if 3^x = 1, find the value of x.​

[tex] \sf \underline{ \red{Solution - }} \\ [/tex]

Given,

[tex] \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\ [/tex]

The denominator is √11 - √5.

We know that

Rationalising factor of √a-√b is √a+√b.

Therefore, the rationalising factor of √11-√5 is √11+√5.

On rationalising the denominator them

[tex] \longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Multiplying (√11 + √5) with both the numerator of the fraction.

[tex] \longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Performing multiplication in the numerator and by using identity (a + b)(a - b) = a² - b², solving further in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\ [/tex]

Writing the squares of the numbers in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\ [/tex]

Performing subtraction in the denominator.

[tex] \longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\ [/tex]

Hence, the denominator is rationalised.

Answer:

Step-by-step explanation:

[tex]y =\dfrac{-3}{4}x -6[/tex]

Multiply the entire equation by 4,

[tex]4*y=\dfrac{-3}{4}x*4 - 6*4\\[/tex]

4y = -3x - 24

Add 3x to both sides

3x + 4y = -24

Add 24 to both sides

3x + 4y + 24 = 0

Answer:

c or d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Slope- intercept form:

In the process of solving it was found that:

The equation therefore is:

Correct choice is D

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Hello haohaoxNienie!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

Show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

[tex] \huge \boxed{\mathfrak{Explanation} \downarrow}[/tex]

To show that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1, we must divide the polynomial by x - 1. If we get the remainder as 0, then we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

So, let's do the division (steps in the attached picture).

__________________

We got the remainder as 0. So, yes p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

x² - 5x + 6

= (x - 3) (x - 2) [use the splitting the middle term method].

So, the zeroes are,

(x - 3)

x - 3 = 0

x = 3 ⇨ 1st zero.

(x - 2)

x - 2 = 0

x = 2 ⇨ 2nd zero.

Now, use the values of x on the equation. If we get 0 as the solution of the equation then we can prove that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

p(x) = x³ - 6x² + 11x - 6

p(3) = 3³ - 6(3)² + 11 (3) - 6

p(3) = 27 - 54 + 33 - 6

p(3) = 0.

p(x) = x³ - 6x² + 11x - 6

p(2) = 2³ - 6(2)² + 11 (2) - 6

p(2) = 8 - 24 + 22 - 6

p(2) = 0

Since we got the solutions as 0 we can say that p(x) = x³ - 6x² + 11x - 6 is divisible by x - 1.

__________________

Hope it'll help you!

ℓu¢αzz ッ

Answer:

the slope is y2 - y1 over

x2 - x1

which means

[tex]( - 3- 2) = - 5[/tex]

[tex](4 - 2) = 2[/tex]

slope is m= -5/2

then you take a y from the first set of points for b

[tex]y = - \frac{5}{2} x \times 2[/tex]

hope it helps.

Answer:

x = 14

Step-by-step explanation:

So because the sides are equal, that means that the angles are equal.

5x = 3x + 28

Step 1.) Subtract 3x from 5x which leaves you with 2x.

2x = 28

Step 2.) Divide 28 by 2, to get the variable on its own. This leaves you with 14

x = 14

Answer:

Sale kute bhan के lole

Tera baap aya ajju(^bhai 94

Answer:

P of rectangle = 2(L + W)

21 units = 2(n units + W)

21 units = 2nunits + 2W

21 = 2n + 2W

2W = 21 - 2n

W = 21 - 2n units.

2

on simplifying

10.5 - n units

The width of the rectangle is units (10.5 - n) units.

Answer:

= 10 tickets

Step-by-step explanation:

= 20% × 50

= 20/100 × 50

= 1000/100

= 10

Answer:

No; the absolute value of a negative number is equal to its opposite

Step-by-step explanation:

Answer:

greater than because 10 is further to the right on a numberline than 5

Step-by-step explanation:

Answer:

x ≥ 18

Step-by-step explanation:

Given the inequality statement, 2/3x + 17 ≥ 29,

Subtract both sides by 17:

2/3x + 17 - 17 ≥ 29 - 17

2/3x  ≥ 12

Multiply both sides by 3/2 to isolate x:

[tex](\frac{3}{2}) \frac{2}{3}x \geq 12 (\frac{3}{2})[/tex]

x ≥ 18

Answer:

[tex]x = 67[/tex]

Step-by-step explanation:

[tex]x = 67[/tex]

[tex]Alternate \:Intrerior \: Angles[/tex]

Answer:

28/15

Step-by-step explanation:

have a wonderful day :)

Answer:

1 13/15

Step-by-step explanation:

7/10 ÷ 3/8

Copy dot flip

7/10 * 8/3

Rewrite

7/3 * 8/10

Simplify

7/3 * 4/5

Multiply

28/15

Change to a mixed number

15 goes into 28 1 time with 13 left over

1 13/15

Answer:

60 DEG

Step-by-step explanation:

Angle on a straight line = 180 DEG

Equation:

4x + 2x + 90 DEG = 180 DEG

6x = 90 DEG

x = 15 DEG

Therefore,

angle LMN = 15 * 4 = 60 DEG

Answer:

33x + 55y

Step-by-step explanation:

1. To simplify this expression, we have to apply the distributive property. To utilize this property means to distribute (or multiply) the quantity outside the parentheses by the quantities inside the parentheses.

Therefore, the answer is 33x + 55y.

Answer:

Step-by-step explanation:

74*5 = 370

370 - 65 - 70 -70 -80 = 85

So. you need to get 85 on your fifth test.

Answer:

2.4hrs or 2hrs 24 minutes

Step-by-step explanation:

3/5 × 4/1 = 12/5

60÷5=12

12×12=144

144÷60=2.4hrs

2√5 exact form

4.47213595 decimal form

Step-by-step explanation:

y = 3x - 6

the slope of a line is always the factor of x in the equation. in our case here : 3 = 3/1.

the slope is the y/x ratio indicating how many units y changes, when x changes by a certain amount of units (e.g. when going from one point on the line to another).

the perpendicular slope (crosses the original line in a right angle = 90 degrees) turns x and y upside-down and flips the sign.

so, in our case, it is -1/3.

the equation for the perpendicular line looks like this then :

y = (-1/3)×x + b

to get b we use the provided point and it's x and y values.

6 = (-1/3)×-3 + b = 1 + b

b = 5

so, the full equation of the perpendicular line is

y = (-1/3)×x + 5

Answer:

he got 5000 rands for it

Step-by-step explanation:

you multiply it

500 x 10 = 5000

Answer:

simple ( principal *rate*time)/100.

3500*4*10/100 = 1400 interest

account balance =3500+1400=4900

compound p(1+r)^t

3500(1+.04)^10 =3500* 1.480=5180

interest earned = 5180-3500= 1680

how much more interest. ; 1680-1400=280

Answer:

Step-by-step explanation:

Simple Interest:

Simple Interest formula is S.I. = P × r × t

Interest Eared: $3,500 × 0.04 × 10 = $1,400

Account Balance formula is A = P ( 1 + rt )

Account Balance: $3,500 + $1,400 = $4,900

Compound Interest:

Compound Interest formula: [tex]A =P(1+r)^{t}[/tex]

Account balance: $5,180.85

Interest Earned: $5,180.85 - 3,500.00 = $1,680.85

Answer:

Ummm..... I would think 10??

Step-by-step explanation:

I don't really know tho.....

Answer:

10

Step-by-step explanation:

4x = 40

/4       /4

x = 10

Answer:

The slope is (4)  which means that the temperature (increases)  by (4) degrees every minute

Step-by-step explanation:

Answer:

5/12 is your answer

=^-^=

Answer:

C. 1.2009

Step-by-step explanation:

1.3240 + 1.4872 = 2.8112

4.0121 - 2.8112 = 1.2009 - C

Answer:

Your answer is   -14k - 14   or     k = -1

Step-by-step explanation:

-17k - 35 + 3k + 21   ( Combine like terms )

-14k - 14

-14k = 14

k = -1

Hope this helps!

Answer:

155.25

Step-by-step explanation:

Answer:

155.25

Step-by-step explanation:

Since 45% is equal to 0.45, simply multiply 0.45 x 345 and youll get 155.25