Food poisoning occurs when bacteria like Salmonella and Listeria grow on food. These microorganisms grow at an
exponential rate. When an initial population of 100 bacteria are left at 98.6°F, they will grow at a rate of b= 100(8)". Which
graph could be used to calculate the number of bacteria after a certain number of hours?

Part (a)

The locus is the set of points that satisfy the given conditions. Namely that the point P needs to be 1 unit from the line given.

Think of a median along a highway. Then imagine the two shoulders of the road. The locus describes the two parallel lines that are to this given median. In other words, the median is y = x+2 and the road shoulders are unknown for now.

Though we do know that parallel lines have equal slopes (but different y intercepts).

Therefore, the answers to the next section will be of the form y = x+k for some real number k.

=============================================================

Part (b)

Use your favorite graphing tool to plot y = x+2. I recommend GeoGebra since I use it all the time, and it's what I used to make the drawing below. Desmos is another tool you can use. Both are free.

Note that point A(0,2) is on the line y = x+2. The line perpendicular to y = x+2 and goes through (0,2) is y = -x+2. From here, plot a circle centered at (0,2) with radius 1. The equation of this circle is x^2 + (y-2)^2 = 1

The intersection points of the circle and y = -x+2 will provide starting points, so to speak, for the two shoulder lines I mentioned in part (a).

The approximate locations of those points are:

B = (0.71, 1.29)

C = (-0.71, 2.71)

From here, it shouldn't be too hard to find the y = mx+b forms of the locus lines. Let me know if you need help with that, or if you need me to check your answers.

Side note: Why is it called a locus? I'm not sure, but my gut feeling tells me it has to do with the insects of a similar sounding name (locus the math term and locust the insect). Imagine millions of them forming various shapes in the sky, similar to how many points are used in the 2D plane to create various curves.

Answer:

The mistake is that the denominators are not the same in these fractions so you cannot add them yet. So, you would have to change the denominators to be the same before adding. The denominators I chose is 15, 2/5 times 3 which is equal to 6/15 and 1/3 times 5 which is equal to 5/15. Now, we can add 6/15 and 5/15 which is equal to 11/15!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

the first car has 25 gallons of gases while the second car has 35 gallons of gases

Answer:

1. 35 minutes

2. 12:15 p.m.

3. 110 minutes

4. 6:05 p.m.

5. 9:21 a.m.

Step-by-step explanation:

1. Subtract 2:55 from 3:30 = 35

2. Subtract 25 minutes from 12:40 = 12:15

3. Subtract 7:20 from 9:10 = 110

4. Add 35 minutes to 5:30 = 6:05

5. Subtract 33 from 9:54 = 9:21

Answer:

[tex]\boxed{\sf{m=-\dfrac{3}{11} }}[/tex]

Step-by-step explanation:

You simply need to use a slope formula that passes through the points in order to solve this problem.

Slope:

[tex]\sf{\dfrac{Y_2-Y_1}{X_2-X_1}=\dfrac{RISE}{RUN} }[/tex]

y2=(-1)

y1=2

x2=5

x1=(-6)

Rewrite the problem down.

[tex]\sf{\dfrac{-1-2}{5-(-6)}=\dfrac{-1-2}{5+6}=\dfrac{-3}{11}=\boxed{\sf{-\dfrac{3}{11} }}}[/tex]

-3/11

Therefore, the slope is -3/11, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

Sum of the interior angles of any triangle equal 180° .

So ;

A + B + ECB = 180°

A = B = μ

So : 2μ + ECB = 180°

→ ECB = 180° - 2μ

_________________________________

ECF + ECB = 180°

ECF + 180° - 2μ = 180°

ECF = 180° - 180° + 2μ

ECF = 2μ

_________________________________

∆ ADE :

A + D + E = 180°

μ + 90° + E = 180°

E = 180° - 90° - μ

E = 90° - μ

_________________________________

AED + AEF = 180°

90° - μ + AEF = 180°

AEF = 180° - 90° + μ

AEF = 90° + μ

_________________________________

AEF + FEC = 180°

90° + μ + FEC = 180°

FEC = 180° - 90° - μ

FEC = 90° - μ (( # ))

_________________________________

∆ BDF :

B + D + F = 180°

μ + 90° + F = 180°

F = 180° - 90° - μ

F = 90° - μ ((★))

_________________________________

((#)), ((★)) say :

FEC = 90° - μ

F = 90° - μ

So : F =~ FEC

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer:

$5.50

Step-by-step explanation:

so if its $3 for an ice cream plus .50 cents per ounce all you have to do is 11 x 0.50 witch would equal $ 5.50.

Answer:

Step-by-step explanation:

The minimum value of sinx is -1 when x = 3π/2, 7π/2, ...

In [2π, 4π), x = 7π/2

The function f(x)=sin(x) achieves its minimum value of -1 at x=3π.

The function f(x)=sin(x) is a periodic function with a period of 2π, meaning it repeats every 2π units. Within the interval [2π,4π), which is one period of the function, the minimum value of sin(x) occurs at x=3π.

This is because at x=3π, the sine function reaches its minimum value of -1. As you move further away from 3π, the sine function starts increasing again.

So, within the interval [2π,4π), the function f(x)=sin(x) achieves its minimum value of -1 at x=3π.

To know more about function:

https://brainly.com/question/30721594?

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Answer:

12 left-handed students

Step-by-step explanation:

The ratio 2:3 indicates 2 left-handed students for every 3 right-handed students.  This means 2 left-handed students are expected for every 5 total students.  You can use this information and set up and solve the proportion 2/5 = x/30

Answer:

h(x)=2x+3

g(x)=3x-2

First we will find goh(x) then we will put the value of x i.e 5.

goh(x)= 3(2x+3)-2

goh(x)=6x+9-2

goh(x)=6x+7

Now put the value of x, we get

goh(5)=6(5)+7

We get the answer 37

Step-by-step explanation:

[tex]t(n) = 2 {n}^{2} + 2n [/tex]

_________________________________

[tex]t(1) = 2 ({1})^{2} + 2(1) [/tex]

[tex]t(1) = 2 \times 1 + 2 \times 1[/tex]

[tex]t(1) = 2 + 2 = 4[/tex]

##############################

[tex]t(2) = 2 ({2})^{2} + 2(2) [/tex]

[tex]t(2) = 2 \times 4 + 2 \times 2[/tex]

[tex]t(2) = 8 + 4 = 12[/tex]

##############################

[tex]t(3) = 2 ({3})^{2} + 2(3) [/tex]

[tex]t(3) = 2 \times 9 + 2 \times 3[/tex]

[tex]t(3) = 18 + 6 = 24[/tex]

##############################

[tex]t(4) = 2 ({4})^{2} + 2(4)[/tex]

[tex]t(4) = 2 \times 16 + 2 \times 4[/tex]

[tex]t(4) = 32 + 8 = 40[/tex]

##############################

[tex]t(5) = 2 ({5})^{2} + 2(5) [/tex]

[tex]t(5) = 2 \times 25 + 2 \times 5[/tex]

[tex]t(5) = 50 + 10[/tex]

[tex]t(5) = 60[/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Ratio remains same

[tex]\\ \sf\longmapsto \dfrac{18}{27}=\dfrac{x}{45}[/tex]

[tex]\\ \sf\longmapsto 2/3=x/45[/tex]

[tex]\\ \sf\longmapsto 3x=90[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Answer:

d=3

Step-by-step explanation:

multiply 2 to d and 2 then you'll have 2D + 4 = 10 then you subtract 4 to 10 you'll have six you divide 6 by 2 and then you'll have three which, d equals 3

Answer: you need 5000 more

Step-by-step explanation: 70000 + 5000= 75000

Answer:

Answer is B

Step-by-step explanation:

Answer:

Hello...

Step-by-step explanation:

The answer is:c)1/2

25/50=5/10=1/2

HOPE IT HELPS YOU DEAR....

Answer:

1rst one

Step-by-step explanation:

Answer:

1st

Step-by-step explanation:

Question :-

Answer :-

Explanation :-

As per the provided information in the given question, we have been given that the Length of a Rectangular Parking Area is Two times the Width . The Perimeter is given as 90 yards . And, we have been asked to calculate the Length and the Width .

Let the Values be like :-

Now, for calculating the Length & Width , we will use the Formula :-

[tex] \bigstar \: \: \boxed{ \sf{ \: Perimeter \: _{Rectangle} \: = \: 2 \times [ \: Length + Breadth \: ] \: }} [/tex]

Therefore , by Substituting the given values in the above Formula :-

[tex] \dag \: \: \: \sf{Perimeter \: _{Rectangle} \: = \: 2 \: \times \: [ \: Length \: + \: Breadth \: ]} [/tex]

[tex] \longmapsto \: \: \: \sf { 90 \: = \: 2 \: \times \: [ \: x \: + \: 2x \: ]} [/tex]

[tex] \longmapsto \: \: \: \sf {90 \: = \: 2 \: \times \: [ \: 3x \: ]} [/tex]

[tex] \longmapsto \: \: \: \sf {90 \: = \: 2 \: \times \: 3x } [/tex]

[tex] \longmapsto \: \: \: \sf {90 \: = \: 6x } [/tex]

[tex] \longmapsto \: \: \: \sf {x \: = \: \dfrac { \: 90 \: }{6}} [/tex]

[tex] \longmapsto \: \: \textbf {\textsf{ x \: = \: 15}} [/tex]

Therefore :-

[tex] \Longrightarrow \: [/tex] Length = x = 15 yards

[tex] \Longrightarrow \: [/tex] Breadth = 2x = 2 × 15 = 30 yards

[tex] \underline {\rule {210pt} {4pt}} [/tex]

Note :-

The Length of Parking Area is 15 yards  and the Width of Parking Area is 30 yards .

The area of the rectangle is the product of the length and width of a given rectangle.

The Perimeter is given as 90 yards. we have been asked to calculate the Length and the Width .

Let the Values be like :-

Length = x

Breadth = 2x

Now, we will use the Formula :-

Perimeter = 2(L + B)

By Substituting the given values in the above Formula :-

Perimeter = 2(L + B)

90= 2(x + 2x)

90= 2(3x)

45 = 3x

x = 15

Therefore :-

Length = x = 15 yards

Breadth = 2x = 2 × 15 = 30 yards

Learn more about the area;

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The yard is obtuse!

[tex]\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Explanation :-}}}}}}[/tex]

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

[tex] \sf \longrightarrow \: {120}^{2} > {85}^{2} + {84}^{2} [/tex]

[tex] \sf \longrightarrow \:14400> 7225 + 7056[/tex]

[tex] \sf \longrightarrow \:14400> 14281[/tex]

[tex] \qquad \mathbb{TRUE}[/tex]

Thus, The triangle is obtuse angled...~

We need angle

Apply law of cosines

[tex]\\ \rm\Rrightarrow c^2=a^2+b^2-2abcos\gamma[/tex]

[tex]\\ \rm\Rrightarrow 2abcos\gamma=a^2+b^2-c^2[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{a^2+b^2-c^2}{-2ab}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{120^2+84^2-85^2}{-2(120)(84)}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14400+7056-7225}{-20160}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14231}{-20160}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=-0.714[/tex]

[tex]\\ \rm\Rrightarrow \gamma=cos^{-1}(-0.714)[/tex]

[tex]\\ \rm\Rrightarrow \gamma=135.56°[/tex]

The yard is obtuse

Answer:

4 hours

Step-by-step explanation:

What I did was since he automatically makes 30 dollars when mowing lawns, you can take it away then you have 8 and divide it by 2 then get 4 hours

Answer:

C is the correct answer

Answer:

7500 ml

Step-by-step explanation:

first times 0.15 x 15

you get 7.5 liters during the 15 days

convert that into milliliters and its 7500ml

Answer:

42 inches²

Step-by-step explanation:

→ Work out area of full triangle

0.5 × 10 × 10 = 50

→ Work out area of smaller triangle

0.5 × 4 × 4 = 8

→ Minus the answers

50 - 8 = 42

Answer:

The slope of the perpendicular line is [tex]-\frac{5}{3}[/tex]

Step-by-step explanation:

Let us solve the question

∵ The equation of a line is y = [tex]\frac{3}{5}[/tex] x - 8

→ The form of the equation is y = m x + b, where m is the slope

∴ The slope of the line is  [tex]\frac{3}{5}[/tex]

→ To find the slope of the line perpendicular to it reciprocal it and

   reverse its sign

∵ The reciprocal of  [tex]\frac{3}{5}[/tex]  is  [tex]\frac{5}{3}[/tex]

→ Change its sign from positive to negative

∴ The slope of the perpendicular line is [tex]-\frac{5}{3}[/tex]

Answer:

The answer is 112ft

Step-by-step explanation:

All you would do is multiply 8x14

Answer:

nothing

Step-by-step explanation:

i live in kregon

Answer:

It is not equivalent.

Step-by-step explanation:

9(4x-1) simplifys out to 36x-9.

Answer:

19

Step-by-step explanation:

First, You want to add all of the data below and you get 133 and with that data you divide 133 by 7 because you have 7 values. I hope i'm right and have a great day :)