Suppose you are determining the growth rate of two species of plants. Species A is 25 cm tall and grows 3 cm per month. Species B is 10 cm tall and grows 8 cm per month. Which system of equations models the height of each species H(m) as a function of months m.

QUESTION POSTED AT 18/01/2020 - 06:45 AM

Answered by admin AT 18/01/2020 - 06:45 AM

Let
HA(m) = the height of species A as a function of months m
HB(m) = the height of species B as  a function of months m

Assuming that the growth rate of the plants is a linear relationship all throughout the growth stages, we have:
HA(m) = 25 + 3m
and
HB(m) = 10 + 8m
Post your answer

Related questions

Which of the following shows a number as a product of prime numbers in exponential form? Choose all that apply. A: 24 · 10 B: 34 · 7 · 4 C: 23 · 52 · 7 D: 33 · 11

Hello there.

Which of the following shows a number as a product of prime numbers in exponential form? Choose all that apply.

B: 34 · 7 · 4

ANSWERED AT 21/02/2020 - 12:33 PM


QUESTION POSTED AT 21/02/2020 - 12:33 PM

HELP PLEASE? Leticia invests $200 at 5% interest. If y represents the amount of money after x time periods, which describes the graph of the exponential function relating time and money? The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time. The initial value of the graph is 200. The graph increases by a factor of 5 per 1 unit increase in time. The initial value of the graph is 500. The graph increases by a factor of 2 per 1 unit increase in time. The initial value of the graph is 500. The graph increases by a factor of 1.02 per 1 unit increase in time.

I know that just the answer is not enough. You need to understand why and how. So I will explaing the steps.

First you need to state the equation that represents the function.

Investment is $200 and interest rate is 5%, y is the amount of money after x periods.

Note that after 1 period the amount of money is 200 plus 5% interest, which is 200 + 5%(200) = 200 (1 +5%) = 200 (1 + 0.05) = 200 (1.05)

After 2 periods the amount is 200(1.05)*(1.05) = 200 (1.05)^2

After 3 periods the amount is 200 (1.05)^3

And now you can deduce that after x periods y = 200 (1.05)^x

You can then analyze the function to predict the shape and critical points of the graph.

The answers are based in the initial value and the increasing factor.

The initial value is when x = 0, which yields to y = 200 (1.05)^0 = 200*1 = 200

And the increasing factor is 1.05 because any value is the previos one times 1.05.

Then the answer is the first option. The initial value is 200 and the graph increases by a factor of 1.05 per 1 unit increase in time. 

ANSWERED AT 21/02/2020 - 11:37 AM


QUESTION POSTED AT 21/02/2020 - 11:37 AM

There are 25 nickels and dimes worth $2.15. You are asked to find how many of each there are. Which is a reasonable answer? A) 7 nickels and 18 dimes Eliminate B) 9 nickels and 18 dimes C) 11 nickels and 16 dimes D) 13 nickels and 15 dimes

The answer is Choice A 7 nickels and 18 dimes why? because the question tells you that There are 25 nickels and dimes worth $2.15. So 18 dimes that is worth $1.80 and 7 nickels that is worth $0.35 so you add $1.80 + $0.35 that = $2.15. So the answer again is Choice A 7 nickels and 18 dimes.

ANSWERED AT 21/02/2020 - 11:28 AM


QUESTION POSTED AT 21/02/2020 - 11:28 AM

Use substitution to solve each system. -3y = -2x - 1 y = x - 1

-3y = -2x - 1 

-3(x - 1) = -2x - 1 

-3x + 3 = -2x - 1 

-x + 3 = -1 

-x = -4

x = 4 
 
y = x - 1

y = (4) - 1 

y = 3

(4,3) is your solution



ANSWERED AT 21/02/2020 - 10:35 AM


QUESTION POSTED AT 21/02/2020 - 10:35 AM

The population of a certain geographic region is approximately 103 million and grows continuously at a relative growth rate of 1.67%. What will the population be in 5 years? Compute the answer to three significant digits.

The population ( now ) : 103 million.
In 5 years:
103  * ( 1.0167 )^5 =
= 103 * 1.08633586 = 
= 111.89259 ≈ 111.893
Answer:
The population will be 111.893 million.

ANSWERED AT 21/02/2020 - 10:10 AM


QUESTION POSTED AT 21/02/2020 - 10:10 AM

1.) what do values a h and k tell about the graph 2.) graph function 3.) state domain/range 4.) are there any intercepts? List all

Attached is a very useful chart for translations. [https://us-static.z-dn.net/files/df7/85ffaebe52d207009f6ed5967a5e05b4.jpg]

A number added or subtracted outside of parentheses shifts the graph vertically up (if number is added) or down (if number is subtracted).
As you can see in the chart,
f(x) + k shifts the graph up k units, and
f(x) - k shifts the graph down k units.

A number that is multiplied to x outside parentheses stretches or shrinks the graph vertically. If that number is greater than 1, then it stretches the graph. If the number is a fraction or between 0 and 1, then it shrinks the graph vertically.

As you can see in the chart,
a * f(x), where a>1 stretches the graph f(x) vertically by a factor a.
a * f(x), where a is between 0 and 1 shrinks the graph f(x) vertically by a factor of a.

When h is added or subtracated from x inside the parentheses, the graph is shifted horizontally right or left. Remember that this is opposite of what the sign is:
If h is positive, f(x + h), then the graph shifts left h units.
If h is negative, f(x - h), the graph shifts right h units.
Note that the attached chart uses c instead of h.

Since the function will be quadratic (degree is 2), the domain will be all real numbers, from -infinity to +infinity (-∞, +∞).
Depending on whether the value of a is positive or negative, the graph will open up like a U (if a is positive) or open down like an upside down U (if a is negative).

Since the equation is in vertex form f(x) = a(x - h)^2 = k, the vertex is (h, k). The range (set of y-values) will be from y-coordinate of the vertex (k) to positive or negative infinity depending on whether the graph opens up or down. 

ANSWERED AT 21/02/2020 - 09:41 AM


QUESTION POSTED AT 21/02/2020 - 09:41 AM

How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3? None One Two Infinitely many

Answer:

Option (d) is correct.

The equation 5x + 3(x − 1) = 10x − 2x − 3 will have infinite many solution.

Step-by-step explanation:

  Given : the equation 5x + 3(x − 1) = 10x − 2x − 3

We have to find the number of solution to the equation 5x + 3(x − 1) = 10x − 2x − 3

Consider the given equation 5x + 3(x − 1) = 10x − 2x − 3

This can be written as two equations as

y=5x + 3(x-1)   .........(1)

and y = 10x − 2x − 3 ......(2)

Simplify, both the equations,

y=5x + 3x - 3 = 8x - 3  

and y = 10x − 2x − 3 = 8x -3

Since, both equations are same.

So, the graph of both equation will overlap each other.

Hence,  the equation 5x + 3(x − 1) = 10x − 2x − 3 will have infinite many solution.

ANSWERED AT 21/02/2020 - 09:26 AM


QUESTION POSTED AT 21/02/2020 - 09:26 AM

Explain why the graphing calculator cannot be used to solve or approximate solutions to all polynomial equations.

Did your explanation include the following?

Some polynomial equations have complex solutions.

Therefore, complex solutions cannot be found by graphing the related system or function in the Cartesian (x-y) plane.

Polynomial functions with all complex solutions do not have x-intercepts, and the related system of equations will not intersect.

ANSWERED AT 20/02/2020 - 11:21 PM


QUESTION POSTED AT 20/02/2020 - 11:21 PM

What are the x-intercepts of the quadratic function? y = x² + x – 2 1 2 and 1 2 and –1 –2 and 1

Your answer should be the last one, -2 and 1. Hope this helps!

ANSWERED AT 20/02/2020 - 11:20 PM


QUESTION POSTED AT 20/02/2020 - 11:20 PM

If i run 10 kilometers in 1 hour how many kilometers do i run in 2 and a half hours

10 kilometers per hour
in 2.5 hours distance = 10 * 2.5 = 25 kilometers

ANSWERED AT 20/02/2020 - 11:18 PM


QUESTION POSTED AT 20/02/2020 - 11:18 PM

Half day hike in 4 hours you hike 10 miles what is the unit rate?

2.5 miles/hour

Because 10 divided by 4 = 2.5

ANSWERED AT 20/02/2020 - 11:14 PM


QUESTION POSTED AT 20/02/2020 - 11:14 PM

Evaluate 2.34 x 10 cubed

2.34 x 10 cubed
2.34 x 1000
2,340

ANSWERED AT 20/02/2020 - 11:13 PM


QUESTION POSTED AT 20/02/2020 - 11:13 PM

Decide whether the following rates are equivalent. 12 pages in 20 minutes or 20 pages in 32 minutes

The two fractions that we can extract from the given rates above are:
                (1) 12 pages / 20 minutes
                (2) 20 pages / 32 minutes
We can reduce the fractions or rates to their lowest term by dividing the numbers by 4 such that,
                 (1) 3 pages / 5 minutes
                 (2) 5 pages / 8 minutes
Therefore, the rates are not equivalent. 

ANSWERED AT 20/02/2020 - 11:12 PM


QUESTION POSTED AT 20/02/2020 - 11:12 PM

Charles has 24 marble. he has 6 more yellow marbles than blue marbles. what is the equation

Answer:

Required Equations are x + y = 24 & x - y = 6

Step-by-step explanation:

let x be the no of yellow marbles that Charles has.

and y be the no of blue marbles that Charles has.

Total Marbles that Charles has = 24

⇒ x + y = 24 ..............(1)

Charles has 6 more yellow marbles than blue marbles.

⇒ x = y + 6

    x - y = 6 ......................(2)

Therefore, Required Equations are x + y = 24 & x - y = 6

ANSWERED AT 20/02/2020 - 11:12 PM


QUESTION POSTED AT 20/02/2020 - 11:12 PM

What is the common ration of 10, 9, 1, 8, -7, 15?

It would be 4 becuase that is the middle 2 numbers multiplied then didvided by 2

ANSWERED AT 20/02/2020 - 11:11 PM


QUESTION POSTED AT 20/02/2020 - 11:11 PM

Jack is buying tables and chairs for his deck party tables cost $25 and chair cost $15 he plans to spend no more than $285 and buy at least 16 items show and describe the solution set nad suggest a reasonable solution solution to the problem?

By the given scenario above, we can formulate two inequalities that best represent the scenario. We let x and y be the number of tables and chairs, respectively such that,
                                 25x + 15y ≤ 285
                                  x + y ≥ 16
The values of x and y if we temporarily change all the inequality signs to equal signs are 4.5 and 11.5, respectively. Since, it is not allowed for a number of item to be in negative, we can then say that the number of tables should be 4 and that of chair is 12. 

ANSWERED AT 20/02/2020 - 11:09 PM


QUESTION POSTED AT 20/02/2020 - 11:09 PM

In which direction does the parabola open? y = 3x² – 5x – 10 up right down left

For this question it opens upwards in

ANSWERED AT 20/02/2020 - 11:09 PM


QUESTION POSTED AT 20/02/2020 - 11:09 PM

Ill give a tip please explain the steps Use this table as a reference for your interest rate percentages. Secured Unsecured Credit APR (%) APR (%) Excellent 4.80 5.25 Good 5.15 5.65 Average 5.85 6.20 Fair 7.00 7.65 Poor 8.20 9.15 8. You (or your parents) purchase a new car for $19,725.00 plus 4.75% sales tax. The down payment is $2,175.00 and you (or your parents) have an average credit rating. How much interest is accrued after the first month? (2 points) 9. You (or your parents) purchase a used car for $15,867.00 plus 5.25% sales tax. The down payment is 10% of the total cost and you (or your parents) have an excellent credit rating. What is your principal balance at the start of the loan? (2 points) 10. You (or your parents) are debating about whether to buy a new car for $19,072.00 or a used car for $15,635.00. Sales tax is 4.5%. You (or your parents) plan to make a down payment of $1,200.00 and your credit rating is fair. What is the difference in interest accrued by the end of the first month? (

Divide the APR by 360 days and multiply it by 30 days to get the monthly interest. Each loan is usually secured by the car you bought. So we will use the secured APR.

8. Average rating secured apr: 5.85% divide by 360 multiply by 30:  0.4875% monthly rate
Cost of car: 19,725 ; sales tax: 4.75% ; down payment: 2,175

19,725 x 1.0475 =  20,661.94 - 2,175 = 18,486.94 loan amount
18,486.94 x 0.4875% = 90.12 accrued interest for the 1st month.

9. Excellent rating secured apr: 4.80% divide by 360 multiply by 30: 0.40% monthly rate
Cost of car: 15,867 ; sales tax: 5.25% ; down payment: 10% of total cost

15,867 x 1.0525 =  16,700.02 x 90% = 15,030.02 the principal balance at the start of the loan.

10. Fair rating secured apr: 7% divide by 360 multiply by 30: 0.5833% monthly rate
Cost of new car: 19,072 ; sales tax: 4.5% ; down payment: 1,200
Cost of used car: 15,365; sales tax: 4.5% ; down payment: 1,200

19,072 x 1.045 = 19,930.24 - 1,200 = 18,730.24
18,730.24 x 0.5833% = 109.25 accrued interest

15,365 x 1.045 = 16,056.43 - 1,200 = 14,856.43
14,856.43 x 0.5833% = 86.66 accrued interest

109.25 - 86.66 = 22.59 is the difference in interest accrued by the end of the first month.

ANSWERED AT 20/02/2020 - 11:06 PM


QUESTION POSTED AT 20/02/2020 - 11:06 PM

HURRY I'LL PICK A BRAINLIEST!!! Solve the equation for a. K = 4a + 9ab A. a = K(4 + 9b) B. a = 4(K + 9b) C. a = 4+9b/K D. a = K/4+9b

Answer:

Step-by-step explanation:

A

ANSWERED AT 20/02/2020 - 11:06 PM


QUESTION POSTED AT 20/02/2020 - 11:06 PM

Solve each system of equations by substitution Y=50x+4. Y-32x=40

Y=4+50x

Y=40+32x

Those are your answers

ANSWERED AT 20/02/2020 - 11:02 PM


QUESTION POSTED AT 20/02/2020 - 11:02 PM

Lisa is painting a fence that is 26 feet long and 7 feet tall a gallon of paint will cover 350 ft.² right and solve a proportion to determine how many gallons of paint lisa will need

1 gallon / 350 ft^2 = x gallon / 182 ft^2

cross multiply (350 • x, 1 • 182)

350x = 182

x = 0.52 gallons

ANSWERED AT 20/02/2020 - 11:02 PM


QUESTION POSTED AT 20/02/2020 - 11:02 PM

Kayla walks 3 2/5 miles each day? wich of the following statements correctly describe how far she walks? a kayla walks 14 2/5 miles in 4 days b kayla walks 23 4/5 miles in 7 days c kayla walks 34 miles in 10 days d kayla walks 102 miles in 31 days

We inspect each of the choices and determine which among them is the best answer by multiplying the given time frames to the speed given.
(a) (3 2/5 miles/day) x (4 days) = 13.6 miles (wrong)
(b) (3 2/5 miles/day) x (7 days) = 23 4/5 miles (correct)
(c) (3 2/5 miles/day) x (10 days) = 34 miles (correct)
(D) (3 2/5 miles/day) x (31 days) = 105.4 miles (wrong)

Thus, the answers are B and C. 

ANSWERED AT 20/02/2020 - 11:02 PM


QUESTION POSTED AT 20/02/2020 - 11:02 PM