-4n - 8 = 4 (-3n + 2)

what is n?

Answer:

b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex]

Step-by-step explanation:

Given

6b² + 12b - 14 = 0 ( add 14 to both sides )

6b² + 12b = 14

To complete the square the coefficient of the b² term must be 1

Factor out 6 from the 2 terms on the left side

6(b² + 2b) = 14

To complete the square

add/subtract ( half the coefficient of the b- term)² to b² + 2b

6(b² + 2(1)b + 1 - 1) = 14

6(b + 1)² + 6(- 1) = 14

6(b + 1)² - 6 = 14 ( add 6 to both sides )

6(b + 1)² = 20 ( divide both sides by 6 )

(b + 1)² = [tex]\frac{20}{6}[/tex] = [tex]\frac{10}{3}[/tex] ( take the square root of both sides )

b + 1 = ± [tex]\sqrt{\frac{10}{3} }[/tex] ( subtract 1 from both sides )

b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex] ← exact solution

Answer:

x = -1 ± √(10/3) = (-3 ± √30)/3

Step-by-step explanation:

Steps to complete this process:

ax² + bx + c = 0

=> (ax² + bx + c)/a = 0/a

=> x² + (b/a)x + (c/a) = 0

=> x² + 2x(b/2a) + (c/a) = 0

Now it seems somewhat like a square (x² + 2x(b/2a), in order to complete:

=> x² + 2(b/2a) + (b/2a)² + (c/a) = (b/2a)²

=> (x + b/2a)² + (c/a) = b²/4a²

=> (x + b/2a)² = (b² - 4ac)/4a²

So on & you can derive quadratic formula.

In the given question:

=> 6b² + 12b - 14 = 0

=> (6b² + 12b - 14)/6 = 0/6

=> b² + 2b - 7/3 = 0

=> b² + 2(1)b + 1² - (7/3) = 1²

=> (b + 1)² - (7/3) = 1

=> (b + 1)² = 10/3 or 30/9

=> b + 1 = ±√(30/9)

=> b = -1 ± √(30)/3

=> b = (-3 ± √30)/3

*this is the rationalized form(rational-denominator), exact answer:

=> (b + 1)² - (7/3) = 1

=> (b + 1) = ± √(10/3)

=> b = -1 ± √(10/3)

You can take LCM, and even rationalize it to (-3 ± √30)/3.

Answer:

7.2 cm

Step-by-step explanation:

The adjacent interior angles of a rhombus must be supplementary.

Let ABCD be the rhombus whose area is 40 cm².

Let the diagonals AC and BD intersect at O.

If s is the side, one-half diagonal = s× sin(25) and the other is s× sin(65) = s × cos(25)

Area of a rhombus = ½× (a×b)²× sin(ø)]

side length, a = b

Area of rhombus = ½× s² × sin(25)cos(25)

40 cm² = ½ × s² × sin(25)cos(25)

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)]

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°sin(a)cos(b) = 2[sin(x+y)]

》40 cm² = ½ × s² × 2sin(50)

》40 cm² = s² × sin(50)

[tex] {s}^{2} = \frac{40}{ \sin(50) } \\ s = \sqrt{ \frac{40}{ \sin(50) } } [/tex]

s = 7.2260841106 cm

Therefore, the length of the side of a rhombus, s is 7.2 cm

Answer:

Option A.

Step-by-step explanation:

An absolute value function can be written in two ways, as the absolute value sign does not allow negative values.

[tex]|x-5|=x-5[/tex]

or

[tex]|x-5|=-(x-5)=-x+5[/tex]

The only options with these equations are A. and D.

D. can be eliminated as the inequalities given for the piecewise function do not match f(x)

To see it visually, you can try graphing it on a calculator or internet graphing service.

Answer:

2

Step-by-step explanation:

The example of speed and time is a basic and appropriate example of inversely proportional. As the speed increases, the time to complete your trip will decrease

Answer:

x = 74.89

Step-by-step explanation:

Because this is a right triangle we can use trigonometric ratios to solve for x

Remember the three main trig ratios are sine, cosine and tangent

Where

Sine = Opposite over Hypotenuse

Cosine = Adjacent over Hypotenuse

and Tangent = Opposite over Adjacent

In order to use trig ratios we must have a known angle that is not a right angle.

We are given ∠J which has a measure of 27°

We are also given ∠J's opposite side length. ( has a length of 34 )

and "x" is the hypotenuse.

When dealing with opposite and hypotenuse we use Sine

SineФ = Opposite over Hypotenuse

Ф = 27, opposite = 34 and hypotenuse = x

Sin(27)  = 34/x

solve for x

Multiply both side by x

sin(27) x = 34

divide both sides by sin (27)

x = 34 / sin (27)

simplify

x = 74.89 ( rounded to the nearest hundredth )

and we are done!

Answer:

The answer is 74.89

Step-by-step explanation:

Well it gives you 2 angles and one side length using the formula Called SAS you can find the missing lengths and side x = 74.891 while the other side equals 66.729. Hope this helps

Answer:

[tex]5x + \frac{1}{3} (3x + 6) > 14 \\ lcm = 3 \\ \\ (3 \times 5x) + 3 \times \frac{1}{3} (3x + 6) > 14 \times 3 \\ \\ 15x + 3x + 6 > 42 \\ 18x + 6 > 42 \\ 18x > 42 - 6 \\ 18x > 36 \\ x > 2[/tex]

Answer is below

x > 2

How I did it

What I first did was divide 3x + 6 by 3 because when you multiply by 1/3 it's basically just dividing by 3.

5x+x+2>14

Simplify

6x+2>14

Subtract 2 on both sides

6x>12

Since you want to get x by itself you divide both sides by 6, singling out x

x>2

Hope this helps!

Step-by-step explanation:

(x+8) (x-5)

multiply

x×x=x

8×-5=-40

Answer:

Im not certain but I think 7.5% If you get another answer which is different trust them not me if u get one which is the same it should be correct

The interest rate was 7.5% when borrowing $600 for one year and paying $45.00 interest.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

We have been given data as:

Principal (P) = $600

Time (T) = 1 year

Simple interest = $45.00

⇒ Simple interest = P × R × T

Substitute the value of P, and T in the above formula, and solve for R

⇒ 45.00 = 600 × R × 1

⇒ 45.00 = 600R

⇒ R = 45.00/600

⇒ R = 0.075

⇒ R = 7.5/100

⇒ R = 7.5%

Therefore, the interest rate was 7.5%.

Learn more about the simple interest here:

brainly.com/question/22621039

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Answer:

2×10⁵ is the same as 200,000 and 3×10⁴ is the same as 30000 so this simply means you have to multiply the 2 figures and give the answer in standard form

200,000×30000

6000000000

which will be written as

6×10⁹

I hope this helps

Answer:

(0,2)

Step-by-step explanation:

Hi there!

[tex]f(x) = 2*3^x[/tex]

The y-intercept of any function occurs when x=0.

To find the y-intercept, solve for f(0):

[tex]f(0) = 2*3^0\\f(0) = 2*1\\f(0) = 2[/tex]

Therefore, the y-intercept is 2 and occurs at (0,2).

I hope this helps!

Answer:

Step-by-step explanation:

Use the identity for the sum of squares of n natural numbers:

Since we have the sum, 56980:

Solve the equation graphically to get a natural solution of n = 55

Answer:

(a)Seven-tenth=

7divde by 10 =0.7

(b) 4 tenth

4 divide by 10=.4

(c) 2 ones

2 multiply by1 =2

Answer:

TR = 23

Step-by-step explanation:

first we have to find TS, so we subtract 16 from 4 to get 12. then we can add 12 and 11 to get TR

Answer:

|x| - 5

Step-by-step explanation:

Subtracting on the outside translates vertically (down).

4x + 4 = 14 + 14

4x + 4 = 28

4x = 24

x = 6

Verification : 3×6 - 4 = 14

4×6+4 = 28

.........

Answer:

√17

Step-by-step explanation:

Since it's a square, the area will simply be the side length squared. Therefore, we can take the square root of 17 to get the exact length. Since 17 is a prime number, it cannot be simplified any further.

Answer:

[tex](x + 2) \: \: and \: \: (x-6)[/tex]

Step-by-step explanation:

[tex] {x}^{2} −14−12 \\ = {x}^{2} + 2x - 6x - 12 \\ = x(x + 2) - 6(x + 2) \\ = (x + 2)(x - 6)[/tex]

(x + 2) and (x-6) are the side lengths which should be used to model the rectangle.

The area of Rectangle is length times of width.

Given that  rectangle with an area of x² - 4x - 12 square units.

We have to find the side lengths which should be used to model the

rectangle.

x² - 4x - 12

x square minus four times of x minus twelve.

x² -6x+2x-12

Now factorize the given expression.

x(x-6)+2(x-6)

(x+2)(x-6)

Hence, (x + 2) and (x-6) are the side lengths which should be used to model the rectangle.

To learn more on Rectangle click:

https://brainly.com/question/20693059

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[tex]Hello[/tex] [tex]There![/tex]

The answer is...

A. f (-1) = 6.

C. The domain for (x) is the set (-2, -1, 0, 1, 2, 3, 4, 5, 6).

Hopefully, this helps you!!

[tex]JesusLoveMeAlways[/tex]

:)

[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sinF=\dfrac{GE}{FG}[/tex]

[tex]\\ \rm\Rrightarrow sinF=\dfrac{a}{c}[/tex]

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

-7 + 5 = -2

Step-by-step explanation:

-7 + 5 = -2 is the correct equation as you can see it ended on -2 so in this equation also it's -2

Answer:

Step-by-step explanation:

cos(2a) = cos^2(a) - sin^2(a)

cos(2a) = 2cos^(a) - 1

cos(2a) = 11/25

11/25 = 2 cos^(a) - 1             Add 1 to both sides

1 + 11/25 = 2 cos^2

25/25 + 11/25 = 2 cos^2(a)

36/25 = 2 cos^2 (a)            Divide by 2

36/50 = cos^2 (a)               Take the square root of both sides.

6/5*sqrt(2) = cos(a)            

One is given the following:

One is asked to prove the following:

In order to prove the statement above, one will need to use a trigonometric identity. In this case, the following identity is the most relevant in the proof.

[tex]cos(2a)=2cos^2(A)-1[/tex]

One can manipulate this identity to suit the needs of the given problem:

[tex]cos(2a)=2cos^2(A)-1[/tex]

[tex]cos(2a)+1=2cos^2(A)[/tex]

[tex]\frac{cos(2a)+1}{2}=cos^2(A)[/tex]

[tex]\sqrt{\frac{cos(2a)+1}{2}}=cos(A)[/tex]

Now substitute the given information into this identity,

[tex]cos(2A)=\frac{11}{25}[/tex]

[tex]\sqrt{\frac{cos(2a)+1}{2}}=cos(A)[/tex]

Substitute,

[tex]\sqrt{\frac{\frac{11}{25}+1}{2}}=cos(A)[/tex]

Simplify, remember, any number over itself equals (1) and, in order to add two fractions, they must have the same denominator.

[tex]\sqrt{\frac{\frac{11}{25}+1}{2}}=cos(A)[/tex]

[tex]\sqrt{\frac{\frac{11}{25}+\frac{25}{25}}{2}}=cos(A)[/tex]

[tex]\sqrt{\frac{\frac{36}{25}}{2}}=cos(A)[/tex]

[tex]\sqrt{\frac{18}{25}}=cos(A)[/tex]

[tex]\frac{3\sqrt{2}}{5}=cos(A)[/tex]

Manipulate so that it resembles the given information; remember, any number over itself is (1), multiplying an equation by (1) doesn't change it,

[tex]\frac{3\sqrt{2}}{5}=cos(A)[/tex]

[tex]\frac{3\sqrt{2}}{5}*\frac{\sqrt{2}}{\sqrt{2}}=cos(A)[/tex]

[tex]\frac{3\sqrt{2*2}}{5*\sqrt{2}}=cos(A)[/tex]

[tex]\frac{6}{5\sqrt{2}}=cos(A)[/tex]

Answer:

Step-by-step explanation:

Please Upload clear image

Answer:

(2.5,-3)

Step-by-step explanation:

midpoint = (x', y')

x' = (x1 + x2)/2

y' = (y1 + y2)/2

x1=0

x2=5

y1=0

y2=-6

solution

(0+5)/2 =2.5---->x'

(0+(-6))/2 = -3--->y'

Answer: Box A is the first 2

Box C is the 3 option

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

3    9

8    

9 times 8

divided by 3 = denominator

9x8÷3=24

Answer:

[tex]\frac{9}{24}[/tex]

Step-by-step explanation:

Skills needed: Identify numerator, Multiplying to change fraction

1) First, we need to know what the numerator is. The numerator is the upper number of the fraction, which is separated by the fraction bar FROM the denominator (the bottom part of the fraction).

2) What we need to do here is rewrite the fraction [tex]\frac{3}{8}[/tex] so that the numerator is 9. Let's look at it in another way:

[tex]\frac{3}{8} * \frac{x}{x} = \frac{9}{z}[/tex] (The reason it is [tex]\frac{x}{x}[/tex] is because we want to multiply the original fraction/ratio by 1 so that we do not change it).

3) Now we know that [tex]3 * x=9[/tex], and if we divide both sides by 3, we get:

[tex]x=3[/tex].

This means it would be:

[tex]\frac{3}{8} * \frac{3}{3} = \frac{9}{z}[/tex]

Now we need to find [tex]z[/tex]. [tex]z=8*3 = 24[/tex]. [tex]z=24[/tex].

The numerator of our fraction would be 9, and the denominator is 24, making our answer: [tex]\frac{9}{24}[/tex].

Hope you understood and have a nice day!! :D (If you have any questions, please comment, and I can try to help!)

Answer:

365.891, 365.892, 365.893, 365.894, 365.895, 365.896

Step-by-step explanation:

Since we want 6 numbers between 365.89 and 365.91, we can add the ten-thousandths digit and count up from there.

Answer:

28minutes

Step-by-step explanation:

Use this simple trick, it can be used almost everywhere

Time taken pieces

20mins 5

? 7

An x shape is always multiply and straight line is divide

So (7 x 20) ÷5

If u still don't understand, just comment again

Answer:

Step-by-step explanation:

No that is incorrect 28 is not the answer:

1. 4 cuts every 20 mins it would take one cut every 5 mins. You only need one more cut because 6 cuts make 7 pieces. If you draw it.

1/5= 6/30 so 30 mins!