If you are standing 23 m for a tree and the angle of elevation from where your standing is 35° what is the height of the tree?

Considering the figure the unknown angles are

Using the angle in a straight line are supplementary we have

60 + a + 55 = 180

a + 115 = 180

a = 180 - 115

a = 65

applying sum of angles in a triangle equal to 180, b is calculated as follows

a + b + 90 = 180 right angle triangle

substituting for a

65 + b + 90 = 180

b + 155 = 180

b = 180 - 155

b = 25

applying vertical angle theorem

angle c = angle b

angle c = 25

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The distance from the top of the tree to the tip of the shadow is 12.8 ft  

According to the Pythagorean theorem, In a right-angled triangle, the sum of the squares of the side will equal the square of the hypotenuse.
Here hypotenuse is the longest side.

=> Hoptenuse² = side² + side²

Here we have

The length of the tree = 10 feet

Length of shadow = 8 feet

Here we need to find the distance from the top of the tree to the tip of the shadow  

If we join the top of the tree to the tip of the shadow we will observe a right-angled triangle as shown below

From the figure,

AC² = AB² + BC²    [ ∵ ABC is right angle triangle ]

=> AC² = 10² + 8²  

=> AC² = 100 + 64

=> AC² = 164

=> AC = 2√41

=> AC = 12.8 ft

Therefore,

The distance from the top of the tree to the tip of the shadow is 12.8 ft  

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Answer:

b) 12.8 feet

Step-by-step explanation:

Now we have to,

→ find the required distance.

Forming the equation,

→ x² = 10² + 8²

Then the distance will be,

→ x² = 10² + 8²

→ x² = 100 + 64

→ x² = 164

→ x = √164

→ [ x = 12.8 feet ]

Hence, distance is 12.8 ft.

The unit rate of change , d with respect to t is =  1.6  .

In the question,

it is given that ,  the relationship between d and t is proportional

also given that "  increase of 5 units in t corresponds to increase of 8 units in d ".

which is represented as 5t = 8d

Divide both sides of the equation  5t = 8d by "5" ,

t = 8/5d

t = 1.6d

next we plot the graph of t = 1.6d

we see that the above equation is a proportional linear equation

and A proportional linear equation is represented as

t = md , Where m represents the unit rate .

So , after comparing , we get

m = 1.6

Therefore , The unit rate of change of d with respect to t is 1.6  .

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Answer:

Let the age of brother be x and that of a sister be y.

(x+y) =16

(x) ×(y) =63

Using the substitution method, x=16-y

Substitute in equation 2

(16-y)(y)=63

16y-y^2=63

Y^2-16y+63=0

P=63

Sum= -16

Factor=(y-7),(y-9)

(y-7)(y-9)=0

Therefore y=7 or y=9

Therefore age of brother = 16-7 =9 0r 16-9=7

Therefore their ages are 9 years and 7 years

The volume of the sphere is 7241.142 m[tex]m^{3}[/tex].

Given:

A sphere has a diameter of 24 mm.

Radius r = diameter/2

= 24/2

r = 12 mm.

volume of sphere = 4/3π[tex]r^{3}[/tex]

= 4/3 * 22/7 * [tex]12^{3}[/tex]

= 88*[tex]12^{3}[/tex]/21

= 88*1728/21

= 152064/21

= 7241.142 m[tex]m^{3}[/tex].

Therefore the volume of the sphere is 7241.142 m[tex]m^{3}[/tex].

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Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.

According to the question,

We have the following information:

Amount to be invested = $15200

Interest earned 1% a year and 4% a year

Total amount interest to be earned at the end of first year = $548

Now, let's take the amount to be invested in 1% interest a year's mutual fund to be $x.

Then, we have the amount to be invested in mutual fund that earns 4% a year:

$(15200-x)

So, we have the following expression by removing percentage sign:

x/100 + (15200-x)4/100 = 548

Taking 100 as the least common factor and using the cross multiplication method:

x+60800-4x = 548*100

-3x = 54800-60800

-3x = -6000

x = 6000/3

x = $2000

Now, the amount invested in second mutual fund:

15200-2000

$13200

Hence, Sherry needs to invest $2000 in a mutual fund that earns 1% interest a year and $13200 in a mutual fund that earns 4% interest a year.

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Answer:

b=98 and a=82

Step-by-step explanation:

b and 98 are corrisponding angles which means that they are both 98

a+b=180 because it is a straight line

a+98=180 subtract 98 from both sides a d you get a=82

The area of the tile in square centimeters is 929cm2

The area in square centimeters is calculated as follows

First, let convert the tile measures 12 inches on each side into centimeters

1 inch = 2.54 centimeters

= 12 x 2.54
= 30.48 centimeters

Next is to find the area of the tile in square centimeters
The area of square = (side) x (side) square units
= 30.48 centimeters x 30.48 centimeters

= 929.0304

= 929 square centimeters (rounded)

So, the area of the tile in square centimeters is 929 square centimeters

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Answer:

The area of the tile in square centimeters is 929cm2

Step-by-step explanation:

I took the exam and got it right

Answer:

-5 with the exponet of 11

Answer:

-1/5 or -0.2 if you are going by fraction or decimal

The complete two-column proof that shows that ΔAKZ ≅ ΔAKC by AAS is explained below.

The AAS congruence theorem states that if two angles and one non-included side in one triangle have measures that are equal to the two corresponding angles and a corresponding side of another triangle, the two triangles are therefore congruent to each other.

In the image above, we are given two triangles that share a common side, AK. We are informed that line AK bisects an angle, ZKC, and also angles Z and C are congruent.

Therefore, using the information we are given, the two-column proof that can be written to show that the triangles are congruent by the AAS is explained below.

Statements                             Reasons                                      

1. ∠Z ≅ ∠C                              1. Given

AK bisects ∠ZKC

2. ∠ZKA ≅ ∠CKA                   2. Definition of bisection

3. AK ≅ AK                             3. Reflexive property

4. ΔAKZ ≅ ΔAKC                   4. AAS

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Answer: 23%

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

The value needs to be added to x²+10x+6 to complete the square is 19.

Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)².

In the presented trinomial, we can immediately find that a = x, and b² = c,

We know that a = x, and , 2ab = 2bx.

Now, 2bx and 30x are corresponding terms, 2bx = 30x.

Take the coefficient of x = 10

Divide by 2

10/2 =5

Then Square it

5 x 5=25

Add this to make a perfect square trinomial;

x² + 10x + 25

In the given equation we need to add 19 to make the perfect square trinomial; x² + 10x + 25.

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AB has endpoints A (1, 7) and B (5, 4) and DE has endpoints D (-6, -2) and E (-2,-5). The translation is by the rule (x - 7, y - 9), is used to transform AB to DE

Translation is a type of transformation that involve a linear movement.

The translation rule is gotten by comparing the points as below

preimage point A (1, 7) and B (5, 4)

image points D(-6, -2) and E(-2,-5)

x coordinate

using point A and D = -6 - 1 = -7

using point B and E = -2 - 5 = -7

y coordinate

using point A and D = -2 - 7 = -9

using point B and E = -5 -  = -9

Therefore the translation rule is (x - 7, y - 9) that got the image, point D and E from the preimage , point A and B

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The width, labelled x in the figure is 162.5 meters

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

Length = 650 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (650 - 2x) * x

Evaluate

A = 650x - 2x²

Differentiate and set to 0

650 - 4x = 0

So, we have

4x = 650

Divide by 4

x = 162.5

Hence, the width is 162.5 meters

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Answer:

Nathan

Step-by-step explanation:

4.76 / 2.5

= (476/100) / (25/10)

= (476/100) * (10/25)

= 238/125

= 1.904

Thus, Nathan is right in saying that the decimal is incorrectly placed in the quotient of the given answer 0.19

A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given sequence, 20 - n²

The 20 - n² represents the nth term of the sequence.

Thus a(n) = 20 - n²

For the third term n = 3

a(3) = 20 - (3)²

a(3) = 20 - 9 = 11

Hence "A sequence or series is the generalized form of the pattern thus the third term of the given sequence 20 - n² is 11".

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The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.

Therefore,

I = Prt

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

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The translation T due to the transformation is (5,3)

Translation can be defined as movement in a straight line

Given the rule: (x,y) → (x + 3, y + 1) as seen in the image. That means  (x,y) translated to (x + 3, y + 1). This is what we use to solve this problem.

From the figure, the value of  (x, y) can be read i.e. (x, y) = (2,2)

Thus the translation will be:

(x,y) → (x + 3, y + 1)

(2,2) → (2 + 3, 2 + 1) = (5, 3)

Therefore, the  translation T of the transformation shown in the graph is (5, 3)

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Answer:

Step-by-step explanation:

first you need to find the nth term

that would be -4n+28

then you just need to substitute 20 into the position of n

-4*20 = -80

-80+28=-52

Answer: x=3

Step-by-step explanation:

5x+2=7x-4
-5x +4    -5x +4
2x=6
divide both sides by 2
x=3

The dimension of each corral should be 25 feet in width and 33⅓ feet in length so that the enclosed area will be a maximum.

Adjacent rectengular corral has length and width with area formula as below.

A = L × W

Given:

Because the dimension of adjacent rectangular corrals are the same, so:

W = 4x

L = 3y

3y + 4x = 200

[tex]y = \frac{200 - 4x}{3} [/tex]

There are two adjacent rectangular corrals, so:

A = 2×L×W

[tex]A = 2 \times \frac{200 - 4x}{3} \times \: x [/tex]

A = ⅓(400x–8x²)

We can differentiate to get the maximum area:

⅓×(400x–8x²) = 0

400–16x = 0

16x = 400

x = 25 feet

Substitute x value (width) to get y value (length):

y = (200–4(25)) ÷ 3

y = (200–100) ÷ 3

y = 100 ÷ 3

y = 33⅓ feet

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Using the concepts of probability, we got that that Stratified sampling is the experiment design which an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs.

In the question, actually the insurance company intends to study and understand the relationship between the health care cost of the customers and the provision of incentives for the preventative care by two groups, each having one of  two given attributes under study, which are;

a) One group consist of the customers having high health care cost and offered incentives for preventative care

b) The other group consist of the customers having only high health care cost without incentives

Therefore, the insurance company customers are stratified into the groups based on health care cost and again into the groups that have high health care cost and are offered preventative care and those that have only the high heath care cost, which is the process used to implement the stratified sampling technique.

Hence, an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs, by selecting a random sample of 200200200 of their customers and using a random number generator to select 100100100 customer account numbers to offer the incentive, the experiment design is named as  Stratified sampling.

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The value of  g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).

Given,

In the question:

f(x) = [tex]x^{2}[/tex]

To find the value of g(x)

To see the graph and analysis

Now, According to the question:

We know that:

g(x) = k f(x) = k[tex]x^{2}[/tex]

In the graph, The value are given as:

Plug (4,1) into g(x):

1 = k. [tex]4^2[/tex]

k = 1/16

=> g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex])

Hence, The value of  g(x) = 1/16[tex]x^{2}[/tex] = (1/4[tex]x^{2}[/tex]). The correct option is (C).

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Answer: $2.08

Step-by-step explanation: First multiply $52 by 4% as a decimal or 0.04. Then, multiply that by the number of years.
=52(0.04)(1)

=2.08

The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

As per the given,5280ft

It is known that 1 ft = 12 inches.

5280ft = 5280 x 12 inches

It is known that 1 inch = 2.54 cm

5280 x 12 inches = 5280 x 12 x 2.54 cm

It is known that 1 cm = 0.01 meter

5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter

⇒  1609.344 meters

Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".

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Check the picture below.