Mathematics College

Solve this rational equation:
Х
1
x – 4
+
=
2
x2 - 6x + 8
x – 2

Solve This Rational Equation:1x 4+=2x2 - 6x + 8x 2

Answers

Answer 1

Hey there! :)

Answer:

x = -1.

Step-by-step explanation:

[tex]\frac{1}{x-4}+ \frac{x}{x-2}= \frac{2}{x^{2}-6x+8 }[/tex]

Make each fraction have a common denominator:

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

Simplify:

[tex]\frac{x-2}{x^{2}-6x+8}+ \frac{x^{2}-4x }{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]

Disregard the denominator and solve the numerators:

x - 2 + x² - 4x = 2

Combine like terms:

x² - 3x - 2 = 2

x² - 3x - 4 = 0

Factor:

(x - 4)(x + 1)

***Only one of these solutions works because if x = 4, the denominator of the first fraction would be 0, which is undefined. Therefore, the only possible solution is x = -1.

Related Questions

1/9 − y2 when factored is:

Answers

Answer:

Step-by-step explanation:

hello

[tex]\dfrac{1}{9}-y^2=(\dfrac{1}{3})^2-y^2=(\dfrac{1}{3}-y)(\dfrac{1}{3}+y)=\dfrac{(1-3y)(1+3y)}{9}[/tex]

hope this helps

Find the distance from R to S on the graph. Round to the nearest tenth.

Answers

Answer:

7.2

Step-by-step explanation

plug the values in in the distance formula

the points are -3,3 and 1, -3

sqrt((-3-1)^2+(3-(-3))^2)

sqrt(16)+(36)

sqrt(52)

approximately 7.2

There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting at least 1 red?

Answers

Answer:

[tex]\dfrac{65}{81}[/tex] or 80.25%

Step-by-step explanation:

Number of blue Marbles = 4

Number of Red Marbles = 5

Total Number of marbles =4+5=9

[tex]P(B)=\dfrac49\\\\P(R)=\dfrac59[/tex]

In the experiment, two marbles are chosen one after the other with replacement.

The possible outcomes are: BB, BR, RB and RR

The probability of getting at least 1 red

=P(BR or RB or RR)

=P(BR)+P(RB)+P(RR)

[tex]=\left(\dfrac49\times\dfrac59\right) + \left(\dfrac59\times\dfrac49\right)+\left(\dfrac59\times\dfrac59\right)\\\\=\dfrac{20}{81}+\dfrac{20}{81}+\dfrac{25}{81}\\\\=\dfrac{65}{81}[/tex]

Expressed as a percentage, we have:

[tex]\dfrac{65}{81}\times100=80.25\%[/tex]

The probability of getting at least 1 red is 80.25%.

find the gradient of the line segment between the points N(-1,2) and M(-6,3)​

Answers

Answer:

1/5

Step-by-step explanation:

Gradient is another word for slope. To find the gradient, we have to use a formula.

Which is greater 36÷(4×3) or 54-48-(16÷4

Answers

Step-by-step explanation:

36 ÷ (4 x 3)

36 ÷ 12

= 3

54 - 48 - (16 ÷ 4)

54 - 48 - 4

= 2

So first one is greater

What is if we divide 8 by 4 multiply by 6 and add 2 then subtract 2 what is the result?

Answers

Answer:

its its 12.

Step-by-step explanation:

=8÷4×6+2-2

=2×6+2-2

=12+2-2

=14-2

=12 is answer..

Answer:

12

Step-by-step explanation:

8÷4×6+2-2

=2×6+2-2

=12+2-2

14-2

=12

how many are 4 x 4 ?​

Answers

16
4+4=8
4+4=8
8+8= 16

The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12π cubic inches 36π cubic inches 64π cubic inches 81π cubic inches

Answers

Answer:

36pi

Step-by-step explanation:

Answer:

36pi

Step-by-step explanation:

i got it right on my test

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.
Coefficients Standard Error
Constant 12.924 4.425
x1 -3.682 2.630
x2 45.216 12.560
Analysis of Variance
Source of Degrees of Sum of Mean
Variation Freedom Squares Square F
Regression 4853 2426.5
Error 485.3
We want to test whether the variable x1 is significant. The critical value obtained from ttable at the 1% level is:_______.
1. ±2.650.
2. ±2.921.
3. ± 2.977.
4. ± 3.012.

Answers

Answer:

4. ± 3.012

Step-by-step explanation:

Hello!

Assuming that for both variables X₁ and X₂ n₁= n₂ = 16

You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.

The hypotheses are:

H₀: β₁= 0

H₁: β₁≠ 0

α: 0.01

[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]

The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"

The rejection region for this test is two-tailed, the critical values are:

±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]

I hope this helps!

WILL GIVE BRAINLIEST TO ANSWER:)) <33
Q: A committee of six people is to be formed from a pool of six grade 11 students and seven grade 12 students. Determine the probability that the committee will have two grade 11 students.

Answers

Answer: 5/26

Step-by-step explanation: 6/13 x 5/12

4) A large number of people were polled and asked which of four different animals were their
favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you
decide to carry out a simulation given these percentages. You decide to select two digits at a
time. Which would be a proper assignment of digits for these teams?
a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtle
b) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtle
c) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtle
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
e) None of these

Answers

Answer:

d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle

Step-by-step explanation:

13 − 01 + 1 = 13

34 − 14 + 1 = 21

56 − 35 + 1 = 22

99 − 57 + 1 + 1 = 44

If two chords in a circle are congruent, then they are
_____

Answers

Answer:

A

Step-by-step explanation:

Two congruent chords in a circle have the same distance from the center.

If two chords in a circle are congruent, then they are the same distance from the center of the circle .

What are the properties of equal chords of a circle?

The properties of Equal Chords of a Circle are:

In a circle equal-chords are equidistant from the center.Equal-chords of congruent circles are equidistant from the corresponding centers.In a circle equal chords subtend equal angles at the center.  

According to the question

If two chords in a circle are congruent, then they are

Now,

By properties of Equal Chords of a Circle

The equal chords will be equal distance from the center of the circle .

Hence, If two chords in a circle are congruent, then they are the same distance from the center of the circle .

To know more about  properties of equal chords of a circle here:

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Suppose that 3 is a factor of a, a is a divisor of 12, and a is positive. What is the number of possible values of a?

Answers

Answer: the number of possible values of a are 3 and 6

Explanation:
Since a is a divisor of 12
Then let’s see what are the divisor for 12
12= 6 x 2
12= 3 x 4
And we know that 3 is a factor of a
So if a was 3 then 3/3 is exactly 1
And if a was 6 then 6/3 is exactly 2 with no remainder

And 3 and 6 are also the divisor of 12
12/6=2
12/3=4
So a should be 3 and 6

Answer:

3

Step-by-step explanation:

12 is divisible by: 1, 2, 3, 4, 6, 12

Because 3 is a factor of a, that means 3 multiplied by another number equals a. Additionally, a is a divisor of 12, meaning a multiplied by another number equals 12.

Out of the numbers, 12 is divisible by, only 3 are also divisible by 3: 3, 6, 12 This gives three possible values of a.

Please help ASAP thanks in advance

Answers

Answer:

P(0,4)

Q(2,0)

Step-by-step explanation:

We khow that both P and Q are lying in the line : 4x+2y=8

4x+2y=82y = -4x+8y= -2x+4 P(0,y) ⇒y= -2*0+4=4 ⇒ P(0,4) Q(x,0)⇒ 0=-2*x+4 ⇒ x= 2⇒ Q(2,0)

A client would like a logo printed onto a canvas that is at least 70 inches tall. The original logo is 4.5 inches wide by 3.6 inches tall. Which dimensions will keep the logo in proportion and large enough to meet the client's requirements?

Answers

Answer:

to find the dimension I would get 3.6/4.5=x/70 amd u get 3.6*70=4.5x and u get 252=4.5x and x=56

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the width of logo printed on canvas = x inches

Dimensions are in proportion

[tex]\frac{70}{x}=\frac{3.6}{4.5}\\[/tex]

Cross multiply

70 * 4.5 = x * 3.6

x * 3.6 = 315

[tex]x=\frac{315}{3.6}\\\\=\frac{3150}{36}\\\\x=87.5inches[/tex]

Find the length of AB. Leave

your answer in terms of 7.

A

20° AB = [ ? ]

27

1B

Enter

Answers

Answer:

AB = 3π

Step-by-step explanation:

See attachment for correct format of question.

Given

From the attachment, we have that

θ = 20°

Radius, r = 27

Required

Find length of AB

AB is an arc and it's length can be calculated using arc length formula.

[tex]Length = \frac{\theta}{360} * 2\pi r[/tex]

Substitute 20 for θ and 27 for r

[tex]Length = \frac{20}{360} * 2\pi *27[/tex]

[tex]Length = \frac{20 * 2\pi * 27}{360}[/tex]

[tex]Length = \frac{1080 \pi}{360}[/tex]

[tex]Length = 3\pi[/tex]

Hence, the length of arc AB is terms of π is 3π

Solve this correctly for brainliest !!!!!! 3(7) + 2 • |7 - 8| - 12

Answers

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

20 pts! If Quadrilateral J K L M is congruent to quadrilateral C B D A, which pair of sides must be congruent? Segment J K and Segment A B Segment J K and Segment C B Segment J M and Segment A D Segment J M and Segment B C

Answers

Answer:

segment I'm and segment ad

Answer:

The answer is B

Step-by-step explanation:

Sean has some candy bars that he wants to give away. He is going to give each person 1/18 of a bar, and he has 2 3/4 to give away How many people will get candy? PLS HELP MEEE

Answers

Answer:

49 people

Step-by-step explanation:

Take the amount of candy and divide by the amount in a serving

2 3/4 ÷ 1/18

Change to an improper fraction

(4*2+3)/4 ÷ 1 /18

11/4 ÷ 1/18

Copy dot flip

11/4 * 18/1

198/4

49.5

Round down since people do not want half a serving

49 people

Answer: 2 29/36

Step-by-step explanation:

A is any nonnegative real number and b is a square root of that number. Is a a function of b, b a function of a, both, or neither?

Answers

Answer:

B is a function of A

Step-by-step explanation:

If you do something to another thing, it is a function of that.

The regular price of a baseball cleats is $80. If the cleats are on sale for 45% off. then: (how to solve this two questions?) a) What is the value of the discount, in dollars? b) What is the final selling price of the cleats, before tax?​

Answers

Answer:

The discount is 36 dollars

The sale price is 44 dollars

Step-by-step explanation:

First find the discount by multiplying the original price by the discount rate

80*45%

Change to decimal form

80*.45

36

The discount is 36 dollars

The sale price is the original price minus the discount

80-36

44

The sale price is 44 dollars

Factor completely 2x⁴y³-12x³y²-8x²y

Answers

This is what I got, hope this helped:)

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 118. ​(a) Determine the 30th percentile for the number of chocolate chips in a bag. ​(b) Determine the number of chocolate chips in a bag that make up the middle 98​% of bags. ​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

Answers

Answer:

(A) 1199.168

(B) 1503.372

(C) 159.17728

Step-by-step explanation:

(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.

Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524

The formula for finding X (the number of items in a given percentile) is:

X = M + Z(S.D.)

Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.

So for the 30th percentile,

X = 1261 + (-0.524)(118)

X = 1261 - 61.832 = 1199.168

(B) The number of chocolate chips that make up the middle 98% of chips in the bag is

X = 1261 + (2.054)(118)

X = 1261 + 242.372 = 1503.372

(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.

This is within 1.34896 standard deviations of the mean.

IQR = (1.34896)(118)

IQR = 159.17728

0.3y+ z y ​ 0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.

Answers

Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  [tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]

If y = x2 + 2x , find the value of y when x = 3
and
If y = x3 - 3 , find the value of y when x = 2 plsss help me

Answers

Answer:

y=15; y=5

Step-by-step explanation:

y=x2+2x

plug in x as 3:

y=3 2+ 2*3

y=9+6

y=15

Next problem:

y=x3-3

plug in x as 2:

y=2 3-3

y=8-3

y=5

BÉ is an angle bisector of ZABC.
If mŁABE = 2x + 20 and mZEBC = 4x - 6,
determine the value of x.
B.
x = [? ]

Answers

angle bisector makes the two split parts equal to each other:
2x+20=4x-6
2x+26=4x
26=2x
x=13

what is 3 + 3 × 3 + 3 =​

Answers

Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

Learn more about BODMAS rule here:

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ASAP will give brainliest Which of the following formulas would find the surface area of a right cylinder where h is the height, r is the radius, LA is the lateral area, and BA is the base area?

Answers

Answer:

A. BA + 2πrh

C. 2πr² + 2πrh

Step-by-step explanation:

height of cylinder = h

Radius of cylinder = r

=>Lateral area of cylinder = LA (THis is the area of the cylinder excluding the area of its circular bases)

L.A of a cylinder = 2πrh

=>Base area = BA (this is the area of both circular bases of the cylinder)

Area of circle = πr²

Area of the 2 circular bases of the cylinder (BA) = 2(πr²) = 2πr²

=>Surface area of a right cylinder = B.A + L.A

= 2πr² + 2πrh

The formulas that can be used to find surface area of a right cylinder from the given options are:

A. BA + 2πrh (note: BA = 2πr², LA = 2πrh)

C. 2πr² + 2πrh

y = 0.8x+ 7.2
20x + 32y = 48

Answers

Step-by-step explanation:

y = 0.8x+ 7.2   ..........(1)

20x + 32y = 48 .........(2)

Substitute (1) in (2)

20x +32*(0.8x+7.2) = 48     expand

20x + 25.6x+230.4 = 48     add

45.6x+230.4 = 48                transpose and simplify

45.6x = 48-230.4 = -182.4

x = -182.4 / 45.6

x = -4

Answer:

x=-4, Y=4

Step-by-step explanation:

20x+32(0.8x+7.2)=48

45.6x =48-230.4

x=-4

substitute x=-4 in y eqn

y=-3.2+7.2

y=4

Determine f(-1) (3). Use the following table of values

Answers

Answer:

  -5

Step-by-step explanation:

The value of x that gives f(x) = 3 is -5.

  [tex]f^{-1}(3)=-5[/tex]

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