Parallelograms in geometry.

Answer:

Step-by-step explanation:

Part A

If the gardener increases the number of dahlia plants by buying the new bulbs,

Let the equation representing year (x) and number of bulbs purchased (y) is,

y = mx + b

Here, m = Number of plants purchased each year

b = Initial numbers of plants

For x = 0, and y = 6,

6 = m(0) + b

b = 6

For x = 1, y = 56,

56 = m(1) + 6

m = 50

Therefore, equation for this method of increasing the numbers of plants will be,

y = 50x+ 6

Let the equation for the second method of increasing the number of plants is represented by the equation,

y = a(b)ˣ

From the data given in the table,

For x = 0, y = 6

6 = a(b)⁰

a = 6

For x = 1, y = 12

12 = 6(b)¹

b = 2

Therefore, equation representing the second method (By diving the existing bulbs) will be,

y = 6(2)ˣ

Part B

By substituting the value of x = 10 years,

Method - 1

y = 50(10) + 6

y = 506 plants

Method - 2

y  = 6(2)¹⁰

y = 6144 plants

Part C

After 5 years number of plants by method - 1,

y = 50(5) + 6

  = 256

After 5 years number of plants by method - 2,

y = 6(2)⁵

y = 192

Similarly, After 10 years number of plants by method - 1,

y = 50(10) + 6

  = 506

By method - 2,

y = 6(2)¹⁰

y = 6144

Since, number of plants after 5 years are less by the second method as compared to method 1

But after 10 years second method results the number of plants more than method-1,

Therefore, gardener should adopt method 2 for increasing the numbers of plants.  

Functions are used to represent tables and equations.

(a) The equation of the functions

The function of "Buy New Bulbs" is a linear function with an initial value of 6, and a rate of 50 (i.e. 56 - 6)

So, the equation is:

[tex]y = 6 + 50x[/tex]

The function of "Divide Existing Bulbs" is an exponential function with an initial value of 6, and a rate of 2 (i.e. 12/6)

So, the equation is:

[tex]y = 6(2)^x[/tex]

Hence, the equations of the functions are [tex]y = 6 + 50x[/tex] and [tex]y = 6(2)^x[/tex]

The expected number of bulbs in 10 years

This means that x = 10.

So, we have:

[tex]y = 6 + 50x =6 + 50*10 = 506[/tex]

[tex]y = 6(2)^x =6 *2^{10} = 6144[/tex]

Hence, the expected number of bulbs in 10 years for both functions are 506 and 6144, respectively

Compare the expected number of bulbs in 5 and 10 years

When x = 5.

We have:

[tex]y = 6 + 50x =6 + 50*5 = 256[/tex]

[tex]y = 6(2)^x =6 *2^5 = 192[/tex]

When x = 15

We have:

[tex]y = 6 + 50x =6 + 50*15 = 756[/tex]

[tex]y = 6(2)^x =6 *2^{15} = 196608[/tex]

By comparison;

In 5 years, the expected number of bulbs for the function of "Buy New Bulbs" is greater than the function of "Divide Existing Bulbs", however the expected number of bulbs for the function of "Buy New Bulbs" is less than the function of "Divide Existing Bulbs" in 15 years

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Answer:

A quadrilateral has a parallelogram if one pair of opposite sides is congruent and parallel. Parallelograms are designed to have diagonals that bisect one another. When ABCD is bisected by — BD and —AC, then ABCD is a parallelogram.

Step-by-step explanation:

Answer:

A quadrilateral has a parallelogram if one pair of opposite sides is  coinciding exactly when superimposed and parallel. Parallelograms are designed to have diagonals that bisect one another. When abcd is bisected by  bd and ac, then abcd is a parallelogram.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

The area can be calculated by Length times width. The length is 10 and the width is 2 so 10 x 2 = 20

Cheers

Answer:

I believe it is 20

Step-by-step explanation:

10 x 2 = 20

Answer:

6=k×2

k=3

g(x)=k f(x)

g(x)=3 |x|

Answer:

it would be 60

Step-by-step explanation

4*5= 20

8*5=40

12*5=  60

We multiply by 5 because if we divide 20/4=5, 40/8=5, 60/12=5.

Answer:

y = 841.25 feet

Step-by-step explanation:

Given that,

The height of the rocket, y in feet, is  related to the time after launch, x in seconds, by the given equation as follows:

[tex]y = -16x^2 + 212x + 139[/tex] ....(1)

We need to find the maximum height reached by the rocket.

For maximum height, put dy/dx = 0

So,

[tex]\dfrac{d(-16x^2 + 212x + 139)}{dx}=0\\\\-32x+212=0\\\\x=\dfrac{212}{32}\\\\x=6.625\ s[/tex]

Pu x = 6.625 in equation (1).

[tex]y = -16(6.625)^2 + 212(6.625) + 139\\\\y=841.25\ feet[/tex]

So, the maximum height reached by the rocket is equal to 841.25 feet.

Answer:

Quadratic

Step-by-step explanation:

Example of linear is 2x + 3

Example of quadratic is x² + 2x + 3

Example of cubic is x³ + 2x² + 3x + 4

Example of quartic is x⁴ + 2x³ + 3x² + 4x + 5

Answer:

7 unites

Step-by-step explanation:

np

Answer:

x²+2x+3

Step-by-step explanation:

We are to simplify the expression;

5x³+10x²+15x/5x

Factor out 5x from the numerator

= 5x(x²+2x+3)/5x

5x will cancel out both at the top and bottom to have;

x²+2x+3

Factorize

x²+2x+3

Hence the simplified form is x²+2x+3

Answer:

83.5km/h

Step-by-step explanation:

To find average you have to add up all the numbers in a given set then divide it by the amount of numbers in that set

Answer:

3/12 - 8/12= 5/12

10/12 - 5/12= 5/12

Answer:

The new cost is $ 2.34 and sales tax is .14.  Total cost is $2.48

Step-by-step explanation:

1.80 x 1.3 = 2.34

2.34 x .06 = .14

Add the two together for the total

Answer: it’s D

Step-by-step explanation:

The domain and the range of an exponential parent function mean that the domain is all real numbers and the range signifies positive real numbers y > 0.

The simplest parent function of an exponential function takes the form:

[tex]\mathbf{f(x) = p^x}[/tex], where p refers to the base.

So, if we have a number such that x = 3 and the base is 2

Therefore, we can conclude that the domain of an exponential parent function is all real numbers, and the range is positive real numbers (y > 0).

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Answer:

Answer is 9/8

Step-by-step explanation:

18/8-9/8=9/8

Answer:

9/8

Step-by-step explanation:

9/4 - 9/8

9/4 x 2 = 18/8 to match denominators

18/8 - 9/8

= 9/8

Answer:

the slope is -2

Step-by-step explanation:

Answer:

3/35, 12/35, 16/35, 4/35

Step-by-step explanation:

The box has a total of 35 squares.

The pink fills 3 squares so the pink section is: 3/35

The dark blue section covers 12 squares

So 12/35 is another fraction.

The light blue area covers 16 squares so another fraction is 16/35

The white covers 4 squares

So the last possible fraction is 4/35.

Answer:

3/4 of a cup or .75 of a cup

Step-by-step explanation:

Answer:

b = -9

Step-by-step explanation:

Given the equation (−34 + 43)+ b = 0

We are to find the value of b

First solve for the value in parenthesis

(−34 + 43)+ b = 0

9+b = 0

Subtract 9  from both sides

9+b-9 = 0 - 9

b+0 = -9

b = -9

Hence the value of b will make the equation a true statement is -9

Answer:

D

Step-by-step explanation:

it states that the snikholes are from underneath when the soil it lose

Answer:

Only those members of the marketing team eating together at the picnic

Step-by-step explanation:

The members of the marketing team eating together at the picnic weren't randomly selected from a larger population. They may not be representative of employees (marketing team or not) beyond their group.

Only members of the marketing team eating together depicts a 80 percent legitimate estimate of the percent of employees who like the new slogan.

This can be defined as the approximate calculation of a set of data or values.

The members of the marketing team eating together will represent 80 percent legitimate estimate because they weren't randomly selected from a larger population.

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Answer:

10.7703296142

Step-by-step explanation:

Using "Desmos" a graphing chart and the hypotenuse formula, i have found the distance diagonally from point (4,7) and (2,2)

Answer:

A = 102m squared (Brainiest?)

Equation = b x h / 2

Step-by-step explanation:

A = (12 x 17) / 2

A = 204 / 2

A = 102m squared

Answer:

[tex]0.5^{3}[/tex]=0.125

Step-by-step explanation:

.5*.5*.5

Answer:

the first one

Step-by-step explanation:

just trust me