Simplify the expression 3x3^ 648x 4 y8

Reading from top to bottom. Answers are as follows:

1. 7(2)^t

2. 3000(0.93)^t

3. 300(1.015)^t

4. 300(0.985)^t

We know that the exponential function is given by:

             [tex]f(x)=ab^x[/tex]

where a is the initial amount.

and b is the change in the amount and is given by:

[tex]b=1+r[/tex] if the function is increasing by a rate of r

and [tex]b=1-r[/tex] if the function is decreasing by a rate of r.

a)

The initial amount of fish in the trout are: 7

i.e. a=7

Also, the population doubles every year.

This means that that b=2

Hence, the population after t years is given by the function P(t) as:

[tex]P(t)=7(2)^t[/tex]

b)

The original amount of the machine is: $ 3,000

i.e. a=3,000

Also, the value of machine decreases by a rate of 7%

i.e.

[tex]r=7\%\\\\i.e.\\\\r=0.07[/tex]

Hence, we have:

[tex]b=1-r\\\\i.e\\\\b=1-0.07\\\\i.e.\\\\b=0.93[/tex]

Hence, the function which represent the price of the machine after t years i.e. P(t) is given by:

[tex]P(t)=3000(0.93)^t[/tex]

c)

The initial population of colony of ants i.e. a=300.

The number of ants increases at a rate of 1.5% every month.

i.e. [tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]

i.e.

[tex]b=1+r\\\\i.e.\\\\b=1+0.015\\\\i.e.\\\\b=1.015[/tex]

Hence, the function P(t) which represents the population of ants after t months is given by:

[tex]P(t)=300(1.015)^t[/tex]

d)

The initial infected cells i.e. a=300

The infected cells are decaying at a rate of 1.5% per minute.

i.e.

[tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]

Since, there is a decay hence,

[tex]b=1-r\\\\i.e.\\\\b=1-0.015\\\\i.e.\\\\b=0.985[/tex]

Hence, the function P(t) which represents the number of infected cells after t minutes is given by:

[tex]P(t)=300(0.985)^t[/tex]

Answer: [tex]x=-5\\y=-7[/tex]

Step-by-step explanation:

Given the system of equations:

[tex]\left \{ {{y=\frac{4}{5}x-3 } \atop {y=-7}} \right.[/tex]

You can apply the Substitution method.

You need to substitute the second equation which gives the value of the variable "y" into the first equation and solve for the variable "x", then:

[tex]y=\frac{4}{5}x-3\\\\-7=\frac{4}{5}x-3\\\\-7+3=\frac{4}{5}x\\\\-4=\frac{4}{5}x\\\\(-4)(5)=4x\\\\x=\frac{-20}{4}\\\\x=-5[/tex]

Let the number of hours driven equal x.

You would multiply the number of hours by his speed, so you would have 50x

You would then want to subtract that from the total miles to see how many more miles he needs to drive.

The answer would be E. y = 470 - 50x

Answer:

The distance between both points would be 14.

Step-by-step explanation:

The y coordinate or -8 stays the same for both points on a coordinate grid. However the x coordinate changes from -4 to 10, which is 14 places away on a coordinate grid. Therefore the distance between these two points is 14.

Answer:

14

Step-by-step explanation:

Use the distance equation:

d² = (x₂ − x₁)² + (y₂ − y₁)²

d² = (10 − -4)² + (-8 − -8)²

d² = 14² + 0²

d = 14

Answer:

8x+16

Step-by-step explanation:

Answer:

(x+7) is not a factor

Step-by-step explanation:

we know that

If (x+7) is a factor of f(x)

then

For [tex]x=-7, f(-7)=0[/tex]

Verify

we have

[tex]f(x)=x^{3}-3x^{2} +2x-8[/tex]

Substitute x=-7

[tex]f(-7)=(-7)^{3}-3(-7)^{2} +2(-7)-8[/tex]

[tex]f(-7)=-343-147 -14-8[/tex]

[tex]f(-7)=--512[/tex]

[tex]-512\neq 0[/tex]

therefore

(x+7) is not a factor

Answer:

[tex]8,101\ bears[/tex]

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

x ----> is the number of years since 2009

y ----> is the population of bears

a ----> is the initial value

b ---> is the base

step 1

Find the value of a

For x=0 (year 2009)

y=1,570 bears

substitute

[tex]1.570=a(b)^{0}[/tex]

[tex]a=1.570\ bears[/tex]

so

[tex]y=1.570(b)^{x}[/tex]

step 2

Find the value of b

For x=1 (year 2010)

y=1,884 bears

substitute

[tex]1,884=1.570(b)^{1}[/tex]

[tex]b=1,884/1.570[/tex]

[tex]b=1.2[/tex]

The exponential function is equal to

[tex]y=1.570(1.2)^{x}[/tex]

step 3

How many bears will there be in 2018?

2018-2009=9 years

so

For x=9 years

substitute in the equation

[tex]y=1.570(1.2)^{9}[/tex]

[tex]y=8,101\ bears[/tex]

Answer:

Step-by-step explanation:

Question 15

1 / 1 pts

In 2009, there were 1570 bears in a wildlife refuge.  In 2010, the population had increased to approximately 1884 bears.  If this trend continues and the bear population is increasing exponentially, how many bears will there be in 2018?

ANSWER = 8,101 GOT IT RIGHT ON TEST

Answer:

6 units

Step-by-step explanation:

We require to calculate the absolute value so as to consider the measure both ways, that is

AB = | 1 - (- 5) | = | 1 + 5 | = 6

BA = | - 5 - 1 | = | - 6 | = 6

Answer:

A

Step-by-step explanation:

A function maps one member in the domain ( x values ) to exactly one member in the range (y values ).

A is the only diagram representing this characteristic.

Answer:

5852 deer.

Step-by-step explanation:

That would be 11 * 532

= 5852 (answer).

Answer:

There are 5852 deer live in the county.

Step-by-step explanation:

The population density of deer in the county is 11 deer per square mile.

That means, there are 11 deer in 1 square mile in that county.

Given that, the total area of that county is 532 square miles.

For getting the total number of deer, we just need to multiply the 'population density' by the 'total area'.

So, the total number of deer [tex]=(11\times 532)= 5852[/tex]

Answer:

[tex]f(x) = (4\sqrt{5})^{x}[/tex]

Step-by-step explanation:

The exponential function looks like the following: [tex]f(x) = b^{x}[/tex].

If the function passes through the point (2, 80), then:

[tex]f(x) = b^{x}[/tex] → [tex]80 = b^{2}[/tex]

Solving for 'b':

[tex]b = \sqrt{80}[/tex] →[tex]b=4\sqrt{5}[/tex]

Then, the equation of exponential function that passes through the point (2, 80) is: [tex]f(x) = (4\sqrt{5})^{x}[/tex]

Answer:

The division was completed in the wrong order

Step-by-step explanation:

To convert [tex]\frac{5}{8}[/tex] to a percent

The numerator is divided by the denominator, that is

    0.625

8 | 5.0

Multiply 0.625 × 100% = 62.5%

Answer:

Step-by-step explanation:

We have:

two squares 10ft × 10ft

three rectangles 14ft × 10ft

two rectangles 9ft × 14ft

two triangles with base 10ft and height 8ft

The formula of an area of a reactangle l × w  (square s × s) :

[tex]A=lw\qquad(s^2)[/tex]

Substitute:

[tex]A_1=10^2=100\ ft^2\\\\A_2=(14)(10)=140\ ft^2\\\\A_3=(9)(14)=126\ ft^2[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{(base)(height)}{2}[/tex]

Substitute:

[tex]A_4=\dfrac{(10)(8)}{2}=40\ ft^2[/tex]

The Surface Area:

[tex]SA=2A_1+3A_2+2A_3+2A_4[/tex]

Substitute:

[tex]SA=(2)(100)+(3)(140)+(2)(126)+(2)(40)=952\ ft^2[/tex]

Answer:

Step-by-step explanation:

-5x+31+3x=3

move everthing to one side

-5+31+3x-3=0

add and subtract common terms

-2x+28=0

divide across by common denominator

-x+14=0

Solve for x

x=14

Answer:

16

Step-by-step explanation:

6+8+10+20=44+16= 60 divided by 5 is 12

Konichiwa~! My name is Zalgo and I am here to help you out on this amazing day. I believe the answer that you would be looking for is (x-1)  (6x-1).

I hope that this answer helps! :3

"Stay Brainly and stay proud!" - Zalgo

(By the way, do you mind marking me as Brainliest? I'd greatly appreciate it! Arigato~! XP)

Answer:

Part a) The elevation of the road is [tex]6\°[/tex]

Part b) The rise is [tex]0.2\ km[/tex]

Step-by-step explanation:

Part a) What is the elevation of the road to the nearest degree?

Let

y-----> the rise of the road ( vertical distance)

x ----> the run of the road (horizontal distance)

we have

y/x=1/10

we know that

The ratio y/x is equal to the tangent of the angle of the elevation of the road

Let

[tex]\theta[/tex] ---->  angle of the elevation of the road

[tex]tan(\theta)=y/x[/tex]

[tex]tan(\theta)=1/10[/tex]

[tex]\theta=arctan(1/10)=6\°[/tex]

Part b)  If the road is two km long, how much does it rise?

using proportion

[tex]1/10=y/2[/tex]

[tex]y=2/10=0.2\ km[/tex]

Answer:

[tex]4h> 14\ cm^{2}[/tex]

Step-by-step explanation:

Let

b -----> the base of parallelogram

h ----> the height of parallelogram

we know that

The area of parallelogram is equal to

[tex]A=bh[/tex]

[tex]A> 14\ cm^{2}[/tex]

so

[tex]bh> 14\ cm^{2}[/tex]

substitute the value of b

[tex]4h> 14\ cm^{2}[/tex] ---->inequality that represents all possible values of h

Answer:

The answer is D

Step-by-step explanation:

Answer: c. area ≈ 5 units²

Step-by-step explanation:

Step 1: Use Law of Sines to find b:

[tex]\dfrac{sinC}{c}=\dfrac{sinB}{b}\\\\\\\dfrac{sin44.9}{4}=\dfrac{sin107.3}{b}\\\\\\b=\dfrac{4sin107.3}{sin44.9}\\\\\\b=5.4[/tex]

Step 2: Use SAS formula to find the area of the triangle:

[tex]Area = \dfrac{1}{2}bcsinA\\\\\\Area=\dfrac{1}{2}(5.4)(4)sin27.8\\\\\\Area = 5.05[/tex]

Answer: A is correct (x+2)/(x-1)

Step-by-step explanation:

Divide the top and bottom by 2, to simplify

[2(x^2+x-2)]/[2(x^2+2x+1)]

The 2's cancel each other out, since 2/2 would be 1.

Now factor (x^2+x-2)/(x^2+2x+1)

[(x+2)(x-1)]/[(x-1)(x-1)]

Now you can cancel out one of the (x-1) on top and bottom. All that's left is (x+2)/(x-1) which is your answer. Hope this helps!

Answer:

[tex]x^{2}+y^{2}=25[/tex]

Step-by-step explanation:

we know that

The equation of a circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center

r is the radius

In this problem we have

(h,k)=(0,0)

r=5 in

substitute

[tex](x-0)^{2}+(y-0)^{2}=5^{2}[/tex]

[tex]x^{2}+y^{2}=25[/tex]

For this case we have that a quadratic equation is of the form:[tex]ax ^ 2 + bx + c = 0[/tex]

Where:

a: is the main coefficient because it accompanies the quadratic variable.

b: It is the linear coefficient

c: It is the constant term.

Then, a quadratic function with a main coefficient of "3" and a constant term of "-12" is:

[tex]f (x) = 3x ^ 2 + 11x-12[/tex]

Answer:

Option B

[tex]f (x) = 3x ^ 2 + 11x-12[/tex]

Answer:

It is B. f(x) = 3x2 + 11x – 12

Step-by-step explanation:

If this question is on Edg, then it is B, & B is Correct.

Answer:

[tex]H'(-3,-18)\\\\J'(3,-9)\\\\K'(-15,-3)\\\\L'(15,-15)[/tex]

Step-by-step explanation:

We know the coordinates of the polygon HJKL:

H(-1,-6), J(1,-3), K(-5,-1), and L(5,-5)

We know that the polygon HJKL is dilated using the scale factor 3. This means that, to find the coordinates of the vertices of polygon H'J'K'L', we need to multiply the x-coordinate and the y-coordinate of each vertex by this scale factor.

Then:

[tex]H'=(-1(3),-6(3))=(-3,-18)\\\\J'=(1(3),-3(3))=(3,-9)\\\\K'=(-5(3),-1(3))=(-15,-3)\\\\L'=(5(3),-5(3))=(15,-15)[/tex]

Answer:

A.

Only function g is even

Option: A is the correct answer.

  A.   Only function g is even.

Here by looking at the graph we observe that the graph of function g satisfies the condition of even function.

( whereas the graph of function f is not symmetric about the y-axis and hence function f is not even )

     Hence,  the function g is an even function.

Answer:

172.5 mg/dl

Step-by-step explanation:

Given the equation y= -2.5x + 222.5, where 'x' is the time spent exercising in minutes. If we want to know the amount of cholesteron for a person exercising 20 minutes a day, we just have to subtitute 20 into the equation for x.

So we have: y= -2x + 222.5 → y= -2.5(20 minutes) + 222.5 = 172.5 mg/dl

Answer:

172.5

Step-by-step explanation:

Confirmed on test

Answer:

156 square inches

Step-by-step explanation:

We are given the two quantities

Let

length = l = 13 inches

and

Width = w = 12 inches

The formula for the area of rectangle is:

[tex]Area=l*w[/tex]

where l is length and w is width

Putting the values of both that are given

[tex]Area = 13*12\\=156[/tex]

so the area is 156 square inches ..

Answer:

True depending on what you are comparing it to.

Step-by-step explanation:

A pulley would help lighten the load that you are trying to pull up, which may make it easier for you to get the load to your designated area. The more complicated it is, usually the more 'lighter' it becomes, or the less force you have to exert.

For example, you will have to give a 100% energy in trying to life a heavy box. However, if you use a simple pulley (only one), you may only have to exert 75% more energy, for the weight is significantly lower.

~

Answer:

156.429

Step-by-step explanation:

52.1428571 in one year x 3

Answer:  I suggest using desmos, since I can't help!! I can't see the function!!

Answer:

I'm sorry but there is no graph if you could take a picture I could try to help.

Answer:

[tex]{\huge \boxed{X<-2}}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

Expand.

4(1-3x)-14=-12x-10

4(2x+3)-9x=-x+12

-12x-10>-x+12

Add by 10 from both sides of equation.

-12x-10+10>-x+12+10

Simplify.

-12x>-x+22

Add by x from both sides of equation.

-12x+x>-x+22+x

Simplify.

-11x>22

Multiply by -1 from both sides of equation.

(-11x)(-1)<22(-1)

Simplify.

11x<-22

Divide by 11 from both sides of equation.

11x/11<-22/11

Simplify, to find the answer.

-22/11=-2

x<-2 is the correct answer.

I hope this helps you, and have a wonderful day!