blue dot located on the number line?

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:

(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:

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:

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: Box A is the first 2

Box C is the 3 option

Step-by-step explanation:

Answer:

9.14 miles an hour

Step-by-step explanation:

Answer:

|x| - 5

Step-by-step explanation:

Subtracting on the outside translates vertically (down).

Answer:

1

Step-by-step explanation:

First plug in x and y:

(3)^2 - 2(3)(2) + (2)^2

Use order of operations (PEMDAS). First, evaluate the exponents:

9 - 2(3)(2) + 4

Then multiplication:

9 - 12 + 4

Then addition and subtraction, which is done from left to right:

-3 + 4

1

Answer:

[tex] {x}^{2} - 2xy + {y}^{2} \\ x = 3 \\ y = 2 \\ then \: we \: can \: written \: as \\ {3}^{2} - 2 \times 3 \times 2 + {2}^{2} \\ = 9 - 12 + 4 \\ = - 3 + 4 \\ = 1 \\ or \: in \: another \: way \\ this \: is \: the \: expansion \: of \: {(x - y)}^{2} \\ so \: put \: x = 3and \: = 2in {(x - y)}^{2} \\ then \: {(3 - 2)}^{2} \\ = {1}^{2} = 1 \\ thank \: you[/tex]

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:

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:

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:

-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

4x + 4 = 14 + 14

4x + 4 = 28

4x = 24

x = 6

Verification : 3×6 - 4 = 14

4×6+4 = 28

.........

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.

[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]

Step-by-step explanation:

(x+8) (x-5)

multiply

x×x=x

8×-5=-40

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:

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:

(a)Seven-tenth=

7divde by 10 =0.7

(b) 4 tenth

4 divide by 10=.4

(c) 2 ones

2 multiply by1 =2

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

Explanation:

The composition of the original function with its inverse will cancel out the operations to yield the input as the output.

Consider the example functions shown below

The first function adds 5 while the second function does the complete opposite and subtract 5. The two functions are inverses of each other.

We see that,

f(x) = x+5

f(g(x)) = g(x)+5

f(g(x)) = x-5+5

f(g(x)) = x

and you should find that g(f(x)) = x for similar steps.

No matter what the x input is, the output will be identical to the input.

For instance, if we plug in x = 7, then adding 5 to it gets us 12. Then undoing that operation to subtract 5 gets us back to 7 again. This is one example showing why both f(g(x)) and g(f(x)) both equal x, where f and g are inverses of each other.

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

#SPJ2

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

#SPJ7

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!

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!

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] - \frac{8}{9} \div ( - \frac{8}{9} ) \\ - \frac{8}{9} \times ( - \frac{9}{8} ) \\ = 1[/tex]

I hope I helped you^_^

Answer:

Step-by-step explanation:

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