explain the difference between

(3z)^3 and 3z^3

Answer:

a) each hour the number is multiplied by 16. Such a geometric sequence is described by an exponential growth function.

b) n = 16^t . . . . . n is number of bacteria; t is hours

c) about 7.923×10^28

d) the rule would be multiplied by 100/16=6.25, so becomes n=6.25·16^t

Step-by-step explanation:

a) We presume the table represents exponential growth because it was formulated with that purpose in mind. ("Why?" is always a tricky question.) It represents exponential growth because each table entry is 16 times the one before. A constant multiplier like that is characteristic of exponential growth.

___

b) In part (a) we noted the common ratio is 16. Since the first term (for t=1) is also 16, we can write the equation as ...

n = 16^t

where n is the number of bacteria and t is time in hours

___

c) Evaluating the formula for t=24, we get ...

n = 16^24 ≈ 7.923×10^28

n = 79,228,162,514,264,337,593,543,950,336

This is the estimate of the number present after 24 hours based on the formula.

___

d) If the starting number is different, the rule is multiplied by a factor that gives the appropriate starting value. The above answer assumes your "starting value" is 100 after 1 hour. If the starting value at 0 hours is 100, then the rule of part (b) gets multiplied by 100, not 6.25

n = 100·16^t . . . . . starting with 100 at t=0

n = 6.25·16^t . . . . starting with 100 at t=1

_____

Comment on exponential bacteria growth

The number of bacteria estimated in part (c) have an approximate volume of 102 cubic kilometers, roughly the volume of Lake Nicaragua.

Since only the first term has ax for coefficients the GCF cant be -3ax^5.

The GCF would be -3a

Factor -3a out of all the terms:

-3a(2x^7)-3a(-4a^5)-3a(a^4)

Now factor -3a out of the equation for the final answer:

-3a(2x^7-4a^5+a^4)

Answer:

Step-by-step explanation:

Answer:

  1/8, 7/8

Step-by-step explanation:

1/2 is 4/8.

3/8 less than 4/8 is 1/8.

3/8 more than 4/8 is 7/8.

Answer:

Step-by-step explanation:

you have to change it into a x and keep change flip and

1/5 / 3/7

1/5 * 7/3 then x

To divide two fractions, you should flip the second fraction to get its reciprocal, then multiply the first fraction with this reciprocal. For instance, in dividing 3/5 by 4/7, you flip 4/7 to get 7/4, then multiply 3/5 by 7/4 to obtain 21/20.

To divide two fractions, you will need to follow a few simple steps. Firstly, you need to flip or find the reciprocal of the second fraction (the one that you are dividing by). Secondly, you will multiply the first fraction (the one being divided) by the reciprocal of the second fraction. This process can also be remembered as 'copy, flip, multiply'.

For example, if we have to divide 3/5 by 4/7, first we flip 4/7 to get 7/4. Then we multiply 3/5 by 7/4. The result is 21/20.

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Answer:

  zero

Step-by-step explanation:

In order for sets A and B to have the same sum of elements, that sum of elements must be the same for each set, and half the sum of elements of the original set.

The sum of elements of the set {1, 2, 3, ..., 42} is an odd number (903), so there cannot be two sets with the same sum that have that total.

Answer:

3^2+7*4~  Addition should be last

Step-by-step explanation:

Parenthesis        ----- Addition is second to last in order of operations

Exponents                    

Multiplication

Division

Addition

Subtraction

Given the problem 3² + 7 × 4, the last operation that should be performed is addition due to the rules dictated by the order of operations (PEMDAS).

In the given problem, 3² + 7 × 4, the operation that should be performed last is addition. This is due to the rule of the order of operations, often remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Therefore, in this expression, you first perform the exponentiation (3²), then multiplication (7x4), and add the results last.

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Answer:

The answers for your two problems, can be found below in the attached images.

Problem 1

Graph

The graph was plotted using a calculator. We can see that the graph opens up.

f(x) = x^2 + 4x +3

Vertex

The vertex is the minimum point of the equation

In this case  Vertex (V) = (-2,-1)

Axis of symmetry

The x axis corresponding to the vertex component

x = -2

y intercept

Interception with the y-axis

From the first attached image, we can see that they y intercept occurs

at x = 0, y = 3  

(0,3)

Problem 2

Graph.

The graph was plotted using a calculator. We can see that the graph opens up.

f(x) = 2x^2 + 3x +1

Vertex

The vertex is the minimum point of the equation

In this case  Vertex (V) = (-0.75,-0.125)

Axis of symmetry

The x axis corresponding to the vertex component

x = -0.75

y intercept

Interception with the y-axis

From the second attached image, we can see that they y intercept occurs

at x = 0, y = 1  

(0,1)

For both problems, expand the left hand side and match up the coefficients.

a. [tex](5x-2)^2=25x^2-20x+4=ax^2-bx+c[/tex]

[tex]\implies a=25,b=20,c=4[/tex]

[tex]\implies a+c^2=25+4^2=41[/tex]

b. [tex](3x+5)^2=9x^2+30x+25=ax^2+bx+c[/tex]

[tex]\implies a=9,b=30,c=25[/tex]

[tex]\implies a+b+c=9+30+25=59[/tex]

Answer:

y=+3

Step-by-step explanation:

the equation of a line is y=mx+c

where m is the slope and c is the y-intercept.

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=3.

Also, let's call the second point you gave, (-5,3), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-5 and y2=3.

Now, just plug the numbers into the formula for m above, like this:

m=[tex]\frac{3-3}{-5-0}[/tex]

or

m=[tex]\frac{0}{-5}[/tex]

or

m=0

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+c like this:

y=0x+c

Now, what about c, the y-intercept?

To find c, think about what your (x,y) points mean:

(0,3). When x of the line is 0, y of the line must be 3.

(-5,3). When x of the line is -5, y of the line must be 3.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=0x+c. c is what we want, the 0 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,3) and (-5,3).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for c for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,3). y=mx+c or 3=0x 0+c, or solving for c: c=3-(0)(0). c=3.

(-5,3). y=mx+c or 3=0x -5+c, or solving for c: =3-(0)(-5). c=3.

See! In both cases we got the same value for c. And this completes our problem.

The equation of the line that passes through the points

(0,3) and (-5,3)  

is  

y=+3

Hope this helps :)

y = 3

First find the gradient of the line:

(Y²-Y¹)/(X²-X¹)

(3-3)/(-5-0)

0/-5 = 0

Your gradient is 0

Now find the y intercept. This is whrre where the line crosses the y axis, when X = 0

(0,3)

Your y intercept is 3.

Now put It into the formula y = mx + c

m = 0

c = 3

y = 0x + 3

y = 0 + 3

y = 3

Answer:

The relation is not a function

Step-by-step explanation:

∵ {(-7 , -7) , (-7 , -8) , (-1 , 4) , (6 , 5) , (10 , -1)}

* The relation is a function if every x-coordinate has only

  one image of y-coordinate, that means x-coordinate

  can not appear more than one time in the order pairs of relation.

* Ex: {(2 , -3 , (2 , 1)} ⇒ not function because 2 has

        two values of y -3 and -1

        means 2 appears twice in the relation so it's not a function

∵ -7 appears twice in the relation (-7 has 2 values of y -7 and -8)

∴ The relation is not a function

Answer:

It is not a function.

Step-by-step explanation:

We have given the relation.

{(-7, -7), (-7, -8), (-1, 4), (6, 5), (10, -1)}

We have to find whether  It is a function or not.

A function is a relation that assigns each input a single output.

This relation is not a function.

Because one input -7  has two outputs -7 and -8.

It is not a function.

To write a percent as a decimal- move the decimal point two places to the left and divide by 100.

Explanation:

Lets take an example.

We have to convert 25% into decimals.

So, we will divide 25 by 100 , [tex]\frac{25}{100} =0.25[/tex]

Here, we can see that we have moved the decimal to two places on the left side.

Answer:

Move the decimal point two places to the left

Divide by 100

Step-by-step explanation:

To write a percent as a decimal, there are two possible options, and they are the same thing.

The first one is moving the decimal point two places to the left. For example, 25% =0.25.

The second one is dividing by 100. 25% = 25/100 = 0.25.

So the answers are:

Move the decimal point two places to the left

Divide by 100

Answer:

The student assumed he was asked to factor

(a^2 - b^2)

Which is equal to

= (a+b)*(a-b)    (His response)

But, he was asked to simplify

(a^2 + b^2)

Which has imaginary roots, and can be factored as:

(b +ai)(b-ai)

Answer:

3 km/h

Step-by-step explanation:

Let c represent the speed of the current in km/h, and t the time in hours after the raft leaves point A. 2 hours 40 minutes is 8/3 hours.

Distance = Speed × Time

The watercraft meet at a point 27 km upstream from B, so we have two equations involving these variables:

27 = 44 - ct

27 = (12-c)(t -8/3)

Equating these two versions of "27", we have ...

44 -ct = 12t -32 -ct +(8/3)c

76 = 12t + 8/3·c . . . . . add 32+ct

9t +2c = 57 . . . . multiply by 3/4

t = (57 -2c)/9 . . . .solve for t

Now, we can substitute this into the first of the above equations, after rearranging it to ...

ct = 17

c(57 -2c)/9 = 17

2c^2 -57c +153 = 0 . . . . multiply by 9, subtract the left side

c = (57-√((-57)^2 -4(2)(153)))/(2·2) = (57 -√2025)/4 = 12/4 . . . . quadratic formula

c = 3

The speed of the current is 3 km/h.

Answer:

(5/6) cup carbonated water

Step-by-step explanation:

We can easily solve this problem by applying a rule of three.

4 cups of orange juice    ------------------------  2/3 cup carbonated water

5 cups of orange juice    ------------------------  x

x = (5/4)*2/3 cup carbonated water

x = (10/12) cup carbonated water

x = (5/6) cup carbonated water

x = 0.8333 cup carbonated water

Answer:

  zero

Step-by-step explanation:

Assuming your intended side lengths are {7 cm, 10 cm, 18 cm}, the sum of the short sides is not long enough to connect to the ends of the long side. No triangle can be formed.

Answer:

where are the pictures

Step-by-step explanation:

Answer:

[tex]y=2\cdot4^x\\y=4\cdot\left(\frac{1}{2}\right)^x[/tex]

Step-by-step explanation:

We're given both the y-intercept and a point on the graphs of both functions, so our work her is largely just substituting x and y values in the general form of the equation for an exponential function.

For the first one, we can start by using the point (0, 2) to solve for a:

[tex]y=a\cdot b^x\\2=a\cdot b^0\\2=a[/tex]

Next, we can use that a-value and the second point to solve for b:

[tex]y=2\cdot b^x\\128=2\cdot b^3\\64=b^3\\4=b[/tex]

This gives us the equation [tex]y=2\cdot4^x[/tex] for the first function.

We can repeat the same process for the second function. Solving for a:

[tex]y=a\cdot b^x\\4=a\cdot b^0\\4=a[/tex]

And then for b, using the point (2, 1):

[tex]1=4\cdot b^2\\\frac{1}{4}=b^2\\\frac{1}{2}=b[/tex]

This gives us the general equation [tex]y=4\cdot\left(\frac{1}{2}\right)^x[/tex]

To write an exponential function in y = a · bx form that represents the given situations, substitute the given points into the equation to find the values of a and b.

To write an exponential function in the form y = a · bx that represents the given situations:

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Answer:

The numbers are 4 and 5

Step-by-step explanation:

Let

x------> the smaller number

x+1----> the bigger number

we know that

[tex]\sqrt{x}=(x+1)-3[/tex] ----> equation that represent the situation

solve for x

[tex]\sqrt{x}=(x-2)[/tex]

squared both sides

[tex]x=(x-2)^{2}\\x=x^{2}-4x+4\\x^{2}-5x+4=0[/tex]

using a graphing calculator to solve the quadratic equation

see the attached figure

the solution is

[tex]x=4[/tex]

[tex]x+1=5[/tex]

The consecutive numbers are 4 and 5 in which the square root of the smaller number is 3 less than the bigger number

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the smaller number and y the larger number, hence:

y = x + 1  (1)

Also:

[tex]\sqrt{x} =y-3[/tex]   (2)

From equation 1 and 2:

x = 4, and y = 5

The consecutive numbers are 4 and 5

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Answer:

  (-√10)/10

Step-by-step explanation:

The trig identity that relates the sine and the tangent is ...

  sin(x) = ±tan(x)/√(1 + tan(x)²)

For your given value of tan(x), this evaluates to ...

  sin(x) = ±(1/3)/(√(1 + (1/3)²) = ±1/√10 = (±√10)/10

The given value of the tangent function is positive, so the sine and cosine functions have the same sign (both are negative in this case).

So, your sine function is ...

  sin(x) = (-√10)/10

_____

You can derive the above relationship using SOH CAH TOA.

  Tan = Opposite/Adjacent

You are given the value of the tangent function as 1/3, so it is convenient to assign Opposite = 1 and Adjacent = 3. Then Hypotenuse is found using the Pythagorean theorem as ...

  Hypotenuse = √(Opposite² + Adjacent²) = √(1² + 3²) = √10

Now, the sine is ...

  Sin = Opposite/Hypotenuse = 1/√10

Rationalizing the denominator, this is ...

  Sin = (√10)/10

__

Now, you need to take into account the quadrant of the angle. Tangent is positive and Cosine is negative in the 3rd quadrant, where the Sine is also negative. Then your sine value is ...

  sin(x) = (-√10)/10

Answer:

[tex](x+2)^2+(y-1)^2=25[/tex]

Step-by-step explanation:

The equation of a circle with center at (h,k) and radius r, is given by

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

Since the given circle contains the point (-5,-3) and it is centered at (-2,1), we can determine the radius of the circle using the distance formula;

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This implies that;

[tex]r=\sqrt{(-2--5)^2+(1--3)^2}[/tex]

[tex]r=\sqrt{(-3)^2+(4)^2}[/tex]

[tex]r=\sqrt{9+16}[/tex]

[tex]r=\sqrt{25}[/tex]

[tex]r=5[/tex]

We now substitute (h,k)=(-2,1) and r=5 into the formula to obtain;

[tex](x+2)^2+(y-1)^2=5^2[/tex]

[tex](x+2)^2+(y-1)^2=25[/tex]

2.52 × 10 = 25.2

2.52 = 240 × 0.008

The total thickness of a stack of 10 textbooks, where each book has 240 sheets of 0.008 cm thickness and two covers of 0.3 cm thick, is 25.2 cm.

The question requires us to find the total thickness of a stack of 10 textbooks. Each book has 240 sheets and two covers. The thickness of each sheet is 0.008 cm and each cover is 0.3 cm thick.

First, we calculate the thickness of one book. The thickness of sheets in one book is 240 multiplied by 0.008 cm (sheet thickness), which equals 1.92 cm. The thickness of the covers of one book is 2 multiplied by 0.3 cm (cover thickness), which equals 0.6 cm. Hence the total thickness of one book is 1.92 cm (sheets) plus 0.6 cm (covers), which equals 2.52 cm.

Therefore, the thickness of a stack of 10 books would be 10 multiplied by 2.52 cm (single book thickness), which equals 25.2 cm

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The equation 5x+8-7x=-4x+1 has exactly one solution

Option B is correct

The given equation is:

5x  +  8  -  7x   =  -4x  +  1

Simplify both sides of the equation

5x  -  7x  +  8  =  -4x  +  1

-2x   +  8   =  -4x  +  1

Collect like terms

-2x  +  4x  =  1  -  8

2x  =   -7

Divide both sides by 2

[tex]\frac{2x}{2} =\frac{-7}{2} \\\\x=-3.5[/tex]

As seen above, the equation has exactly one solution

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Final answer:

The equation 5x+8-7x=-4x+1 simplifies to 2x = -7, which means that there is exactly one solution for x, which is x = -7/2. The correct option is:  B)exactly one solution

Explanation:

To determine how many solutions the equation 5x+8-7x=-4x+1 has, let's first simplify and solve for x:

Combine like terms on the left side: (5x - 7x) + 8 = -2x + 8.

Bring the term involving x from the right side to the left: -2x + 8 + 4x = 1.

Combine like terms involving x: (4x - 2x) + 8 = 1, which simplifies to 2x + 8 = 1.

Subtract 8 from both sides: 2x = 1 - 8, which simplifies to 2x = -7.

Divide by 2 to solve for x: x = -7/2.

Since we have found a single value for x, the equation has exactly one solution.

Answer:

  90.04 °F

Step-by-step explanation:

Evaluate the expression.

  (9×10) + (4×.01) = 90 + .04 = 90.04

5/6=f/15

15•5=6•f

75=6•f

75/6=f

12.5=f

The flag pole is 12.5 ft tall

¶

. |

__& ____|

Answer:

  The flagpole is 12.5 ft tall.

Step-by-step explanation:

The ratio of object height to shadow length is ...

  (teen height) : (teen shadow) = (5 ft) : (6 ft) = 5 : 6

so the height of an object is 5/6 the length of its shadow. Then the height of the flagpole is ...

  (5/6) · (15 ft) = 12.5 ft

_____

A suitable scale drawing can show you the answer.

35 round to the nearest 10 equal 40

37 round =40

Answer:

If a scatter plot has no association then it's ordered pairs have no predictable pattern.

Step-by-step explanation:

Answer:

the answer is .75 as a decimal or 3/4 as a fraction.

Step-by-step explanation:

Lara and three girl friends share three sandwiches. They can share .75