Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{14 {x}^{2} - 96}{ {x}^{4} - 13 {x}^{2} + 36}}}}}} [/tex]
Step-by-step explanation:
[tex] \sf{ \frac{2}{x - 2} + \frac{1}{x - 3} - \frac{2}{ x + 2} - \frac{1}{ x + 3}}[/tex]
⇒[tex]\sf{ \frac{2(x - 3)(x + 3)(x + 2) + (x - 2)(x + 2)(x + 3) - 2(x - 2)(x - 3)(x + 3) - (x - 2)(x + 2)(x - 3)}{(x - 2)(x - 3)(x + 2)(x + 3)}} [/tex]
Use the formula : a² - b² = ( a + b ) ( a - b )
⇒[tex] \sf{ \frac{2( {x}^{2} - 9)(x + 2) + ( {x}^{2} - 4)(x + 3) - (2x - 4)( {x}^{2} - 9) - ( {x}^{2} - 4)(x - 3) }{( {x}^{2} - 4)( {x}^{2} - 9)}} [/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{ \frac{(2 {x}^{2} - 18)(x + 2) + ( {x}^{2} - 4)(x + 3) - (2x - 4)( {x}^{2} - 9) - ( {x}^{2} - 4)(x - 3)}{( {x}^{2} - 4)( {x}^{2} - 9) } }[/tex]
Multiply the algebraic expressions
⇒[tex] \sf{ \frac{2 {x}^{3} + 4 {x}^{2} - 18x - 36 + {x}^{3} + 3 {x}^{2} - 4x - 12 - (2 {x}^{3} - 18x - 4 {x}^{2} + 36) - ( {x}^{3} - 3 {x}^{2} - 4x + 12) } {( {x}^{2} - 4)( {x}^{2} - 9)} }[/tex]
When there is a ( - ) in front of an expression, change the sign of each term in the expression
⇒[tex] \sf{ \frac{2 {x}^{3} + 4 {x}^{2} - 18x - 36 + {x}^{3} + 3 {x}^{2} - 4x - 12 - 2 {x}^{3} + 18x + 4 {x}^{2} - 36 - {x}^{3} + 3 {x}^{2} + 4x - 12}{( {x}^{2} - 4)( {x}^{2} - 9) } }[/tex]
Since two opposites add up to zero, it would be better to remove them from the expression
⇒[tex] \sf{ \frac{4 {x}^{2} - 36 + 3 {x}^{2} - 12 + 4 {x}^{2} - 36 + 3 {x}^{2} - 12}{( {x}^{2} - 4)( {x}^{2} - 9)} }[/tex]
collect like terms and simplify
⇒[tex] \sf{ \frac{14 {x}^{2} - 48 - 36 - 12}{( {x}^{2} - 4)( {x}^{2} - 9) } }[/tex]
⇒[tex] \sf{ \frac{14 {x}^{2} - 84 - 12}{( {x}^{2} - 4)( {x}^{2} - 9) } }[/tex]
⇒[tex] \sf{ \frac{14 {x}^{2} - 96}{ ({x}^{2} - 4)( {x}^{2} - 9)} } [/tex]
Multiply : ( x² - 4 ) and ( x² - 9 )
⇒[tex] \sf{ \frac{14 {x}^{2} - 96}{ {x}^{4} - 13 {x}^{2} + 36}} [/tex]
Hope I helped!
Best regards! :D
Related Questions
19) If x an y are odd numbers which of the following is even?
a)(X+y)/3
b) (x+y) x^y
c) x^y
d)x^y/2
Answers
Answer:
(x+y)x^y
Step-by-step explanation:
i hope it helped you. thankyou
Which equation can be used to solve for b? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 30 degrees. The length of side B C is 8 feet, the length of B A is c, and the length of C A is b.
Answers
Answer:
b = 8tan30°
Step-by-step explanation:
Find the diagram of the triangle in the attachment. Using SOH CAH TOA to find the side AC which is b. Side AC will be the opposite of the triangle since it is facing the acute angle 30° and side BC will be adjacent.
Using TOA;
Tan<CBA = CA/BC
Given <CBA = 30°, BC = 8feet
CA = BCtan<CBA
CA = 8tan30° = b
Hence the equation that can be used to solve for b is 8tan30°
Answer:
B
Step-by-step explanation:
let f(x) = 12/4x+2. find f(-1)
Answers
8 + 56/-7 х -4
-24
-40
0
40
Answers
Answer:
0
Step-by-step explanation:
8+56/-7x-4
8+(-8)x-4
0x-4
0
Hope this helps ;) ❤❤❤
Find the value of x/y if (3/5)^4*(15/10)^4=x/y^4
Answers
Answer:
9/10
Step-by-step explanation:
3^4/5^4 × 15^4/10^4=x^4/y^4
81/625 × 50625/10000= x^4/y^4
multiply
4100625/6250000=x^4/y^4
break it down by dividing it by 5
820125/1250000
divide by 5
164025/250000
divide by 5
32805/50000
divide by 5
6561/10000 = x^4/y^4
4√6561/4√10000=x/y
9/10= x/y
Match the verbal expression to its correct algebraic expression. Five more than the square of a number Five more than twice a number Five less than the product of 3 and a number Five less the product of 3 and a number Twice the sum of a number and 5 The sum of twice a number and 5 The product of the cube of a number and 5 The cube of the product of 5 and a number.
Answers
Answer:
[tex]x^{2}[/tex]+5
2x+5
3x-5
2(n+5)
3([tex]x^{3}[/tex]+5)
5x(x^3)
Step-by-step explanation:
What is the exact area of a circle with a diameter of 20 cm?
Answers
Answer:
314 cm^2
Step-by-step explanation:
pi(r^2)
r= d/2
pi= 3.14
3.14(10^2)
3.14(100)
314
Answer:
100π cm^2
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr^2
where r represents the radius, which is half the diameter. For a circle of radius 10 cm, the area is ...
A = π(10 cm)^2 = 100π cm^2
How far will Danny travel in12 hours at a speed of 99 kilometers per hour?
Answers
Answer: 1,188 km
Step-by-step explanation:
99 x 12 = 1,188
What is the slope m of a line that is perpendicular to the line represented by x = 8? (If an answer is undefined, enter UNDEFINED.)
Answers
Answer:
slope = 0
Step-by-step explanation:
x = 8 is a vertical line parallel to the y- axis
A line perpendicular to it is a horizontal line parallel to the x- axis.
The x- axis has a slope of zero thus the line perpendicular to x = 8 is zero
The slope of a line is simply the ratio of a change in the vertical axis to the horizontal axis. The line perpendicular to [tex]x = 8[/tex] has a slope of 0
Given that
[tex]x = 8[/tex]
See attachment for the line of [tex]x = 8[/tex]
First, we determine the slope of [tex]x = 8[/tex]
The slope of a line (m) is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]x = 8[/tex] means that, the value of x is always 8; irrespective of the y-value.
So:
[tex]x_2 = x_1 = 8[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes
[tex]m = \frac{y_2 - y_1}{8-8}[/tex]
[tex]m = \frac{y_2 - y_1}{0}[/tex]
Assume the slope of the line perpendicular to [tex]x = 8[/tex] is [tex]m_2[/tex].
[tex]m_2[/tex] is calculated as follows:
[tex]m_2 = -\frac{1}{m}[/tex]
Substitute [tex]m = \frac{y_2 - y_1}{0}[/tex]
[tex]m_2 = -\frac{1}{(y_2 - y_1)/0}[/tex]
This gives
[tex]m_2 = -\frac{1\times 0}{y_2 - y_1}[/tex]
[tex]m_2 = -\frac{0}{y_2 - y_1}[/tex]
[tex]m_2 = -0[/tex]
[tex]m_2 = 0[/tex]
The slope of the line perpendicular to [tex]x = 8[/tex] is 0.
Read more about slopes at
https://brainly.com/question/3605446
1. Describe the figure using precise mathematical language
please help
Answers
What is 0.895 repeating simplified in a fraction
Answers
Answer:
[tex]\dfrac{887}{990}[/tex]
Step-by-step explanation:
Multiply by 100, subtract the original and divide the result by 99.
[tex]x=0.8\overline{95}\\100x=89.5\overline{95}\\100x-x=89.5\overline{95}-0.8\overline{95}=88.7\\99x=88.7\\\\x=\dfrac{88.7}{99}=\boxed{\dfrac{887}{990}}[/tex]
Write 2.3181818... as a mixed number.
Answers
Describe how to draw a tape diagram to represent and answer 3÷3/5=? 3 ÷ 3/5 = ? for a friend who was absent.
Answers
Answer:
The numerical answer is 5
Please see the tape diagram evolution in the attached image
Step-by-step explanation:
Start by drawing three unit tapes, and divide each one of them in 5 equal parts since we need to be dividing the quantity 3 by 3/5 (denominator 5)
In the second step, join the three tapes in one long one maintaining the original divisions.
In the third step, select groups of 3 divisions (recall you need to divide by 3/5) which will identify in your tape how many of these 3/5 groups you have.
Finally count the number of 3/5 groups you found in the collection of the three original tapes placed together. You should count a total of 5 of these 3/5 groups.
5 then tells you what is the quotient of 3 divided in 3/5
This set has me absolutely confused. Can anyone help with the first problem?
Answers
Answer:
The other endpoint is ( -1,15)
Step-by-step explanation:
21.
The x coordinate of the midpoint is the sum of the x coordinate of the endpoints divided by 2
(-5 +x)/2 = -3
Multiply each side by 2
-5+x = -6
Add 5 to each side
-5+x+5 = -6+5
x = -1
The y coordinate of the midpoint is the sum of the y coordinate of the endpoints divided by 2
(-1 +y)/2 = -8
Multiply each side by 2
-1+y = -16
Add 1 to each side
-1+y+1 = -16+1
y = -15
The other endpoint is ( -1,15)
solve for x by first setting up two equations. Then find the PRODUCT of your solutions |2x+5|=7
Answers
Answer: see below
Step-by-step explanation:
|2x+5|=7
2x+5=±7 ⇔ since the absolutely value of any number is all positive, so the value in side can be either positive or negative
2x+5=7 or 2x+5=-7
2x=2 2x=-12
x=1 or x=-6
----------------------------------------
The product of the two solutions
1 × -6=-6
Hope this helps!! :)
Please let me know if you have any question
Answer: 2x−5=7 and 2x−5=−7
Hello! I need some help figuring out what 12 x 6,012 is. Ty!
Answers
Answer:
12 times 6012 u can type in calculator is 72144
Answer:
72144 is the answer.
Hope this helps
17. Tonya's mother is 1.5 times as tall as
Tonya was when she was 6. How tall
is Tonya's mother? Use the correct
number of significant digits.
Answers
The question is incomplete:
17. Tonya's mother is 1.5 times as tall as Tonya was when she was 6. How tall is Tonya's mother? Use the correct number of significant digits.
The image with the information about Tonya's height is attached.
Answer:
68 in.
Step-by-step explanation:
According to the information given, you can write the following expression:
x=1.5y
x=Tonya's mother height
y= Tony's height when she was 6
Also, you know from the table that Tonya's height when she was 6 was 45 in. and you can replace this value in the formula:
x=1.5*45
x=67.5
Because of this, the answer is that Tonya's mother height is 68 in.
PLEASE PLEASE PLEASE HELP ME!
Answers
Answer: 50 Minutes = 309 gal
Step-by-step explanation: Every 10 minutes the amount of water goes up by 18, so after 50 minutes the water would be equivalent to 309 gallons.
Answer:
[tex]y=1.8x+219[/tex]
309 gallons
Step-by-step explanation:
So to find the linear equation, we can use the data from the table.
First, use the data from the table to find the slope. Pick any two points. I'm going to use (10,237) and (20,255).
Let (10,237) be x₁ and y₁ and let (20,255) be x₂ and y₂.
The formula for slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\frac{255-237}{20-10}[/tex]
Simplify:
[tex]m=18/10=1.8[/tex]
Thus, the slope is 1.8. This means that 1.8 gallons of water flow into the tank every minute.
Now, let's find the slope-intercept. To do this, we can use the point-slope form. The point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Let's use (10,237) for consistency. Plug in 237 for y₁ and 10 for x₁. Also use 1.8 for m. Thus:
[tex]y-237=1.8(x-10)[/tex]
Distribute:
[tex]y-237=1.8x-18[/tex]
Add 237 to both sides:
[tex]y=1.8x+219[/tex]
What this means is that there is initially 219 gallons of water in the tank already. Every minute, 1.8 gallons is added further.
And that's our linear equation :)
So, to find the amount of gallons after 50 minutes, plug in 50 for x and solve:
[tex]y=1.8(50)+219\\y=90+219=309[/tex]
After 50 minutes, there will be 309 gallons of water.
Whats the quotient or -42/-7
Answers
Answer: 6
Step-by-step explanation: when you divide two negative numbers, the answer will always be positive .
A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant
records information including the type, age, weight, and height of each pet. Which of the variables is a categorical
variable?
Answers
The correct answer is Type
Explanation:
Categorical variables differ from other types of variables because these involve categories or defined groups. For example, sex is a categorical variable because in a population individuals are either classified as females or males (categories). This concept applies to types of pets because this variable involves categories or defined groups such as dogs, cats, hamsters, turtles, etc. Also, other variables such as age, weight, or height are not naturally categorical because these can be understood using numbers rather than categories.
Answer: The answer is definitely TYPE
Step-by-step explanation: For example the brand of a car is a category. You could have a Toyota. Toyota is a category of a car. Therefore, this can be applied in this problem; the Type of a pet is a category. The pet could be a dog or a cat e.t.c.
Adam would like to build a deck thatbis 60,feet long by 8 feet hiw much wood would he need
Answers
Answer:
136 ft of woods
Step-by-step explanation:
1. Let us assume that we are solving for the frame of the deck alone
2. And also from the given parameters the deck has a rectangular shape
we know that the total amount of woods to be used is same as the perimeter of the rectangle.
Given that
length l= 60 ft
width w= 8 ft
The formula for the perimeter of a rectangle is given as
Perimeter= 2l+2w
perimeter= 2*60+ 2*8
perimeter= 120+16
perimeter= 136 ft
Hence in other to construct the frame of the deck Adam needs a total of 136 ft of woods
Solve for a: 2.2a + 3.4 b = 1.2a + 2.6
What is the value of a when b = 2? b =
1.5?
Answers
Answer:
when b=2 , a = -4.2
when b=1.5 , b=-2.5
Step-by-step explanation:
When b = 1.5
[tex]2.2a + 3.4b = 1.2a + 2.6 \\ a = \\ b = 1.5 \\ 2.2a + 3.4(1.5) = 1.2a + 2.6 \\ 2.2a + 5.1 = 1.2a + 2.6[/tex]
[tex]2.2a - 1.2a = 2.6 - 5.1 \\ a = - 2.5[/tex]
When b = 2
[tex]2.2a + 3.4(2) = 1.2a + 2.6 \\ 2.2a + 6.8 = 1.2a + 2.6[/tex]
Collect like terms and simplify
[tex]2.2a - 1.2a = 2.6 - 6.8 \\ a = - 4.2[/tex]
11. Listed below are the temperature in °C for 10 days.
-6.-8. 0. 3. 2. 0. 1, 5, 4, 4
What is the range of the data?
Answers
Answer:13
Step-by-step explanation: range is the biggest value - the smallest value, in this case, the biggest value= 5 and the smallest value= -8 so, 5--8= 5+8 ( when it is a minus minus it is automatically changed to a plus)= 13.
which of the following is equivalent to complex number i6 ?
A 1
B i
C -1
D -i
Answers
Answer:
-1
Step-by-step explanation:
please answer!!! I really need this
Answers
Answer:
A
Step-by-step explanation:
a would be the correct answer to create a rectangle
Megan purchased 12 square yards of flooring for a total of $432. What was the price of this
flooring per square foot
Answers
Answer:
$5184
Step-by-step explanation:
1 per square foot =$432/1
12 square =12×$432/1
$5184
f(x)= 2x+5, g(x)=x+10, f-g (x)
Answers
Answer:
x -5
Step-by-step explanation:
f(x)= 2x+5, g(x)=x+10,
f-g (x) = 2x+5 - (x+10)
Distribute the minus sign
= 2x+5 - x-10
=2x-x +5-10
Combine like terms
x -5
Which equation does not represent y as a function of x? Group of answer choices A. 5x2 + 5y = 3 B. 2x = 8y C. –4y = –8 D. 3x + 6y = –5 E. 7y2 + 8x = 9 Please Post the explanation!! I want to understand it.
Answers
Answer:
The correct option is (C).
Step-by-step explanation:
We need to find the correct option that does not represent y as a function of x.
In options A, B, D and E, both x and y are involved. It means we can represent y as a fucntion of x.
But in option (c), it has only y as a variable i.e.
-4y=-8
y=(8/4)
y = 2
So, this option does not represent y as a function of x.
42 divided by (14-6)
Answers
Answer:
5 r 2
Step-by-step explanation:
Steps :
Please help me!! the pic with the graph is the question & the other 2 pics are the numbers given to me!! pls help
Answers
This question was answered earlier at this link below
https://brainly.com/question/17274617
Let me know if you have any questions about any of the steps.