MATHEMATICS MIDDLE SCHOOL

Jada is standing 10 feet away from the base of the tree and spots a nest sitting on a branch. The angle of elevation from the ground where she is standing to the nest is 55 degrees. Find the height of the nest.

Answers

Answer 1

Answer:

Answer:

14.3 feet

Step-by-step explanation:

Let the height of the tree = x feet.

It is given that the horizontal distance from the base of tree = 10 feet and the angle of elevation to the nest is 55°.

So, we get the following figure.

As, we are obtaining a right angled triangle.

Using the trigonometric form for the angles of a right angled triangle, we get,

$\tan x=(opposite)/(adjacent)$

i.e. $\tan 55=(x)/(10)$

i.e. $x=10* \tan 55$

i.e. $x=10* 1.43$

i.e. $x=14.3$

Hence, the height of the tree is 14.3 feet.

Answer 2

Answer:

Answer:

here is your answer ..have a good day.

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The n term of a geometric sequence is denoted by Tn and the sum of the first n terms is denoted by Sn.Given T6-T4=5/2 and S5-S3=5.Calculate (a)the common ratio. (b)the first term of this geometric sequence

Answers

1 step: $S_(5)=T_(1)+T_(2)+T_(3)+T_(4)+T_(5)$ , $S_(3)=T_(1)+T_(2)+T_(3)$ , then
$S_(5)-S_(3)=T_(4)+T_(5)=5$ .

2 step: $T_(n)=T_(1)*q^(n-1)$ , then
$T_(6)=T_(1)*q^(5)$
$T_(5)=T_(1)*q^(4)$
$T_(4)=T_(1)*q^(3)$
$T_(3)=T_(1)*q^(2)$
and $\left \{ {{T_(6)-T_(4)= (5)/(2) } \atop {T_(5)+T_(4)=5}} \right.$ will have form $\left \{ {{T_1*q^(5)-T_(1)*q^(3)= (5)/(2) } \atop {T_(1)*q^(4)+T_(1)*q^(3)=5} \right.$ .

3 step: Solve this system $\left \{ {{T_1*q^(3)*(q^(2)-1)= (5)/(2) } \atop {T_(1)*q^(3)*(q+1)=5} \right.$ and dividing first equation on second we obtain $(q^(2)-1)/(q+1)= ( (5)/(2) )/(5)$ . So, $((q-1)(q+1))/(q+1) = (1)/(2)$ and $q-1= (1)/(2)$ , $q= (3)/(2)$ - the common ratio.

4 step: Insert $q= (3)/(2)$ into equation $T_(1)*q^(3)*(q+1)=5$ and obtain $T_(1)* (27)/(8)*( (3)/(2)+1 ) =5$ , from where $T_(1)= (16)/(27)$ .

An architect makes a model of a new house with a patio made with pavers. In the model, each paver in the patio is 1/3 in. long and 1/6 wide. The actual dimensions of pavers are shown: 1/8 ft and 1/4ft. What is the constant of proportionality that relates the length of a paver in the model and the length of an actual paver? What is the constant of proportionality that relates the area of an actual paver?

Answers

Answer:

The constant of proportionality between the actual dimensions of the pavers and the model is 9.

The proportionality constant for the area is 81.

Step-by-step explanation:

To solve this problem, let's transform all quantities to the same units (inches)

The actual dimensions of the pavers are:

$Width = (1)/(8) ft * (12in)/(1 ft) = (3)/(2) in\n\n Length = (1)/(4) ft * (12in)/(1 ft) = 3in$

Then we divide the real dimensions between those of the model:

Width:

$((3)/(2))/((1)/(6))= 9$

Long =

$(3)/((1)/(3))= 9$

Then, the constant of proportionality between the actual dimensions of the pavers and the model is 9.

Actual length = model length * (9)

The "A" area of a paver is the product of its width multiplied by its length.

So:

(real width) * (real length) = ((9) Model width) * ((9) model length)

(real width) * (real length) = $9 ^ 2$ * (Model width) * (model length)

(real area) = 81 * (Model area)

The proportionality constant for the area is 81.

Answer:

The length of a paver in the model and the length is 1/9.

The constant of proportionality that relates the area 1/81.

Step-by-step explanation:

Area of rectangle is

$A=length* width$

Dimensions of paver in model:

$Length=(1)/(3)in$

$width=(1)/(6)in$

Area of model

$A=length* width$

$A=(1)/(3)* (1)/(6)=(1)/(18)$

The area of the model is 1/18 square inches.

We know that 1 ft = 12 inches

Actual dimensions of paver:

$Length=(1)/(4)ft=3 in$

$width=(1)/(8)ft =1.5in$

Actual area is

$A=length* width$

$A=3* 1.5=4.5$

The actual area is 4.5 square inches.

The constant of proportionality that relates the length of a paver in the model and the length of an actual paver is

$\text{Constant of proportionality of length}=\frac{\text{Length of model}}{\text{Actual length}}=(1/3)/(3)=(1)/(9)$

The length of a paver in the model and the length is 1/9.

The constant of proportionality that relates the area of an actual paver is

$\text{Constant of proportionality of area}=\frac{\text{Area of model}}{\text{Actual area}}=(1/18)/(4.5)=(1)/(81)$

The constant of proportionality that relates the area 1/81.

19) At a local river, there were 48 alligators lying on the riverbank. If of the alligators wereasleep, how many were not asleep?20) At a charity bike rally, offhe student population of oakleaf Junior High Schodparticipated. If there are 1students at ouJH, how many participated in the bike rally?

21) out of 18 times at bat, Kayla got a hitof the time and Tia got a hitof the time. Whogot more hits? How many more?

Answers

19) 48 alligators; 7/8 of the alligators were asleep. How many were not asleep?

8/8 - 7/8 = 1/8
48 * 1/8 = 48/8 = 6 alligators were not asleep.

20) 2/3 of the student population participated. 1,500 is the student population of the school. HOw many attended the bike rally?

1500 * 2/3 = 1500*2 / 3= 3000 / 3 = 1000 students attended.

21) 18 times at bat:
Kayla 5/6 of the time = 18 * 5/6 = 18*5 / 6 = 90/6 = 15 hits
Tia 8/9 of the time = 18 * 8/9 = 18*8 / 9 = 144/9 = 16 hits

Tia got more hits.

Your bill is $49.64 you want to give a tip if 15% how much would the tip be? Round to nearest dollar. Part B what is exact estimated tip round to nearest cent.
Please help I do not get this!❤️

Answers

Answer:

$63.25

Step-by-step explanation:

Answer:

Part A : $7

Part B : $7.44

Step-by-step explanation:

49.64/0.15 = 7.446 ($7)

Tonya took out a loan to help pay for her house. She borrowed $40,000 for 15 years at a yearly simple interest rate of 5%. How much interest will she end up paying the bank? A. $300 B. $30,000 C. $6,000 D. $300,000

Answers

Answer is B. Need an explanation?

6 divided by four sevenths

Answers

First step - make both the numbers into fractions.6/1 divided by 4/7Second step - reciprocal ( you flip the second fraction)6/1 divided by 7/4Third step - multiply6*7=421*4=442/4Fourth step - simplifySo, in this case, you change it into a mixed number, because it is an improper fraction. You do this by dividing 42 by 4 and you get 10 1/2.The answer is 10 1/2

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