Jackson places the mirror on the ground so that he is able to look at the mirror and see the top of the mountain.
The mirror is 5 feet in front of him and is approximately 40 feet from the base of the mountain. Jackson is 6’4” tall. Approximately how high is the top of the mountain?

Answer:

Question 42

area of a triangle = 1/2 × base × height

Given:

Substituting given values into the formula:

⇒ 14 = 1/2 × x × (x + 3)

⇒ 28 = (x + 3)x

⇒ 28 = x² + 3x

⇒ x² + 3x - 28 = 0

⇒ (x - 4)(x + 7) = 0

⇒ x = 4, x = -7

As length is positive, x = 4 only.

⇒ height = 4 + 3 = 7 in

⇒ base = 4 in

-----------------------------------------------------------------------------------------

Question 43

volume of a cuboid = length x width x height

Given:

Substituting given values into the formula:

⇒ 72 = 6 × (2x - 5) × x

⇒ 12 = (2x - 5)x

⇒ 12 = 2x² - 5x

⇒ 2x² - 5x - 12 = 0

⇒ (x - 4)(2x + 3) = 0

⇒ x = 4, x = -1.5

As length is positive, x = 4 only.

⇒ height = 4 in

⇒ width = 2(4) - 5 = 3 in

-----------------------------------------------------------------------------------------

Question 44

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting given values into the formula:

⇒ (x - 7)² + x² = 13²

⇒ x² - 14x + 49 + x² = 169

⇒ 2x² - 14x - 120 = 0

⇒ x² - 7x - 60 = 0

⇒ (x - 12)(x + 5) = 0

⇒ x = 12, x = -5

As length is positive, x = 12 only.

⇒ one leg = 12 m

⇒ other leg = 12 - 7 = 5 m

Answer:

\( 300000= 100000 e^{0.12 t}\)

We divide both sides by 100000 and we got:

\( 3 = e^{0.12 t}\)

Now we can apply natural logs on both sides;

\( ln(3) = 0.12 t\)

And then the value of t would be:

\( t = \frac{ln(3)}{0.12}= 9.16 years\)

And rounded to the nearest tenth would be 9.2 years.

Step-by-step explanation:

For this case since we know that the interest is compounded continuously, then we can use the following formula:

\(A =P e^{rt}\)

Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.

For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means \( A= 300000\) and we want to find the value for t.

\( 300000= 100000 e^{0.12 t}\)

We divide both sides by 100000 and we got:

\( 3 = e^{0.12 t}\)

Now we can apply natural logs on both sides;

\( ln(3) = 0.12 t\)

And then the value of t would be:

\( t = \frac{ln(3)}{0.12}= 9.16 years\)

And rounded to the nearest tenth would be 9.2 years.

Answer:

y = 6x

Step-by-step explanation:

To write an equation, find the unit rate or constant of proportionality (k).

Using a point on the line, (3, 18):

Constant of proportionality, k = y/x = 18/3

k = 6

To write an equation, substitute k = 6 into y = kx.

Thus:

y = 6x

Answer:

3/8

Step-by-step explanation:

He has a total of 80 which is your bottom number

30 is what he gave away so that is her top number

30/80 you simplify or reduce that down by dividing both top and bottom number by 10

30÷10=3

80÷10=8

your answer is 3/8

Mohan has total 80 pens from which he gave 30 pens to his friend, then the fraction of pens he gave to his friend will be 8/3.

In mathematics, a fraction is represented by a specific number that designates a portion of an entire.

A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.

As per the information given in the question,

Total number of pens = 80

Pen's given to his friend = 30

Then, the fraction will be,

= 80/30 = 8/3

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The greatest number of coin in each stack using the GCD principle is 36.

The greatest common divisor (GCD) of 756 and 360. The GCD represents the largest number that divides both 756 and 360 evenly.

Let's calculate the GCD using an algorithm known as the Euclidean algorithm:

Step 1: Divide 756 by 360.

756 ÷ 360 = 2 remainder 36

Step 2: Divide 360 by 36 (the remainder from the previous step).

360 ÷ 36 = 10 remainder 0

Step 3: Since the remainder is 0, the GCD is the divisor from the previous step, which is 36.

Therefore, the greatest number of coins that Suyin can place in each stack is 36.

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The score that you need to make in your final exam to ensure you make at least an 80 for the class is; 71

To calculate the Grade point Average, the unit value for each course that a student receives one of the utilized grades is multiplied by the number of grade points that are assigned for that grade. Then, the sum of these products is then divided by the sum of the units. Thereafter, the cumulative GPA is the sum of the grade points divided by the sum of the units.

We are told that;

You need to make on your final exam to make an 80 for this class S1.

T1 = 73, T2 = 90, grades count as 3/7 each.

The final is 1/7.

Thus, we can develop the equation with x as the required final score as;

(219/7) + (270/7) + (x/7) = 80

Multiply through by 7 to get;

219 + 270 + x = 80

489 + x = 560

x = 560 - 489

x = 71

Thus, that is the required score.

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Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Answer:

see below

Step-by-step explanation:

You could write it as 2+2+2+2+2 or 5+5 bc multiplication is like repeated addition.

Answer:

You can use the repeated additional as given below.

Step-by-step explanation:

2+2+2+2+2 or 5+5

Answer:

Step-by-step explanation:

1 to find AB

in triangle ADB

here 4 and 2\(\sqrt{6}\)  are the legs of the right triangle so let them be a and b respectively.

AB is the hypotenuse (longest side ) and let it be x

using pythagoras theorem

a^2 + b^2 = c^2

4^2 + \((2\sqrt{6} )^2\) = AB^2

16 + 4*6 = AB^2

16 + 24 = AB^2

40 = AB^2

\(\sqrt{40}\) = AB

\(2\sqrt{10}\) = AB

therefore AB =v\(2\sqrt{10}\) .Hence proved .

In triangle ADC

here 6 and \(2\sqrt{6}\) are the legs of the right angle so let them be a and b respectively. AC is the hypotenuse (longest side) so let it be c

usinfg pythagoras theorem

a^2 + b^2 = c^2

6^2 + \((2\sqrt{6} )^2\) = AC^2

36 + 4*6 = AC^2

36 + 24 = AC^2

60 = AC^2

\(\sqrt{60}\) = AC

\(2\sqrt{15}\) = AC

To prove triangle ABC is a right angled triangle

AD and BD are the legs and AB is hypotenuse

according to pythagoras theorem to be the right angle triangle the sum of square of two smaller sides of a triangle must equal to the square of hypotenuse(longest side)

let two smaller sides be a and b respectively and c be hypotenuse

using pythagoras theorem

a^2 + b^2 = c^2

4^2 + \((2\sqrt{6} )^2\) = \((2\sqrt{10} )^2\)

16 +2^2*6 = 2^2*10

16 + 4*6 = 4*10

16 + 24 = 40

40 = 40

since both sides are equal it is proved that the triangle ABC is a right angled triangle.

Hope this helps u !!

Answer:

2 square root 10

Step-by-step explanation:

firstly you must find the hipotenus using the hipotenus formula AB is the hipotenus

(4)*2 + (2 square root 10)*2 = 40 juat press a calculator if you dont know

and then you press square root of 40 then you will get 2 square root 10 so you already prove that AB is 2 square root 10

The quantity of the water in the water bottle is 648ml

Find the area,

Area of the bottle = 6 x 6

= 36cm²

To determine the quantity of the water in the bottle, multiply the area by the level of the water in the bottle:

area of the bottle x level of the water

= 36 x 18

= 648cm

When you convert it to ml, it becomes 648ml

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The complete question goes thus:

A water bottle has a square base of side 6 cm . If the bottle is filled up to a height of 18 cm .How much water is in the water bottle ?

Answer:

On the diagram, construct lines BY, XY and DY.

Now, consider triangles ΔXBY and ΔXDY. We can say that these triangles are congruent by the SAS postulate (they share side XY, XY bisects ∠BYD so ∠BYX=∠DYX, and BY=DY=radius). If they're congruent, their sides are the same so BX=DX.

BX=DX

AB+radius = CD +radius

AB=CD

The volume of the water that was displaced will be equal to 0.06 cubic feet.

Suppose that a finite amount of substance is there having its properties as:

mass of substance = m kg

density of substance = d kg/m³

volume of that substance = v m³

Then, they are related as:

\(d = \dfrac{m}{v}\)

If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water, then the volume of the water that was displaced will be

We know that the density of the water is 62.4 pounds per cubic foot.

Then we get

3.7 = 62.4 × volume

Volume = 0.059

Volume ≅ 0.06 cubic-foot

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Step-by-step explanation:

' MLB

ML Ĺ

bryon yuuù 6553w2 wasmay what is this portion insulator used for

The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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Answer:

$37.50

Step-by-step explanation:

They are asking you to find the average and to do that you have to add all the numbers together in a given set then divide that total by the amount of numbers in that set to get your average.

Answer:

The answer is, 37.50

Step-by-step explanation:

In statistics, spread refers to a data set's variability, or how the data is spread out and differs from the mean.

The range, quartiles, deciles, and percentiles; the five-number summary; standard deviation, and variance are all examples of spread measures.

According, to the question:

Adding the all the value, 25.50, 49.75,and 37.25

= 25.50+49.75+37.25

= 112.5

To get your average, divide the sum by the number of numbers in the set.

= 112.5/3

= 37.50

The equal share of the class is 37.50.

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Answer:

Use dimensional analysis to answer each of the following questions. To find the distance light travels in a year for part a, convert sec to yr by using unit ratios with min, hr, and days in their denominators. Thus, a light year is approximately 5,874,589,152,000 mi

The number of miles that the light covers in a light year will be 5.89 × 10¹² miles.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

At 186282 miles per second.

We know that in one light year, the number of seconds will be 31.536 × 10⁶.

Then the distance is given as,

186282 = d / (31.536 × 10⁶)

d = 31.536 × 10⁶ × 186282

d = 5.89 × 10¹² miles

The number of miles that the light covers in a light year will be 5.89 × 10¹² miles.

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Answer:

there is ia $30,000 range in which you are eligible and $14,000 and $46,000 thousand dollars are not eligible

The range of this scenario interpret a salary that would be eligible for the tax programs,

45000 > n > 15000.

A salary that would not be eligible,

n ≤ 15000 and n ≥ 45000.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

To be eligible for certain tax programs,

you can't make $15,000 or less per year nor $45,000 or more per year.

That means,

n > 15000

And n < 45000.

The range of this scenario interpret a salary that would be eligible for the tax programs,

45000 > n > 15000.

A salary that would not be eligible,

n ≤ 15000 and n ≥ 45000.

Therefore, the required values are given above.

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I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

the length of the box is represented by (8m2)

does that mean 8m^2?

in English that would be 8 times m^2 or 8 * m * m.

if that is true, then the volume of the box would be equal to (8*m^2)^3 which is equal to 8^3 * m^6 which is then simplified further to 512 * m^6 which can also be written as 512m^6.

if we assume that m is 3, then the side of the box is equal to 8 * 9 which is equal to 72 and that is cubed to get 373248.

working that out algebraically, it would look like this:

(8*3^2)^3 equals 8^3 * (3^2)^3 which is equal to 8^3 * 3^6 which is equal to 512 * 729 which is equal to 373248

The simplified expression that represents the volume of the box is D. 512m.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.

The volume of a cube or a square box can be calculated by multiplying the length of one side by itself twice since all sides of a cube are equal. Therefore, the volume of the square wooden box in the question is:

Volume = (8m')³

= 8m' * 8m' * 8m'

= 64m' * 8m'

= 512m"³

So the simplified expression that represents the volume of the box is 512m"³. Both options C and D in the original question have the same answer, but there is a typo in option D where it only says "512m" instead of "512m³".

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Missing information:

How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point

\(P = (\frac{1}{2}, \frac{\sqrt 3}{2})\)

Answer:

\(Rate = 0.935042^\circ /cm\)

Step-by-step explanation:

Given

\(P = (\frac{1}{2}, \frac{\sqrt 3}{2})\)

\(T(x,y) =x\sin2y\)

\(r = 1m\)

\(v = 2m/s\)

Express the given point P as a unit tangent vector:

\(P = (\frac{1}{2}, \frac{\sqrt 3}{2})\)

\(u = \frac{\sqrt 3}{2}i - \frac{1}{2}j\)

Next, find the gradient of P and T using: \(\triangle T = \nabla T * u\)

Where

\(\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j\)

So: the gradient becomes:

\(\triangle T = \nabla T * u\)

\(\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j]\)

By vector multiplication, we have:

\(\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}\)

\(\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)\)

\(\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5\)

\(\triangle T = 0.935042\)

Hence, the rate is:

\(Rate = \triangle T = 0.935042^\circ /cm\)

Given:

To find:

The point-slope form of the equation.

Explanation:

The general point-slope form of the equation is,

Substituting m = -6/5 and c = 2, we get

Therefore, the equation of the line in the point-slope form is,

Final answer:

The equation of the line in the point-slope form is,

Given the information about the circle, the value of x is 7.3

A circle is simply a round shape that has no corners or line segments. It is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

The value of x based on the information given will be:

10x + 38 = 111

10x = 111 - 38

10x = 73

Divide

x = 73 / 10

x = 7.3

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The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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Answer:

100

Step-by-step explanation:

You're correct :) good job

Answer:

$17 per day

4 days= $17 x 4= $68

$200-$68= $132

$0.33x=$132

_____.  ____

$0.33.    $0.33

x= 400

His policy will cover 400 miles of driving

Step-by-step explanation:

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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Answer:

The angle of elevation for this example is  θ  =  30.96 o

Step-by-step explanation:

For this situation we will use the Tangent function of

tan  θ  =  o p p/ a d j

tan θ  =  30 50  

tan − 1 ( .60 ) = θ

0 =   30.96 o  

Humanity would achieve a life expectancy of 110 years in approximately 60 years.

To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.

In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.

110 years - 80 years = 30 years

Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:

30 years / 5.3 years per decade ≈ 5.66 decades

Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.

To calculate the number of years, we multiply the number of decades by 10:

6 decades * 10 years per decade = 60 years

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