As part of his math assignment, Santos has to estimate the height
of a lighthouse. He decides to use what he knows about 30-60-90
triangles. Santos makes the measurements shown below. About how
tall is the tower? Explain.
60
5ft
58 ft.
Not drawn to scale

Answer:

a + b + c = 12

Step-by-step explanation:

The given information are;

a² + b² + c² = 138

a·b + b·c + c·a = 3

The required data = a + b + c

Using an online tool, we have;

(a + b + c)² = (a + b + c) × (a + b + c) = 2·a·b + 2·b·c + 2·c·a + a² + b² + c²

∴ (a + b + c)² = 2·(a·b + b·c + c·a) + (a² + b² + c²)

Where;

a·b + b·c + c·a = 3, and a² + b² + c² = 138, we have;

(a + b + c)² = 2 × 3 + 138 = 144

(a + b + c)² = 144

(a + b + c) = √144 = 12

a + b + c = 12.

Answer:

25

Step-by-step explanation:

Answer:

x = 25

Step-by-step explanation:

Okay so as you can see there is an x shape and whenever you have that it means they are verticle angles. So we can conclude that 25 is verticle to x and so x is equal to 25.

f(-6) = 5

Just look at the graph when x= -6 , y = 5

Answer:

Step-by-step explanation:

See image -->Answer

Answer:

The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h

Step-by-step explanation:

At noon the location of Lan = 300 km north of Makenna

Lan's direction = South

Lan's speed = 60 km/h

Makenna's direction and speed = West at 75 km/h

The distance  Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km

The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km

The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km

Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.

By Pythagoras' theorem, we have;

s² = x² + y²

The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61

ds²/dt = dx²/dt + dy²/dt

2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt

2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900

ds/dt = 900/(2×30·√61) ≈ 1.92

The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h

Answer:

952

Step-by-step explanation:

If you have anything else that has to do with donuts it goes straight to me.

Answer:

102 more donuts

Step-by-step explanation

when dealing with how much percent increase you multiply the amount by the percent in decimal form . So 850x0.12 is 102.

Answer:

5 men and 2 women = 7 people with no restriction

a) Two women must sit next to each other:

b) The two women must not sit next to each other:

3 men and 5 women with no restriction:

Answer:

x = [tex]\frac{3+\sqrt{105} }{8} , \frac{3-\sqrt{105} }{8} x=1.655,-0.905[/tex]

Step-by-step explanation:

3x+6 = 4x^2

4x^2 -3x -6 = 0

x = [tex]\frac{3+\sqrt{105} }{8} , \frac{3-\sqrt{105} }{8} x=1.655,-0.905[/tex]

Answer:

6.66 kg/m is the correct answer

Answer:

An arithmetic sequence is defined by:

[tex]a_n = a_{n-1} + d[/tex]

Here, we know that:

[tex]a_3 = 14\\a_{10} = 98[/tex]

Using the recursive relation, we can write:

[tex]a_{10} = 98 = a_9 + d[/tex]

And can keep applying the recursive relation, so we will have:

[tex]98 = a_9 + d = (a_8 + d) + d = a_8 + 2*d[/tex]

And so on, until we get to a known term:

[tex]98 = a_8 + 2*d = a_7 + 3*d = a_6 + 4*d = a_5 + 5*d = a_4 + 6*d = a_3 + 7*d[/tex]

[tex]98 = a_3 + 7*d = 14 + 7*d[/tex]

Then we can solve:

98 = 14 + 7*d

for d:

98 - 14 = 7*d

84 = 7*d

84/7 = d = 12

Now we know the value of d, we can keep using the recursive relation to find the first 3 terms:

Here, we can rewrite the recursive relation as:

[tex]a_{n-1} = a_n - d[/tex]

Then:

[tex]a_2 = a_3 - d = 14 - 12 = 2\\a_2 = 2[/tex]

[tex]a_1 = a_2 - d = 2 - 12 = -10\\a_1 = -10[/tex]

[tex]a_0 = a_1 - d = -10 - 12 = -22\\a_0 = -22[/tex]

Then the first 3 terms are:

-22, -10, 2

Answer:

Step-by-step explanation:

none in the first 3 box

none in the second 3 boxes

2 in the third 3 boxes

1 in the 4th three boxes

1 in the 5th three boxes

3 in the 6th three boxes

and none in the last 3 boxes

hope this helped :D

Answer:

300

Step-by-step explanation:

A: 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25 +26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+ 67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100

A=5,050

B: 4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25 +26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+ 67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100+101+102+103

B=5,350

B-A

=5,350-5,050

=300

Answer:

6.9 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 35 = x /12

12 sin 35 = x

6.882917236=x

To the nearest tenth

6.9 =x

Answer:

[tex]x=100\\y=60[/tex]

Step-by-step explanation:

The shape of the figure is quadrilateral, that means overall it will be 360 degrees.....

Angle of straight line to find x:

[tex]x+80=180[/tex]

[tex]x=180-80[/tex]

[tex]x=100[/tex]

Now, both the values of x will be 100

Find the value of y:

[tex]y+100+120+80=360[/tex]

[tex]y+300=360[/tex]

[tex]y=360-300[/tex]

[tex]y=60[/tex]

Therefore, [tex]x=100[/tex] and [tex]y=60[/tex]

hope this helps, have a good day.....

Answer:

We taking the same final exam

Step-by-step explanation:

I don’t know the answer that’s why I came here

Answer:

2

Step-by-step explanation:

take any point

i am taking F

coordinate of F is (5 , 3)

F' is (10,6)

so use formula

(x , y) = (kx , ky)

(5 , 3) = (5k , 3k) = (10 , 6)

compare corresponding elements

5k = 10

k = 10/5

k = 2

3k = 6

k = 6/3

k = 2

note here k means scale factor

Answer:

p = 2(l+w)

= 2 ( 13 + 6)

2 ( 19)

= 38

C = 2pie r(radius)

= 2 × 22/7 × 3

= 18/6/7

38 - 18/6/7

answer = 19.14

HOPE ITS HELPS!!

plzz brainliest..

Answer:

1. The two triangles are ASA congruent

2. The two triangles are SAS congruent

Answer:

40

Step-by-step explanation:

the line in the middle shows the median

Answer:

7x

Step-by-step explanation:

Common ratio = 2nd term ÷ first term

[tex]= \frac{35x^{2}}{5x}=\frac{35 * x * x}{5 *x}\\\\= 7x[/tex]

Answer:

8

Step-by-step explanation:

x+x+7=23

2x=16

x=8

There were 8 males in the meeting.

Let us assume,

The number of males = x

Number of females = 7+x

Total people = 23

x + x+ 7= 23

2x + 7 =23

2x = 23 - 7

2x = 16

x= 8

There were 8 males in the meeting.

To learn more about How many males were there refer to:

https://brainly.com/question/734405

#SPJ2

Answer:

B

Step-by-step explanation:

4 scores add all together divided by 4 needs to be greater or equal to his goal

Let G be some point on the diagonal line away from point E.

Angle DEG represents angle 1.

We're given that angle DEF is a right angle which means it's 90 degrees. Angle DEG is some angle smaller than 90 degrees. By definition, that must mean angle 1 is acute. Any acute angle is smaller than 90 degrees. There's not much else to say other than this is just a definition problem.

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

Extra side notes:

If angle 1 was a right angle, then that would mean angle GEF would have to be 0 degrees; however the diagram shows this isn't the case.

If angle 1 was obtuse, then there's no way we'd be able to fit it into angle DEF. In other words, there's no way to have an angle larger than 90 fit in a 90 degree angle.

Answer:

25.2 in.

Step-by-step explanation:

Given:

RQ = 7 in.

QL = 24 in.

LK = 3 in.

Required:

Length of diagonal RK

Solution:

Apply the extension of the Pythagorean theorem which is:

d² = x² + y² + z²

Where,

d = RK

x = RQ = 7 in.

y = QL = 24 in.

z = LK = 3 in.

Plug in the values

d² = 7² + 24² + 3²

d² = 634

d = √634

d = 25.1793566 ≈ 25.2 in. (nearest tenth)

Answer:

x = 21º

Step-by-step explanation:

∆ ABC is isosceles therefor

Angles B and C are congruent

(180  - 18)/2 = 162/2 = 81º

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

∆ BCD is equilateral  therefor all angles are 60º

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

x = = 81 - 60

x = 21º

Answer:

20

Step-by-step explanation:

320 = 16x

Our objective here is to isolate the variable (x) using inverse operations

First we want to get rid of 16

16x is the same as 16 times x( which is multiplication)

The inverse of multiplication is division so to get rid of the 16 we divide by 16 ( but note: whatever you do to one side you must do to the other ) so we divide both sides by 16

320/16=20

16x/16 = x

We would be left with x = 20

This meaning that they would need 20 first grade classes

Answer:

The school will need 20 first grade classes

Step-by-step explanation:

So think about it. There are 320 first grade students and each class can have 16 students which represents the equation 16x=320

All you need to do is solve the equation 16x=320

The equation is multplication. To undo multiplication you need to do division

So, x=320/16

x=20

So overall, your awnser is 20.

Answer:

Since i don't know what formula is mentioned. I just used the easiest way to solve :)

Step-by-step explanation:

[tex](3x^2 + 3)^3 = (3x^2)^3 + 3^3 + 3((3x^2)^2)(3) + 3(3x^2)(3^2)[/tex]

              [tex]= 27x^6 + 27 + 3(9x^4 \times 3) + 3(3x^2 \times 9)\\\\=27x^6 + 27 + 81x^4 + 81x^2\\\\=27x^6 + 81x^4 + 81x^2 + 27\\\\[/tex]

[tex]\int\limits {(3x^2+3)^3} \, dx = \int\limits {27x^6 + 81x^4+81x^2 + 27} \, dx[/tex]

                      [tex]= \frac{27}{7}x^7 + \frac{81}{5}x^5+\frac{81}{3}x^3 + 27x +C\\\\= \frac{27}{7}x^7 + \frac{81}{5}x^5+27x^3 + 27x +C\\\\[/tex]

Answer:

The expressions are not equivalent.

Step-by-step explanation:

Here we have two expressions:

4*(2 + p)

14 + p

We want to evaluate these two expressions in two different values of p to check if the expressions are equivalent or not.

First, we evaluate both of them in p = 2, this is just replace p by 2 in each expression and then solve it.

4*(2 + 2) = 4*4 = 16

14 + 2 = 16

In this case, we can see that both expressions yield the same number, so we could think that the expressions are equivalent, now let's try with other value of p.

Now let's do it with p = 8

4*(2 + 8) = 4*10 = 40

14 + 8 = 22

Now we can see that the results are different, then we can conclude that the expressions are not equivalent.

Answer:

Use p = 2 and p = 8 to determine if the two expressions are equivalent.

   4(2 + p)    14 + p

Complete the statements.

If both expressions have the same value after substituting two different values and simplifying, then they are

✔ equivalent expressions

.

When p = 2, the first expression is

✔ 16

and the second expression is 16.

When p = 8, the first expression is 40 and the second expression is

✔ 22

.

The expressions are

✔ not equivalent

.

Answer:

There isn't a plot.

Step-by-step explanation: