Mathematics High School

100 points brainliest!!! plz answer all to the best of your ability no links they don't work for me
Answer the following questions using what you've learned from this unit. Write your responses in the space provided.
1. Part I: The degree of a polynomial is the (greatest / least) of the degrees of its terms. (Circle the term that correctly completes this definition.) (1 point)
Part II: In order to write a polynomial in descending order, you must write the terms with the exponents (decreasing / increasing) from left to right. (Circle the term that correctly completes this rule.) (1 point)
Part III: For each polynomial, determine the degree and write the polynomial in descending order. (4 points: 2 points each)
A. –4x2 – 12 + 11x4 B. 2x5 + 14 – 3x4 + 7x + 3x3
2. Use addition and subtraction to simplify the following polynomials.
A. Add polynomials: (3 – 4x + 8x2) + (–6 + 2x – 5x2)
Step 1: Rewrite the polynomials without the parentheses. (1 point)
Step 2: Write the polynomial in descending order and use parentheses around like terms. (1 point)
Step 3: Add the like terms identified in Step 2 to simplify the polynomial. (1 point)
B. Subtract polynomials: (3x – 5 – 7x2) – (–2 + 6x2 – 5x)
Step 1: Rewrite the polynomials without the parentheses. Remember to multiply each term in the second parentheses by –1. Show your work. (2 points)
Step 2: Write the polynomial in descending order and use parentheses around like terms. (1 point)
Step 3: Add the like terms identified in Step 2 to simplify the polynomial. (1 point)
3. Use the FOIL method to multiply binomials.
Part I: When multiplying binomials, the FOIL method helps you to organize the multiplication of each term of the first binomial by each term of the second. Fill in each blank with the word used to show how the binomials' terms are multiplied. (2 points: 0.5 point each)

F

O

I

L

Part II: Using the FOIL method, multiply the terms in the binomials below. Show your work in the blanks provided. Then, add any like terms and write the polynomial in standard form in the space provided. Show your work. (8 points: 2 points each)
A. (3x + 7)(2x – 5) B. (x2 + 2x)(5x2 – 3x)

______ + _______ + _______ + _______
______ + _______ + _______ + _______
______________________
______________________

C. (5x + 4)(5x – 4) D. (x2 – 7)(x2 – 4)

______ + _______ + _______ + _______
______ + _______ + _______ + _______
______________________
______________________
4. Use the distributive property to multiply the trinomial by the binomial.
Circle the first term in the trinomial, multiply it by each term in the binomial, and place each result in the blank spaces provided. Repeat this process for the second and third terms of the trinomial until all of the spaces are filled in. Finally, in the space provided beneath the blanks, simplify the expression by combining like terms and arranging the terms from highest to lowest order. Show your work. (4 points)

(3x2 – 2x + 7)(x2 + 2x)
______ + _______ + _______ + _______ + ______ + _______
5. Use the vertical method to multiply two trinomials.
Step 1: Multiply the top trinomial by the last term in the bottom trinomial. Place each result in the blank spaces provided. (2 points)
Step 2: Multiply the top trinomial by the middle term in the bottom trinomial. Place each result in the blank spaces provided. (2 points)
Step 3: Multiply the top trinomial by the first term in the bottom trinomial. Place each result in the blank spaces provided. (2 points)
Step 4: Add the three partial products to find the final answer. Place the result at the bottom. (1 point)
6. Sabrina is making an open box from a piece of cardboard that has a width of 12 inches and a length of 18 inches. She'll form the box by making cuts at the corners and folding up the sides. If she wants the box to have a volume of 224 in3, how long should she make the cuts?
Part I: Each dimension (width, length, and height) of the finished box can be represented by a polynomial expression. If the height is x inches, what is the length in terms of x? (2 points)
Height = x
Width = 12 – 2x
Length =
Part II: The formula for volume is v = l • w • h. Use the polynomial expressions from Part I to write an equation to represent the volume of the box. Simplify on the right side by multiplying the polynomials and writing the answer in descending order. Show your work.
HINT: First multiply the binomials representing length and width. Next, multiply the resulting trinomial by the expression representing height. (3 points)
v =
Part III: The length of each cut at the corners is represented by x. To make a box, x must fall in a certain range of values. For example, x cannot be 15 because that would make the flap longer than the width of the box. Identify one reasonable value of x. Why did you choose that value? (2 points)
Part IV: Use the polynomial equation you wrote in Part II to find the volume of the box for each value of x. Show your work. (5 points)

Answers

Answer 1

Answer:

Part I:  The degree of a polynomial is the greatest of the degrees of its terms.

Part II:  In order to write a polynomial in descending order, you must write the terms with the exponents decreasing from left to right.

Part III: A. -4x² + 11x - 12, degree = 2,

B. 5x³ + 4x + 14, degree = 3.

Step-by-step explanation:

Part I : Since the degree of a polynomial is the highest power of its monomials ( single term ),

e: degree of is 5.

Thus, in part I, the correct option is 'greatest'

Part II: When we write a polynomial then we write the terms of the polynomial in descending order of their degrees.

Thus, in part II the correct option is 'least'

Part III: A.  

∵ -4x² has the highest power in the polynomial.

⇒ Degree = 2,

Also, in the polynomial descending order of degrees,

2 > 1 > 0

⇒ polynomial in descending order,

B.  

Combining like terms,

∵ 5x³ has the highest degree,

⇒ Degree = 3,

Also, the order of the degrees in the polynomial is,

3 < 2 < 1 < 0

Thus, the polynomial in descending order,

Answer 2

Answer: I had trouble with this one too.

Step-by-step explanation:

Related Questions

Round 4,368 to the nearest ten

Answers

Answer:

4,370

Step-by-step explanation:

.....just round the tenths place (6) up sense 8 is above 5 it rounds up so

4,370

sorry for bad explanation

1. Find the coordinates of the center and the measure of the radius for a circle whose equation is
(x - 8) + (y + 4) = 12

Answers

Answer:

the center of this circle is (8, -4) and the radius is 2√3.

Step-by-step explanation:

Compare this equation

(x - 8) + (y + 4) = 12      Don't forget to type in the " ^ " symbol to indicate exponentiation.

(x - 8)^2 + (y + 4)^2 = 12

to the standard equation of a circle with center at (h, k) and radius r:

(x - h)^2 + (y - k)^2 = r^2

In this way we learn that h = 8, k = -4 and r^2 = 12 (or r = 2√3).

Then the center of this circle is (8, -4) and the radius is 2√3.

On a standardized exam, the scores are normally distributed with a mean of 120 and
a standard deviation of 10. Find the z-score of a person who scored 115 on the exam

Answers

Answer: z= -0.5

Step-by-step explanation: mean m=120 and deviation s=10.

Z = (x-m)/s= (115-120)/10

Answer: z=−1.1

Step-by-step explanation:

z=\frac{x-\mu}{\sigma}

z=

σ

x−μ

​

z-score formula

z=\frac{104-115}{10}

z=

10

104−115

​

Plug in values

z=\frac{-11}{10}

z=

10

−11

​

Subtract

z=-1.1

z=−1.1

Divide

The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet

Answers

Complete question :

The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet. Find length of the ladder.

Answer:

17

Step-by-step explanation:

From Pythagoras :

Hypotenus = sqrt(opposite² + adjacent²)

From the diagram

l = sqrt((l-9)² + 15²)

l² = (l² - 18x + 81 + 225)

Square both sides

l² = l² - 18x + 306

l² - l² = 306 - 18x

18l = 306

l = 306/18

l = 17

A rectangle has a width of 8cm and a length given by the expression 2n +3. What is the correct expression to find the area of the rectangle?

Answers

Answer:

16n + 24

Step-by-step explanation:

Area of a rectangle= Length × width

= (2n+3) × 8

= 16n + 24

Please Help!
Factor the following trinomial
[tex]9x^2-24x+16[/tex]
Please show work

Answers

=> 9x² - 24x + 16

Split the middle term(term with x) in such a manner so that the product of those parts is equal to the product of term with x² and constant. Here, those parts are 12 & 12 as 12*12 = 9*16.

=> 9x² - 24x + 16

=> 9x² - (12 + 12)x + 16

=> 9x² - 12x - 12x + 16

=> 3x(3x - 4) - 4(3x - 4)

=> (3x - 4)(3x - 4)

Method 2

=> 9x² - 24x + 16

=> (3x)² - 2(3x*4) + 4²

=> (3x - 4)²

=> (3x - 4)(3x - 4)

Method 3

In case if you can't find the factors of the middle term.

Say f(x) = 0, find the zeroes using quadratic formula. Zeroes of this eqⁿ are [-(-24) ± √24²-4(9)(16)] / 2(9) = 4/3 & 4/3

Therefore, f(x) = (x - 4/3)(x - 4/3) = (3x - 4)(3x - 4)/9

Ignore the numeric constant.

f(x) = (3x - 4)(3x - 4)

Can someone help me on this

Answers

Answer:

Y = 10 I believe

Step-by-step explanation:

To solve this we need to find what number, times 6, equals 18 - it's fairly easy to find the answer is three.

So what, minus seven, equals 3?

I need help with my homework ​

Answers

Answer:

Step-by-step explanation:

1. b. Alt. Exterior angles

  a. 7x + 8 = 6x + 18

   c.    x + 8 = 18

          x = 10

   d. 6(10) + 18 = 60 + 18 = 78

       7(10) + 8 = 70 + 8 = 78

2. 15x + 10 + 12x + 8 = 180

     same side angles

   27x + 18 = 180

   27x = 162

   x = 6

15(6) + 10 = 90 + 10 = 100 degrees

12(6) + 8 = 72 + 8 = 80 degrees

3. 12x + 2 = 11x + 6

    x + 2 = 6

    x = 4

12(4) + 2 = 48 + 2 = 50 degrees

11(4) + 6 = 44 + 6 = 50 degrees

corresponding angles

     

Which one would result an integer

Answers

Answer:

c is the only one that would result in an integer

Step-by-step explanation:

i hope this helps :)

Option c ∛ 27 would result in an integer.

what are integers?

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Given here, ∛27= 3 while the other options ∛60 is not an integer because 60 is not  cubic number similarly for 9 , 18 are not cubic numbers and thus their subsequent cubic roots will not yield an integer.

Hence, Option c ∛ 27 would result in an integer.

Learn more about integers here:

https://brainly.com/question/15276410

#SPJ2

Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)

Answers

Answer:

it does not form a triangle

Step-by-step explanation:

brainliest give me pls pls pls

Answer:

It forms a obtuse triangle

Step-by-step explanation:

Because two sides are the same.

jada says she can write an equivalent fraction with a denominator of 100 by multiplying 5 by 5, then writing the number of hundredths as a decimal ​

Answers

It’s going to be 845.64 and 2.52

A cylindrical gas tank holds approximately 401.92 cubic feet of fuel. The radius of the tank is 4 feet. Find the height of the tank in feet. Use 3.14 for π. PLEASE HURRY I NEED THIS

Answers

Answer:

8 ft

Step-by-step explanation:

Given:

Volume = 401.92

radius = 4 feet

Volume of cylinder: [tex]\pi[/tex]r^2h

3.14 * 4^2 * h = 401.92 cubic feet

3.14 * 16 * h = 401.92 cubic feet

50.24 * h = 401.92

h = 8 ft

Simplify 4(3n + 2b + k)
a. 12nbk
b. 12n + 2bk
c. 12n + 8b + 4k
d. 24bkn

Answers

Answer:

C

Step-by-step explanation:

4(3n+2b+k)

12n+8b+4k

So it would be C.

---

hope it helps

PLEASE HELPP !!! it’s due today

Answers

Answer:

18

Step-by-step explanation:

If f(x) = x is changed to g(x) = -f(x + 3) + 2, how is the graph transformed?

Answers

Answer:

f(x) is flipped, and each point is moved 3 units to the left and 2 units up

Step-by-step explanation:

Can someone please help

Answers

Answer:

First row of blanks: -3 -3

Second row of blanks: 2 2 3

Third row blank: 6

Step-by-step explanation:

x/2 + 3 = 6

The objective is to isolate the variable:

Subtract both sides by 3

x/2 = 3

Multiply both sides by 2

x = 6

Which amount is largest?

1 kg
1 dg
100 g
1,000 mg

Answers

1 kg is the biggest.

Answer:

1 kg here you go this is the answer

Porter read 20% of the Star Wars book. He read 8 pages of the book. Write the number of pages in the Star Wars book

Answers

Answer: 40 pages in total

Explanation: Porter has read 20% of the book and this translates to 8 pages of the book.

20% = 8 pages

Assume the total number of pages is x:

20% * x = 8

0.2x = 8

x = 8 / 0.2

x = 40 pages in total

Answer:

40 pages in the book

Step-by-step explanation:

8/40 = .20

Rewrite as an addition equation and determine the answer: -3 - - 8 =

Answers

Answer:

-3 + 8 = 5

Step-by-step explanation:

When we have a "minus a negative", it's a positive. So the - -8 is the same as + 8.

LMK if you have questions.

-3 + -8 = -11

is that a nice one or something

IVE BEEN STUCK ON THIS FOR AN HOUR PLEASE HELP WHAT IS 9.85714285714 X 7

Answers

Answer:

69

Step-by-step explanation:

lol

A tub contained 80 gallons
of water. The water drained from
the tub at a rate of 5 gallons every 4
minutes. At this rate, how many
minutes did it take
for all the water to
drain from the tub?

Answers

Answer:

its 64 because 4x16= 64

Step-by-step explanation:

Can someone help me with this. Will Mark brainliest.

Answers

Answer:

[tex]\sqrt{53}[/tex]

Step-by-step explanation:

Use the distance formula:

[tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]

plug in (-5,6) for (x1,y1) and (-3,-1) for (x2,y2)

[tex]\sqrt{(-5-(-3))^2+(6-(-1))^2}[/tex]

[tex]\sqrt{4+49}[/tex]

[tex]\sqrt{53}[/tex]

Hope that helps :)

joshua is planting a triangular garden he sketched his diagram measurements are 12m and 10m the questions asks to find the missing side PLZ THIS IS URGENT

Answers

Answer:

It's 16m

Step-by-step explanation:

Let's say the missing side is C, and since the triangle is right-angle triangle, you can use Pythagoras theorem. Which is

C squared is equal to A squared plus B squared

Like this: c^2 = a^2+b^2

Then

c^2= (10)^2 + (12)^2

c^2= 100 + 144

c^2= 244

c=

[tex] \sqrt{244} [/tex]

c = 15.6

Hope this helps :)

what is x - (14x-4) + 12 = 6x + 32

Answers

Answer:

x=  -16/19

Step-by-step explanation:

x−14x+4+12=6x+32

−13x+16=6x+32

16=6x+32+13x

16=19x+32

16−32=19x

−16=19x

-16/19=x

 

6,6 and 7 units down and 5 units left where is t'

Answers

Answer:

it's 1,-1

Step-by-step explanation:

hoped I helped. I'm good at these.

Which point is not on the line

Answers

Definitely C, or (5,10)

Hope this helped!

40
in.
in?
What is the area of this trapezoid?
b2 = 5 in.
h = 4 in.
2 in.
3 in.
b = 10 in.

Answers

The area of the trapezoid is 30

Identify the measure of the angle indicated.
76
х
The value of 2 that makes lines a and b parallel is

Answers

Answer:

x = 76°

Step-by-step explanation:

76° and x are alternative interior angles, so they are congruent when lines a and b are parallel

Solve the system of equations shown below?

Answers

(6,4) x=4 and y=6. hope this helps

I need help fast and for real no bots

Answers

Answer: d. 201.06

Step-by-step explanation:

To find area of a circle we use the equation 2pi(r) or in this case 2*pi(16)= 804.25in^2 but since we are looking for the shaded region which is 1/4 or one-fourth of the circle so divide 804.25/4 to get 201 or specifically 201.06

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