A nursery plants a new tree and attaches a guy wire to help support the
tree while its roots take hold. An eight foot wire is attached to the tree
and to a stake in the ground. From the stake in the ground the angle of
elevation of the connection with the tree is 42°. Find to the nearest tenth
of a foot, the height of the connection point on the tree.

Answer:

[tex]A = 43.0^o[/tex]

[tex]B = 55.0^o[/tex]

[tex]BC = 20.0[/tex]

Step-by-step explanation:

I will solve this question with the attached triangle

From the attachment, we have:

[tex]\angle C =82^o[/tex]

[tex]AB = 29[/tex]

[tex]AC = 24[/tex]

Required

Solve the triangle

First, we calculate [tex]\angle B[/tex] using sine law:

[tex]\frac{AC}{\sin(B)} = \frac{AB}{\sin(C)}[/tex]

This gives:

[tex]\frac{24}{\sin(B)} = \frac{29}{\sin(82^o)}[/tex]

[tex]\frac{24}{\sin(B)} = \frac{29}{0.9903}[/tex]

Cross multiply

[tex]\sin(B) * 29 = 24 * 0.9903[/tex]

[tex]\sin(B) * 29 = 23.7672[/tex]

Divide both sides by 29

[tex]\sin(B) = 0.8196[/tex]

Take arcsin of both sides

[tex]B = \sin^{-1}(0.8196)[/tex]

[tex]B = 55.0^o[/tex]

Next, calculate [tex]\angle A[/tex] using:

[tex]A + B + C = 180^o[/tex] --- angles in a triangle

[tex]A + 55^o + 82^o = 180^o[/tex]

Collect like terms

[tex]A = 180^o-55.0^o - 82^o[/tex]

[tex]A = 43.0^o[/tex]

Next, calculate BC using sine laws

[tex]\frac{BC}{\sin(A)} = \frac{AB}{\sin(C)}[/tex]

This gives:

[tex]\frac{BC}{\sin(43.0)} = \frac{29}{\sin(82)}[/tex]

[tex]\frac{BC}{0.6820} = \frac{29}{0.9903}[/tex]

Make BC the subject

[tex]BC = \frac{29*0.6820}{0.9903}[/tex]

[tex]BC = 20.0[/tex]

Answer:

$9,763

Step-by-step explanation:

Using the compund interest formula;

A = P(1+r)^t

A is the amount = $10,200

rate r = 6.5%= 0.065

time t = years

n = 1/365 ((daily compounding)

Substitute into the formula and get Pincipal P

10,200 = P(1+0.065(365))^5/365

10200 = P(1+23.725)^0.01369

10200 = P(24.725)^0.01369

10200 = P(1.0448)

P = 10200/1.0448

P = 9,762.6

Hence the amount invested is $9,763 to nearest dollars

Answer:

∠ BOC = 40°

Step-by-step explanation:

∠ AOC = 90° , then

5x + 2x + 20 = 90

7x + 20 = 90 ( subtract 20 from both sides )

7x = 70 ( divide both sides by 7 )

x = 10

Then

∠ BOC = 2x + 20 = 2(10) + 20 = 20 + 20 = 40°

Answer:

The negative sign is put before numbers to make them negative, or make their signs the opposite of what the are.

You have a 20.

+ 20

You don't need to put the + there if there is nothing before it, but that is a positive 20.

If you put a negative in front of it;

- (+ 20) = - 20

If you have a negative in front of parenthesis;

50 - (2x - 20)

50 - 2x + 20

70 - 2x

Answer:

144.84

Step-by-step explanation:

Answer:

No solution is possible from the information provided.

Step-by-step explanation:

"A floor plan of the room is shown below. "

You failed to provide the floor plan so it is not possible to answer your question.

Responder:

15 m e 75 m

Explicação passo a passo:

Deixar :

Largura = x

Comprimento = 5x

Perímetro = 180

Já o terreno tem uma forma retangular; usamos a relação;

Perímetro = 2 (comprimento + largura)

180 = 2 (5x + x)

180 = 2 (6x)

180 = 12x

180/12 = x

15 = x

Largura = x = 15 metros

Comprimento = 5x = 15 * 5 = 75 metros

Medida de largura e comprimento, respectivamente:

15 m e 75 m

Answer:

400 total .... 120 officers

Step-by-step explanation:

.7 X = 280

x=400

Answer:

30% of 280 is 84.

What I did to find the answer was multiply 280 by 3 then divide by 10.

I checked it with a calculator and got the same result being 84.

Answer:

The volume is 942.478

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4 * 2=8. Don't really know how else to explain it

Answer:

x = 9

Step-by-step explanation:

These are alternate exterior angles and alternate exterior angles are equal if m is parallel to n

6x+5 = 7x-4

Subtract 6x from each side

6x -6x+5 = 7x-6x-4

5 = x -4

Add 4to each side

5+4 =x-4+4

9 =x

Answer:

x = 9°

Step-by-step explanation:

The two angles are alternate exterior angles, so they both are congruent.

The equation is :

6x + 5 = 7x - 4

Add 4 to both sides

6x + 9 = 7x

Subtract 6x from both sides

9 = x

x = 9

Lets check:

6(9) + 5 = 7(9) - 4

54 + 5 = 63 - 4

59 = 59

Correct!

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Let's imagine the image of the zoo.

The diameter is basically the length of the circle.

The penguin swam the radius.

To find the radius, we need to divide the diameter by 2.

The diameter is 20 meters.

20 [tex]\div[/tex] 2 = 10 meters.

2 x pi x 10 = 62.83185307

62.83185307/2 = 31.41592654

Answer = 31.41592654

Answer:

The distance through which penguin swim = 10π meters

Step-by-step explanation:

The island is given to be in a shape of circle and the distance around any circle is known as circumference.

The diameter of the island = 20 meters

So, to find the distance traveled by penguin we need to find the circumference or the circular island.

⇒ Circumference = π·diameter

⇒ Circumference = π × 20

                             = 20π meters

Now, it is given that the penguin only travels the half of the island So, the distance traveled by penguin is half the circumference of the island.

Distance traveled by penguin = 1/2 × 20π = 10π

The distance through which penguin swim = 10π meters

9514 1404 393

Answer:

  36

Step-by-step explanation:

Let the digits of the number be represented by t for the tens digit and u for the units digit.

  u = 2t . . . . . . . . the units digit is twice the tens digit

  2(10t +u) = (10u +t) +9 . . . . . double the number is 9 more than its reverse

Substituting for u, we have ...

  2(10t +2t) = 10(2t) +t +9

  24t = 21t +9 . . . . . . . . . . . collect terms

  3t = 9 . . . . . . . . . . . . . subtract 21t

  t = 3 . . . . . . . . . . . divide by 3

  u = 2t = 6 . . . . find u

The number is 36.

Answer:

x = 25

Step-by-step explanation:

The two angles form a straight line which is 180 degrees

2x+10 + 4x+20 = 180

Combine like terms

6x+30 = 180

Subtract 30 from each side

6x+30-30 = 180-30

6x = 150

Divide by 6

6x/6 = 150/6

x=25

Answer:

30°

Step-by-step explanation:

because the sum of all interior angles in a triangle is 180 degrees

180°= ∡ADE+∡DAE+∡AED

∡ADE = 180°-∡DAE -∡AED

because the diagonals are perpendicular so they form 90° angles, and ∡BRC≅∡AED(vertical angles)

∡AED =90

To find ∡DAE we need to find the value of y

11y+2  =90

11y =90-2

y=88/11

y=8

∡DAE=7y+4=7 ·8 +4= 56+4 =60°

now we know what we need to find ∡ADE

∡ADE = 180°-∡DAE -∡AED

∡ADE = 180°-60° -90°

∡ADE = 30°

Answer:

3 1/2 is between 3 and 4  in the MIDDLE. 3/12 would be between 3 and 3 1/10

Answer:

Step-by-step explanation:

3 1/2 > 3 1/12

so 3 1/2 is right of 3 1/12.

Answer:

The answer is "[tex]b=\frac{A}{h}[/tex]".

Step-by-step explanation:

Therefore in this question the "bh" were the multiplied and these values includes the variable which is solving by the isolating of "b".

Let's Divides the both sides for h.

[tex]\to \frac{A}{h} = \frac{bh}{h}\\\\\to \frac{A}{h} = b\\\\\to b= \frac{A}{h}[/tex]

Answer:

B

Step-by-step explanation:

i know math

Answer:

Step-by-step explanation:

Answer: t=-8

Step-by-step explanation:

1/2t-4(2+t)=20 then multiplied by two so t-16-8t=40 -7t=56 then divide -7 by 56 and you will get your answer t=-8

Answer:

x = 2

Step-by-step explanation:

[tex] log_{3}x(x+ 30) = log_{3}64 \\ x(x + 30) = 64 \\ {x}^{2} + 30x - 64 = 0 \\ x = 2 \: or \: x = - 32[/tex]

-32 is rejected because in logarithms you cannot use negative value so x=2

9514 1404 393

Answer:

  a) see attached

  b) 1/3

Step-by-step explanation:

Your grid doesn't come with any coordinate axes, so you will need to draw those and label them. You will also need to determine the number of grid squares for each unit. (I suggest 2 grid squares per unit to give you a little more distance between the points you plot. The attachment shows 5 small squares per unit. You may not have this much space on your graph.)

Plot the points. Once you do this, you can see that their horizontal difference is 3 units and their vertical difference is 1 unit. The right point is above the left point, so the slope is positive:

  m = (rise)/(run) = 1/3 . . . slope of the line

Answer:

Adjacent

Step-by-step explanation:

Because supplementary angles make 180 degrees, complementary make 90 degrees, vertical angles are pairs of opposite angles made by two intersecting lines.

Answer:

8

Step-by-step explanation:

7779.949783~7779.94978

Answer:

The missing digit is 8

Step-by-step explanation:

An educated guess, but i'm pretty sure it's right

Answer:

Step-by-step explanation:

according to the question ur algebraic expression is

8-w

The algebric function will be 8-w

Answer:

True.

Step-by-step explanation:

first solid

A=72

second solid

A= 72

Answer:

True

Step-by-step explanation:

Both the surface areas = 72.

Step-by-step explanation:

Circumference is

2 x pi x r

r= 1

plug and chug

Answer:

x = 63.8°

Step-by-step explanation:

[tex]tan x = \frac{opposite}{adjacent} \\\\tan x = \frac{5.9}{2.9}\\\\x= tan^{-1} (\frac{59}{29})\\\\x = 63.82 = 63.8[/tex]

The measure of the angle [x] is equivalent to 26.6°.

Given is a triangle ΔPON as shown in the image.

From the triangle ΔPON, we can write -

tan (x°) = ON/OP

tan (x°) = (5.9/2.9)

tan (x°) = (59/29)

tan (x°) = 2.1

x° = tan⁻¹ (2.1)

x° = 26.6°

Therefore, the measure of the angle [x] is equivalent to 26.6°.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ2

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Explanation:

Check out the diagram below. I've drawn a horizontal line to split the orange region into two parts: a triangle on top and a rectangle down below.

The triangle has base 11 cm and height 7 cm. The area is base*height/2 = 11*7/2 = 77/2 = 38.5 sq cm.

The rectangle has area 11*8 = 88 sq cm.

The total area of the entire orange figure is 38.5+88 = 126.5 square cm