PLs help with these 2 problems

PLs Help With These 2 Problems
PLs Help With These 2 Problems

Answers

Answer 1

The expressions are simplified to 2x and [tex]\frac{2}{(x+ 1)(x - 1)}[/tex]

How to simply the expressions

1.

Given the expression;

[tex]\frac{8x^2 - 4x}{4x - 2}[/tex]

Let's factorize the numerator;

[tex]\frac{2x( 4x - 2)}{4x - 2}[/tex]

Factor the common terms, we have;

2x

2. [tex]\frac{1}{x-1} - \frac{2}{x} + \frac{1}{x + 1}[/tex]

Find the Lowest common multiple

[tex]\frac{x(x+ 1) - 2 (x+ 1)(x - 1) + x(x-1)}{x(x-1)(x+ 1)}[/tex]

expand the brackets

[tex]\frac{x^2 + x -2(x^2 -x + x -1) + x^2 -x}{x(x-1)(x+ 1)}[/tex]

[tex]\frac{x^2+x - 2x^2 -2 + 2x + 2 + x^2 - x}{x(x+1) (x -1)}[/tex]

collect like terms

[tex]\frac{2x}{x(x+ 1) (x-1)}[/tex]

Divide common terms

[tex]\frac{2}{(x+ 1)(x - 1)}[/tex]

Thus, the expressions are simplified to 2x and [tex]\frac{2}{(x+ 1)(x - 1)}[/tex]

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Related Questions

Solve the equation below by factoring, then select ALL of the possible solutions.

f (x) = x^2 - 9x - 36

a . x = - 12
b. x = - 9
c. x = - 6
d. x = - 4
e. x = - 3
f. x = - 2
g. x = 2
h. x = 3
i. x = 4
j. x = 6
k. x = 9
l. x = 12

Answers

factored: f(x) = (x-12)(x+3)
possible x values: 12 and -3

Two numbers are in the ratio 2:5 .If their sum is 28 ,find the numbers​

Answers

8:20 are the two numbers ur welcome :)

Answer:

8:20

Step-by-step explanation:

8+20=28 and all that has happened is the ratio got bigger.

giving brainliest !!!!

Answers

Answer:

It is A or D but mostly A is correct.

Step-by-step explanation:

give brainliest

Solve the equatuon

x/2-(2/(x+1))=1

x=?

Answers

[tex]\frac{x}{2}-\frac{2}{x+1}=1[/tex]

We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.

Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)

[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)][/tex]

Then shorten the fractions.

[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)[/tex]

Distribute in all.

[tex]x^2+x-4=2x+2[/tex]

We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.

[tex]x^2+x-4-2x-2=0\\x^2-x-6=0\\[/tex]

We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)

[tex](x-3)(x+2)=0\\x=3,-2[/tex]

Thus, the answer is x = 3, -2

What fraction is equivalent to the expression
21
16
÷
7
4
?

Answers

Answer:

3/4

Step-by-step explanation:

21/16 ÷ 7/4

21/16 × 4/7

3/4

What is the volume of a cylinder, in cubic ft, with a height of 9ft and a base diameter
of 16ft? Round to the nearest tenths place

Answers

Answer:

Volume of cylinder is: Volume=1808.64 ft³

Step-by-step explanation:

Height of cylinder = 9 ft

Base diameter of cylinder = 16 ft

We need to find volume of cylinder .

The formula used is: [tex]Volume=\pi r^2h[/tex]

We need radius:

The radius = diameter/2 = 16/2 = 8 ft

Putting values and finding volume of cylinder

[tex]Volume=\pi r^2h[/tex]

[tex]Volume=3.14\times (8)^2\times (9) \\Volume=3.14\times 64\times (9) \\Volume=1808.64 \: ft^3[/tex]

So, Volume of cylinder is: Volume=1808.64 ft³

Suppose a and b are positive integers such that lcm(a,b) = 90 and gcd(a,b) = 3. If b is three more than a, then what are the values of a and b?​

Answers

Given:

LCM(a,b) = 90 and GCD(a,b) = 3.

b is three more than a.

To find:

The values of a and b.

Solution:

We have,

LCM(a,b) = 90

GCD(a,b) = HCF(a,b) = 3

According to the question,

[tex]b=a+3[/tex]

If a and b are two positive integers, then

[tex]a\times b=HCF(a,b)\times LCM(a,b)[/tex]

[tex]a\times (a+3)=3\times 90[/tex]

[tex]a^2+3a=270[/tex]

[tex]a^2+3a-270=0[/tex]

Splitting the middle terms, we get

[tex]a^2+18a-15a-270=0[/tex]

[tex]a(a+18)-15(a+18)=0[/tex]

[tex](a+18)(a-15)=0[/tex]

Using zero product property, we get

[tex]a+18=0[/tex] and [tex]a-15=0[/tex]

[tex]a=-18[/tex] and [tex]a=15[/tex]

a is a positive integer so it cannot be negative. So, a=15.

Now,

[tex]b=a+3[/tex]

[tex]b=15+3[/tex]

[tex]b=18[/tex]

Therefore, the value of a is 15 and the value of b is 18.

Which graph represents an even function?

Answers

Answer:

one that looks like triangle

Step-by-step explanation:

I can't seem to figure this one out. Could someone show how to do it and the answer? Thanks in advance!

Answers

Answer:

[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]

Step-by-Step explanation:

We have the function:

[tex]\displaystyle y=\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt[/tex]

And we want to find the interval for which y is concave upwards.

Therefore, we will need to find the second derivative of y, find its inflection points (where y''=0), and test for values.

So, let's take the derivative of both sides with respect to x. So:

[tex]\displaystyle y^\prime=\frac{d}{dx}\Bigg[\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt\Bigg][/tex]

By the Fundamental Theorem of Calculus:

[tex]\displaystyle y^\prime=\frac{1}{3+x+3x^2}[/tex]

So, we will take the derivative again. Hence:

[tex]\displaystyle y^\prime^\prime=\frac{d}{dx}\Big[\frac{1}{3+x+3x^2}\Big]=\frac{d}{dx}\Big[(3+x+3x^2)^{-1}\Big][/tex]

We will use the chain rule. Let:

[tex]\displaystyle u=x^{-1}\text{ and } v=3+x+3x^2[/tex]

Differentiate:

[tex]\displaystyle y^\prime^\prime=-(3+x+3x^2)^{-2}(1+6x)[/tex]

Rewrite:

[tex]\displaystyle y^\prime^\prime=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]

So, points of inflection, where the concavity changes, is whenever the second derivative is 0 or undefined.

We can see that the second derivative will never be undefined since the denominator can never equal 0.

So, our only possible inflection points are when it's equal to 0. Hence:

[tex]\displaystyle 0=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]

Multiplying both sides by the denominator gives:

[tex]0=-(6x+1)[/tex]

Then it follows that:

[tex]\displaystyle x=-\frac{1}{6}[/tex]

So, our only possible point of inflection is at x=-1/6.

We will test for values less than and greater than this inflection point.

Testing for x=-1, we see that:

[tex]\displaystyle y^\prime^\prime=-\frac{6(-1)+1}{3+(-1)+3(-1)^2}=1>0[/tex]

Since the result is positive, y is concave up for all values less than -1/6.

And testing for x=0, we see that:

[tex]\displaystyle y^\prime^\prime=-\frac{6(0)+1}{3+(0)+3(0)^2}=-\frac{1}{3}[/tex]

Since the result is negative, y is concave down for all values greater than -1/6.

Therefore, the interval for which y is concave up is:

[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]

Note that we use parentheses instead of brackets since at exactly x=-1/6, our graph is neither concave up nor concave down.

I can write linear equations

1. Through: (-1,3), Slope=2

2.Through: (3,3), slope= -2

Answers

1. Y=2x+5

2. Y= -2x-3

Evaluate 1/8 + 3/4 Fhffh

Answers

Answer:

7/8

Step-by-step explanation:

1/8 + 3/4 =

1/8 + 6/8 =

7/8

9-3x/9=-11 what is x and how you did it in a way that isn’t complicated please

Answers

First you want to move every term without the x on the other side and when you do remember to change the sign:

-3x/9 = -11 -9

Now you can do the sum

-3x/9 = -20

And in the end you multiply both sides for -9/3 to find the x:

x = -20*(-9/3)

x = 60

-60+x-23=70
Need help

Answers

Answer:

x-83=70

x = 70 + 83

x= 153

Let f(x) = 2x^2-2x+ 7 and g(x) = x^2 + 9x -6z Find f(x) - g(x).

A. X^2-11x+13

B. X^2-11x+1

C. X^2+7x+1

D. X^2+7x+13

Answers

Heres the answer welcome btw

C is the answer im pretty sure

13 more than x times 5 as an expression

Answers

Answer: I believe it's 13 > 5x or 5x+13. . But I'm not completely sure.

Your answer is 65 I think

The cube of the product of 8 and a number.

Answers

8 cubes equals 512 because 8x 8x= 512

The unknown number will be equal to 64.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the cube of the product of 8 and the number is 512. The unknown number will be calculated as,

8 x = 512

x = 512 / 8

x = 64

The number which is the product of 8 will be equal to 64.

The complete question is given below.

The cube of the product of 8 and the number is 512. What is the number?

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Anna's favorite pool toys are the beach balls. If the radius of one of the beach balls
is 6 inches, to the nearest whole number, what is the volume of the beach ball?
Leave your answer in terms of a.
Inches Cubed

Answers

Answer:

288

Step-by-step explanation:

please review the attachment for step by step soluation

question is in the picture.

Answers

Answer: About 16 snaps

Step-by-step explanation:

In a box and whisker plot, the rightmost line in the "box" of the plot is the third quartile, which represents the 75th percentile.

In this graph, although it is difficult to pinpoint the EXACT number of snaps sent, the 75th percentile would be marked at about 16 snaps.

I need help with this one

Answers

Answer:

that's your answer

Evaluate the function rule for the given value. y = 12 • 3^-2 for x = –2

Answers

Your answer is: y = 4/3

Hope this helps and happy holidays!!

how is 1/14x42=3 can someone? explain

Answers

Answer:

This is why [tex]\frac{1}{14}[/tex] x 42 = 3

Step-by-step explanation:

[tex]\frac{1}{14}[/tex] x 42 can also be written as [tex]\frac{1}{14}[/tex] x [tex]\frac{42}{1}[/tex]

we can reduce diagonally by 7 so [tex]\frac{1}{14}[/tex] x [tex]\frac{42}{1}[/tex] = [tex]\frac{1}{2}[/tex] x [tex]\frac{6}{1}[/tex]

now we multiply across [tex]\frac{1}{2}[/tex] x [tex]\frac{6}{1}[/tex] = [tex]\frac{6}{2}[/tex]

6 divided by two or [tex]\frac{6}{2}[/tex] = [tex]\frac{3}{1}[/tex] or 3

2x<6 solve the following inequality

Answers

Answer:

x<3

Step-by-step explanation:

2x<6
/     /

2    2


x<3

Answer: x < 3

Hope this helps!

The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1999 his card was worth $4.99. The value has increased by $1.73 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2006? Express the relationship with an equation. y=(Use integers or decimals for any numbers in the expression.)​

Answers

Answer: $15.37

Yes, proportional

Step-by-step explanation:

Ok So the Equation Here is

y = 1.73x + 4.99

The reason why 4.99 doesn't have a variable is because of the fact it's not being manipulated by time like the 1.73 is. It's a flat rate of 4.99 for the card itself, no increase or decrease in years. However, the 1.73 is affected by how ever many years the player is in retirement. That's why it has X because the amount of 1.73 needs to be multiplied by however many years hes been in retirement.

So Substitute 6 (because 2006 is what year we need to find) for x and we get

y = 1.73(6) + 4.99

Which if you simplify in a calculator or do it in your paper, comes out to be $15.37

*If this Helped I'd Also Appreciate 5* and a ♥ Thanks!*

Please help me with my question

Answers

Answer: use mahthway it hels

Step-by-step explanation:

Help? Will give brainliest!

Answers

Answer:

Top one

Step-by-step explanation:

It is more appropriate to measure the speck of dust using millimeters because that is most similar to the scale of the speck's size.

Need this ASAP thanks

Answers

Answer:

In Step 2.

Step-by-step explanation:

They should have distributed the 2 to the x and 1 instead of subtracting it.

1. If 5 lbs of apples cost $2.99, How much would 3 lbs cost?

Answers

The answer will be 1.80
I divided 2.99 by 5 to find the price of each lb which is 0.6 and then multiplied by 3 which equals to 1.80

PLEASE HELP ME!!!!! WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!

Answers

Answer:

Domain: -3 ≤ x ≤ 3

Range: -2 ≤ y ≤ 4

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x) Range is the set of y-values that are outputted by function f(x)

Step-by-step explanation:

According to the graph, our x-values span from -3 to 3. Since both are closed dot, they are inclusive in the domain:

[-3, 3] or -3 ≤ x ≤ 3

According to the graph, our y-values span from -2 to 4. Since both are closed dot, they are inclusive in the range:

[-2, 4] or -2 ≤ y ≤ 4

Determine the intercepts of the line.
x-intercept ( , )
y-intercept ( , )

Answers

Answer:

y-100

x-250

Step-by-step explanation:

because the lines are insecting the other lines on that line

The average daily maximum temperature in Syracuse is 21.85°C, and the average daily minimum temperature is -4.7°C. The average daily maximum temperature is BLANK °C higher than the average daily minimum temperature.

Answers

Answer:

The average daily maximum temperature is

26.56 °C higher than the average daily minimum temperature

Step-by-step explanation:

Here, we simply want to calculate how higher is the average daily maximum temperature to average daily minimum temperature

We simply proceed to subtract the two

Mathematically, that will be;

21.85 - (-4.7)

= 21.85 + 4.7

= 26.56 °C

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