Directions - Identify the key components, create an exponential equation, then answer the questions.
Exponential Form: y=a.6, a is the starting value, b is the base (rate).
In a small town, the stray dog population is rapidly increasing there are currently 15 stray dogs, and it is estimated that the population will triple every year.
How many dogs will there be after 1 year? 2 years? 3 years?
1) a =
4) Dogs after 1 years =
2) b =
5) Dogs after 2 years =
3) Equation:
6) Dogs after 3 years =

Answer:

Step-by-step explanation:

It would be easier to just show you.

Because we're using variables, I'm going to plug in a random set of numbers to stand for x and y.

(x+y)^2

(2+4)^2=36

vs.

x^2+y^2

2^2+4^2=20

The difference is because, following the order of operations, in the first situation you must first take care of what is in the parenthesis, which means you add x and y together-then you multiply that combined number by the 2nd power. Whereas in the second situation, you multiply x and y by the 2nd power separately, and then add the product of that together. So opposite order. In the first situation you add, then multiply. In the second, you multiply then add.

Answer:

angle 8= 82 degrees

angle 7 = 98

angle 6 = 82

Step-by-step explanation:

5 and 7 are congruent because vertical angles.

5 and 8 are supplementary.

Answer: 7) No   8) No

Step-by-step explanation:

According to the Pythagoras theorem of the right triangle,

Square of largest side = Sum of square of other two sides.

8) Given sides: 5cm, 12cm, 14cm

Here, Largest sides = 14 cm

[tex]5^2+12^2=25+144=169\neq14^2 \ \ \ [14^2=196][/tex]

These sides do not represent a right triangle.

7) Given sides:  9m, 4m, 5m

Largest side = 9 m

[tex]4^2+5^2=16+25=49\neq 9^2 \ \ \ \ \ [9^2=81][/tex]

These sides do not represent a right triangle.

Answer:

first option

Step-by-step explanation:

Given

f(x) = [tex]\frac{2x^2+5x-12}{x+4}[/tex] ← factorise the numerator

     = [tex]\frac{(x + 4)(2x-3)}{x+4}[/tex] ← cancel (x + 4) on numerator/ denominator

     = 2x - 3

Cancelling (x + 4) creates a discontinuity ( a hole ) at x + 4 = 0, that is

x = - 4

Substitute x = - 4 into the simplified f(x) for y- coordinate

f(- 4) = 2(- 4) - 3 = - 8 - 3 = - 11

The discontinuity occurs at (- 4, - 11 )

To obtain the zero let f(x) = 0, that is

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

There is a zero at ( [tex]\frac{3}{2}[/tex], 0 )

Thus

discontinuity at (- 4, - 11 ), zero at ( [tex]\frac{3}{2}[/tex], 0 )

Answer:

The rule for the linear function will be:

f(x) = -2x+1

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear  as shown in the attached graph

Taking two points

Finding the slope between (0, 1) and (1, -1)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

                =  [-1 - 1] / [1 - 0]

                = -2 / 1  

                = -2

Thus, the slope of the line = m = -2

We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 1

Thus, the y-intercept b = 1

Now, substituting m = -2 and b = 1 in the slope-intercept form of linear function

y = mx+b

y = (-2)x + 1         ∵ m = -2, b = 1

y = -2x+1

f(x) = -2x+1

Therefore, the rule for the linear function will be:

f(x) = -2x+1

Answer:

Well when simplified your answer would be

-8-32g

Step-by-step explanation:

So distribute -4 to each number in the parentheses

-4*2= -8

-4*8g= -32g

Now the answer is

-8-32g

Answer:

8.6

Step-by-step explanation:

From the above question, we know that the length of the third side is the longest. Hence, we apply Pythagoras Theorem

c² = a² + b²

a = 5, b = 7

c = Third side

c = √a² + b²

c = √5² + 7²

c = √25 + 49

c = √74

c = 8.602325267

Approximately c = 8.6

Possible length of the third side = 8.6

Answer:

Step-by-step explanation:

[tex] \frac{5(x + 6) - 15(2 - x)}{3x - 1} = 10 \\ [/tex]

[tex] = > 5(x + 6) - 15(2 - x) = 10(3x - 1)[/tex]

[tex]5x + 30 - 30 + 15x = 30x - 10[/tex]

[tex] = > 20x = 30x - 10 \\ = > 20x - 30x = - 10 \\ = > - 10x = - 10 \\ = > x = 1[/tex]

hope it helps:)

Answer: 6.25 cm

Step-by-step explanation:

Area of parallelogram [tex]A=base\times height[/tex]

Using base as AB and height as DE

[tex]Area=8\times 5[/tex]

Now, using base BC and height as DF

[tex]Area=6.4\times x[/tex]

Equating area

[tex]8\times5=6.4\times x\\x=6.25\ cm[/tex]

Answer:

3 Quarters 9 dimes 14 pennies

Step-by-step explanation:

so dimes are x, quarters are y, and pennies are z. Next we know that x*3 y is what dimes are and 5 more pennies then dimes so z+5. Now we do 3 quarters since thats about 100  but less then 3*3=9 so 190 we have 90+75 cents now then we add 14 the cursed number lol but we add 14 because 9+5 is 14 and there are 5 more pennies then dimes.

Answer:

I believe B could be wrong

Answer:

7 green cars.

Step-by-step explanation:

Look at the totals of all of the colors at the bottom. The least of them is green (at 7 cars). That's the answer.

Answer:

4(2+t)

Step-by-step explanation:

A term is a single mathematical expression.  We can see in this expression there are four terms, each separated by an operation:

8, 6t, -3t, and 1.

Coefficients are the numbers that multiply variables.  You can also just think of them as the number in front of any variable.  Here we see we have two terms with variables:

6t, -3t

and therefore our coefficients are:

6, -3

Constants are numbers that are, well, constant - you could also just think of them as "normal" numbers.  We can see in this expression you have two:

8, 1

Like terms are terms of the same type.  We have two like terms with a variable in them:

6t, -3t

and two like terms that are constants:

8, 1

Answer:

the equation only has 1 solution

Step-by-step explanation:

Answer:

One solution

x = -4/13

Explanation:

Image below

Answer:

The value of n is 5

Step-by-step explanation:

Here, we want to get the value of n

To get this, we will need to use the appropriate trigonometric identity

As we can see, n represents the opposite as it the side that faces the angle given

m is the hypotenuse as it is the side that faces the right angle

The last side is called the adjacent

The trigonometric identity we want to use is that which connects the opposite to the adjacent

The appropriate trigonometric identity to use in this case is the tan

Thus;

Mathematically, the tan is the ratio of the opposite to the adjacent

hence;

tan 30 = n/ 5 √3

n = 5 √3 * 1/ √3

n = 5

Answer:

V = hπr^2

V = 5 X π X 15^2

V = 3534.29173

V = 3534.2 cubic feet

The equation that can be used to find the volume V of the swimming pool is πr²h

The swimming pool is circular and has a diameter of 30 feet and a depth of 5 feet.

This simply means the swimming pool follows the shape of a cylinder. The

two bases are circular and has a height of 5 feet.

Therefore, the volume of the swimming pool in cubic feet is the volume of a cylinder.

volume = πr²h

where

r = radius = 30 / 2 = 15 feet

h = 5 feet

volume = 3.14159 × 15² × 5 = 3.14159 × 225 × 5 = 3534.28875 = 3534.3 ft³

learn more about cylinders here: https://brainly.com/question/20766511?referrer=searchResults

Step-by-step explanation:

x² + 4x + y² + 16y - 20 = 0

(x² + 4x + 4) + (y² + 16y + 64) - 4 - 64 - 20 = 0

(x + 2)² + (y + 8)² = 88.

Answer:

125

Step-by-step explanation:

3000 divided by 24 (hours in a day)=125 days

Answer: -9

Step-by-step explanation: Your welcome

Answer:

19.5 or 19 1/2

Step-by-step explanation:

9y + (2x + 1)

9y + (2 x 7 +1)

9y + (14 +1)

9y + 15

9 x 1/2 +15

4.5 + 15

= 19.5

Answer:

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0

y-intercept:

(0,392)

Step-by-step explanation:

sorry if this isn't the answer you were looking for.

Answer:

12 x 3 = 36

Step-by-step explanation:

This is a Multiplication problem Because the Factory can produce 12 shoelaces in 3 minutes so take 12 and multiply it by 3 and your answer is  36. So the factory made 36 shoelaces in that time.

Answer:

12*3=36

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

We can write the ratio of first graders to students as 56:24.

We have to find the total amount of students so we add those two up and we get 70

Out of 70, there are 56 first graders, so we can write that as a fraction which will be 56/70

To get this to a percent, we have to get it so the denominator is 100, I can do some weird thing, multiplying a decimal over decimal to get to the answer, but that isn't what you would most likely do

The best thing to do in this scenario is to simplify this equation so it has a denominator of 10, so we do divide by 7 on the bottom, divide by 7 on the top, and we get the more simplified fraction, 8/10. And 8/10 is also equal to 80/100 which makes the percent 80%

Answer:

The height of the building is 21.38 m

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.

It's required to find the height of the building H.

The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:

[tex]\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

[tex]\displaystyle \tan 22^\circ=\frac{H}{D+B}[/tex]

Multiplying by D+B:

[tex]\tan 22^\circ(D+B)=H[/tex]

Dividing by tan 22°

[tex]\displaystyle D+B=\frac{H}{\tan 22^\circ}[/tex]

Subtracting B:

[tex]\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1][/tex]

Applying to the smaller triangle:

[tex]\displaystyle \tan 33^\circ=\frac{H}{D}[/tex]

Multiplying by D:

[tex]\tan 33^\circ D=H[/tex]

Substituting from [1]:

[tex]\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H[/tex]

Substituting values:

[tex]\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H[/tex]

Operating:

[tex]1.6074H-12.988=H[/tex]

[tex]1.6074H-H=12.988[/tex]

[tex]0.6074H=12.988[/tex]

[tex]H = 12.988/0.6074[/tex]

H = 21.38 m

The height of the building is 21.38 m

Answer:

$6120  (Plz GIve me BRailiest)

Step-by-step explanation:

Answer:

50

Step-by-step explanation: