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3 years ago

What is the 30th term of the sequence 7, 16, 25, 34,

1 answer:

7 0

First, find the difference between each number in the sequence.... 34 - 25 = 9. 25 - 16 = 9 and 16 - 7 = 9... So, there is a constant difference of 9 between each number of the sequence. To find the 30th term, you could expand the sequence out to 30 (which is a good way to check your answer, but tedious)... So, simply add the 1st value of the sequence to the difference and multiply by 30 to find your 30th value.... 7 + 9 x 30 = 16 x 30 = 480.

Therefore, the 30th term is 480.

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Can someone please help me

anyanavicka [17]

Answer:

x=12 the other answer is 144.

Step-by-step explanation:

You set the expressions equal to each-other which gives you what x equals. then you substitute that in the A expression which gives you 144

5 0

3 years ago

Can someone help me with this plsssss

cupoosta [38]

Answer:

15 cm

Step-by-step explanation:

Given:

The two cylinders shown in the figure are similar to each other.

Therefore, when two figures are similar their measures are in proportion.

So, radius and height of both the cylinders are in proportion.

Radius of both the cylinders are 2 cm and 5 cm respectively. Height of the smaller cylinder is 5 cm. Now,

$\frac{2}{6}=\frac{5}{x}$

Doing cross multiply, we get:

$2x=6\times 5\\2x=30$

Dividing both sides by 2, we get:

$\frac{2x}{2}=\frac{30}{2}\\x=15\ cm$

Therefore, the height of the larger cylinder must be 15 cm in order to make both the cylinders similar to each other.

4 0

3 years ago

6. The angle of depression from the top of a tower to a boulder on the ground is 38°. If the tower is 25 m high,

gizmo_the_mogwai [7]

Tan38 = 25/x
.781 = 25/x
31.998 = x

3 0

3 years ago

Use the rectangle hexagon with side length 10 meters to fill in the missing information

Vlada [557]

Answer:

$A_h=150\sqrt{3}\ m^2$

Step-by-step explanation:

Regular Hexagon

For the explanation of the answer, please refer to the image below. Let's analyze the triangle shown inside of the hexagon. It's a right triangle with sides x,y, and z.

We know that x is half the length of the side length of the hexagon. Thus

$x=5 m$

Note that this triangle repeats itself 12 times into the shape of the hexagon. The internal angle of the triangle is one-twelfth of the complete rotation angle, i.e.

$\theta=360/12=30^o$

Now we have $\theta$ , the height of the triangle y is easily found by

$\displaystyle tan30^o=\frac{x}{y}$

Solving for y

$\displaystyle y=\frac{x}{tan30^o}=\frac{5}{ \frac{1} {\sqrt{3} }}=5\sqrt{3}$

The value of z can be found by using

$\displaystyle sin30^o=\frac{x}{z}$

$\displaystyle z=\frac{x}{sin30^o}=\frac{5}{\frac{1}{2}}=10$

The area of the triangle is

$\displaystyle A_t=\frac{xy}{2}=\frac{5\cdot 5\sqrt{3}}{2}=\frac{25\sqrt{3}}{2}$

The area of the hexagon is 12 times the area of the triangle, thus

$\displaystyle A_h=12\cdot A_t=12\cdot \frac{25\sqrt{3}}{2}=150\sqrt{3}$

$\boxed{A_h=150\sqrt{3}\ m^2}$

6 0

3 years ago

What is the length of each side of a square that has the same area as a rectangle that is 14 mm long and 16 mm wide? Round to th

swat32

1. You have the following information:

- The square has the same area as a rectangle.
- The dimensions of the rectangle are: 14 mm long and 16 mm wide.

2. You must use the formula for calculate the area of a square, which is shown below:

A=S²

"A" is the area of the square.
"S" is the lenght of the side of the square. (It is important to remember that the sides of a squre have equals lenghts.

3. The square and the rectangle have the same area. Therefore:

Arectangle=(14 mm)(16 mm)
Arectangle=224 mm²

A=224 mm²

4. Now, you must substitute the value A=224 mm² into the formula A=S² and clear "S":

A=S²
 S=√A
 S=√(224 mm²)
 S=15 mm

The answer is: 15 mm

7 0

3 years ago