(x2 + 4)(x2 - 4) please help

Answer:

[tex]\large\boxed{x=-\dfrac{1}{11}}[/tex]

Step-by-step explanation:

[tex]34x+5-12x=3\qquad\text{subtraxct 5 from both sides}\\\\34x-12x=3-5\\\\22x=-2\qquad\text{divide both sides by 22}\\\\x=\dfrac{-2}{22}\\\\x=-\dfrac{2:2}{22:2}\\\\x=-\dfrac{1}{11}[/tex]

To solve the equation 34x+5−12x=3, we combine like terms to get 22x+5=3, then isolate x to find that x=-1/11.

The student's question, 34x+5−12x=3, presents a linear equation where we need to find the value of x.

To solve for x, we shall first consolidate like terms on the left side of the equation.

We have:

34x - 12x + 5 = 3

22x + 5 = 3

22x = 3 - 5

22x = -2

x = -2/22

x = -1/11

The value of x in this equation is -1/11.

Answer: 90°

Step-by-step explanation:

The two arcs made by the angle will add up to twice the value of the angle in degrees

89 * 2 = 178

178 - 88 = 90

a. Your answer and reasoning are correct.

b. If O is the center of the circle, then angle ABO has measure 72º, so that by the law of cosines

[tex]AB^2=6^2+6^2-2\cdot6\cdot6\cos72^\circ\implies AB=3\sqrt{10-2\sqrt5}[/tex]

just to add to the superb reply above by @LammettHash

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=6\\ \theta =72 \end{cases}\implies s=\cfrac{\pi (72)(6)}{180}\implies s=\cfrac{12\pi }{5}\implies s\approx 7.54[/tex]

Answer: Congruent

Step-by-step explanation:

Congruent describes the shapes below that are the same shape but not the same size.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

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Answer:

B. 24

Step-by-step explanation:

it takes 60 minutes for one and 40 for another. since you don't know the time. the denominator is going to be x. The equation to solve this problem will be x/60 + x/40 = 1. Since you're adding, you want to have the same denominator. ( i chose to do 120) this will change the problem to 2x/120 + 3x/120 = 1. which will simplify to 5x/120=1. Multiply each side by 120 to get 5x=120 and divide each side by 5 to get x=24.

Answer:

a) The equation to find the elevation of Mt. Wilson is [tex]28,784.31=x+11,510.21[/tex]  

b) The elevation of Mt. Wilson is [tex]17,274.10\ ft[/tex]  

Step-by-step explanation:

Let

x ----> represent the elevation of Mt. Wilson

y ----> represent the elevation of Snow Crest

we know that

[tex]y=x+11,510.21[/tex] ----> equation A

we have

[tex]y=28,784.31\ ft[/tex]

Substitute the value of y in equation A and solve for x

[tex]28,784.31=x+11,510.21[/tex]  

[tex]x=28,784.31-11,510.21[/tex]

[tex]x=17,274.10\ ft[/tex]  

The elevation of Mt. Wilson is 17,274.1 feet.

To find the elevation of Mt. Wilson, you can set up an equation based on the information given. You're told that Snow Crest is 11,510.21 feet higher than Mt. Wilson, so you can write the equation as follows:

Elevation of Snow Crest = Elevation of Mt. Wilson + 11,510.21

Now, you can plug in the elevations you have:

Elevation of Snow Crest = 28,784.31 feet

Elevation of Mt. Wilson = x (since you're using x to represent the elevation of Mt. Wilson)

So, the equation becomes:

28,784.31 = x + 11,510.21

Now, you need to solve for x, which represents the elevation of Mt. Wilson. To isolate x, you can subtract 11,510.21 from both sides of the equation:

x = 28,784.31 - 11,510.21

x = 17,274.1

So, the elevation of Mt. Wilson is 17,274.1 feet.

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Answer:

1. P(5 U 6) =2/3

2. P(2 U 5 U 6) = 5/6

3. P(1 U 2) = 1/3

4. P(4) = 0

Step-by-step explanation:

As the number cube has 6 sides,

So,

Total outcomes = {1,2,5,5,6,6}

n(S) = 6

Now,

1. P(5U6) = P(5) + P(6)

P(5)=2/6=1/3

P(6)=2/6=1/3

P(5U6)= 1/3 + 1/3 = 2/3

2. P(2 U 5 U 6) = P(2) + P(5) + P(6)

P(2)=1/6

P(5)=2/6

P(6)=2/6

P(2 U 5 U 6) = 1/6 + 2/6 + 2/6

= 5/6

3. P(1 U 2) = P(1) + P(2)

P(1) = 1/6

P(2)= 1/6

P(1 U 2) = 1/6 + 1/6

= 2/6 = 1/3

4. P(4) = 0

As 4 is not in the outcomes, it's probability will be zero ..

ANSWER

all real numbers

EXPLANATION

The given absolute value function is

[tex]f(x) = |x + 2| [/tex]

This function is obtained by shifting the graph of

[tex]y = |x| [/tex]

to the left by 2 units.

Since the domain of the parent function is all real numbers, the domain of the transformed function is also all real numbers because the shifting the parent function horizontally or vertically does not affect the domain.

Answer:

(0,0) (-6,0), (-2,0)

Step-by-step explanation:

Answer:

The correct choice is A. (-6,0), (-2,0) and (0,0).

Step-by-step explanation:

Consider the provided information:

The provided function f(x) is an even function and has 5 x-intercept.

Therefore,

f(x) = f(-x)

Thus, there will be positive and negative pairs of zeros.

As it is given that the x intercept is at (6,0). Therefore, the another x intercept will be on (-6,0).

If there are an odd number of intercepts and function is even then, (0,0) will be the x intercept because of its own negation.

The only choice with (-6,0) and (0,0) is A.

Therefore, the correct choice is A. (-6,0), (-2,0) and (0,0).

Answer:

Solve the equation inside the parentheses

-3(28) = -30

Multiply the constants

-84 = -30

The equation is false because  -84 ≠ -30. So, the equation is false

To solve the logarithmic equation with different bases, one must recognize the importance of base conversion and utilize logarithmic properties to guide conversion or comparison, not just directly equate the logarithmic arguments, which was a misunderstanding.

To solve the equation log_4(x + 3) = log_2(2 + x), we need a system that represents this equation effectively by considering logarithmic properties and base conversion.

Steps for Solving the Equation

Recognize that both sides of the equation are logarithms, which implies their arguments must be equal if their outputs are equal. Thus, it means x + 3 = 2 + x.

This simplification does not directly solve our original equation due to the different bases of the logarithms. We utilize the property that allows us to convert between bases: log_a(b) = log_c(b) / log_c(a), specifically focusing on changing base 4 logarithm to base 2.

We apply this to convert log_4(x + 3) to a base 2 logarithm, yielding a new equation: log_2(x + 3)/log_2(4) = log_2(2 + x).

Since log_2(4) = 2, the equation simplifies to 0.5 * log_2(x + 3) = log_2(2 + x).

This step reveals that the initial transformation inadvertently simplified through a direct comparison, which doesn't correctly express the conversion between bases or the nature of the original problem.

To correctly translate the given logarithmic equation into a system of equations, acknowledge that the original task was misunderstood in Step 1, as it did not account for the different log bases and their properties.

Instead, consider equations that capture the essence of converting bases or applying logarithmic identities to derive a solution.

A more accurate representation would involve recognizing the base conversion and understanding that without a direct means of converting or equating the logarithms due to their different bases and the variables involved, it does not straightforwardly lead to a solvable system without further information or manipulation that squarely addresses the base disparity.

Answer:

B

Step-by-step explanation:

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

Given m = - [tex]\frac{5}{6}[/tex], then

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{-\frac{5}{6} }[/tex] = [tex]\frac{6}{5}[/tex]

Since m > 0 then lines LM and No are the 2 possible lines

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = L(- 5, - 3) and (x₂, y₂ ) = M(0, 3)

m = [tex]\frac{3+3}{0+5}[/tex] = [tex]\frac{6}{5}[/tex]

Hence the required line is LM

Answer:

Line LM

Step-by-step explanation:

Answer:

c is the answer. (Assuming that's a positive 5)

Step-by-step explanation:

You would use the slope formula: (y1 - y2)/(x1-x2).

Plugging in gives

(3--2)/(2-1)

(3+2)/(2-1)

which simplifies to:

5/1

= 5

Hope this helps!

Answer:

The correct option is C.  5

Step-by-step explanation:

Points to remember

slope of the line  passing through the point (x₁, y₁) and (x₂, y₂) is given by

Slope m = (y₂ - y₁)/(x₂ - x₁)

To find the slope of the given line

Here (x₁, y₁) = (2, 3)  and (x₂, y₂) = (1, -2)

Slope m = (y₂ - y₁)/(x₂ - x₁)

 = (-2 - 3)/(1 - 2)

 = (-5)/(-1)

 = 5

Therefore the slope of given line is 5

The correct option is C.  5

Answer:

-1/2 b

Step-by-step explanation:

Answer:

Hi there!

The answer is: 2 and -2

Step-by-step explanation:

Case 1: An absolute value of positive number will still be a positive number

so absolute value of 2 is 2

Case 2: An absolute value of negative number will be positive number so absolute value of -2 is 2

Answer:

The Absolute Value of Both 2 and -2 is 2

Step-by-step explanation:

An Absolute Value (abs) is the non-negative value of that number or to put it in other words, it is the amount of space between that number and 0 on a number line. Every Absolute Value other than 0 has two values (a positive and a negative) since the Absolute Value is always a positive. For Example,

abs(-2) = 2 = abs(2) ......The Absolute Value of both 2 and -2 is 2

abs(-75) = 75 = abs(75) .... The Absolute Value of both 75 and -75 is 75

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

this is the diagram

Step-by-step explanation:

Answer:

11 has 85° because it is opposite to 9

Step-by-step explanation:

Answer:

ED = 5π/6

Step-by-step explanation:

First convert angles into radians by using formula 1° = π/180 rad

So, 50° becomes 5π/18.

Now using formula,

angle = length of arc / radius of circle

we get,

5π/18 = length of arc / 3

Hence , length of arc = 5π/6

Answer:

ED ≈ 2.62 in

Step-by-step explanation:

The length of the arc ED is calculated as

ED = circumference × fraction of circle

     = 2πr × [tex]\frac{50}{360}[/tex]

     = 2π × 3 × [tex]\frac{5}{36}[/tex]

     = 6π × [tex]\frac{5}{36}[/tex]

     = [tex]\frac{5\pi }{6}[/tex] ≈ 2.62 in ( to 2 dec. places )

Answer:

9 boxes were packed. 10 brownies were left over.

Step-by-step explanation:

127 ÷ 13 =  9 R10

13 x 9 = 10 x 9 + 3 x 9 = 90 + 27 = 117

127 - 117 = 10

Answer:

x = 7

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Hence

[tex]log_{x}[/tex] 343 = 3 ⇒ 343 = x³

Take the cube root of both sides

x = [tex]\sqrt[3]{343}[/tex] = 7

Answer:

C ) Inverse variation  .

Step-by-step explanation:

Given  : Graph.

To find : What type of variation do the adjacent side lengths exhibit.

Solution : We have given graph between width and height of the rectangle .

Width shown by the x axis  .

Height shown by the y axis .

Coordinates are ( 1, 4) ( 2,2) ( 8 ,0.5) ( 16 ,0.25) .

We can see from the given coordinates :

As the values of width coordinates increases , the values of height coordinates is decrease .

That mean width and height are inverse of each other .

Therefore, C ) Inverse variation  .

A type of variation which the adjacent side lengths exhibit is an: C. inverse variation.

An inverse variation can be defined as a type of proportionality which shows the relationship between two (2) variables, wherein, as the value of one variable increases, the value of the other variable decreases.

Based on the graph, we can logically deduce that there is an inverse variation between the height and width of this rectangle because they are inversely proportional.

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Answer:

F(x) = 2.15(2x^2-4x-6)

x=9

F(x)= 2.15[2(9)^2 - 4(9) - 6

F(x)=258

$258

Your answer is B.

Answer:

D. y - 5 =3(x + 1)

Step-by-step explanation:

y = -1/3x -6

The slope is -1/3

Take the negative reciprocal to find the slope of the line that is perpendicular

- (-3) = 3

The slope would be 3

We have the slope and a point

Using point slope form

y-y1 = m(x-x21)

y-5 = 3(x--1)

y-5 = 3(x+1)

Answer:

D. y - 5 =3(x + 1)

Step-by-step explanation:

Given equation of line:

[tex]y = -\frac{1}{3}x-6[/tex]

Comparing it with the standard form of equation of line

y=mx+b

m = -1/3

Let m1 be the slope of line perpendicular to the given line.

We know that the product of slopes of two perpendicular lines is -1.

[tex]m*m_1 = -1\\-\frac{1}{3} * m_1 = -1\\ m_1 = -1 * -\frac{3}{1}\\ m_1 = 3[/tex]

The equation of line in point slope form is:

[tex]y-y_1 = m(x-x_1)[/tex]

where x_1 and y_1 is the point from which the line passes.

So, putting the values of slope and point,

[tex]y-5 = 3[x-(-1)]\\y-5=3(x+1)[/tex]

Option D is correct ..

If x is 12 units away from 20 it is either 20-12 or 20+12 so the two possibilities would be 8 or 32

Hope this helps!!

The equation is x = 20 + 12 or x = 32 if "x is 12 units from 20" into an equation here x is the real number.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Translate "x is 12 units from 20" into an equation.

Here x is a real number.

The linear equation can be framed as follows:

x = 20 + 12

x = 32

Thus, the equation is x = 20 + 12 or x = 32 if "x is 12 units from 20" into an equation here x is the real number.

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Answer:

9%

Step-by-step explanation:

To find the percentage of Team B's mean absolute deviation difference in the means, you have to subtract the two means, 59.32-59.1.

After this, divide your answer the the mean absolute deviation of Team B, or you could put it all in the calculator or paper like this:

[tex]\frac{59.32-59.1}{2.4}[/tex]

You'd then end with the decimal: .0916, which you would multiply by 100 to get about 9%

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\sqrt{x+4}-1=8\\\\\text{Domain:}\ x+4\geq0\to x\geq-4\\\\\sqrt{x+4}-1=8\qquad\text{add 1 to both sides}\\\\\sqrt{x+4}=9\qquad\text{square both sides}\\\\\left(\sqrt{x+4}\right)^2=9^2\\\\x+4=81\qquad\text{subtract 4 from both sides}\\\\x=77\in D[/tex]

You want the formula for conditional probability.

P(X | B) = (X and Y)/P(Y)

Final answer:

P(X | Y) = P(X and Y) / P(Y).

Explanation:

The formula P(X | Y) represents the probability of event X occurring given that event Y has already occurred.

This concept is often used in the context of conditional probability, which differs from the calculation of independent events where the probability of both events X and Y occurring is simply the product of their individual probabilities, denoted as P(X) · P(Y).

When events are not independent, to find the conditional probability P(X | Y), you would typically use the formula

P(X | Y) = P(X and Y) / P(Y),

where

P(X and Y) is the joint probability of events X and Y occurring together, and

P(Y) is the probability of event Y occurring.

Answer:

5, − one third , one half

Step-by-step explanation:

If the number 'n' is a zero of f(x), then f(n)=0.

We could solve this problem by factorizing the polynomial, but the quickest way is by plugging the options into the equation.

We know that f(x) = 6x3 − 31x2 + 4x + 5.

Then:

Then, the correct option is: 5, − one third , one half.

Finally, the factorized form is: (x−5)(2x−1)(3x+1). If you expand it, you will get the original polynomial.

Answer:  The correct option is

(B) 5, − one third , one half.

Step-by-step explanation:  We are given to select the correct option that represents the zeroes of the following cubic function :

[tex]f(x)=6x^3-31x^2+4x+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

if for any number a, the function f(x) is zero at x =a , then x = a is a zero of the function f(x).

We have, for the given function, at x = 5,

[tex]f(5)\\\\=6\times5^3-31\times5^2+4\times5+5\\\\=125\times6-31\times25+20+5\\\\=750-775+25\\\\=0[/tex]

So, x = 5 is a zero of the function f(x).

Now, we have

[tex]f(x)\\\\\=6x^3-31x^2+4x+5\\\\=6x^2(x-5)-x(x-5)-(x-5)\\\\=(x-5)(6x^2-x-1)\\\\=(x-5)(6x^2-3x+2x-1)\\\\=(x-5)(3x(2x-1)+1(2x-1))\\\\=(x-5)(3x+1)(2x-1)[/tex]

The zeroes of f(x) are given by

[tex]f(x)=0\\\\\Rightarrow (x-5)(3x+1)(2x-1)=0\\\\\Rightarrow x-5=0,~~3x+1=0,~~2x-1=0\\\\\Rightarrow x=5,-\dfrac{1}{3},\dfrac{1}{2}.[/tex]

Thus, the zeroes of f(x) are 5, -one-third, one half.

Option (B) is CORRECT.