a 50ft ladder is placed against a large building. the base of the ladder is resting on an oil spill, and it slips at the rate of 3 ft. per minute. find the rate of change of the height of the top of the ladder above the ground at the instant when the base of the ladder is 30 ft. from the base of the building.

The statement that best justifies the conclusion based on the given information is given as follows:

C) If a plane contains a line, it contains the points on the line.

We are given these two pieces of information:

When a line belongs to a plane, as is the case in this problem, with Line l belong to plane M, then all the points of the line will belong to the plane.

Hence, point x belongs to the plane M in this problem, as the plane M contains the line l for which point x belongs, and thus statement c is correct.

(basically, the transitive property can be applied to conclude that every point on a line belonging to a plane also belong to the plane).

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In his account balance now $3215

Tyler withdraws $35 from his bank account every week until he runs out of

money. He started the year with $3245 in his bank account.

Tyler withdraws $35.

He started with $3245.

In his account balance now

Tyler withdraws -His started accound.

$3245 - $35 = $3215

Currently, he has $3215 in his account.

In his account balance now $3215

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Answer:

graph D

Step-by-step explanation:

x - 1 ≥ 0

x ≥ 1

if x ≥ 1

x - 1 < 4

x < 4 + 1

x < 5

1≤ x < 5

if x < 1

-x + 1 < 4

-x < 4 - 1

- x < 3

x > -3

-3 < x < 1

final solution

-3 < x < 5

The proportion that correctly represents the similar figures is the one in option B:

8/5 = 3/x

If two figures are similar, then the quotient between the correspondent sides must be equal.

Then we can write the equation:

8ft/3ft = 5ft/x

8/3 = 5/x

Now we can divide both sides by 5 and multiply both sides by 3, then we will get:

8/5 = 3/x

That is the proportion we wanted, then we conclude that the correct option is B.

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Answer:

Subtotal: $250.00

Savings: $62.50

New Subtotal: $187.50

Total: $195.00

Step-by-step explanation: First, multiply 25 by 10. You'd get 250. Then, recall the formula to find the worth after a percent is applied:

Worth = Whole number * part percent / 100

Plug in the numbers:

Worth = 250 * 25 / 100

6250 / 100

=  62.50

Now, since it's a discount we need to subtract the discount price from the current subtotal. This would look like this:

250 - 62.50 = 187.50

Now, use the same formula to find the sales tax:

187.50 * 4 /100

750 / 100

= 7.5

So, since we need to pay the tax, we add the amount to our current subtotal:

187.50 + 7.5 = 195

So, our total is $195.00

The remainder when f(x) = 3x³ + 24x² − 45x − 162 is divided by (x + 8) is 198.  

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Therefore, the remainder when f(x) = 3x³ + 24x² - 45x - 162 is divided by (x + 8) is as follows:

The dividend is x + 8.

Hence, let's Set the dividend to 0

x + 8 = 0

x = -8

Substitute x = - 8 in f(x) = 3x³ + 24x² - 45x - 162

f(-8) = 3(-8)³ + 24(-8)² - 45(-8) - 162

f(-8) = - 1536 + 1536 + 360 - 162

f(-8) = 198

Therefore, the remainder is 198.

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A parabola is a graph of a quadratic equation of the form

In order to write the equation of a parabola in vertex form, we need to first determine the values of a, b, and c.

To find the vertex of the parabola, we know that the vertex lies at the point (0,0), so the x-coordinate of the vertex is 0. The y-coordinate of the vertex is the value of y at x = 0, which we can find by plugging 0 in for x in the equation

So the vertex of the parabola is (0, c).

Since the parabola passes through the point (6,9), we can plug in these values for x and y into the equation y = ax^2 + bx + c to find the values of a, b, and c. We get the equation

We can now write the equation of the parabola in vertex form. In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. In our case, the vertex is (0,c), so we can write the equation as y = a(x - 0)^2 + c. Plugging in the values we found earlier, we get

Finally, we can simplify the equation by dividing both sides by 36a. This gives us

Since c/36a is a constant, we can simplify the equation even further by letting d = c/36a, so the final equation is

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Answer:

Step-by-step explanation:

Which is a solution for the equation y= 6x + 6

y = 6x + 6   (there is no possibility to simplify)

y = 6x + 6

6x + 6 = y

6x = y − 6

divide both side by 6

A data series contains the actual values that are plotted on the chart. So the option c is correct.

In the given question, we have to find the answer to fill in the blanks.

The given statement is:

"A ________ contains the actual values that are plotted on the chart."

As we know that;

A data series, such as a list of quarterly corporate profits, is a row or column of figures that are input in a worksheet and plotted in your chart. Even if you generated your chart in a different software, like Word, Office automatically associates charts with an Excel-based worksheet.

A data series contains the actual values that are plotted on the chart.

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The complete question is:

A ________ contains the actual values that are plotted on the chart.

(1) data source

(2) category values

(3) data series

(4) legend

If a fraction's denominator is not a factor of 10 or 100, we can divide the number in the numerator by the number in the denominator to obtain a decimal.

Let us take an example. Say we have a fraction- 3/2

here numerator = 3 and denominator = 2

To convert this into a decimal, we need to divide 3 by 2

2 goes in 3 one time and remainder left is 1.

Then we put a decimal and divide 10 by 2 which gives us 5

Thus, on dividing 3 by 2, we get a quotient of 1.5

Hence the fraction 3/2 becomes 1.5 as a decimal.

Similarly, we can convert any fraction into decimal.

Thus, we can see that if a fraction's denominator is not a factor of 10 or 100, we can divide the number in the numerator by the number in the denominator to obtain a decimal.

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The length of BR is 40 cm.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

YN is parallel with BR.

Triangle HYN is congruent with Triangle HBR.

HN = 5 cm

NR = 15 cm

YN = 10 cm

Now,

HR = HN + NR

HR = 5 + 15 = 20 cm

YN/HN = BR/HR

10/5 = BR/20

2 = BR/20

BR = 20 x 2

BR = 40 cm

Thus,

The value of BR is 40 cm.

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4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.

Given that,

A cyclist travels at a speed of 24 miles per hour on average.

We have to find what is the required riding time (in hours) if she wants to cycle 180 km.

We know that,

The velocity is a vector quantity (has magnitude and direction) that is calculated by dividing the distance by the amount of time needed to travel the distance in question.

So, the distance is 180 km, and the speed is 24 miles per hour.

To calculate the amount of time needed to travel the distance, we divide the distance by the speed.

The distance is first converted to miles as 1 mile is equal to 1.6098 kilometers,

180 kilometers are equal to 111.84681 Miles.

111.84681 miles traveled in 24 hours

111.84681/24

4.66 hours.

Therefore, 4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.

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Answer: 23 spools of thread

Step-by-step explanation:

0.2 times 9 = 1.8 spools of thread

25 - 1.8 = 23.2 spools of thread

point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

Given that,

We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.

We know that,

First we write the co-ordinates of the triangle in the given graph.

P is (-3,3)

Q is (2,1)

R is (-4,-2)

The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.

Midpoint Formula is

(x₁+x₂/2, y₁+y₂/2)

So,

The midpoint of the side PR is

(-3+(-4)/2, 3+(-2)/2)

(-3-4/2, 3-2/2)

(-7/2,1/2)

So, S point is (-3.5, 0.5)

The midpoint of the side QR is

(2+(-4)/2, 1+(-2)/2)

(2-4/2, 1-2/2)

(-2/2,-1/2)

So, T point is (-1, -0.5)

Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

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x as his total income

x = 12(25 000) + 0.065(100 000)

x = 300 000 + 6 500

x = 306 500

12(25 000) = 300 000 (12 months salary)

0.065(100 000) = 6 500 (bonus)

= 306 500

Therefore, the salesman total income is 306 500 in 2014.

Step-by-step explanation:

The points with black dots on the number line represent the fractions.

In elementary mathematics -

Given are the fractions -

5/6 and 2[tex]\frac{2}{3}[/tex]

We can write -

2[tex]\frac{2}{3}[/tex] = 8/3

5/6 = 5/6

Refer to the number line attached. The points with black dots represent the numbers.

Therefore, the points with black dots on the number line represent the fractions.

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To solve for x in this equation, we must first perform the operations inside the parentheses. This gives us:

X = 40 * (25x^2 + 75x + 75x - 75)

Next, we can distribute the 40 and combine like terms to get:

X = 1000x^2 + 3000x - 3000

Now, we can set this expression equal to X and solve for x.

1000x^2 + 3000x - 3000 = X

We can use the quadratic formula to find the solutions for x:

x = (-3000 +/- sqrt(3000^2 - 4 * 1000 * (-3000))) / (2 * 1000)

This simplifies to:

x = (-3000 +/- sqrt(9000000 + 24000000)) / 2000

Finally, we can simplify further to get:

x = (-3000 +/- sqrt(33000000)) / 2000

Thus, the solutions for x are:

x = (-3000 + sqrt(33000000)) / 2000

x = (-3000 - sqrt(33000000)) / 2000

These are the possible values for x that satisfy the given equation.

25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

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Although part of your question is missing, you might be referring to this full question: Right triangles MNP and QRS are congruent. What is the area of △MNP? (Picture as attached)

The area of △MNP is 60 m².

Since △MNP and △QRS are congruent, then SQ = MP, NM = RQ, and RS = NP.

The formula to find the area of a triangle is:

= 1/2 * base * height

As shown in the picture, height = 15, and base is unknown.

To find the base, we use Pythagoras theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle), or, in familiar algebraic notation, a² + b² = c².

So, MP = √ 17² – 15²

MP = 8m = the base

Hence, area of △MNP:

= 1/2 * 8 * 15

= 60 m²

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The time on clock shows at the instant you see the clock at the origin showing 3.80 μs is 5.47 × [tex]10^{-6[/tex] s.

As per the given data the values of x and y are as follows:

x = 300 m

y = 400 m

Here you are standing at the point (300, 400) in a reference frame with synchronized clocks.

Here we have to determine the time on clock shows at the instant you see the clock at the origin showing 3.80 μs.

The point where you're standing (300, 400) is 500 m from the origin.

Therefore my distance from the origin is 500 m

Speed of light , c = 3 × [tex]10^8[/tex] m/s

The clock at the origin showing, [tex]T_0[/tex] = 3.80 μs

[tex]T_0 = 3.8 \times 10^{-6}[/tex] s

Time shown by my clock , T = distance ÷ c + [tex]T_0[/tex]

T = [tex]\frac{500}{(3 \times 10^8)} + 3.8 \times 10^{-6[/tex]

T = 5.47 × [tex]10^{-6[/tex] s

Therefore the time shown by my clock is 5.47 × [tex]10^{-6[/tex] s.

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Answer: The answer is B: 0.9

The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $21,000 and the standard deviation is $1000. Use the 68-95-99.7 Rule the percentage of buyers that paid between $20,000 and $21,000 is 68%

68 percent of the data falls within one standard deviation of the mean,

95 percent falls within two standard deviations, and

99.7 percent falls within three standard deviations.

In the problem, it was given that the mean is $21 000 and the standard deviation is $1 000

The deviation between $20,000 and $21,000

= $21,000 - $20,000

= $1,000

The standard deviation is $1000 hence buyers within $20,000 and $21,000 are within one standard deviation. according to the 68-95-99.7 Rule they are 68%

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The rate of the boat approaching the dock when 125 ft of rope is out is 101.6 ft/min

let x be the horizontal distance to the dock. And the rope is attached to the boat 10 feet below the pulley

Using Pythagorean theorem

x^2=R^2-10^2

where R is the rope length to the pulley.

Differentiates with respect to time t

2x dx/dt=2RdR/dt

Xdx/dt = RdR/dt ...... (1)

If the boat is approaching the dock when 125 ft of rope is out

This is R = 125ft

Using Pythagorean theorem again

X^2 = R^2 - 10^2

X^2 = 125^2 - 10^2

X^2 = 15525

X = 124.6 ft

The rate the boat approaching the dock = dx/dt

While the rope is pulled through the pulley at a rate of 20 ft/min = dR/dt

Solve for dx/dt when R is 125, x= 124.6, and dR/dt= 20ft/min

Substitute all in equation 1

124.6 dx/dt = 125 × 20

dx/dt = 2500/124.6

dx/dt = 101.6 ft/min

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Answer:

Step-by-step explanation: : 630°, 990°, -90°, -450°

The scalar quantities in Fourier's law is the temperature and the conductivity whereas heat flux is vector.

Heat moves from a higher temperature to a lower temperature, which is explained by the minus sign.

Fourier's law

q = -k ▽T

Where,

q is the local heat flux density in W.m2

k is the conductivity of the material in W.m-1.K-1

▽T is the temperature gradient in K.m-1

The terms "force," "speed," "velocity," and "work" are frequently used, and they all refer to scalar or vector quantities. Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.

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Answer: The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.

Step-by-step explanation:

To find the angles and sides of a triangle, you need to know at least three pieces of information about the triangle. In this case, you are given the lengths of sides AB and AC, and the measure of angle BAC.

You can use the Law of Sines to find the measure of the third angle and the length of the third side. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles in the triangle. In other words, if we let a, b, and c represent the lengths of the sides of the triangle and A, B, and C represent the measures of the angles opposite those sides, then the following equation holds:

a/sin A = b/sin B = c/sin C

In triangle ABC, we are given the lengths of sides AB and AC and the measure of angle BAC. We can use the Law of Sines to find the measure of angle BCA and the length of side BC.

First, we can find the measure of angle BCA using the equation:

a/sin A = b/sin B = c/sin C

Substituting the known values, we get:

14/sin BAC = 12/sin BCA

Solving for sin BCA, we get:

sin BCA = 14/12 * sin BAC

Plugging in the given value for sin BAC, we get:

sin BCA = 14/12 * sin 68°

Using a calculator, we find that sin 68° = 0.906308

So sin BCA = 0.763696

To find the measure of angle BCA, we can use the inverse sine function on our calculator. The inverse sine of 0.763696 is about 50.6°.

Now that we know the measures of angles BAC and BCA, we can use the fact that the angles in a triangle sum to 180° to find the measure of angle ABC:

BAC + BCA + ABC = 180°

Substituting the known values, we get:

68° + 50.6° + ABC = 180°

Solving for ABC, we get:

ABC = 180° - 68° - 50.6°

This simplifies to:

ABC = 61.4°

Now that we have found the measures of all three angles, we can use the Law of Sines again to find the length of side BC.

We can use the equation:

a/sin A = b/sin B = c/sin C

Substituting the known values, we get:

14/sin BAC = 12/sin BCA = BC/sin ABC

Solving for BC, we get:

BC = 14/sin BAC * sin ABC

Plugging in the values we found earlier, we get:

BC = 14/0.906308 * sin 61.4°

Using a calculator, we find that sin 61.4° = 0.875

So BC = 14/0.906308 * 0.875 = 13.68

The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.

Option D is the correct answer. AK + BK = AC is not a true statement.

All the statements are not true except:

AK + BK = AC

Since BK = KC, so

AK + KC = AC

DB=BK is not necessarily true since it is not stated whether AB = BC

B is the midpoint of AC is not necessarily true since again it's not stated that AB = BC

D bisects AK is not necessarily true since it is not stated that D and K lie on the same line.

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