When sitting atop a tree and looking down at his Pal Joey, the angle of depression of Mack’s line of sight is 53°51. If a Joey is known to be standing 25 feet from the base of the tree, how tall is the tree( to the nearest foot)? A 36 ft B 38ft C 34ft D 40ft

The solution to the equation -3(h + 5) + 2 = 4(h + 6) - g is h = -12 and g = -18.

Distribute the negative signs:

-3(h + 5) + 2 = -3h - 15 + 2

Combine constant terms:

-3h - 15 + 2 = 4(h + 6) - g

-3h - 13 = 4h + 24 - g

Isolate h on one side:

-7h - 13 = 24 - g

-7h = 37 - g

h = (37 - g) / -7

Substitute h back into the original equation to solve for g:

-3(h + 5) + 2 = 4(h + 6) - g

-3((37 - g) / -7 + 5) + 2 = 4((37 - g) / -7 + 6) - g

-3(-12 - g + 35) + 2 = 4(-12 - g + 42) - g

Simplify both sides:

11g + 66 = -36g + 108

47g = 42

g = -18

Therefore, the solution is h = -12 and g = -18.

Answer:

Center: (-5,10)

Radius: 2

Step-by-step explanation:

The equation of the circle in center-radius form is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the point (h,k)  is the center of the circle and "r" is the radius.

Subtract 121 from both sides of the equation:

[tex]x^2+y^2+121-20y-121=-10x-121\\x^2+y^2-20y=-10x-121[/tex]

Add 10x to both sides:

[tex]x^2+y^2-20y+10x=-10x-121+10x\\x^2+y^2-20y+10x=-121[/tex]

Make two groups for variable "x" and variable "y":

[tex](x^2+10x)+(y^2-20y)=-121[/tex]

Complete the square:

Add [tex](\frac{10}{2})^2=5^2[/tex] inside the parentheses of "x".

Add  [tex](\frac{20}{2})^2=10^2[/tex]  inside the parentheses of "y".

Add [tex]5^2[/tex] and [tex]10^2[/tex] to the right side of the equation.

Then:

[tex](x^2+10x+5^2)+(y^2-20y+10^2)=-121+5^2+10^2\\(x^2+10x+5^2)+(y^2-20y+10^2)=4[/tex]

Rewriting, you get that the equation of the circle in center-radius form is:

 [tex](x+5)^2+(y-10)^2=2^2[/tex]

You can observe that the radius of the circle is:

[tex]r=2[/tex]

And the center is:

[tex](h,k)=(-5,10)[/tex]

Answer:

Step-by-step explanation:

x²+y²+121-20y=-10x

(x²+10x)+(y²-20y)+121=0

(x²+10x+25)-25+(y²-20y+100)-100+121=0

(x+5)² + (y-10)²= 2²

the center is : A(-5;10)  and radius : r = 2

Answer:

A. 10

Step-by-step explanation:

This is a right triangle with a hypotenuse between the vertices (-4,-2) and (4,4). You can now solve for the length to get 10.

The answer is -- 10 days

Answer:

  2. 90°

  3. 65°

Step-by-step explanation:

2. Points A, B, and D are on a semicircle centered at C. The angle A is inscribed in that semicircle, so is 90°. Then angles B and D sum to 90°.

__

3. Triangle ABC is similar to triangle EDC by SAS, so angle x has the same measure as the third angle of triangle EDC: 180° -80° -35° = 65°.

___

The relevant relationship in both cases is that the sum of angles in a triangle is 180°. Also, for problem 2, you need to know that an inscribed angle has half the measure of the arc it subtends. And for problem 3, it helps to understand the relationships in similar triangles.

Answer:

The lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

Step-by-step explanation:

Without graphing, this is the equation of a circle with center at the origin,

(0, 0) and with a radius of 3 units. The general equation of a circle with center (a, b) and with radius r units is given as;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]  

The graph of the function is as shown in the attachment below;

A line of symmetry cuts the graph of a function into two equal parts such that these parts become mirror images of each other.

For the case of a circle, the line that divides the circle into two equal portions is the diameter. Any given circle has infinite number of diameters.

Therefore, the lines of symmetry are the diameters, any straight line passing through the origin and touching both ends of the circle.

Check the picture below.

so is filled with those cubes, recall that a cube has all equal sides, in this case 1/3, so the volume of each cube is simply the product of length*width*height.

[tex]\bf \stackrel{\textit{volume of one cube}}{\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\implies \cfrac{1}{27}}\qquad \qquad \stackrel{\textit{if there are \underline{x} cubes inside then their total volume is}}{\cfrac{1}{27}x~~~~=~~~~\stackrel{\textit{volume of prism}}{4}} \\\\\\ x=27\cdot 4\implies x=108[/tex]

Answer:

  10.  D. 5 1/3

  11.  C. 285 cm

  12.  A. 42 units

Step-by-step explanation:

The first two are simple addition problems. (In problem 11, you can replace the addition of 5 identical numbers with a multiplication by 5.) The last problem is also an addition problem, but figuring out what to add can take a little effort.

___

10. The segment addition theorem tells you that for R between S and T:

  ST = SR + RT

  ST = 3 2/3 + 1 2/3 = (3 +1) + (2/3 +2/3) = 4 + 4/3 = 4 + 1 1/3

  ST = 5 1/3

__

11. The definition of a regular polygon is that all of its sides and angles are congruent. A "pentagon" is 5-sided polygon, so your regular pentagon will have 5 sides, each of measure 57 cm. The perimeter is the total length of the sides, so is ...

  P = 57 cm +57 cm +57 cm +57 cm +57 cm

  P = 5×57 cm

  P = 285 cm

__

12. Again, the perimeter is the sum of the side lengths. Here, the length of the top side is easily figured by the difference of x-coordinates (6 units). The length of the left side is recognizable as double the length of the hypotenuse of a 3-4-5 right triangle (10 units). The lengths of the other two sides can be found using the distance formula with the end point coordinates:

  MN = √((-10-8)^2 +(-6-(-3))^2) = √(324 +9) = √333 ≈ 18.248

 LM = √((8-2)^2 +(-3-2)^2) = √(36 +25) = √61 ≈ 7.810

So, the perimeter is ...

  P = 6 + 10 + 18.248 +7.810 = 42.058 ≈ 42 units

_

Here, it is helpful to be familiar with the 3-4-5 right triangle. It has several interesting properties, one of which is that it shows up in algebra problems a lot. Any triangle with this ratio of side lengths is also a right triangle.

In this problem, the difference in coordinates K - N = (-4-(-10), 2-(-6)) = (6, 8) which we recognize as having the ratio 3:4. We could continue with the distance formula:

  NK = √(6^2 +8^2) = √100 = 10

or, we can simply recognize this will be the result based on our familiarity with this triangle.

_

An alternate approach to this problem will also work. You can estimate the length of the perimeter.

The distance between two points is more than the maximum difference of their coordinates and less than the sum of differences of their coordinates. For example, the distance between points N and K will be more than 8 and less than 8+6=14.

If you need to refine this very crude estimate further, you can add 40% of the smallest difference to the largest difference. In this case, that would be ...

  8 + 0.40·6 = 10.4 . . . . . we already know the length is actually 10, so we see this estimate is within 4% of the real length.

For the coordinates in this problem, we can see that the perimeter will be more than the sum of the longest coordinate differences: 6+6+18+8 = 38. This is an important fact, because it eliminates all of the answer choices except 42. If there were any remaining ambiguity as to the answer, we could refine our estimate by adding 40% of the sum of the shortest coordinate differences: 0.40·(0+5+3+6) = 5.6. That would bring our estimate to 38+5.6 = 43.6, within 4% of the actual value of the perimeter.

Answer:

y = 700 (0.969)^t

Step-by-step explanation:

Using the depreciation formula after a given period of time.

A = P (1- r/100)^n

Where, A is the initial value

P is the original value

r is the rate of depreciation and

n is the time taken in years

Therefore;

A will be the new mass of the sample after decay,y

P is the original mass of the sample before decay, 700 mg

r is the rate of decay each year, 3.1% and

n is the number of years, t

Hence;

y = 700 (1- 3.1/100)^t

y = 700 (96.9/100)^t

y = 100(0.969)^t

The relationship between the mass of the radioactive sample (y) and the number of years since the start of the study (t) can be represented by the exponential function y = 700 * (1 - 0.031) ^ t.

This is a problem related to exponential decay. In general, the formula for an exponential decay is given as Y = A * (1 - r) ^ t where 'A' represents the initial amount, 'r' is the rate of decay (as a decimal), and 't' is the time period.

For this problem, the initial amount of the radioactive substance is 700 milligrams (A = 700), the rate of decay is 3.1% per year (r = 0.031), and 't' is represented as the number of years since the start of the study.

Using these values, we can write the exponential function showing the relationship between the mass of the sample 'y' and the number of years 't' as follows:

y = 700 * (1 - 0.031) ^ t

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Answer:

6.9

Step-by-step explanation:

12 x 4 = x^2

48 = x^2

x = 6.9

Answer:

6.9

explanation:

I did the test.

hope this helps you!

:D

Answer:

ΔADB~ΔCDB; SAS~

Step-by-step explanation:

Due to the tick marks on AD and DC, we know that those sides are congruent

We also know that the angle D is congruent due to the marks

As they share line BD, that side is also congruent.

This means that we have a side, an angle, and another side.

This leaves us with the last two options

The only difference between them is what angle corresponds to which

In the case of this triangle, A and C correspond with each other and B and D are shared. This means we are looking for when the locations of A and C, and B and D are matched

This would mean that the 4th option

ΔADB~ΔCDB; SAS~

Answer:

m∠DAB = 90°

Step-by-step explanation:

* Lets revise some facts about the circle

- If two tangent segments drawn from a point outside the circle, then

 the two tangent segments are equal in length

- The radius and the tangent perpendicular to each other at the point

 of contact

* Lets solve the problem

∵ AB and AD are two tangent segments to circle C at B and D

 respectively

∴ AB = AD ⇒ (1)

∵ CD and CD are two radii

∴ AB ⊥ BC and AD ⊥ DC

∴ m∠ABC = m∠ADC = 90°

∵ m∠BDC = 45°

∵ ∠BDC + m∠ADB = m∠ADC

∴ 45° + m∠ADB = 90° ⇒ subtract 45° from both sides

∴ m∠ADB = 45° ⇒ (2)

- In Δ ABD

∵ AB = AD ⇒ proved in (1)

∴ m∠ABD = m∠ADB ⇒ isosceles triangle

∵ m∠ADB = 45° ⇒ proved in (2)

∴ m∠ABD = 45°

- The sum of the measure of the interior angles of a Δ is 180°

∴ m∠DAB + m∠ABD + m∠ADB = 180°

∴ m∠DAB + 45° + 45° = 180° ⇒ simplify

∴ m∠DAB + 90° = 180° ⇒ subtract 90° from both sides

∴ m∠DAB = 90°

Answer:

The area of the circle is [tex]36\pi\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle subtends a central angle of [tex]2\pi[/tex] radians

so

By proportion find the area of the circle

[tex]\frac{33\pi }{(11\pi /6)}=\frac{x}{2\pi}\\ \\ x=2\pi*( 33*6)/11\\ \\x=36\pi\ units^{2}[/tex]

Answer:

its just 36 pi

Step-by-step explanation:

just did this one

She will take 6 weeks.

Answer:

She will take 6 weeks.

hope this helps

Answer:

Your Awnser would be 597,000

Step-by-step explanation:

Answer:

The actual answer for this question should be 200.

Step-by-step explanation:

Answer:

2nd one: AB = 6

Step-by-step explanation:

Because PQ is 4 (Pythagorean triples), you can prove that triangle PBQ is congruent to PAQ by HL. You can then say AQ is equal to 3 becasue of CPCTC. AQ+QB=AB, or 3+3=6. AB=6

ANSWER

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

EXPLANATION

We need to use the Pythagoras Theorem to find the height of the triangle.

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] ({2 \sqrt{3}) }^{2} + {b}^{2} = {4}^{2} [/tex]

[tex]12 + {b}^{2} = 16[/tex]

[tex] {b}^{2} = 16 - 12[/tex]

[tex]{b}^{2} = 4[/tex]

Take positive square root to get;

[tex]b = \sqrt{4} = 2[/tex]

Area =½bh

[tex]Area = \frac{1}{2} \times 2\sqrt{3} \times 2[/tex]

[tex]Area = 2\sqrt{3} \: {cm}^{2} [/tex]

Answer: [tex]x=-11[/tex]

Step-by-step explanation:

You can use the Method of substitution.

Substitute the equation [tex]y=3-\frac{1}{2}x[/tex] into the equation [tex]3x + 4y = 1[/tex] and then you must solve for the variable x:

[tex]3x + 4y = 1\\\\3x + 4(3-\frac{1}{2}x) = 1\\[/tex]

Apply Distributive property:

[tex]3x + 12-\frac{4}{2}x = 1\\3x+12-2x=1[/tex]

Subtract 12 from both sides of the equation and then add the like terms. Then you get:

[tex]3x+12-2x-12=1-12\\3x-2x=-11\\x=-11[/tex]

[tex]\ln(n+3)-\ln n=\ln\dfrac{n+3}n=\ln\left(1+\dfrac3n\right)[/tex]

We can show the sequence is bounded and monotonic.

Boundedness: [tex]1+\dfrac3n>1[/tex] for all [tex]n>0[/tex], so [tex]\ln\left(1+\dfrac3n\right)>\ln1=0[/tex] for all [tex]n>0[/tex].

Monotonicity: Consider the function

[tex]f(x)=\ln\left(1+\dfrac3x\right)[/tex]

which has derivative

[tex]f'(x)=\dfrac{1+\frac3x}{-\frac3{x^2}}=-\dfrac3{x^2+3x}[/tex]

which has negative sign for all [tex]x>0[/tex], and so [tex]f(x)[/tex] is strictly decreasing.

[tex]\ln(n+3)-\ln n[/tex] is bounded and monotonic, so the sequence converges.

As [tex]n\to\infty[/tex] we have [tex]\dfrac3n\to0[/tex], leaving us with the limit

[tex]\displaystyle\lim_{n\to\infty}(\ln(n+3)-\ln n)=\lim_{n\to\infty}\ln\left(1+\frac3n\right)=\ln\left(1+\lim_{n\to\infty}\frac3n\right)=\ln1=0[/tex]

The sequence an = ln(n + 3) - ln(n) converges with a limit of 0. This is determined by simplifying the expression and observing its behavior as n approaches infinity.

Firstly, the question pertains to the study of the convergence or divergence of a sequence. In this case, we're looking at the sequence an = ln(n + 3) - ln(n). Using logarithmic properties, this can be rewritten as ln((n+3)/n). As n approaches infinity, the sequence converges to the limit ln(1), which equals 0. Therefore, the sequence converges and its limit is 0.

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Answer:

  x = 12 cm

Step-by-step explanation:

The product of lengths from the secant intersection point to the "near" and "far" circle intersection points is the same for both secants. When one "secant" is a tangent, the lengths to the circle intersection points are the same (so their product is the square of the tangent segment length).

  8^2 = 4·(4 +x) . . . . . . measures in centimeters

  16 = 4 +x . . . . . . divide by 4

  12 = x . . . . . . . . . subtract 4

Answer:

  y = 11.2 in

Step-by-step explanation:

The square of the tangent length is equal to the product of the lengths of the secant from the intersection with the tangent to the near and far circle intersection points.

  9^2 = 5(5+y)

  16.2 = 5+y . . . . . divide by 5

  11.2 = y . . . . . . inches

The scale factor of the lengths of two similar octagons with areas 4 m² and 9 m² is obtained by taking the square root of the ratio of their areas, yielding a scale factor of 1.5.

The subject of this question is Mathematics, particularly dealing with geometry and scale factors. For two similar shapes, the ratio of their areas is equal to the square of the scale factor of their lengths.

Given the areas of the two similar octagons as 4 m² and 9 m², we find the square root of the ratio of the areas to obtain the scale factor of the lengths. That is, √(9/4) = √2.25 = 1.5.

Therefore, the scale factor of the lengths of the two similar octagons is 1.5.

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The scale factor of the lengths of the two similar octagons is 1.5.

To find the scale factor of the lengths of two similar octagons, we can use the formula:

Scale factor = sqrt(Area2 / Area1)

Where Area1 is the area of the first octagon, and Area2 is the area of the second octagon.

Plugging in the given values, we get:

Scale factor = sqrt(9 m² / 4 m²) = sqrt(2.25) = 1.5

Therefore, the scale factor of the lengths of the two octagons is 1.5.

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Answer:

21.5

Step-by-step explanation:

x is the radius of the circle.

If we draw a line from the circle's center to either end of the horizontal line, that line will also be a radius, so it will have length x.  This forms a right triangle with side lengths 10 and 19 and hypotenuse x.

Using Pythagorean Theorem:

c² = a² + b²

x² = 10² + 19²

x² = 461

x ≈ 21.5

Answer:

The value of [tex]cos\theta[/tex] would be Base/Hypotenuse = EF/DF

Step-by-step explanation:

In figure, we are given a triangle

There is a 90 degree angle in the triangle. Therefore, the triangle is a right triangle.

In a right triangle,

[tex]Sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]

[tex]Cos\theta = \frac{Base}{Hypotenuse}[/tex]

[tex]Tan\theta = \frac{Perpendicular}{Base}[/tex]

In triangle, the side with right angle and given angle is called base, Therefore

Base = EF

The side opposite to the right angle is called the hypotenuse, so

Hypotenuse = DF

and

Perpendicular = DE

Therefore, the value of [tex]cos\theta[/tex] would be Base/Hypotenuse = EF/DF

Answer:

Hi ! I hope you're doing good

Here is your graph ...I hope it's helpful for you

Step-by-step explanation:

The first one u circled is a single rotation

Answer:

The upper left figure has a single rotation.

Step-by-step explanation:

In math and geometry single rotation is what we call a figure that has been rotated by only 90º from an original point and it is usually measured to the right, so in this case from the option the figure that has been rotated only 90º is the one in the upper left corner of the image.

Answer:$76

Step-by-step explanation:

JEANS: (5x8)= 40

SHIRTS:(4x6)= 24

SHOES BUY ONE GET ONE FREE: (12x2 - 12)= 12

40 + 24 + 12 = 76

Some simplification:

[tex]\dfrac{x^{-1}}{x^{-1}+1^{-x}}=\dfrac{x^{-1}}{x^{-1}+1}=\dfrac1{1+\frac1{x^{-1}}}=\dfrac1{1+x}[/tex]

Then

[tex]f(2)=\dfrac1{1+2}=\dfrac13[/tex]

Answer:

$726.02 I had to guess cause I used a calculator but it didn't get to an exact number this is the closet

Answer:

$726.02

Step-by-step explanation:

Answer:

125,970

Step-by-step explanation:

Even if jury are assigned numbers, the order in which they are picked has no importance.  That means that it's a combination, not a permutation.

The formula to calculate possible combinations is:

[tex]C(n,r) = \frac{n!}{(r! (n-r)!)}[/tex]

Where n is the global population, and r is the number of selected items.

In our case, n = 20 and r = 12, so...

[tex]C(20,12) = \frac{20!}{(12! (20-12)!)} = 125970[/tex]

There are 125970 different ways to select 12 jury members out of 20 people.

there are 125970 different 12 person juries that can be chosen from a pool of 20 people.

The question is asking how to determine the number of different ways to choose a 12-person jury from a pool of 20 potential jurors. This type of problem is solved using the concept of combinations in mathematics, specifically the binomial coefficient formula which is given by the following:

C(n, k) = n! / (k!(n - k)!)

where:

n represents the total number of items (in this case, jurors).

k represents the number of items to choose (jurors to be selected for the jury).

n! means factorial of n, which is the product of all positive integers up to n.

In this scenario, n = 20 and k = 12. Therefore, the number of different 12 person juries that can be chosen is calculated as:

C(20, 12) = 20! / (12!(20 - 12)!)

Further calculation yields:

C(20, 12) = 20! / (12!8!) = 125970

Therefore, there are 125970 different 12 person juries that can be chosen from a pool of 20 people.