The graph below represents the data from Part A. Use the data from Part A to correctly label the graph. Drag the labels to their appropriate locations on the graph.

The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

            After 1 hour, the population is 3*10

            After 2 hours, -> 3*3*10

            After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

              number of the  insects per hour

              This can be generalized as a function of t, the time in hours:

              f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                             P = (3^t) * 10

             Since 20 minutes is equal to (1/3) hours, t can be substituted for

             (1/3) in order to calculate the population size after 20 minutes:

                  P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

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Answer:The population after 20 minutes is 14.

We have starting point that is 10 and increasing with 3 times per hour. So, in every hour the data varies as :-        

           After 1 hour, the population is 3*10

           After 2 hours, -> 3*3*10

           After 3 hours, -> 3*3*3*10

Make a function from above observation in the increasing

             number of the  insects per hour

             This can be generalized as a function of t, the time in hours:

             f(t) = (3^t) * 10

putting the values in the function and get the desired answer,

                            P = (3^t) * 10

            Since 20 minutes is equal to (1/3) hours, t can be substituted for

            (1/3) in order to calculate the population size after 20 minutes:

                 P = (3^(1/3)) * 10 = 14.422 ≈ 14

The population after 20 minutes is 14.

Step-by-step explanation:

The interval where the function is negative is (–∞, –6)

The function is given as:

[tex]f(x) = \sqrt[3]{x + 6}[/tex]

Set the radicand to less than 0

x + 6 < 0

Subtract 6 from both sides

x < -6

Rewrite as an interval notation.

(–∞, –6)

Hence, the interval where the function is negative is (–∞, –6)

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Step-by-step explanation:

that means nothing else than

y = k×x

24 = k×6

k = 24/6 = 4

y = k×-4 = 4×-4 = -16

The first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}

Given the nth term of a recursive expression shown below

an =an-1 - 1.4

where

an-1 is the preceding term

a1 is the first term

an is the nth term

an-1 is

Given the following

a1 = 0

For the second term a2

a2 = 0 - 1.4

a2 = -1.4

For the third term a3

a3 = -1.4 - 1.4

a3 = -2.8

For the fourth term a4

a4 = -2.8 - 1.4

a4 = -4.2

For the fifth term a2

a5 = -4.2 - 1.4

a5 = -5.6

Hence the first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}

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Answer:

  (d)  1 unit

Step-by-step explanation:

The length of the dilated line segment is the product of the dilation factor and the length of the original line segment. It can also be computed as the length of the segment between the dilated coordinates.

The length of the original horizontal line segment BC is the difference of its x-coordinates:

  BC = 6 -4 = 2 . . . . units

(We know the segment is horizontal because the y-coordinates of the end points are the same.)

Multiplying the length of the original segment by the dilation factor, we find the length of B'C':

  B'C' = dilation factor × BC

  B'C' = 0.5×(2 units)

  B'C' = 1 unit

The dilation factor multiplies each coordinate value:

  B' = 0.5B = 0.5(4, 3) = (2, 1.5)

  C' = 0.5C = 0.5(6, 3) = (3, 1.5)

The length of B'C' is the difference of x-coordinates: 3 -2 = 1 unit.

I don't think this question is complete but here's ur answer

The equation of line with the given slope and y-intercept is y = (3/4)x + 4.

Given that;

We use the formula for equation of line to determine the equation.

y = mx + b

Where m is the slope and b is the y-intercept.

We plug in our values

y = mx + b

y = (3/4)x + 4

Therefore, the equation of line with the given slope and y-intercept is y = (3/4)x + 4.

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Step-by-step explanation:

To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.

Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0

⇒ 3 + 2√5 = p/ q

⇒ 2√5 = p/ q - 3

⇒ √5 = (p - 3q ) / 2q

⇒ (p - 3q ) / 2 q is a rational number.

However, √5 is an irrational number

This leads to a contradiction that 3 + 2√5 is a rational number.

There are 105 comparisons made with 15 statistically independent scenarios.

According to the statement

we have given value of n is 15.

Then r = 2. so,

we use the formula NcR then

Substitute the values in it then

15c2

we open it according to ncr formula

In this formula we arrange the terms according to the following

NcR formula = n! /r! * (n-r)!

then the terms will arrange in this way.

So,

ncr = 15! / 2! * 13!

After solving the statement some terms will be cancel with each other and remaining terms are

ncr = 15*14/2

ncr = 210/2

ncr = 105

here the value becomes 105.

So, There are 105 comparisons made with 15 statistically independent scenarios.

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Answer:

x = 2 ;   x = -8

Step-by-step explanation:

 [tex]\sf \ log_4 \ x +log_4 \ (x +6) = 2\\\\ log_4 \ (x)*(x +6) = 2\\\\[/tex]

    log₄  ( x² + 6x) = 2

                        4² = x² + 6x

         x² + 6x - 16 = 0

   x² - 2x + 8x - 16 = 0  

   x(x - 2) + 8(x - 2) = 0

       (x - 2) (x + 8)   = 0

x - 2 = 0  or x + 8 = 0

    x  = 2  or      x  = - 8

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

Explanation:

The 3y in the first equation must add to -3y so the y terms go away. We have -y in the second equation, which is why we triple everything in that equation

2x-y = 1 becomes 6x - 3y = 3 after tripling everything. This is the same as multiplying both sides by 3.

This is the updated equivalent system

[tex]\begin{cases}x+3y = 42\\6x-3y = 3\end{cases}[/tex]

Add the terms straight down

We have the equation 7x = 45 which solves to x = 45/7.

Unfortunately it doesn't turn into a nice single whole number because 45 isn't a multiple of 7. So I would leave it as a fraction.

Optionally you could note that 45/7 = 6.42857 approximately. But I prefer the fraction form since it's most exact.  

--------------

Use this x value to find y. Pick any equation involving x and y. Plug in that x value and solve for y.

x + 3y = 42

45/7 + 3y = 42

3y = 42 - 45/7

3y = 42*(7/7) - 45/7

3y = 294/7 - 45/7

3y = (294 - 45)/7

3y = 249/7

y = (249/7)*(1/3)

y = 83/7

Like with x, we also don't get a nice whole number.

I used WolframAlpha to confirm the solutions. GeoGebra is another tool you could use.

Answer:

No, L and S are parallel.

Step-by-step explanation:

Perpendicular lines go directly opposite from each other, making a + looking arrangement. While parallel lines go in the exact same direction, making a = looking arrangement. The only way both S and L can both be perpendicular to R is if they are both parallel to each other. An illustration by yours truly is placed below to represent it visually.

                    L                                              |

_______________________________|_____

                                                                    |

                                                                    |

                                                                    |   R

                                                                    |

_______________________________|_____

                     S                                             |  

                                                                    |

Now, if this were on the outside of a sphere, then it would be totally possible to have three lines all be parallel, because they can curve with the sides of the sphere and create a triangle with all right angles.

Answer:

she rides her bike at a rate of 8mph during the second part of the trip.

Step-by-step explanation:

for the first part of the trip, she rides 18 miles in 2 hours which means that she bikes at a rate of 9 miles per hour.

subtracting 18 from 58 gives us the distance she biked during the second part of her trip (which is 40 miles). subtracting 2 from 7 gives us that she biked for 5 more hours. Putting this together means she biked 40 miles in 5 hours.

Now divide miles by hours [tex]\frac{40mi}{5hrs} =8mph[/tex] to get your average rate of change for the second part of the trip.

Answer:

Use the slope and one of the points to solve for the y-intercept (b). One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.

Step-by-step explanation:

The answer choice which represents the quotient of the expression given is; 1/(t+4)².

It follows from the task content that the quotient which is to be evaluated is;

(t+3)/t+4) ÷ (t²+7t +12)

The quotient can therefore be evaluated as follows;

= (t+3)/t+4) ÷ (t+3)(t+4)

= (t+3)/t+4) × 1/(t+3)(t+4)

= 1/(t+4) × 1/(t+4)

= 1/(t+4)².

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Answer:

c

Step-by-step explanation:

c

Answer: Y-intercept: (0,5) X-intercept: (3,0)

Step-by-step explanation: Set x and y equal to 0.

Answer:

The statement is false.

Step-by-step explanation:

Given,

[tex] \sqrt{4 \times - 3} = 5[/tex]

To Prove

Soln:

=[tex]2i \sqrt{3} [/tex]

=>[tex]2i \sqrt{3} ≠5[/tex]

Hence, 2i√3 is not equal (≠) to 5.

The total earnings for the year is $18,900.

The total earnings is a sum of the annual salary, commission and Christmas bonus.

Commission = 6% x (160,000 - 20,000) =

6% x $140,000

0.06 x 140,000 =  $8,400

Total earnings =  $8,400 + 10,000 + $500 = $18,900

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Answer:

7a + b

Step-by-step explanation:

5a + 2a + 3b - 2b

= 7a + 3b - 2b

= 7a + b

Answer:

(3x − 1)(x 8)

Step-by-step explanation:

Answer:

25,132.74 miles

Step-by-step explanation:

Hello!

We are basically asked to find the circumference of the Earth's cross-section.

Circumference: [tex]C = 2\pi r[/tex]

We can replace 2r with the diameter, because the diameter is 2 times the radius.

Multiply the Diameter by pi:

It is around 25,132.74 miles around.

The first 3 iterates of the function are D. 3, -3, 9.

The function given is:

f(x) = -2x + 3

= -2(0) + 3

= 3

When x = 3

f(x) = -2x + 3

= -2(3) + 3

= -6 + 3

= -3

When x = -3

f(x) = -2x + 3

= -2(-3) + 3

= 9

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The graph of the exponential function f(x) = 5(2)ˣ is as shown in the attached file.

We want to draw the graph of the exponential function;

f(x) = 5(2)ˣ

At input of x = 0, we have;

f(x) = 5(2)⁰ = 5

At input of x = 1, we have;

f(x) = 5(2)¹ = 10

At x = -1, we have;

f(x) = 5(2)⁻¹ = 2.5

At x = -2, we have;

f(x) = 5(2)⁻² = 1.25

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Answer:

[tex]\frac{4}{15}[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{1}{5} \div\frac{3}{4}[/tex]

To find the answer we will use KCF (Keep, Change, Flip) apply it to the following question and then complete by multiplying and reducing. If needed of course.

[tex]\frac{1}{5} \div\frac{3}{4}[/tex]
Apply KCF:
[tex]\frac{1}{5} \div\frac{3}{4}=\frac{1}{5} \times\frac{4}{3}[/tex]
[tex]\frac{1}{5} \times\frac{4}{3}[/tex]
Solve:
[tex]1\times4=4[/tex]
[tex]5\times3=15[/tex]
[tex]=\frac{4}{15}[/tex]
Answer is in simplest terms.

Which means your answer is the first option or "4/15."

Hope this helps.

The total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape

The two cubes are stacked upon one another, so they form a composite figure.

The side lengths of the cubes are given as

Cube 1 = 4p

Cube 2 = 2q^2

The volume of each cube is calculated as:

Volume = Side length^3

So, the total volume is

Total = (4p)^3 + (2q^2)^3

Evaluate the exponents

Total = 64p^3 + 8q^6

Using the sum of cubes, we have the factored form to be

Total = (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

Hence, the total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

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Complete question

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?

The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

If an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;

Cos120 = cos(90 + 30)

Using the cosine rule of addition

cos(90 + 30) = cos90cos30 - sin90sin30

cos(90 + 30) = 0(√3/2) - 1(0.5)

cos(90 + 30) = 0 - 0.5

cos(90 + 30) = 0.5

Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5

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Answer:

It's -0.5

Explanation:
Answered it

14) theorem

15) sides

16) separately

17) equilateral

18) supplementary