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eduard
2 years ago
5

A, B & C lie on a straight line.

Mathematics
1 answer:
Liono4ka [1.6K]2 years ago
8 0

Answer:

x = 129°

Step-by-step explanation:

∠ ABD and ∠ DBC are a linear pair and sum to 180° , then

y + ∠ DBC = 180°

107° + ∠ DBC = 180° ( subtract 107° from both sides )

∠ DBC = 73°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then

x = ∠ DBC + z = 73° + 56° = 129°

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Three equals parentheses five squared 1/2 parentheses you parentheses X squared 1/2
Aliun [14]

Answer:

Can you give me a picture of the question? Or be more specific?

3 0
3 years ago
Warren brought $41.50 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as th
melomori [17]

Answer:

Warren paid $2.5 for the brush, $15 for the sketchbook and $20 for the paint set.

Step-by-step explanation:

If Warren went to the store with $41.5 and left with only $4 then the total amount he spent on the store was:

total spent = 41.5 - 4 = 37.5

Since he bought a brush, a sketchbook and a paint set we have:

brush + sketchbook + paint = 37.5

The prices of each item are related in the following manner:

brush = (1/6)*sketchbook

sketchbook = (3/4)*paint

brush = (1/6)*(3/4)*paint = (3/24)*paint = (1/8)*paint

Using these expressions on the one that represents the total value we will be abble to have only one variable, paint. We have:

(1/8)*paint + (3/4)*paint + paint = 37.5

(1/8)*paint + (6/8)*paint + (8/8)*paint = 37.5

(15/8)*paint = 37.5

paint = 37.5/(15/8) = 37.5*(8/15) = 20

brush = (1/8)*paint = (1/8)*20 = 2.5

sketchbook = (3/4)*paint = (3/4)*20 = 15

Warren paid $2.5 for the brush, $15 for the sketchbook and $20 for the paint set.

6 0
3 years ago
Read 2 more answers
Principal = $2,400<br> Rate = 4%<br> Time = 30 months
grandymaker [24]

Answer:

$240

Step-by-step explanation:

I = prt

I = (2,400) (0.04) (2.5)  

note: I changed 4% to a decimal and 30 months to 2.5 years

I = 96 (2.5)

I = 240   <-- The interest

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

The simple interest accumulated on a principal of $ 2,400.00  at a rate of 4% per year for 2.5 years (30 months) is $240.00.

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

* Last time I did interest was in 6th grade and I don't remember much. So I am very sorry if my answer is wrong *

3 0
3 years ago
Need answer to 4 and 5
algol13

Answer:

Substitute n =1, 2, 3, 4, 5 to get the first five terms.

Step-by-step explanation:

(4). $ g_n  = 2 . 3^{n - 1} $

To find the first term, substitute n = 1.

Therefore, $ g_1 = 2 . 3^{1 - 1} = 2 . 3^{0} = 2 . 1  $ = 2

$g_2 = 2 . 3^{2 - 1} = 2 . 3 $ = 6

$ g_3 =  2 . 3^{3 - 1} = 2 . 3^{2} = 2 . 9 $ = 18

$ g_4 = 2 . 3^{4  - 1} = 2 . 3^{3} = 2 . 27 $ = 54

$ g_5 =  2 . 3^{5 - 1} = 2 . 3^{4} = 2 . 81 $ = 168

Therefore the first five terms of the sequence are: 2, 6, 18, 54, 168.

(5). $ t_n = \frac{2}{3}t_{n - 1} $

$ t_2 = \frac{2}{3} t_{2 - 1} = \frac{2}{3}t_1  = \frac{2}{3}6 $ = 4

$ t_3 = \frac{2}{3} t_2 = \frac{2}{3}. 4 = \frac{8}{3} $

$ t_4 = \frac{2}{3}t_3 = \frac{2}{3}\frac{8}{3} = \frac{16}{9} $

$ t_5 = \frac{2}{3}t_4 = \frac{2}{3}\frac{16}{9} = \frac{32}{27} $

Therefore the first five terms in the sequence are: 6, 4, 8/3, 16/9, 32/27.

8 0
3 years ago
Find the volume of a right circular cone that has a height of 15.6 cm and a base with a radius of 7.8 cm. Round your answer to t
sergey [27]

Answer:

356.8cm3

Step-by-step explanation:

Volume of a cone= 1/3 * base area * height.

Note: don't be confused by right circular cone ; a cone is gotten from a cylinder by dividing it into three parts. One from the right vertex slanted to the middle of the base; another from the left vertex slanted to the middle of the base and the remaining portion with the surface base at the top.

Going forward; base area =pi * raduis * raduis [ area of a circle; the base is a circle]

Volume= 1/3 * (3.142 * 7.8 * 7.8 *5.6) = 356.83cm3

Volume= 356.8cm3 [ to the nearest tenth].

Tenth means 1/10= 0.1; that is value after the decimal point.

5 0
3 years ago
Read 2 more answers
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