If a math student squared all three sides of a right triangle and the results were 49, 625, and 576, what is the length of the longest leg of that triangle?

Answer:

[tex]x^{5/12}[/tex]

Step-by-step explanation:

Having a power to a power means that you multiply them:

[tex]x^{5/8 * 2/3} = x^{(5 * 2)/ (8 * 3)} = x^{10/24} = x^{5/12}[/tex]

The simplified expression is  [tex]x^{(\frac{5}{12} )[/tex].

Given that an expression [tex](x^{\frac{5}{8}} )^\frac{2}{3}[/tex], we need to simply it.

To simplify the expression, first, we raise the fraction to the power of 2/3:

Step 1: [tex](x^{\frac{5}{8}} )^\frac{2}{3}[/tex]

Now, when raising a power to another power, we multiply the exponents:

Step 2: [tex]x^{\frac{5}{8} \times \frac{2}{3}[/tex]

To simplify further, we multiply the fractions:

Step 3: [tex]x^{\frac{10}{24}[/tex]

Now, we can simplify the exponent by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case:

Step 4: [tex]x^{(\frac{5}{12} )[/tex]

So, the simplified expression is  [tex]x^{(\frac{5}{12} )[/tex].

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Answer:

The measure of the arc it creates from the central angle is 124°

Step-by-step explanation:

Remember that a central angle's vertex is located on the center of the circle. The measure of the arc, is the same as the measure of the central angle. If it's an inscribed angle, the measure of the arc is two times the measure of the inscribed angle.

Answer:

124

Step-by-step explanation:

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 ..

Answer:

[tex]6.25x+7.50=26.25[/tex]

Clara played 3 rounds of golf.

Step-by-step explanation:

The admission fee is = $7.50

Let the number of rounds be = x

Each round costs = $6.25

Total money Clara paid = $26.25

We can denote this in equation form as:

[tex]6.25x+7.50=26.25[/tex]

Now we will solve for x

[tex]6.25x=26.25-7.50[/tex]

=> [tex]6.25x=18.75[/tex]

=> x = 3

Hence, Clara played 3 rounds of golf.

The equation used to determine the number of rounds, x, that Clara golfs is 6.25x + 7.50 = 26.25

An equation is an expression that is used to show the relationship between two or more variables and numbers.

Let x represent the number of rounds that Clara golfs.

The total amount Clara pays for admission and the number of rounds she golfs is $26.25, hence this is given by:

The equation used to determine the number of rounds, x, that Clara golfs is 6.25x + 7.50 = 26.25

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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:

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

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

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:

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:

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:

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 ..

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:

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:

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.

Konichiwa~! My name is Zalgo and I am here to help you out on this beautiful day. The answer is -7x-1. When you input it into the equation, you should get f (-7x-1) = -8.

Answer:

A.  

The model is not a good fit.

Step-by-step explanation:

The correlation coefficient is a measure of the degree of association between two quantitative variables , such as weight and height.

On the other hand, the quantity R-squared is an indicator of the predictive power of a model. It is an indicator of how well the model fits the data. R-squared is the coefficient of determination.

R-squared = the square of the correlation coefficient

                  = 0.6 * 0.6

                  = 0.36

Therefore, only 36% of the variations in the dependent variable can be explained by the model. More than 50% can thus not be explained by the model. The model is thus not a good fit.

Answer:

A the model is not good

Step-by-step explanation:

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

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:

Option B and C  are correct.

Step-by-step explanation:

We need to find the pattern of the values in the table and find the values of a and b.

6³ = 216

216/6 = 36

6² = 36

36/6 = 6

6¹ = 6

6/6 = 1

6⁰ = 1

1/6 = 1/6

6⁻¹ = 1/6

1/6*1/6 = 1/36

6⁻² = 1/36

So, value of a = 1/6

and value of b = 1/36

And we have seen as the exponent is decreasing, each previous value is divided by 6.

So, Option B and C  are correct.

Answer:  The correct options are

(B) the value of b is [tex]\dfrac{1}{36}.[/tex]

(C) As the value of the exponent decreases, each previous value is divided by 6.

Step-by-step explanation:  We are given that Tori examined the pattern of exponents in the following table :

[tex]\textup{power of 6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{value}\\\\6^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~216\\\\6^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~36\\\\6^1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6\\\\6^0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1\\\\6^{-1}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a\\\\6^{-2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b[/tex]

We are to select the true statements based on the above pattern.

We will be using the following property of exponents :

[tex]x^{-y}=\dfrac{1}{x^y}.[/tex]

Therefore, we get

[tex]a=6^{-1}=\dfrac{1}{6^1}=\dfrac{1}{6}.[/tex]

and

[tex]b=6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}.[/tex]

Also, the value of the exponent is decreasing and we see that

[tex]\dfrac{216}{36}=\dfrac{36}{6}=\dfrac{6}{1}=\dfrac{1}{\frac{1}{6}}=\dfrac{\frac{1}{6}}{\frac{1}{36}}=6.[/tex]

So, each previous value is divided by 6.

Thus, the correct options are

(B) the value of b is [tex]\dfrac{1}{36}.[/tex]

(C) As the value of the exponent decreases, each previous value is divided by 6.

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:

-1/2 b

Step-by-step explanation:

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:

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:

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:

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:

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:

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.