[tex]5x- \dfrac{ \sqrt{ 9 { x }^{ 2 } -6x+1 \phantom{\tiny{!}}} }{ 1-3x }[/tex]

Answers

Answer 1

Answer:

[tex]=5x+1[/tex]          or          [tex]=5x-1[/tex]

Step-by-step explanation:

One is given the following equation:

[tex]5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]

The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation.  Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]

[tex]=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}[/tex]

Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,

[tex]=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}[/tex]

[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]

Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:

[tex]|a-b|\\=a -b[/tex]           or           [tex](-a-b) = b-a[/tex]

[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]

[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex]          or          [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]

Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,

[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex]          or          [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]

[tex]=5x-(-1)[/tex]          or          [tex]=5x-(1)[/tex]

Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.

[tex]=5x-(-1)[/tex]          or          [tex]=5x-(1)[/tex]

[tex]=5x+1[/tex]          or          [tex]=5x-1[/tex]


Related Questions

Have to finish these by the 23rd :(

Answers

Answer:

5/6

Step-by-step explanation:

x²- 3x + 7 / x + 4

when [x = 2]

Putting the value of x,

2² - 3(2) + 7 / 2 + 4

= 4 - 6 + 7 / 6

=5 / 6

x+y=4
x-2y=-5
If the first equation is multiplied by 2 and then the equations are added, the result is
=3
3 = 13
o3х=3 3

Answers

Answer:

3x = 3

Step-by-step explanation:

x + y = 4 × 2

= 2x + 2y = 8

2x + 2y = 8 + x - 2y = -5

3x = 3

If p:q=3:4 and q:r=14:9, find p:r

Answers

Answer:

7/6

Step-by-step explanation:

p=3/4*q

q=14/9*r

so p=3/4*14/9r=7/6r

PLEASE HELP! ASAP
Sarah is five years old. When she asked her father about his age, he gave her this answer. "When you are my age, I will be 67." How old is her dad?

Answers

Her dad = 36

Sarah = 5

After 31 years sarah = 36

And her dad = 67

Answered by Gauthmath must click thanks and mark brainliest

I think of a number I multiply it by 4 subtract by 6 and the divide by 5 if the answer is 10 what was the original number

Answers

Answer:

Step-by-step explanation:

(4x-6)/5 = 10

4x-6 = 50

4x = 56

x = 14

This is for geometry, please help ASAP

Answers

Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH


What are the solutions to the system of equations graphed below?

Answers

Answer:

The answer is B (4, 8) and (0, -8)

If mBAC = 90°, and mZDAC = 68°,
then mBAD = [?]

Answers

Answer:

22 degrees

Step-by-step explanation:

BAC=90 and DAC=68

DAC+BAD=BAC=90

so BAD=BAC=DAC

so BAD=90-68

= BAD=22 degrees

Answer:

The answer according to my calculations would be 22 degrees

Step-by-step explanation:

Fill in the box 22


Solve for both x and y in the parallelogram below.

Answers

Answer:

x is 14 and y is 13

Step-by-step explanation:

[tex]{ \sf{(4y - 5) = (3y + 8)}} \\ { \sf{y = 13}}[/tex]

[tex]{ \sf{(x + 12) = 2y}} \\ { \sf{x + 12 = 2(13)}} \\ { \sf{x + 12 = 26}} \\ { \sf{x = 14}}[/tex]

4y-5=3y+8( opposite sides of parallelogram are equal)

or, 4y-5-3y=8

or, 4y-3y=8+5

.•. y=13

now,

x+12=2y

x+12=2*13

x=26-12

.•. x=14

1. The sum of x and 10 is -1. Find x.​

Answers

Answer:

0 ,1cyvkdcbdfiiihh7v6ctc6e5a5ise5aasusti

If a^2+1/a^2=79 where (a>0), find the value of a^3 +1/a^3

Answers

Note the binomial expansion,

(a + 1/a)³ = a ³ + 3a + 3/a + 1/a ³

so

a ³ + 1/a ³ = (a + 1/a)³ - 3 (a + 1/a)

Similarly,

(a + 1/a)² = a ² + 2 + 1/a ²

We're given a ² + 1/a ² = 79, so

(a + 1/a)² - 2 = 79

(a + 1/a)² = 81

a + 1/a = ±9

but a > 0, so we ignore the negative solution.

Then

a ³ + 1/a ³ = 9³ - 3×9 = 702


Solve for x in the drawing above.

Answers

Answer:

x is 28°

Step-by-step explanation:

Alternate angles of parallel lines:

[tex]{ \sf{x = \frac{1}{2} \times 56 \degree }} \\ { \sf{x = 28 \degree}}[/tex]

Answer:

Hello,

28°

Step-by-step explanation:

Calculate the complementary angle of x =y

In the triangle on the right :

y+y+56°=180°

y=62°

So x=90°-62°=28°

Can someone help me with this answer?

Answers

[tex](4.2 \times {10}^{5}) \times (3.2 \times {10}^{6}) = 15.54 \times {10}^{11} = 1.554 \times {10}^{12} [/tex]

I hope I helped you ^_^

PLEASE HELPPP

Which statement correctly compares the reading speed of Danika and Kevin?

A. Each hour, Kevin reads 10 fewer pages than Danika.

B. Each hour, Kevin reads 10 pages more than Danika.

C. Each hour, Kevin reads 5 fewer pages than Danika.

D. Each hour, Kevin reads 5 pages more than Danika.​

Answers

Answer:

No.B is correct statement

What is the total surface area of the square pyramid below?
14 cm
10 cm
10 cm
O 100 cm
O 200 cm
O 280 cm?
O 380 cm?
a

Answers

Answer:

D

Step-by-step explanation:

380

Write the function for the graph.

Answers

Answer:

B)

Step-by-step explanation:

exponential function given by:

[tex] \displaystyle f(x )= a \cdot{b}^{x} [/tex]

where:

a is the y-interceptb can be any number

since the function crosses y-axis at (0,4) point

[tex]a = 4[/tex]

to find a we can consider (1,8) point it tells us when x is 1 then y is 8 thus:

[tex] \displaystyle 8= 4 \cdot{b}^{1} [/tex]

[tex] \displaystyle 8= 4 \cdot{b}^{} [/tex]

divide both sides by 4:

[tex] \displaystyle \boxed{b = 2}[/tex]

altogether substitute:

[tex] \displaystyle f(x)= 4 \cdot{2}^{x} [/tex]

hence our answer is B)

The perimeter of a rectangular park is 300 feet. The length of the park is 10 feet longer than the width.
Find the length of the park.
What is the length of the park?
feet=?​

Answers

Answer:

80 ft

Step-by-step explanation:

width = w

length = w+10

Perimeter of a rectangle

P = 2(l+w)

300 = 2(w+10+w)

300 = 2(2w+10)

Divide by 2

300/2 = 2/2(2w+10)

150 = 2w+10

Subtract 10

150-10 = 2w+10-10

140 = 2w

Divide by 2

140/2 = 2w/2

70 = w

l = w+10

l = 70+10

w = 80

Tìm x
(x+1)^2=x+1
Help me!!Pls

Answers

x^2+2x+1=x+1
x^2+2x-x+1-1=0
x^2-x=0
x(x-1)=0
x=0
x-1=0
x=1

What is the value of x in the equation 1/5x - 2/3y
=
30, when y = 15?

Answers

Answer:

x = 200

Step-by-step explanation:

Plug in 15 as y into the equation and solve for x:

1/5x - 2/3y = 30

1/5x - 2/3(15) = 30

1/5x - 10 = 30

1/5x = 40

x = 200

So, when y = 15, x = 200

Find the missing angles indicated by small letters in each of the diagram. ​

Answers

Answer:

a) X=75°

y= 105°

b) b= 120°

a=45°

d) r=75°

q=37°

p= 37°

e) y=100°

X= 143°

Step-by-step explanation:

soln no. a

here,

X+50+55=180(sum of all angle of triangle)

or, X= 180-105

or, X= 75°

again,

X+y = 180 (straight angle)

or, y= 180-75

or, y= 105°

soln no b

here,

b+60=180(straight angle)

or, b = 180 - 60

or, b = 120°

again,

a+60+75=180(sum of all angle of triangle)

or, a = 180- 135

or, a = 45°

soln no. d

here,

r=70°( alternate angle)

again,

73°+q+r=180( sum of all angle of triangle)

or,q=180-143

or,q=37°

again,

p=q=37(alternate angle)

soln no. e

y+80=180(straight angle)

or,y= 180-80

or, y = 100°

again,

63+80+<RMB=180(sum of all angles of triangle)

or, 143+<RMB=180

or, <RMB=180-143

or,<RMB= 37°

again,

X+ <RMB= 180(straight angle)

or,X= 180°-37°

or, X = 143°

Wich graph is the result of the reflection f(x) =1/4(8)^x across the y axis and then across the x- axis

Answers

Answer:

I assume that the function is:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

Now let's describe the general transformations that we need to use in this problem.

Reflection across the x-axis:

For a general function f(x), a reflection across the x-axis is written as:

g(x) = -f(x)

Reflection across the y-axis:

For a general function f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

Then a reflection across the y-axis, and then a reflection across the x-axis is just:

g(x) = -(f(-x)) = -f(-x)

In this case, we have:

[tex]f(x) = \frac{1}{4}*8^x[/tex]

then:

[tex]g(x) = -f(-x) = -\frac{1}{4}*8^{-x}[/tex]

Now we can graph this, to get the graph you can see below:

A spinner numbered 1 to 6 is spun ten times, giving the results : 2, 5, 3, 5, 1, 2, 3, 3, 4, 6. The experimental probability of getting a 2 is:

Answers

Answer:

1 / 5

Step-by-step explanation:

Given the outcome of number cube spin : 2, 5, 3, 5, 1, 2, 3, 3, 4, 6

The experimental probability of an event, A is given as :

P(A) = number of times A occurs / total number of trials

Therefore, the experimental probability of getting 2 ;

P(getting 2) = Number of times 2 occurs / total number of trials

P(getting 2) = 2 / 10 = 1/5

calculate the area of a sector with radius 13m and angle 93​

Answers

Answer:

137.16

Step-by-step explanation:

we have a formular of the area of a sector:

S= pi*(its angle)/360*R^2

so apply to it

S= pi*(93/360)*13^2=137.16

solve for x. Round to the nearesr tenth of a degree if necessary.

Answers

Answer:

im not sure but i got 30.1

Step-by-step explanation:

[tex] \cos(x) = \frac{45}{52} \\ x = 30.1[/tex]

cho tam giác ABC vuông tại A < góc B=a chứng minh: a) 1+[tex]tan^{2}[/tex]a=[tex]\frac{1}{sin^{2}a }[/tex]
làm giúp mình với

Answers

LHS:-

[tex]\\ \sf\longmapsto 1+tan^2A[/tex]

[tex]\boxed{\sf tanA=\dfrac{sinA}{cosA}}[/tex]

[tex]\\ \sf\longmapsto 1+\dfrac{sin^2A}{cos^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{cos^2A+sin^2A}{cos^2A}[/tex]

[tex]\boxed{\sf cos^2A+sin^2A=1}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{cos^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{1-sin^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{1}-\dfrac{1}{sin^2A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{sin^2A}[/tex]

Hence verified

ILL GIVE POINTS!!

Suppose a triangle has two sides of length 3 and 4 and that the angle
between these two sides is pi/3 What is the length of the third side of the
triangle?
A. sqrt13
B. 4sqrt3
C. sqrt3
D. 3

Answers

Answer:

no A

Step-by-step explanation:

sqrt13 is the ans

hope it helps

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 7 miles. Find the probability of the following events: a. The car travels more than 69 miles per gallon. Proba

Answers

Answer:

0.28386

Step-by-step explanation:

Given that :

Mean, μ = 65 miles

Standard deviation, σ = 7 miles

Probability that car travels more than 69 miles per gallon :

Recall,

Z = (x - μ) / σ ; x = 69

Z = (69 - 65) / 7 = 0.5714

The probability :

P(Z > z) = P(Z > 0.5714) = 1 - P(Z < 0.5714)

P(Z > 0.5714) = 1 - P(Z < 0.5714) = 1 - 0.71614 = 0.28386

P(Z > 0.5714) = 0.28386

Graph the relation shown in the table. Is the relation a function? Why or why not?

Answers

Answer:

what can i help u with

Step-by-step explanation:

No; the relation passes the vertical-line test. Yes; only one range value exists for each domain value

Yes; two domain values exist for range

yes; only one range value exists for each domain.

The slope of a line is -4 and Y negative intercept is -3 what is the equation of the line written in slope intercept form

Answers

Answer:

y = mx + c

m = -4

at y intercept x = 0

(x,y) =(0,-3)

-3 = -4(0) + c

c = -3

therefore the answer is y = -4x + c

8abx−10a2b+12ax2−15a2x plz regroup and factories this expression​

Answers

Answer:

2x (4a-5b)2+ 3x (3a-4b)

I hope this answer was helpfull for you

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