Write a rational expression that simplifies to (x-1)/(x+2), x≠-4, -2

Answers

Answer 1

Answer: [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)}[/tex] which is the same as [tex]\frac{x^2+3x-4}{x^2+6x+8}[/tex]

If the math notation does not load properly, or the font size is too small, then it says ( (x+4)(x-1) )/( (x+4)(x+2) ) which is the same as (x^2+3x-4)/(x^2+6x+8)

==========================================================

Explanation:

We see that x cannot equal -2, as this prevents the denominator (x+2) from becoming zero. If x = -4, then x+4 = 0. So x not allowed to be -4 means (x+4) is prevented in being zero, and this is the missing factor in the denominator. We can never divide by zero.

Multiply top and bottom of this given fraction by (x+4) to get [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)}[/tex]

Note how the (x+4) terms divide and cancel to get back to the original fraction given. The portion [tex]x \ne -4[/tex] sticks around to make sure the domains line up properly.

----------

Optionally you can expand out each product in the numerator and denominator to get

(x+4)(x-1) = x^2-x+4x-4 = x^2+3x-4

(x+4)(x+2) = x^2+2x+4x+8 = x^2+6x+8

I used the FOIL rule

So, [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)} = \frac{x^2+3x-4}{x^2+6x+8}[/tex]


Related Questions

What is the simplified form of each expression? a. (6 + 3)2 − 4 b. 23 + (14 − 4) ÷ 2

Answers

Answer:

a. 14

b. 28

Step-by-step explanation:

a. ex: (6+3)2 - 4 = 9(2) - 4

18 - 4 = 14

b. ex: 23 + (14 - 4) / 2

Use PEMDAS

P 1st

10

D over A

5

A

28

Hope this helps!

Express the ratio 700g to 1.75kg in its lowest terms.

Give your answer in the form m:n where m and n are integers​

Answers

Answer:

2 : 5

Step-by-step explanation:

700 g : 1.75 kg

Since ratio should be between same units, so we'll convert either g into kg or kg into g. For convenience, kg will be converted to g

700 g : 1.75 kg × 1000

700 g : 1750 g

÷ 50 ÷50

14 : 35

÷7 ÷7

2 : 5

Which measure is always the 50th percentile?
mean
median
upper quartile

Answers

Answer:

median

Step-by-step explanation:

the median is literally the middle number--half the numbers are higher, half the numbers are lower.

2.
Name the quadrant in which the point lies:
(a) A (1, 1)
(b) B (2,4)
(c) C (-3,-10)
(d) D (-1,2)
(e) E (1, -1)
() F (-2,-4)
(9) G (-3, 10)
(h) H (1, -2)​

Answers

Answer:

hope this helps! pls mark brainliest

Step-by-step explanation:

a = quadrant 1

b = quadrant 1

c = quadrant 3

d = quadrant 2

e = quadrant 4

f = quadrant 3

g = quadrant 2

h = quadrant 4

En un colegio hay dos grupos de 1º ESO con 24 alumnos cada uno.
a) Si las chicas de 1º A son el doble que los chicos, ¿cuántas chicas hay en la clase?
b) Si el número de chicas de 1º B supera en cuatro al de chicos, ¿cuántos chicos
hay?

Answers

Answer:

I will answer in English.

In each group, A and B, we have 24 students.

a) The number of girls in A is twice the number of boys in A.

Then, if G is the number of girls and B the number of boys.

G + B = 24

G = 2B

Now we can replace the second equation into the first one:

2B + B = 24

3B = 24

B = 24/3 = 8

G = 24 - 8 = 16

We have 16 girls in class A.

b) In B we have 4 more girls than boys, then:

G  = B + 4

G + B = 24

we can replace the first equation into the second one:

B + (B + 4) = 24

2*B = 24 - 4 = 20

B= 20/2 = 10

We have 10 boys in class B:

make b the subject of the formula a = sqrt(b+6)

Answers

Answer:

a = √(b+ 6)

a² = b + 6 (Square both sides)

b = a² - 6 (subtract 6 from both sides)

Answer:

b = a^2 - 6

Step-by-step explanation:

a = sqrt(b+6)

Find the square of both sides

a^2 = (b+6). Open brackets

a^2 = b+6

Subtract 6 from both sides

a^2 - 6 = b + 6 -6

b = a^2 - 6

Suppose that you received an unexpected inheritance of ​$39,200.You have decided to invest the money by placing some of the money in stocks that pay 4.8% and the rest in bonds that pay 8%.How much should you place in each investment in order to earn 6%or ​$2352 annually?

Answers

I’m not going first to tell y’all that I’m not going first because I’m gonna the way you are the most likely one that will make you a

What is the average rate of change from x = −1 to x = −2?

Answers

Answer:

Step-by-step explanation:

this graph is probably : 2(x+1)^(2)+5:

it was transformed :

vertically stretched by a factor of 2

left 1 unit

up 5 units

from the graph, we can see that the points are (-1, 5) and (-2, 7)

m=(y2-y1)/(x2-x1)

m=(7-5)/(-2-(-1))

m=2/-1

m=-2

How do I find the area of this figure?

Answers

Answer:

140 units^2

Step-by-step explanation:

Area of a parallelogram is base times height, A = bh. Multiply the height (10) times the base (14) to get your final answer.

A = bh

A=14(10)

A=140units^2

Expand and simplify ( √2 + 3)to the power of 2

Answers

Answer:

Step-by-step explanation:

[tex](\sqrt{2}+3)^2=(\sqrt{2})^2 + 6\sqrt{2}+9 = 6\sqrt{2} +9+2=6\sqrt{2}+11[/tex]

hope this helps

!35 POINTS! Find the total surface area of the following prism! ​

Answers

Total surface area is 152 cm

Answer:

152

Step-by-step explanation:

Why is this still worth 18 points?
because if you math 12+273 it = 8281 or something free point thank

Need answers quick. Find the endpoint of the line segment with the given endpoint and midpoint. Endpoint: (−6,−6) Midpoint: (−2,0)

Answers

Answer: The second endpoint is  (2,6)

Step-by-step explanation:

[tex]\frac{-6 +x}{2}[/tex] = -2  solve for x  

-6 +x = -4

+6        +6

x= 2

[tex]\frac{-6+y}{2} = 0[/tex]  

-6 + y = 0

+6         +6

 y= 6

Look how many points u get on this.
What is the mean of this data set?
12, 17, 16, 10, 20, 13, 14, 14, 12, 12, 19, 18

A 13.50

B 14.00

C 14.75

D 15.75

Answers

Answer:

C. 14.75

Step-by-step explanation:

To find mean is fairly easy. All you have to do is add all of the numbers in your data set, and then divide it by the total amount of numbers in the set. So:

12 + 17 + 16 + 10 + 20 + 13 + 14 +14 + 12 + 12 + 19 + 18

Total numbers in the set: 12

All numbers added together: 177

177 / 12 = 14.75

brainliest is always epic :)

Answer:

Step-by-step explanation:

1. First add all the listed numbers which equals to 177

2. Divide 177 by the amount of number given above so there are

12 numbers

So 177÷12= 14.75

Answer is c

Find the volume of the sphere. Use 3.14 for Pi. Round your answer to the nearest thousandth. A sphere with diameter 10 inches. a. 4186.667 cu. in. b. 523.333 cu. in. c. 104.667 cu. in. d. 294.375 cu. in. Please select the best answer from the choices

Answers

General Formulas and ConceptsGeometry

Volume of a Sphere Formula:
[tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]

[tex]\displaystyle r[/tex] is the radius

Diameter/Radius Relationship:
[tex]\displaystyle r = \frac{d}{2}[/tex]

[tex]\displaystyle r[/tex] is the radius[tex]\displaystyle d[/tex] is the diameter

ApplicationStep 1: Define

Let us clearly sort out what information this specific problem gives us:

We are given that the shape is a sphere.We are also given that the diameter of the sphere is equal to 10 inches.Finally, we are asked to find the volume of the sphere.

We can consolidate this into mathematical symbols:

[tex]\displaystyle d = 10 \ \text{in}[/tex][tex]\displaystyle V_{\text{Sphere}} = \ ?[/tex]

Step 2: Work

Given what we know, we now need to find the volume of the sphere. With knowledge implied, found under the General Formulas and Concepts section above, we can first solve for the radius [tex]\displaystyle r[/tex]:

[tex]\displaystyle\begin{aligned}r & = \frac{d}{2} \\& = \frac{10 \ \text{in}}{2} \\& = \boxed{5 \ \text{in}} \\\end{aligned}[/tex]

∴ the radius of the sphere is equal to 5 inches.

Now that we have our radius, we can substitute this value into our volume of a sphere formula and evaluate:

[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \boxed{ \frac{500}{3} \pi \ \text{in}^3 } \\\end{aligned}[/tex]

∴ the volume of the sphere is equal to [tex]\boxed{ \frac{500}{3} \pi \ \text{in}^3 }[/tex].

To estimate our answer, we can simply substitute the value of [tex]\displaystyle \pi[/tex] for 3.14, as defined by the problem, and evaluate once more:

[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \frac{500}{3} \pi \ \text{in}^3 \\& = \frac{500}{3} (3.14) \ \text{in}^3 \\& \approx \boxed{ 523.333 \ \text{in}^3 }\end{aligned}[/tex]

∴ the volume of the sphere is approximately equal to [tex]\displaystyle \boxed{ 523.333 \ \text{in}^3 }[/tex].

Answer

∴ the best answer choice that corresponds to our gathered result is answer choice b. 523.333 cu. in.

___

Learn more about volume: https://brainly.com/question/27749754

Learn more about geometry: https://brainly.com/question/16893579
___

Topic: Geometry

Unit: Volume

What is the perimeter of the triangle?

Answers

Count the boxes and add the sides and the bottom and that’s the perimeter

Answer:

36 units

Step-by-step explanation:

The short leg is 9 units and the long one is 12 units.

Use pythagorean theorem to find the hypotenuse, a² + b² = c²

Plug in the numbers: 9² + 12² = c²

81 + 144 = c²

225 = c²

√225 = c

15 = c

Find perimeter by adding all 3 sides: 9 + 12 + 15 = 36 units.

Find sin3A, cos
3A and tan 3A when sin=1/2

Answers

Answer:

Sin 3A = 1

cos 3A = 0

tan 3 A = undefined

Step-by-step explanation:

[tex]\sin A = \frac{1}{2} \\ \therefore \: \sin A = \sin \: 30 \degree.. \bigg( \because \: \sin \: 30 \degree = \frac{1}{2} \bigg) \\ \therefore \: A = 30 \degree \\ \\ now \\ \sin 3A =\sin (3 \times 30 \degree)= \sin \: 90 \degree = 1 \\ \\ \cos 3A =\cos (3 \times 30 \degree)= \cos \: 90 \degree = 0\\\\ \tan 3A =\tan (3 \times 30 \degree)= \tan \: 90 \degree = \infty [/tex]

work out the circumference of the circle when the radius is 6mm and give the answer in terms of pie.

Answers

_______________________________

Hey!!

Solution,

Radius(r)= 6 mm

Circumference of circle=?

Now,

Circumference of circle=2 pie r

=2*pi*6

=12 pie

So the answer is 12 pie.

Hope it helps...

Good luck on your assignment

______________________________

The circumference of the circle is 12[tex]\pi[/tex] mm.

What is circumference of circle ?

The boundary of a circle, i.e. the length of the full arc of a circle is called circumference of circle.

What is the formula of circumference of circle ?

Let, radius of the circle be r

Then, Circumference of circle = [tex]2\pi r[/tex] unit

What is the value of required circumference ?

Given, The radius is 6 mm

Circumference of the circle = [tex]2\pi r[/tex]

                                                  = ([tex]2\pi[/tex]× 6) mm

                                                  = 12[tex]\pi[/tex] mm

Hence, Circumference of the circle = 12[tex]\pi[/tex] mm

Learn more about circumference of circle here :

https://brainly.com/question/164719

#SPJ2

Solve 3^x - 5. What are the exact and approximate solutions?​

Answers

Answer:

x = log(5) / log(3)

x=1.46497

Step-by-step explanation:

3^x - 5 =0

Add 5 to each side

3^x = 5

Take the log of each side

log 3^x = log 5

We know log a^b = b log (a)

x log (3) = log (5)

Divide side by log (3)

x = log(5) / log(3)

x=1.46497

nothing to do + tired = ????

Answers

Sleepy and tired nothing to do

Answer: Go and do something :)

Step-by-step explanation:

Get off your phone and get the motivation to fo and find something to do for now :)

Solve the following math problem using Roman numerals.

VII + X =

XIV
XVII
XV
XX

Answers

Answer:

XVII

Step-by-step explanation:

VII + X =

V = 5

I = 1

X = 10

5+1+1 + 10 = 17

XVII

Looking at the histogram, where would the median fall?

Answers

Answer:

The median would be found in the middle of the histogram

Step-by-step explanation:

It looks like 70-79, would fall in being the median because it is in the middle and it has the most results. In this case, I think it 70-79.

Hope this helps.

Answer:

70-79

Step-by-step explanation:

I took the test :)

10 pts!
How can you determine if two triangles have a scale factor?

Answers

Answer:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1 , Δ ABC∼ Δ DEF. Figure 1 Similar triangles whose scale factor is 2 : 1. The ratios of corresponding sides are 6/3, 8/4, 10/5. hope that helps love!

Answer:

i dont know but here is some help

Step-by-step explanation:

Scale Factor. Suppose you have two similar figures , one larger than the other. The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Example: Here, XYUV=123=4 .

Tina throws a baseball straight up from a height of 3 feet and at a speed of 50 feet per second. The height of the ball in feet is given by the polynomial -16t^2+50t+3, where t is the time in seconds. How high is the ball after 3 seconds?

Answers

Answer:

9 feet

Step-by-step explanation:

The height of the ball in feet is given by the polynomial:

[tex]h(t) = -16t^2+50t+3[/tex]

where t is the time in seconds.

After 3 seconds, t = 3:

[tex]h(3) = -16(3)^2 + 50(3) + 3 \\\\h = -144 + 150 + 3 = 9 feet[/tex]

The height of the ball after 3 seconds is 9 feet.

Let a be a non-zero rational number and be an irrational number. Is a/b rational or irrational?

Answers

Answer: Irrational, assuming b is irrational

Step-by-step explanation:

You didnt state what "b" is, but:

Youre dividing "a" by an irrational number. you could do something simple like 4 divided by pi. Youre going to get an irrational number

Which similarity postulate or theorem can be used to verified that the two triangles shown below are similar? PLEASE HELP ASAPP

Answers

Answer:

Correct option: A -> AA postulate

Step-by-step explanation:

In the figure we can see that in triangle ABC we have:

A = 53°

B = 72°

And we can see in the triangle LMN that:

L = 53°

M = 72°

We have two pairs of angles (A - L  and B - M) that are congruent, and therefore we can use the case AA (angle-angle) to affirm that these triangles are similar.

So the correct option is A: AA postulate.

tell whether this has one solution, infinitely many solutions, or no solution. Explain your reasoning. y=2x+7, y=3x-1

Answers

Answer:

One solution

Step-by-step explanation:

They have isolated y for you in both equations so you can plug either one into the other.

y = 3x - 1

2x + 7 = 3x - 1

isolate the x

7 = x - 1

x = 8

Go back to the original and plug 8 into x to get y.

y = 2 (8) + 7

y = 16 + 7

y = 23

This means at (8, 23) y = 2x+7 is equal to y = 3x-1. In other words they share a point at (8, 23). This is the only solution because for any other x and y they'd not be equal.

Using the midpoint method (show your work), calculate the price elasticity of demand when the price of a barrel of gosum berries rises from $10 to $20. What kind of elasticity is this value that you computed for the price elasticity of demand and what does it mean for how demand will change based on a change in price within this price range?

Answers

Answer:

0.18

Step-by-step explanation:

Given that:

P₁ = $10, P₂ = $20

From the tables Q₁ = 900, Q₂ = 800

Using midpoint method:

Percentage change in quantity = [tex]\frac{Q_2-Q_1}{(Q_1+Q_2)/2} *100\%=\frac{800-900}{(900+800)/2}*100\%= -11.76\%\\[/tex]

Percentage change in price =

[tex]\frac{P_2-P_1}{(P_1+P_2)/2} *100\%=\frac{20-10}{(20+10)/2}*100\%= 66.67\%\\[/tex]

Price of elastic demand = Percentage change in quantity/ Percentage change in price = -11.76% / 66.67% = 0.18

The Price of elastic demand is positive because we took the absolute value and elasticity are always positive

Therefore since Price of elastic demand < 1, the demand is inelastic in this interval.

This means that, along the demand curve between $10 to $20, if the price changes by 1%, the quantity demanded will change by 0.18%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 1.8% decrease in quantity demanded and a 10% decrease in the price will result in only a 1.8% increase in the quantity demanded

The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven

in fact, there is more than one way to arrange the numbers in such a way in the circle. Determine all different arrangments. Note that we will consider two arrangments to be the same if one can be obtained from the other by a series of reflections and rotations

Answers

Answer:

[tex]\fbox{\begin{minipage}{4em}36 ways\end{minipage}}[/tex]

Step-by-step explanation:

Step 1: Re-state the problem in an easier way to set up a permutation problem

"The numbers 1,6,8,13,15,20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven"

The series above can be represented again, in form of:

7a + 1, 7b - 1, 7c + 1, 7d - 1, 7e + 1, 7f - 1

with a, b, c, d, e, f are non-negative integers.

=> 3 numbers are multiply of 7 plus 1

=> 3 numbers are multiple of 7 minus 1

Step 2: Perform the counting:

For the 1st number, there are 6 ways to select

To satisfy that each pair of numbers creates a multiple of 7, then:

For the 2nd number, there are 3 ways left to select

For the 3rd number, there are 2 ways left to select

For the 4rd number, there are 2 ways left to select

For the 5th number, there are 1 way left to select

For the 6th number, there are 1 way left to select

=> In total, the number of possible ways to select:

N = 6 x 3 x 2 x 2 x 1 x 1 = 72

However, these numbers are located around a circle, each option is counted twice.

=> The final number of possible ways:

N = 72/2 = 36

Hope this helps!

:)

4. In parallelogram PQRS, QP is extended to point T and ST is drawn. If ST SP and
m 130°
80°
65°
50°

Answers

In parallelogram PQRS, QP is extended to point T and ST is drawn. If ST = SP and m∠R = 130°, what is m∠PST?

Answer: 80°

Step-by-step explanation:

ST = SP and m∠R = 130°

If m∠R = 130°, then,

QPS = 130° ( Opposite angles of a parallelogram are equal)

QPS + SPT = 180° (angle on a staght line)

130° + SPT = 180°

SPT = 180° - 130° = 50°

PTS = SPT = 50° (Base Angle of an isosceles triangle)

m∠PST = 180° - (50° + 50°) (sum of Angle in a triangle)

m∠PST = 80°

41 points. What is the range of this data set? 2.1, 2.6, 7.2, 5.5, 4.1, 5.5, 7.5, 6.1 A. 5.1 B. 5.5 C. 5.4 D. 7.5

Answers

Answer:

C. 5.4

Step-by-step explanation:

Range means highest number minus lowest number.

7.5 - 2.1 = 5.4

[tex]answer =5.4 \\ given \: data = 2.1 , 2.6 , 7.2 , 5.5 ,4.1 , 5.5 ,7.5 , 6.1 \\ range = highest \: score - lowest \: score \\ \: \: \: \: \: \: \: \: = \: 7.5 - 2.1 \\ \: \: \: \: \: = 5.4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

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