C

He forgot the negative sign on 1/2x

Answer:

Please see attached picture

Step-by-step explanation:

A rectangular prism has its volume defined as

V_rect_prism = length * height * width

V_rect_prism = (x+9) * (x-1) * (x-7)

The volume expressed as a polynomial can be seen in the picture below.

Answer:

Step-by-step explanation:

Let the number of games played be x.  68% of x comes out to 17 games.

Then 0.68x = 17.  Mult. both sides by 100:  68x = 1700.

Divide 68 into 1700 to obtain x, the number of games played:  x = 25

The team plays in 25 games.

The correct answer is C. The graph of the function [tex]y = (1/3)^x[/tex] decreases from left to right, exhibiting exponential decay as x increases.

To complete the table for the function [tex]y = (1/3)^x[/tex], we need to substitute the given values of x into the equation and calculate the corresponding values of y.

Let's start by substituting -3 into the equation:

y = (1/3)^(-3)

y = 1/(1/3)^3

y = 1/1/27

y = 27

Next, let's substitute -1 into the equation:

y = (1/3)^(-1)

y = 1/(1/3)^1

y = 1/(1/3)

y = 3

Then, let's substitute 0 into the equation:

y = (1/3)^0

y = 1

After that, let's substitute 1 into the equation:

y = (1/3)^1

y = 1/3

Lastly, let's substitute 2 into the equation:

y = (1/3)^2

y = 1/9

Therefore, the completed table is as follows:

x | -3 | -1 | 0 | 1 | 2 | 3

y | 27 | 3 | 1 | 1/3 | 1/9 | 1/27

To graph the function y = (1/3)^x, we plot the points from the completed table on a graph. The graph of this function is an exponential decay curve that starts at (0, 1) and decreases as x increases. The curve is steeper for larger x values and approaches the x-axis as x approaches infinity.

In terms of the given options, the correct answer would be C. The graph of the function decreases from left to right.

Answer:

Step-by-step explanation:

t(1) = 4

t(n) = -4 * t(n - 1)

common ratio: -4

t(1) = -4 * t(0)

4 = -4 * t(0)

t(0) = -1

t(n) = -4n * -1

t(1) = -4 (1) * -1

= 4

t(n) = -4n * -1

t(6) = -4*6 * -1

t(6) = 24

Answer:

45%

Step-by-step explanation:

It is 45% because is 1/4 of the circle

Answer:

37.5%

Step-by-step explanation:

The probability is 3/8, which is 37.5%.

Answer:

28 times

Step-by-step explanation:

18 x 28 = 504

It’s 4! Those seem wrong lol

Answer: is A 4

Step-by-step explanation:

Answer: 26.8 feet

Step-by-step explanation:

In the figure attached you can see two right triangles  triangle ABD and a triangle ACD.

You are located at point B and the other person at point C.

The approximate height of the lifeguard station is x.

Keep on mind that:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

Therefore:

For the triangle ABD:

[tex]tan(36\°)=\frac{x}{DC+11}[/tex]    [EQUATION 1]

For the triangle ACD:

[tex]tan(46\°)=\frac{x}{DC}[/tex]    [EQUATION 2]

Solve from DC from [EQUATION 2]:

[tex]DC=\frac{x}{tan(46\°)}[/tex]

Substitute into [EQUATION 1] and solve for x:

[tex]tan(36\°)=\frac{x}{(\frac{x}{tan(46\°)}+11)}\\tan(36\°)(\frac{x}{tan(46\°)}+11)=x\\11*tan(36\°)=x-\frac{xtan(36\°)}{tan(46\°)}\\7.991=0.298x[/tex]

[tex]x=26.81ft[/tex]≈26.8ft

Answer would be D which is L

Answer:

L

Step-by-step explanation:

Most people prefer to use a unit of measurement that gives a number they can easily visualize, usually between 0.1 and 1000.

You wouldn't use centimetres, because that is a unit of length, and grams are a unit of mass.

The amount of milk in a half-gallon carton is about 2 L or 2000 mL, so you would measure the milk in litres (L).

I think it’s b I’m currently learning the same thing in my class

Answer:

The answer is A. 2.0

Step-by-step explanation:

One of the angles is a right angle, because x is the tangent of that circle. The other radius is 1.5, since all radius are equal to each other. Then you use the Pythagorean theorem (a²+b²=c²). C is always the hypotenuse. The hypotenuse in this triangle is the 1.5 + 1 line. A and b can be changed within each other. I put A = 1.5, B = x, and C = 2.5. My equation was 1.5²+x²=2.5². Remember the formula can also be x²+1.5²=2.5² as well. Then you solve the equation you just made. You multiply everything by each other, because of the ² (I forgot the name of it, hehehe). You will get 2.25+x²=6.25. Then you subtract 2.25 to both side. x²= 4. Then you square root both sides to make x by itself. x=2. That's how you get 2 as your answer

Answer:

Option C From day 7 to day 8

Step-by-step explanation:

The given graph shows the total number of hours Katrina worked over the period of 10 days.

Now we will calculate the number of hours worked by Katrina for every given options in the question.

Option A - From day 1 to day 2

Katrina worked (6 - 3) = 3 hours

Option B - From day 4 to day 5

Katrina worked (12-12) = 0 hours between the period of 4 to 5 days

Option C - From day 7 to day 8

Katrina worked (18-12) = 6 hours

Option D - From day 9 to day 10

Katrina worked ( 18 - 18) = 0 hours so she took the rest.

According to this, options C represents the work done for maximum hours in one day interval.

Answer:

Yes

-2(3x-7) is equivalent to 5+6x-19-12x

Step-by-step explanation:

Given in the question two expression

-2(3x-7)

5+6x-19-12x

We will apply distributive law to solve first expression

a(b + c) = ab + ac

-2(3x-7)

-2(3x) + -2(7)

-6x -14

For the second expression rearrange the terms

5+6x-19-12x

-12x+6x -19+5

-6x -14

Since both equations when expanded have same answers, hence they are equivalent

the answer is (-2,-9) because x's cannot repeat

Final answer:

To find the probability that the red die shows an even number or the green die shows an even number, we can use the concept of probability of a union of two events. The probability is 3/4.

Explanation:

To find the probability that the red die shows an even number or the green die shows an even number, we can use the concept of probability of a union of two events. Let's denote the event that the red die shows an even number as E and the event that the green die shows an even number as F.

Since each die has 6 equally likely outcomes, the probability of rolling an even number on the red die is P(E) = 3/6 = 1/2, and the probability of rolling an even number on the green die is P(F) = 3/6 = 1/2.

To find the probability of the union of two events (E or F), we add the probabilities of E and F and subtract the probability of their intersection (E and F) to avoid double-counting. In this case, the intersection is the event that both dice roll an even number, which has a probability of P(E and F) = (1/2) × (1/2) = 1/4.

Therefore, the probability that the red die shows an even number or the green die shows an even number is P(E or F) = P(E) + P(F) - P(E and F) = 1/2 + 1/2 - 1/4 = 3/4.

Solution: 6 x 9 / 2 = 27

If its a triangle its divided by 2 found the sum of base x height.

The area of the triangle is 27  sq.ft

The area can be defined as the space occupied by surface of an object.

The area of a figure is the number of square unit that cover the surface of a closed figure.

The area of a triangle is given  by

= (1/2) * base * height

The base of the triangle = 6 feet

The height of the triangle = 9 feet

Therefore the area of the triangle = (1/2) * 6 *9

= 27 sq.ft

Therefore the area of the triangle is 27  sq.ft.

To know more about Area

https://brainly.com/question/27683633

#SPJ2

1) 2 and 3

2) skewed right

3) skewed left

(−1

2  )(n^3)+

1

2 n^2+4.6n+(−

1

2)(n^3)+

1

2  n^2+4.5n

=

−1

2  n^3+

1

2  n^2+4.6n+

−1

2  n^3+

1

2  n^2+4.5n

Combine Like Terms:

=

−1

2  n^3+

1

2  n^2+4.6n+

−1

2  n^3+

1

2  n^2+4.5n

=(−1

  2   n^3+

−1

2   n^3)+(

1

2  n^2+

1

2   n^2)+(4.6n+4.5n)

=−n^3+n^2+9.1n

Answer:

=−n^3+n^2+9.1n

     Everything underlined means its a  fraction/divided hope this helps :D

Hey there!

The first thing we should do is to make the fractions have a common denominator.

The least common multiple of 4 and 6 is 12, which we can find by taking the multiples of both and finding the smallest one they have in common.

What we should do it multiply both sides of the equation by 12, which eliminates both fractions.

We now have:

9x - 60 = 10

Hope this helps!

The results of the equation without fraction is 118x = 175

Given the equation

[tex]\frac{3}{5} x - 5 = \frac{5}{6}\\[/tex]

Step 1: Add 5 to both sides of the equation:

[tex]\frac{3}{5} x - 5 +5= \frac{5}{6} + 5\\\frac{3}{5} x= \frac{5}{6} + 5\\[/tex]

Multiply through by 30:

[tex]\frac{3}{5} x \times 30= (\frac{5}{6} \times 30 )+( 5 \times 30)\\(3x \times 6) = (5\times 5) + 150\\18x = 25 + 150\\18x = 175[/tex]

Hence the result of the equation without fraction is 118x = 175

Learn more here: https://brainly.com/question/17788156

Again, scale factor is 12 / 4 = 3.

So Perimeter = 16 * 3 = 48.

The perimeter of the larger flag, which is a square with each side measuring 8 inches, is 32 inches. This is calculated by multiplying the side length by 4, as a square has four sides.

To find the perimeter of the larger flag, which resembles a larger square, you need to know the length of one of its sides. Since the problem states that the dimensions are twice that of a smaller square, first, determine the side length of the smaller square. If the side length of the larger square is 8 inches, obtained by scaling up the smaller square's side length by a factor of 2 (4 inches x 2 = 8 inches), you can find the perimeter by multiplying the side length of the larger square by 4 (since a square has four sides).

The calculation for the perimeter of the larger square is as follows: 8 inches x 4 = 32 inches. Therefore, the perimeter of the larger flag is 32 inches.

A card shuffling machine picks cards from a standard deck.

Step-by-step explanation:

Parking lot:

Angie=x

Sister=x+12

Amom=2•(sister) or 2(x+12)=2x+24

Betty=x-3

Bmom=4•(betty) or 4(x-3)=4x-12

--------

Part A: Amom=2x+24

Part B: Bmom=4x-12

PartC:

x=angie

Amom=Bmom+6

2x+24=4x-12+6

2x+24=4x-6

24-6=4x-2x

18=2x

9=x

Angie is 9 years old.

Answer:

Choice B best fits the data shown

Step-by-step explanation:

We employ the scatter-plot feature in Ms. Excel and then add an exponential trend line selecting the display equation on chart option. The attachment below is an image from the excel workbook where the task was performed.

From the attachment the regression equation was obtained as;

[tex]y=3.799e^{0.7x}[/tex]

But;

[tex]e^{0.7}=2.01[/tex]

Thus, the regression equation can be expressed as;

[tex]y=3.80*2.01^{x}[/tex]