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1 year ago

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A plant is already 52 centimeters tall, and it will grow one centimeter every month. Let H be the plant's health (in centimeters

) after M months. Write an equation relating H to M. Then use this equation to find the plant's height after 31 months.
Equation:

Plant's height after 31 months: _______ centimeters

1 answer:

Tasya [4]1 year ago

5 0

Plant's height after 31 months:82 centimeters

<h3>How to find the height of the plant</h3>

The equation that can be used to find the height of the plant is given as

h = 52 centimeters + 1m

We have that the plant grows at 1 centimeter every month hence we have 1m in the equation.

Then the number of periods is m, Now we are to find the height in this period of time

h = 52 + 1*31

= 51 + 31

= 82

Hence the height after 31 months is given as 82 centimeters.

Read more on height here:

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The Students' Conjectures Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Po

noname [10]

Complete Question:

Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x) They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

Answer:

$A = B$

Step-by-step explanation:

<em>See comment for complete question</em>

Given

$A: (4x^2 - 4x)(x^2 - 4)$

$B: (x^2 + x - 2)(4x^2 - 8x)$

Required

Determine how they can show if the products are the same or not

To do this, we simply factorize each polynomial

For, Polynomial A: We have:

$A: (4x^2 - 4x)(x^2 - 4)$

Factor out 4x

$A: 4x(x - 1)(x^2 - 4)$

Apply difference of two squares on x^2 - 4

$A: 4x(x - 1)(x - 2)(x+2)$

For, Polynomial B: We have:

$B: (x^2 + x - 2)(4x^2 - 8x)$

Expand x^2 + x - 2

$B:(x^2 + 2x - x - 2)(4x^2- 8x)$

Factorize:

$B:(x(x + 2) -1(x + 2))(4x^2- 8x)$

Factor out x + 2

$B:(x -1) (x + 2)(4x^2- 8x)$

Factor out 4x

$B:(x -1) (x + 2)4x(x- 2)$

Rearrange

$B: 4x(x - 1)(x - 2)(x+2)$

The simplified expressions are:

$A: 4x(x - 1)(x - 2)(x+2)$ and

$B: 4x(x - 1)(x - 2)(x+2)$

Hence, both polynomials are equal

$A = B$

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2 years ago

Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

JulijaS [17]

A:

(f+g)(x)=f(x)+g(x)

(f+g)(x)=4x-5+3x+9

(f+g)(x)=7x+4

B:

(f•g)(x)=f(x)•g(x)

(f•g)(x)=(4x-5)(3x+9)

(f•g)(x)=12x^2-15x+36x-45

(f•g)(x)=12x^2+21x-45

C:

(f○g)(x)=f(g(x))

(f○g)(x)=4(3x+9)-5

(f○g)(x)=12x+36-5

(f○g)(x)=12x+31

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2 years ago

What’s 7/12+1/3 in fractions show your work

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The answer is 11/12. (:

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2 years ago

Read 2 more answers

Please solve these questions for me. i am having a difficult time understanding.

s2008m [1.1K]

Answer:

1) AD=BC(corresponding parts of congruent triangles)

2)The value of x and y are 65 ° and 77.5° respectively

Step-by-step explanation:

1)

Given : AD||BC

AC bisects BD

So, AE=EC and BE=ED

We need to prove AD = BC

In ΔAED and ΔBEC

AE=EC (Given)

$\angle AED = \angel BEC$ ( Vertically opposite angles)

BE=ED (Given)

So, ΔAED ≅ ΔBEC (By SAS)

So, AD=BC(corresponding parts of congruent triangles)

Hence Proved

2)

Refer the attached figure

$\angle ABC = 90^{\circ}$

In ΔDBC

BC=DC (Given)

So, $\angle CDB=\angle DBC$ (Opposite angles of equal sides are equal)

So, $\angle CDB=\angle DBC=x$

So, $\angle CDB+\angle DBC+\angle BCD = 180^{\circ}$ (Angle sum property)

x+x+50=180

2x+50=180

2x=130

x=65

So, $\angle CDB=\angle DBC=x = 65^{\circ}$

Now,

$\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90$

So, $\angle ABD=90-x=90-65=25^{\circ}$

In ΔABD

AB = BD (Given)

So, $\angle BAD=\angle BDA$ (Opposite angles of equal sides are equal)

So, $\angle BAD=\angle BDA=y$

So, $\angle BAD+\angle BDA+\angle ABD = 180^{\circ}$ (Angle Sum property)

y+y+25=180

2y=180-25

2y=155

y=77.5

So, The value of x and y are 65 ° and 77.5° respectively

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3 years ago

This is a challenging problem ? can someone help

Dafna11 [192]

The opposite sides of a rectangle are equal, so we can write the following equations:
2x = 3y + 5 ...........(1)
x = 2y + 2 .............(2)
Multiply equation (2) by 2, to get:
2x = 4y + 4 ...........(3)
The right hand sides of equations (1) and (3) are equal, so we can write:
3y + 5 = 4y + 4
which gives y = 1 as the solution.
Plugging y = 1 into equation (2), we find the x = 4.
So the full solution is: x = 4, y = 1.

4 0

2 years ago