Need help understanding this question

This can be solved by using the geometric mean theorem. The altitude drawn to the hypotenuse is the geometric mean of the lengths of the segments of the hypotenuse. The geometric mean is numbers for which this statement is true: a/x = x/b where a and b represent 2 numbers. So filling in a/x = x/b with the given information gives you 36/x = x/9. You can then solve by using the means-extremes property. x^2 = 324  

x = 18

In the triangle  ΔJKL,  the length of side k found using the law of cosines is approximately 1764 inches.

What is meant by the law of cosines?

The law of cosines, commonly referred to as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

If ABC is a triangle, then as per the statement of cosine law,  we have:

c = [tex]\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}[/tex]

where,

c = length of side c

a = length of side a

b = length of side b

γ = angle opposite c

Given a triangle, ΔJKL

The length of side l= 920 inches

The length of side j = 880 inches

∠K = 157°

According to the law of cosines,

k² = l² + j² - 2.l.j . cos K

  = 920² + 880² - 2 * 920 * 880  * cos (157°)

=  846400+ 774400 - (-1490481.46)

= 3111281.46

k = 1763.88 = 1764 inches.

Therefore the length of side k found using the law of cosines is approximately 1764 inches.

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A compound event is any event combining two or more simple events.

From the question, we have the following parameters that can be used in our computation:

combining two or more simple events.

As a general rule

When two or more simple events are combined, the result is a compound event

An example is selecting 1 in a die and head in a coin

This means that the statement that completes the blank is compound event

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Answer:

6x-5= 7.62345791436

Step-by-step explanation:

Answer: The conversion of a raw score to a scaled LSAT score is a complex process that involves several steps. The Law School Admission Test (LSAT) is a standardized test used by law schools in the United States and Canada to assess applicants' critical thinking, reading comprehension, and analytical reasoning skills.

Here's a general overview of the process of converting a raw score to a scaled LSAT score:

- Raw score calculation: The raw score is the number of questions answered correctly on the LSAT. There is no penalty for incorrect answers, so it is in your best interest to answer every question, even if you are unsure of the correct answer.

- Equating: The LSAT is equated to account for differences in difficulty between test forms. This means that the raw scores of test-takers are adjusted so that the scaled scores are consistent across different test forms.

- Scaling: The raw scores are then scaled to a range of 120 to 180, with a median score of 150 and a standard deviation of 10. This scaling process allows for meaningful comparisons between test-takers, regardless of the difficulty of the specific test form they took.

It is important to note that the LSAT score is not based solely on the number of questions answered correctly, but also on the difficulty of the questions. This means that a high raw score on a particularly difficult test form may result in a lower scaled score than a lower raw score on a less difficult test form.

Step-by-step explanation:

The required y-coordinate of system of equation is -3.

The second component of an ordered pair is a y-coordinate. The y-coordinate denotes the directional separation of the point from the x-axis when an ordered pair is graphed as the coordinates of a point in the coordinate plane. The ordinate is another term for the y-coordinate.

We have,

y = x/2 - 4 and y = -2x + 1

Equate both equation

x/2 - 4 = -2x + 1

x - 8 = -4x + 2

5x = 10

x = 2

Then,

y = -2x + 1

y = -2(2) + 1

y = -4 + 1

y = -3

Thus, required y-coordinate of system of equation is -3.

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Answer:

a

Step-by-step explanation:

The justification for step 1 in the solution process of equation 8x + 15 = 11x + 2 will be to substitute the negative sign before the number 13.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The equation is given below.

8x + 15 = 11x + 2

Simplify the equation for 'x', then we have

8x + 15 = 11x + 2

8x = 11x + 2 - 15

8x = 11x - 13

The justification for step 1 in the solution process of equation 8x + 15 = 11x + 2 will be to substitute the negative sign before the number 13.

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Answer:

the answer should be negative one and one-fourth, negative one -half

Step-by-step explanation:

hope this helps

x^2 + (y – 3)^2 = 36

Step-by-step explanation:

The standard equation of a circle with center at (h, k) and radius r is

(x - h)^2 + (y - k)^2 = r^2.

If the center lies on the y-axis, then h = 0:  (x - 0)^2 + (y - k)^2 = r^2

If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36

So, among the given equations, your

x^2 + (y – 3)^2 = 36 is correct (but only if you use " ^ " for exponentiation).

Answer:180-128=52

Step-by-step explanation:

opposite supplementary angles

Answer:

Step-by-step explanation:

y(xy+1)

Answer:

xy^2+y = y(xy + 1)

Step-by-step explanation:

If x is a continuous random variable then P(x≥A) =  P(X>A). So, the correct option is C, i.e., P(X>A).

For a continuous random variable, the probability of X taking any specific value is zero, since there are infinitely many possible values that X could take. Instead, we calculate the probability that X falls within a certain range of values.

To find the probability that X is greater than or equal to A, we can use the cumulative distribution function (CDF) of X, denoted as F(X). The CDF F(X) gives the probability that X is less than or equal to a certain value x, i.e., F(X) = P(X ≤ x).

Now, since the event X ≥ A is the complement of the event X < A, we can use the complement rule to write:

P(X ≥ A) = 1 - P(X < A)

Using the definition of CDF, we get:

P(X ≥ A) = 1 - F(A)

Therefore, the probability of a continuous random variable X being greater than or equal to a certain value A is P(X>A) = 1 - F(A). This is the correct option C in the given question.

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Complete question is:

If x is a continuous random variable then P(x≥A)=

A. P(X<A)  

B. 1-P(X>A)

C. P(X>A)

D. 1-P(X≥A-1).

The Option that is common to the formation of all fossil fuels is: fossils are converted into carbon-rich fuels. The Option A is correct.

Fossil fuels are gotten from the decomposition of plants and animals. These fuels, which can be found in the Earth's crust and contain carbon and hydrogen, can be burned for energy. Fossil fuels include coal, oil, and natural gas.

Coal is a material that is typically found in sedimentary rock deposits where layers of rock and dead plant and animal matter are piled up. More than half of the weight of a piece of coal must come from fossilized plants. Oil was discovered as a solid material between layers of sedimentary rock, such as shale.

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Answer:

  1/3

Step-by-step explanation:

You want to know the ratio of the difference in median wait times to the IQR for the box plots shown.

The median is the line in the middle of the box. The medians are ...

The difference in median wait times is 11 -9 = 2 min.

The IQR is the difference between the upper end of the box and the lower end. The IQRs are ...

The ratio of the difference in medians to the IQR is ...

  (median difference) / (IQR) = (2 min)/(6 min) = 1/3

The difference in medians is 1/3 times the IQR.

__

Additional comment

The problem already tells you the difference of medians and the IQR, so all you need to do is express than as a ratio.

  difference = k × IQR

  k = difference/IQR = 2/6 = 1/3

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ABCD is a parallelogram.

The proof is given below.

A special form of quadrilateral called a parallelogram has both pairs of opposite sides parallel and equal.

Given:

ABCD is a quadrilateral.

The diagonal of ABCD are AC and BD.

∠1 ≅ ∠2

That means AB = CD. (the sides of opposite angles)

And BE = ED.

and BD bisect AC at E.

That means BE = BD.

To prove ABCD is a paralleogram:

∠AED ≅ ∠BED (opposite angle)

And EC = AE (given)

So, BC = AD.

The sides are equally spaced because the diagonals bisect each other.

So, the opposite sides are parallel.

Therefore, ABCD is a parallelogram.

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The graph will show a proportional relationship if it is a linear function with an intercept of zero.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Hence from the definition the features of the graph of a proportional relationship are given as follows:

The problem is incomplete, hence the procedure to verify if the graph is a proportional relationship is presented.

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The value of the given expression increases, because as x decreases, 5/x increases

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, what happens to the value of the expression 5/x+5 as x decreases from a large positive number to a small positive number,

We know that, If the denominator of the fraction is decreased, the value of a fraction is increased while the numerator remains unchanged.

Therefore, if the value of x in the given starts decreasing the value of the whole fraction will start increasing.

Hence, the value of the  expression increases, because as x decreases, 5/x increases

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Answer:

The sale price of the shoes is $52.

Step-by-step explanation:

100-35=65

x    =     65

80   =    100

x=65*80/100

x=52

Have a good day :)

The coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis include the following:

P" = (-4, 0).

Q" = (-(3), 1) = (-3, 1).

R" = (1, -2).

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of triangle P′Q′R′, the coordinates of triangle P′′Q′′R′′ include the following:

(x, y)                               →              (-x, y)

Coordinate P' = (4, 0)   →  Coordinate P" = (-(4), 0) = (-4, 0).

Coordinate Q' = (3, 1)   →  Coordinate Q" = (-(3), 1) = (-3, 1).

Coordinate R' = (-1, -2)   →  Coordinate R" = (-(-1), (-2)) = (1, -2).

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Answer:[tex]x=12[/tex]

Step-by-step explanation:

answer: $13.14

$7.24 + $2.65 = $9.89

6.4% sales tax to $9.89 = $10.52

$10.52 + 25% tip = $13.14

The variable that the friends must consider when calculating the cost of the mountain bike tour is the number of hours they would be on the tour.

The group of friends will have to pay $ 90 to rent the equipment needed for the bike tour which means this is a cost that cannot change and so there is no need worrying about it as a variable.

The only variable that the friends should consider is the number of hours that they would need to go on the mountain bike tour as the total cost will increase based on the number of hours that they spend on the bike tour.

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The question is:

At the campground, the friends sign up to go on a mountain bike tour. It costs $90 to rent the equipment and $100 per hour for a group of four.

What variable must the friends consider when calculating the cost of the mountain bike tour?

The angles Θ are:

Θ = 45°

Θ = 225°

If tan = 1, the angle can be found by taking the inverse tangent (or arctan) of 1.

Because tangent is positive in the first and third quadrants, we must examine angles ranging from 0° to 360° that fall within those quadrants:

We have the following in the first quadrant:

arctan(1) = 45° if tan = 1

We have the following in the third quadrant:

225° = tan = 1 + 180° = arctan(1)

As a result, the possible angles for are 45° and 225°, which satisfy the equation tan = 1.

As a result, the angles are:

Θ = 45°

Θ = 225°

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Answer:

90 degrees

Step-by-step explanation:

10 + 3 + 7 = 20

10/20 x 180 = 90 degrees

Hope this helped :)

Answer:

The largest angle is 90 degree[10]

Step-by-step explanation:

Let 10:3:7 be x

10x+3x+7x = 180 [ angle sum property of a triangle ]

20x = 180

x=180/20

 =9/1

 =9

10x=10*9=90

3x=3*9=27

7x=7*9=63

90>63>27

therefore the largest angle is 90 degree.

Answer: 7/80

Step-by-step explanation: This is already the simplest form of this fraction.

Answer: 7/80

Step-by-step explanation:

Answer:

236

Step-by-step explanation:

number of chairs left = total chairs - 7 chairs

total chairs = 9 × 27

= 243

243 - 7

= 236

Answer: 236

Step-by-step explanation:

We have to figure out how many chairs there are in total so you will do 9*27. That is 243. If 7 were removed, you would do 243-7 which is 236. Therefore, there are 236 chairs left.

The side lengths form a proportional relationship, and the ratios are given as follows:

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Similar triangles are triangles that share these two features presented as follows:

For this problem, the triangles are similar, as they have the same angle measures, and thus the side lengths form a proportional relationship, as the equivalent side lengths have a ratio of 1.5.

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The total number number of creamy peanut butter jars are 8556.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Given is that a factory made 9200 jars of peanut butter. 93% of the jars contained creamy peanut butter.

We can write the total number number of creamy peanut butter jars as -

{x} = 93% of 9200
{x} = 93/100 x 9200
{x} = 93 x 92
{x} = 8556

Therefore, the total number number of creamy peanut butter jars are 8556.

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