Mathematics High School

5. Realizar las siguientes operaciones y simplificar el resultado:
a. 3(x3 − x2 + 5) − 8(x3 − 4x2 + 7x)
b. 7x2 + 2x + 5 + x(x + 7)
c. 10 (t3 − 4t2 + 1) − t(2t + 6) + 8(t3 − t − 5)
d. (x − 1)(x + 2)(x − 3)
e. (3a − 2b2)(3a + 2b2) − 3(4a − b2)2 + 2(−2a − b2)(2a − b2)

Answers

Answer 1

Answer:

a. -5x³ + 29x² - 56x + 15

b. 8x² + 9x + 5

c. 18t³ - 42t² - 14t - 30

d. x³ - 2x² - 5x + 6

e. -2b⁴ + a² + 6b² - 24a

Step-by-step explanation:

a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)

3x³ - 3x² + 15 - 8x³ + 32x² - 56x

-5x³ + 29x² - 56x + 15

b. 7x² + 2x + 5 + x(x + 7)

7x² + 2x + 5 + x² + 7x

8x² + 9x + 5

c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)

10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40

18t³ - 42t² - 14t - 30

d. (x − 1)(x + 2)(x − 3)

(x - 1)(x + 2)

x(x + 2) - 1(x + 2)

x² + 2x - x - 2

x² + x - 2(x - 3)

x(x² + x - 2) - 3(x² + x - 2)

x³ + x² - 2x - 3x² - 3x + 6

x³ - 2x² - 5x + 6

e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

3a(3a - 2b²) + 2b²(3a - 2b²)

9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)

(−2a − b²)(2a − b²)

-2a(2a - b²) - b²(2a - b²)

-4a² + 2ab² - 2ab² + b⁴

-4a² + b⁴

2(-4a² + b⁴)

-8a² + 2b⁴

9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴

-2b⁴ + a² + 6b² - 24a

Related Questions

Given f(x) = -x - 1, find ƒ (1).

Answers

Answer:

You've gotta be kidding me...It's easy come on

-2 is the answer

Step-by-step explanation:

f(x)= -x-1 JUST SUBSTITUTE 1 FOR X

f(1)= -(1)-1

f(1)= -2

A store owner mixes 2 lbs of candy that cost x dollars pound with 3 lb of candy that costs $1.50 per pound. she sells the mix for $2.50 per pound. how much did the 3lb of the second type cost the owner?

Answers

Algebraic equations are mathematical equations that consist of unknown variables. These unknown variables can be represented with any letter of the alphabet.

The cost of 2 pounds(lb) of the first type of candy is $8

Note that: x represents the cost per pound (lb) of the first type of candy

The Algebraic equation for the above statement is given as:

2lb × $x + 3 Ib × $1.50 = $2.50(2lb + 3lb)

2x + 4.5 = 12.5

Collect like terms

2x = 12.5 - 4.5

2x = 8

Divide both sides by 2

2x/2 = 8/2

x = 4

The cost of the 1 pound of first type of candy is $4

The cost of 2 pounds(lb) of the first type of candy is calculated as:

2 x $4

= $8

hope it will be helpful

C is the center of the circle with a diameter whose endpoints are the points A(-2, 1) and B(6, 9).
What is the equation of circle C?

Answers

well, the midpoint of segment AB is the center of the circle, so

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}[/tex]

now since we know AB is the diameter, so half that distance AB is its radius, so

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}[/tex]

The cost of Sara’s Cell Phone is $200 plus $45 per month.

How much will she spend on the cell phone in 3 years?

…. If Sara spent $1500, how long would she have had the phone?

(Use Cost ((y=mx+b))

Answers

1. 1,820
2. Around 29 months

Answer: The cost of her phone is $1,820.

45*12=540 per year

540*3=1,820 every 3 years.

She would have had the phone between 2 and 3 years if she had spent 1,500.

Congruent triangles
Please answer this question

Answers

A.Congruent triangles)

In a survey of 1,900 people who owned a certain type of car, 855 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?

Answers

Answer: 45%

Step-by-step explanation: 45% of 1,900 is 855

ANSWER QUICK I WILL GIVE BRAINLIEST
Determine which expression is equivalent to the expression 2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12. 4 over 15 times g plus negative 17 negative 4 over 15 times g plus negative 17 2 over 15 times g plus negative 7 negative 4 over 15 times g plus negative 7

Answers

Answer:

-4/15 - 17

negative 4 over 15 plus negative 17

Step-by-step explanation:

2/3g - 5 - 11/15g - (1/5g +12)

Your wording is extremely confusing but I tried :]

-4/15 - 17

is the correct answer (I think)

The required simplified value of the given expression is -4/15 - 17.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12 is given as

= 2/3g - 5 - 11/15g - (1/5g +12)

Adding the alike terms,
= 2/3g -11/15g -1/5g -5 -12
= [10 - 11 -3] /15 g - 17
= -4g/15 -17

Thus, the required simplified value of the given expression is -4/15 - 17.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

Mrs. Gomez earns $19.50 per hour and gets a 5% raise. Use compatible numbers to estimate her new hourly rate.

Answers

The new hourly rate using compatible numbers is $21.

Given,

The earnings of Mrs. Gomez = $19.50 per hour

She gets a raise of 5%

We have to estimate her new hourly rate by using compatible numbers.

Compatible numbers:

Compatibility in mathematics refers to the mental ease with which a number can be added, subtracted, multiplied, or divided. Compatibility refers to the proximity of the compatible numbers to the real numbers, which facilitates estimation of the solution and simplifies problem-solving.

So,

Compatible number of 19.50 is 20.

The amount raised = 20 × 5/100 = 5/5 = $1

Now, the new hourly rate = 20 + 1 = $21.

That is, the new hourly rate using compatible numbers is $21.

Learn more about compatible numbers here:

https://brainly.com/question/627054

#SPJ1

3=british paintings
t=painting from 2th century
b=british paintings
a painting is chosen at random
work out the probability that it is british

Answers

The probability of choosing a painting random and it is British is 0.50.

Given,

The total number of paintings = 30

Then,

x (x - 2) + x + (2x - 8) + 10 = 30x = 3

T = Painting from 20th century

B = British paintings

We have to find the probability of choosing a painting random and it is British.

Here,

Probability = British/ Its from 20th century

Probability = n (B and T) / n(T)

= x / (x + x(x-2))

= 3 / (3 + 3(3 - 2))

= 3 / (3 + 9 - 6)

= 3 / 6 = 1/2 = 0.5

Here, the probability of choosing a painting random and it is British is 0.50.

Learn more about probability here:

https://brainly.com/question/15534943

#SPJ1

Dracula needs to mix 4 quarts of liquid iced tea concentrate with 5.5
quarts of water to make iced tea. He wants to make 66.5 quarts of
iced tea. How much iced tea concentrate will he need?

Answers

28 quarts.

First find out how many quarts of iced tea are made from 4 quarts of concentrate and 5.5 quarts of water. Then set up a proportion to solve for the amount of concentrate required for 66.5 quarts of iced tea.

See details:

Solve for X.
Help please!!!

Answers

Answer:

x=17

Step-by-step explanation:

2x-3+3x+8=90

5x=85

x=17

if f(x)=8-5x find f(4-+3)

Answers

The required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function ,

f(x) = 8 - 5x
put x = 4
f(4) = 8 - 5(4)
f(4) = 8 - 20
f(4) = -12

Again,
put x = 3
f(3) = 8 - 5(3)
f(3) = 8 - 15
f(3) = -7

Thus, the required value of the function at x = 4 and 3 is f(4) = -12 and f(3) = -7.

learn more about function here:

brainly.com/question/21145944

#SPJ1

Draw the graph of each circle given its equation below.

Answers

Step 1:

First, write the general equation of a circle

[tex]\begin{gathered} (x-a)^a+(y-b)^2=r^2 \\ r\text{ is the radius} \\ (a,\text{ b) is the center} \end{gathered}[/tex]

Step 2:

Question 1

[tex]\begin{gathered} x^2+y^2\text{ = 121} \\ x^2+y^2=11^2 \\ \text{radius r = 11} \\ \text{center = (0 , 0)} \end{gathered}[/tex]

Question 2

[tex]\begin{gathered} (x-2)^2+y^2\text{ = 64} \\ (x-2)^2+y^2=8^2 \\ \text{Center = (2, 0)} \\ r\text{ = 8} \end{gathered}[/tex]

Question 3

[tex]\begin{gathered} (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = 36} \\ (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = }6^2 \\ \text{Center = (-}\frac{3}{2}\text{ , -}\frac{5}{8}) \\ r\text{ = 6} \end{gathered}[/tex]

Question 4

[tex]\begin{gathered} (x-1)^2+(y+7)^2\text{ = 9} \\ (x-1)^2+(y+7)^2\text{ = }3^2 \\ \text{Center = (1, -7)} \\ r\text{ = 3} \end{gathered}[/tex]

Question 5

[tex]\begin{gathered} (x+8)^2+(y-3)^2\text{ = 7} \\ (x+8)^2+(y-3)^2\text{ = (}\sqrt[]{7})^2 \\ \text{Center = (-8, 3)} \\ \text{radius r = }\sqrt[]{7} \end{gathered}[/tex]

x = -4z - 19
y= 5x + z - 4
-5y - z = 25

Answers

Answer:

x = 1, y = -4, z = -5

Step-by-step explanation:

Solve the following system:

{x = -4 z - 19 | (equation 1)

{y = z + 5 x - 4 | (equation 2)

{-z - 5 y = 25 | (equation 3)

Express the system in standard form:

{x + 0 y + 4 z = -19 | (equation 1)

{-(5 x) + y - z = -4 | (equation 2)

{0 x - 5 y - z = 25 | (equation 3)

Swap equation 1 with equation 2: