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zzz [600]
3 years ago
15

Please help. I've been working on this problem for more than 2 hours. Thank you.

Mathematics
1 answer:
I am Lyosha [343]3 years ago
6 0

Answer:

20° and 70°

Step-by-step explanation:

(4x-10)+(2x-20)=90

6x-30=90

6x=90+30

6x=120

x=20

2(20)-20=20

4(20)-10=70

20+70=90

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On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter
andrezito [222]

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0
3 years ago
76.8 of what is 40.32
bearhunter [10]
Hey there

Lets solve this question together,

Convert 76.8% to a decimal.

0.768 * x=40.32

Multiply 0.768 by x to get 0.768x.

0.768x=40.32

Multiply each term by 1 / 0.768 and simplify.

Cancel the common factor of 0.768.

x=40.32 / 0.768

Divide 40.32 by 0.768 to get 52.5

x=52.5
6 0
3 years ago
Pleaseee help !! I’ll give brainliest !
Luda [366]

Answer: 8 in

Step-by-step explanation:

mAB= 8 inches because AB is the difference of AD and BD. The postulate I used for this is the Part Whole Postulate, or PWP.

8 0
3 years ago
Find the value of x. The diagram is not drawn to scale.
GarryVolchara [31]

Step-by-step explanation:

y = 180 \degree - 116 \degree = 64 \degree \\  \\ x = 360 \degree - (125 \degree + 72 \degree + 64 \degree) \\  = 360 \degree -261 \degree \\  = 99\degree \\ \\   \huge \red{ \boxed{\therefore \: x = 99\degree }}\\ \\

Thus, option C is the correct answer.

7 0
3 years ago
PLEASE HELP ASAP !!!
SSSSS [86.1K]

Answer:

The answer to your question is below

Step-by-step explanation:

From the picture we can infer that:

The side OP is proportional to NP, is half the length of NP.

The side QP is proportional to the side RP, is half the length of RP

The triangle OPQ is proportional to the triangle NPR because the have to proportional sides and the ∠P is the same for both.

Finally, if the triangles are proportional, the side OQ is proportional to the side NR. (is half the side of NR)

4 0
3 years ago
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