Mathematics, 24.10.2021 14:00 joey333

Please help me to solve problems

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Answer from: tami5

Step-by-step explanation:

4a)

the principle of similar triangles : they have the same angles.

and we do not forget : the sum of all angles in a triangle is always 180 degrees.

a = 180 - 65 - 45 = 70 degrees

b = 65 degrees

c = 70 degrees

same principles.

x = 58 degrees

y = 52 degrees

z = 180 - 58 - 52 = 70 degrees

same principles.

plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.

x = 85 degrees

y = 180 - 40 - 85 = 55 degrees

z = 180 - 85 = 95 degrees

again same principles.

y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).

the angle POQ is again complementary with 87 degrees,

POQ = 180 - 87 = 93 degrees

x + y + 93 = x + 2x + 93 = 180

3x = 87

x = 29 degrees

y = 2x = 2×29 = 58 degrees

Answer from: Quest

use an equation of ratios to determine the amount of gas needed to fill the tank.

0.2 0.8

288.75 x

231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal $3

* = $3465 (answer)

1 1 gal

hope this you

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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