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The top of the escalator exists 9 feet far from the ground floor.

Let h denote the distance between the top of the escalator from the ground floor.

We have existed given that the angle of depression from the top of the escalator to the floor stands 36.84°, and the escalator exists 15 feet long.

The side h exists opposite side and 15 feet side exists hypotenuse of a right triangle.

[tex]$&\sin =\frac{\text { Opposite }}{\text { Hypotenuse }} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right)=\frac{h}{15} \\[/tex]

[tex]$&\sin \left(36.84^{\circ}\right) * 15=\frac{h}{15} * 15 \\[/tex]

[tex]$&0.599582468446 * 15=h \\[/tex]

8.993737 = h

[tex]$&h \approx 9[/tex]

Therefore, the top of the escalator exists 9 feet far from the ground floor.

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The value of the constant of variation is 3.

The correct option is C.

Direct variations occur when variables in a variation vary proportionately, that is, when they both increase or decrease at the same time. As a result, you can write X Y symbolically if X and Y are in direct variation. The variables alter disproportionally in inverse or indirect variations.

According to the given information:

Let the constant of variation be k

A quantity h varies directly with w and inversely with p

That is,

h∝ w/p

Introducing the constant of variation, k, we get

h = k(w/p)

Also, from the give information,

w = 4

p = 6

h = 2

Putting the parameters into the relation, we get

2  = K x 4/6

6 x 2= 4K

K = (6 x 2)/4

K = 3

Hence, the value of the constant of variation is 3.

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I understand that the question you are looking for is:

A quantity h varies directly with w and inversely with p. If h = 2, w = 4, and p = 6. What is the constant of variation?

A. 1/2

B. 4/3

C. 3

D. 12

Answer:

C

Step-by-step explanation:

The verified user said so

Answer:

He is 2 years old.

Step-by-step explanation:

She is 22, in 8 years she will be 30. 30 is 3×10. At that time, her brother will be 10; that is 8 years from now. So now, the little brother is 10-8 = 2 years old.

If you must show algebra work:

x = brother's age now.

x+8=brother's age in 8 years.

YingYu's age in 8 years = 3 × brother's age in 8 years

22+8 = 3(x+8)

30 = 3x +24

6 = 3x

2 = x

The percentage reduction of the price of the video game from 60 to 45 was 25%.

The percentage reduction refers to the fractional reduction in the price of the video game.

This implies that a percentage is a fraction of a value.  Percentages are calculated over 100.

A percentage is, therefore, a number or ratio expressed as a fraction of 100, often denoted using the "%" sign.

The old price of the video game = 60

The new price of the video game = 45

Reduction in price = 15 (60 - 45)

Percentage reduction = 25% (15/60 x 100)

Thus, the percentage reduction of the price of the video game from 60 to 45 was 25%.

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Answer:

1. <1 ~= <4 (Given)

2. <2 is supplementary to <1; <3 is supplementary to <4 (Because <1 & <2, <3 and <4 form linear pairs, they are supplementary by the linear pair postulate.)

3. <2 ~= <3 (By the definition of supplementary angles, m<1 + m<2 = 180 and  m<3 + m<4 = 180. By definition of congruent angles, m<1 = m<4, therefore m<2 = m<3 by substitution property of equality.)

4. AB ~= BC (Converse of Isosceles Triangles Theorem)

5. Triangle ABC is isosceles (Definition of Isosceles Triangles)

Answer: 2

Step-by-step explanation:

1) substitute

2) calculate the difference before the absolute value

3) calculate the absolute value

4) convert into whole numbers/reduce

5) subtract the whole numbers

this is what i think might be wrong

The graph is in the attached image.

The percentage of respondents who play only hockey is 27.24%.

According to the given question.

Total number of respondents = 2302

And, the number of reposdents who play only hockey = 627

Therefore,

The percentage of respondents said that they play only hockey

= (number of respondents who play only hockey/ total number of respondents)  × 100

[tex]= \frac{627}{2302} \times 100[/tex]

= 27.237 %

≈ 27.24%

Hence, the percentage of respondents who play only hockey is 27.24%.

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Answer:

Domain: (-∞, ∞), Range: [-3, ∞)

Step-by-step explanation:

Domain is all of the possible x-values in a solution set, in this case since the solution extends infinitely horizontally it would be:

(-∞, ∞)

The range is just all of the possible y-values in a solution set, which in this set starts from -3 and proceeds on infinitely, making the range:

[-3, ∞)

Answer:

36 units

Step-by-step explanation:

to find the distance take the absolute value of the difference, that is

| - 42 - (- 78) | = | - 42 + 78 | = | 36 | = 36

or

| - 78 - (- 42) | = | - 78 + 42 | = | - 36 | = 36

Answer:

-36

Step-by-step explanation:

-78 - (-42)

= -78 + 42

= -36

Answer:

y=[-4]x+[10]

Step-by-step explanation:

For a line to be perpendicular to another it must have the reverse reciprocal of the opposite line, to find the reverse reciprocal you take your slope, flip the numerator and denominator, and multiply it by -1.

The slope [tex]\frac{1}{4}[/tex] turns into [tex]\frac{4}{1}[/tex] and is then multiplied by -1 to become [tex]\frac{-4}{1}[/tex] which can be simplified down to: [tex]-4[/tex]

Now that we know the slope we need the line to pass through a point, so we will use point slope form:

[tex]y-y1=m(x-x1)[/tex]
Substitute in our slope and point values:

[tex]y-2=-4(x-2)[/tex]

Now solve for y:

[tex]y-2=-4(x-2)\\y-2=-4x+8\\y=-4x+10[/tex]

Then you will find that line [tex]y=-4x+10[/tex] runs perpendicular to [tex]y=\frac{1}{4}x-8[/tex] and intersects point (2,2).

Inequalities help us to compare two unequal expressions. For all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the inequality x²<4, whose solution can be calculated as shown below.

x² < 4

x² - 4 < 0

x² - 2² < 0

(x+2)(x-2)<0

x = (-2, 2)

Hence, for all real numbers x such that x²<4, the interval which will satisfy the given inequality is (-2,2).

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Answer:

1.8 tonne

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

divide the total mix by 5 to find the value of one part of the mix

3 tonne ÷ 5 = 0.6 tonne , then

3 parts = 3 × 0.6 = 1.8 tonne ← amount of gravel in the mix

The value of the function w(5) is 53

The function is given as:

w(x) = 9x + 8

The expression w(5) implies that the value of x is 5

i.e. x = 5

Substitute the known values in the above equation

w(5) = 9 * 5 + 8

Evaluate the product

w(5) = 45 + 8

Evaluate the sum

w(5) = 53

Hence, the value of the function w(5) is 53

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Answer:50%

Step-by-step explanation:  It doesn't matter how many questions there are because for each question, you have a 50% chance of getting it right. So, the probability is 50%.

Answer:

B

Step-by-step explanation:

The number of hours spent repairing televisions. after how many hours does he break even is 7 hours

These are equations that contains several equations with unknowns. Given the function that modelled the revenue generated from television repair as;

y = 25 + 30x

where:

x is the number of hours spent repairing televisions.

If his overhead cost, in dollars, is modelled by the equation y=5x^2−10, the company breaks even when;

25 + 30x = 5x^2 -10

Divide through by 5

5 + 6x = x^2 - 2

Equate to zero to have:

x^2 - 6x  -2 - 5 = 0

x^2 - 6x - 7 = 0

x^2 - 7x + x - 7 = 0
x(x-7)+1(x-7) =0

x = -1 and 7

Hence the number of hours spent repairing televisions. after how many hours does he break even is 7 hours

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The answer is y - 3 = -1/2 (x - 2).

First, let's find the slope.

Then, the point slope form will be :

Answer: y=-0,5x+4.

Step-by-step explanation:

[tex]A(-4;6)\ \ \ \ B(2;3)\\Straight \ line\ equation\ is:\\\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}} \\\frac{x-(-4)}{2-(-4)}=\frac{y-6}{3-6} \\ \frac{x+4}{2+4}=\frac{y-6}{-3} \\\frac{x+4}{6}=\frac{y-6}{-3} \\ Multiply\ the\ left\ and\ right\ sides\ of\ the\ equation \ by\ -3:\\\frac{-(x+4)}{2} =y-6\\-0,5x-2=y-6\\y=-0,5x+4.[/tex]

Answer:

1/4

Step-by-step explanation:

Change is y (f9x) over the change in x.

Look at the f(x) column.

What is the change from -2 to -1?  1

What is the change from -1 to 0? 1

What is the change from 0 to 1? 1

What is the change from 1 to 2? 1

We see that this change is constant.  It is always 1.

Look at the x column.

What is the change from -8 to -4? 4

What is the change from -4 to 0? 4

What is the change from 0 to 4? 4

What is the change from 4 to 8? 4

We see that the change is constant.  It is always 1.

When we put this change the form a/b we get 1/4

Answer:

The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     [tex]\frac{1}{12}[/tex] turns

9 hours     ⇒     [tex]\frac{1}{12}[/tex]  × 9 = [tex]\frac{9}{12}[/tex]

                                     = [tex]\bf \frac{3}{4}[/tex] turns    (simplified)

∴ The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.

The answer is  [tex]\boxed{\frac{3}{4}}[/tex].

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

Answer:

The second choice is correct.

Step-by-step explanation:

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

The second choice that is B≥ C is correct.

The basics of this question requires us to read the number line perfectly

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

Thus option 2) is correct

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Answer:

(2,4)

Step-by-step explanation:

1. Add the 2 x-values together, then divide. The resulting number is the x-value of the midpoint. -4+8=4 and 4/2=2, so the x-value is 2

2. Do the above steps (add & divide) for the two y-values. 6+2=8 and 8/2=4, so the y-value is 4

3. put the two values together in a coordinate pair & you have your midpoint! so if x=2 and y=4, then the midpoint is (2,4)

hope this helps :)

The question given is incomplete. Completed question is given below the answer.

The set,  {(x, y)|9<x2+y2<25} is open and connected.

The following set, {(x, y)|9<x2+y2<25} is:

A. is open (all points of the set are interior)

B. is connected (since it can not be divided into parts)

C. it is not simply connected (it has holes)

D. False, according to the previous answers

Open Set:

In mathematical terms, a set is said to be open if all its points are interior.

That is to say, no point that belongs to the border of the set or is isolated belongs to the set.

Determine the qualities of the given set. (Select all that apply.)

{(x, y)|9<x2+y2<25}

A. open

B. connected

C. simply connected

D. none of the above

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Answer:

A. W

Step-by-step explanation:

Because their is a rhythm and pattern

The required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

Given that,

The endpoints of the circle's diameter (-2, -1) and (4,7).
The equation of the circle is to be determined.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r².

where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

Center of the circle(h, k) = (-2 + 4)/2 ,(-1+7)/2
                                  = 1  , 3
Radius of the circle,
[tex]r^2 =\sqrt{(1+2)^2+(3+1)^2}\\r^2 =\sqrt{9+16} \\r^2 = 25[/tex]

Equation of the circle with center (1, 3)
[tex]r^2 = (x - 1)^2 + (y-3)^2[/tex]
[tex]25 = (x - 1)^2 + (y-3)^2[/tex]

Thus, the required equation of the circle whose endpoint of the diameter  (-2, -1) and (4,7) is  (x - 1)² + (y - 3)² = 25 ​. Option D is correct.

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Anderson could provide 0.5x2 + 4x + 8 = 0 has exactly one real root if the discriminant is 0,

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

A polynomial's discriminant is a quantity that depends on the coefficients and enables for some root attributes to be inferred without actually computing them. It is actually a polynomial function of the original polynomial's coefficients.

0.5x^2 + 4x + 8 = 0

The discriminant is computed utilizing:

d = b^2 - 4ac

Thus, we have:

d = 4^2 - 4 * 0.5 * 8

Evaluate

d = 0

The equation has only one real root since the discriminant is 0,

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The size around the circular edge of the plate is 37.68 inches

The circumference of a circle can be solved as follows:

The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .

The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.

Hence, the distance around the edge of the plate is the circumference of the plate.

Therefore,

circumference of the circular plate = 2πr

circumference of the circular plate = 2 × π × 6

circumference of the circular plate = 12π

circumference of the circular plate = 12 × 3.14

circumference of the circular plate = 37.68 inches

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Answer:

OA=95

Step-by-step explanation:

JL = 19Z = OA = 4Z+75

19Z = 4Z+75

19Z-4Z=75

15Z=75

Z=75÷15

Z=5

OA=4(5)+75

OA=95

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Answer:

it's side length equals to 8.

Step-by-step explanation:

An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.

Perimeter: 3 x side of equilateral triangle

[tex]24 = 3 \times each \: sides[/tex]

divide both sides by 3

[tex]one \: of \: its \: side = 8[/tex]

Thus, as all the three sides equals to 8.

Hope it helps!