Part 1: Assume that a bacteria population triples every hour. Which of the following three tables of data, with
x representing time in hours and y the count of bacteria, could represent the bacteria population? Circle the
letter of your choice.

The slope of the given line is:

                        [tex]\dfrac{4}{5}[/tex]

We know that if a line is represented in the slope intercept form i.e.

             [tex]y=mx+c[/tex]

then m represents the slope of the line and c represents the y-intercept of the line.

Here we are given a equation of a line as follows:

                [tex]y=\dfrac{4}{5}x-3[/tex]

i.e. on comparing the equation with  the slope-intercept form of the line we have the slope  of the line is:

             [tex]m=\dfrac{4}{5}[/tex]

Final answer:

The slope of the equation y=4/5x-3 is 4/5, which represents the consistent rise over run for the line.

Explanation:

The slope of the line is represented by the equation [tex]y = \frac{4}{5}x - 3 is \frac{4}{5}.[/tex] In the standard form y = mx + b, where m is the slope and b is the y-intercept, and the coefficient of x represents the slope of the line.

Therefore, by comparing the given equation to the standard form, the number 4/5 in front of x is the slope of the line. The slope indicates a rise of 4 units on the vertical axis for every increase of 5 units on the horizontal axis. The slope of a line remains constant along the entire length of the line.

7 is the prime number.

7 × 1000 = 7000

Answer:

The fraction number is [tex]\frac{34}{9}[/tex]

Step-by-step explanation:

we have

[tex]3.777...[/tex]

This is a repeating decimal  (a decimal that has a digit, that repeat over and over and over again without ever ending)

Convert to fraction number

Let

[tex]x=3.777...[/tex]

[tex]10x=37.777...[/tex]

we know that

[tex]10x-x=37.777...-3.777...[/tex]

[tex]9x=34[/tex]

[tex]x=\frac{34}{9}[/tex]

therefore

The fraction number is [tex]\frac{34}{9}[/tex]

Answer:

The given equation is y=-x+3.

The equation for the table is y=-x-3.

The slopes are the same (both are -1) but the y-intercepts are different (the given equation has y-intercept 3 while the table has y-intercept -3). The two lines are parallel.

Also, if you plug a point from the table into the equation, the point renders the equation false.

Step-by-step explanation:

You can use your equation and plug in your points from the table.

So let's see if (-4,1) is a point on the graph of the line of y=-x+3.

1=-(-4)+3

1=4+3

1=7 is not true so the point isn't on the graph of the line y=-x+3.

Let's see if we can find the appropriate equation for the points in the table.

I'm going to first see if there is a constant slope.

In the first two points, the y's are going down by 2 while the second are going up by two.

So the slope of line going through the first two points is -2/2=-1.

So looking at the middle points...the y's are going down by 3 while the x's are going up by 3. So the slope is still retaining -1 since -3/3=-1.

Finally, lets see if the slope still remains the same for the last two points. The y's are going down by 2 while x's are going up by 2. So the set of points do represent a line since the points follow a constant slope per pair of points.

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We know m is -1 so our line is of the form

y=-x+b.

To find b I will use a point from the table such as (-4,1).

1=-(-4)+b

1=4+b

Subtract 4 on both sides:

1-4=b

-3=b

So the equation for the line in the table is

y=-x-3.

So the two are both lines with the same slope but different y-intercept. The lines are therefore parallel.

Answer:

The given equation is y=-x+3.

The equation for the table is y=-x-3.

The slopes are the same (both are -1) but the y-intercepts are different (the given equation has y-intercept 3 while the table has y-intercept -3). The two lines are parallel.

Also, if you plug a point from the table into the equation, the point renders the equation false.

Step-by-step explanation:

You can use your equation and plug in your points from the table.

So let's see if (-4,1) is a point on the graph of the line of y=-x+3.

1=-(-4)+3

1=4+3

1=7 is not true so the point isn't on the graph of the line y=-x+3.

Let's see if we can find the appropriate equation for the points in the table.

I'm going to first see if there is a constant slope.

In the first two points, the y's are going down by 2 while the second are going up by two.

So the slope of line going through the first two points is -2/2=-1.

So looking at the middle points...the y's are going down by 3 while the x's are going up by 3. So the slope is still retaining -1 since -3/3=-1.

Finally, lets see if the slope still remains the same for the last two points. The y's are going down by 2 while x's are going up by 2. So the set of points do represent a line since the points follow a constant slope per pair of points.

Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

We know m is -1 so our line is of the form

y=-x+b.

To find b I will use a point from the table such as (-4,1).

1=-(-4)+b

1=4+b

Subtract 4 on both sides:

1-4=b

-3=b

So the equation for the line in the table is

y=-x-3.

So the two are both lines with the same slope but different y-intercept. The lines are therefore parallel.

Answer:

10

Step-by-step explanation:

Answer:

y = 2x - 16

Step-by-step explanation:

Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE Rate of Changes [Slopes]:

-½ → 2

-4 = 2[6] + b

-16 = b

y = 2x - 16 >> Perpendicular Line in Slope-Intercept Form

I am joyous to assist you anytime.

The equation of the line that is perpendicular to y = -1/2x - 5 and passes through the point (6, -4) is y = 2x - 16. This is found using the concept of negative reciprocals and the point-slope form of the line equation.

The equation of the original line given is y = -1/2x - 5. The slope of this line is -1/2. Since a line perpendicular to this line will have a slope which is the negative reciprocal of -1/2, the slope of the line we're seeking is 2 (because -1 divided by -1/2 is 2).

We also know from the question that the line we're seeking passes through the point (6, -4). Using the slope-intercept form of the equation of a line (y = mx + b), where m is the slope and b is the y-intercept, we substitute the slope and the coordinates of the point into the equation to solve for 'b': -4 = 2*6 + b. Solving this equation gives us b = -16.

Therefore, the equation of the line that is perpendicular to y = -1/2x -5 and passing through the point (6, -4) is y = 2x - 16.

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Answer:

f(x) = 4x − 12

Step-by-step explanation:

It's not quadratic.  It's linear.  Each time x increases by 1, f(x) increases by 4.  So the slope is 4.  The y-intercept (when x=0) is -12.  The equation of the line is therefore:

f(x) = 4x − 12

Answer:14

Step-by-step explanation:

Answer:

it's 15

Step-by-step explanation:

Answer:

About 151.500

Step-by-step explanation:

Actual answer is 151.528 Just go with mental math.

Answer:

Step-by-step explanation:

move x to the right making the equation 5y=-9x-1 then divide both sides by 5 to get y= -9/5x-1/5. the slope of a perpendicular line is the opposite reciprocal of the slope from the og eq. so the slope of the new line is 5/9x and the y-intercept stays the same so the equation should be y=5/9x-1/5

Answer:

a = -5

Step-by-step explanation:

(5 - 3)/(5 - a)

2/(5 - a)

perpendicular of 2/(5 - a) = -(5 - a)/2

(a - 0)/(1 - 0) = -(5 - a)/2

a/1 = -(5 - a)/2

2a = -5 + a

a = -5

Answer:

0 I think

Step-by-step explanation:

Answer:

25/12 or 2 1/12

Step-by-step explanation:

4/3 - (-3/4) =

= 4/3 + 3/4

= 16/12 + 9/12

= 25/12

= 2 1/12

Answer:

129,407.

Step-by-step explanation:

12 ten-thousands = 12*10000=120,000.

8 thousands = 8*1000=8000;

this gives us 120,000+8,000=128,000.

14 hundreds = 14*100=1400;

this gives us 128,000+1,400=129,400.

7 ones = 7*1=7;

this gives us 129,400+7=129,407.

Answer:

12,000 8,000 1,400 7

Step-by-step explanation:

I hope u get a tutor if u dont know how to do this I hope this helps

Answer: He burned 800 calories per hour playing basketball.

Step-by-step explanation:

Let be "b" the amount of calories  per hour Jason burned playing basketball and "c" the amount of calories  per hour Jason burned canoeing.

Set up a system of equations:

[tex]\left \{ {{b+2c=1,400} \atop {2b+3c=2,500}} \right.[/tex]

You can apply Elimination Method:

Therefore, you get:

[tex]\left \{ {{-3b-6c=-4,200} \atop {4b+6c=5,000}} \right.\\.............................\\b=800[/tex]

Answer:

[tex]8x - 26 \\ -16x - 4 \\ -12x + 15[/tex]

Step-by-step explanation:

2(4x - 8) - 10

8x - 16 - 10

|_______|

8x - 26

-5x + 8 - 11x - 12

___ ___ _____ ____

___ ____

-16x - 4

-3(4x - 5)

-12x + 15

For the third and first exercises, you just use the Distributive Property, and for the second exercise, all you are doing is combining like-terms.

I am joyous to assist you anytime.

Answer:

-6

Step-by-step explanation:

[tex] | - 2| = 2 \\ {( - 2)}^{3} = ( - 2)( - 2)( - 2) = ( - 8) \\ \\ | - 2 | + {( - 2)}^{3 } = 2 - 8 = - 6[/tex]

To evaluate the expression |b|+b^3 when b=-2, substitute -2 for b, evaluate |b| and b^3 separately and then add the results.

To evaluate the expression |b|+b^3 when b=-2, we substitute -2 for b in the expression.

The absolute value of a number is that number's distance from zero on a number line, regardless of which direction. This means that the absolute value of any negative number is its positive equivalent. Thus, |b| is the same as |-2|, which equals 2.

Secondly, b^3 means b multiplied by itself twice. So (-2)^3 equals -2*-2*-2 which is -8.

First, we evaluate |b|. The absolute value of -2 is 2, so |b| = 2.

Next, we evaluate b^3. (-2)^3 = -8.

Finally, we add the two results together: 2 + (-8) = -6.

Therefore, when b=-2, the expression |b|+b^3 evaluates to -6.

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Answer:

Step-by-step explanation:

I don't know exactly how simplified it will be, but you can get the square root smaller.

180: 2*2 * 3*3 *5

For every pair of prime factors you can take 1 of the pair outside the the square root and throw the other one away

sqrt(2*2*3*3*5) = 2 * 3 * sqrt(5) = 6*sqrt(5)

Answer:

7 is rmthe correct answer as it's value is 3 the answer is on no 7.

Answer:rational

Step-by-step explanation:

Answer:

Step-by-step explanation:

Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

Answer:

(40-y)^3

Step-by-step explanation:

Make the unknown y

(40-y)^3

Answer:

The difference can be expressed as

y=x³+120x²-4800x+64000

Or

y=(40-x)³

Step-by-step explanation:

Step one

To solve the problem problem let us first initialize the number to be x

By breaking the statement into component parts and implementing

Step two

1. The difference between 40 and the number

=(40-x)

2. The cube of the difference

= (40-x)³

Let us equate the expression to y

y=(40-x)³

Step three

Expanding the expression we have

y= (40-x)(40-x)(40-x)

Opening bracket we have

y=(1600-40x-40x+x²)(40-x)

y=64000-1600x-

1600x+40x²-1600x+40x²+40x²-x³

y=x³+120x²-4800x+64000

Answer:

273

Step-by-step explanation:

8736÷32=273

273×32=8736

Answer:

A, C, and D are correct

Step-by-step explanation:

A. (0.32)(-2)

(0.32)(-2) = -0.64

Correct.

B. 1.6(-4)

1.6(-4) = -6.4

Wrong.

Divide by 10.

[tex]\dfrac{-6.4}{10} = \mathbf{-0.64}[/tex]

C. 0.64(-1)

0.64(-1) = -0.64

Correct.

D. (1.28)(-0.5)

(1.28)(-0.5) = 0.64

Correct.

E. (-4)(-0.16)

(-4)(-0.16) = 0.64

Wrong.

Multiply by -1.

(0.64)(-1)= -0.64

Answer:

1, 2, 3, 4, 6, 8, 9

The number 3456 is divisible by the single-digit numbers 2, 3, 4, 6, and 8.

The number 3456 is divisible by the single-digit numbers 2, 3, 4, 6, and 8.

To determine if a number is divisible by another, we check if the remainder is 0 when dividing the number being tested by the potential divisor. In this case, for example, if we divide 3456 by 2, we get no remainder, so it is divisible by 2.

Similarly, if we divide 3456 by 3, 4, 6, or 8, we get no remainder in each case, so it is also divisible by these numbers.

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tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,

[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}[/tex]

The next number in the sequence is 36.

Starting from 1, the number increases by 3, 1 + 3 = 4. But the next number, the number it's being increased by increases by 2. 3 + 2 = 5, 4 + 5 = 9. And again, 5 + 2 = 7, 7 + 9 = 16. And again. 7 + 2 = 9, 16 + 9 = 25. Therefore, it is increased to + 11, and the next number is 36.

I hope this helped, and you have a great day!

Answer:

36

Step-by-step explanation:

Greetings!

First off, we should know that there are 60 minutes in an hour. Therefore, the first step we will need to do, is divide 60 by 10.

60 ÷ 10 = 6

As shown above, we now know we will have to double the number 6 times. If we start with 30, this will be our first problem.

(1)   30 + 30 = 60

And so on and so forth...

(2)   60 + 60 = 120

(3)   120 + 120 = 240

(4)   240 + 240 = 480

(5)   480 + 480 = 960

(6)   960 + 960 = 1920

And after our sixth time we have our answer:

1920 bacteria

Hope this helps!

~Fluerie

The farmer can determine the dimensions of the fenced area by solving the formula L + 2W = 180 feet, where L is the length of the fenced region along the river bank and W is the width.

This is a classic application of the perimeter of a rectangle in the field of Mathematics. If the farmer is using part of a straight river bank instead of fencing for one side of the rectangle, then he only needs fencing for the other three sides. The formula to calculate the perimeter of a rectangle is 2(length) + 2(width), but since one side is not fenced, it is length + 2(width) in this case.

If we assume the length (L - along the river bank) and width (W) of the rectangular area, then the equation can be expressed as:

L + 2W = 180 feet

This formula can help the farmer calculate the dimensions of the fenced area needed in order to use his materials most effectively. He needs to solve this equation to find the values of length and width that add up to 180 feet.

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