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ruslelena [56]
3 years ago
14

HELP ASAP!!!!!!!!PLEASE Solve for x. Please explain. Thank you

Mathematics
1 answer:
Stella [2.4K]3 years ago
8 0

The values are x=8 and y=10

Explanation:

From the figure, we can see that the two quadrilaterals are similar.

Thus, by the property of quadrilateral, for similar quadrilaterals, their corresponding angles and sides are congruent. Thus, we have,

∠D = ∠S, ∠E = ∠P, ∠G = ∠R and ∠F = ∠Q

Also, GF = QR and DE = PS

Where QR = 2x-4 and ∠D = 102°, ∠G = 84° and ∠F = 68°, ∠Q = (6y+x)°

Hence, to determine the value of x for the side QR, we have,

Equating the values in GF = QR,we get,

12=2x-4\\16=2x\\8=x

Thus, the value of x is 8.

Substituting x in the angle Q to determine the value of y.

Thus, we have,

∠F = ∠Q

68=6y+x\\68=6y+8\\60=6y\\10=y

Thus, the value of y is 10.

Hence, The values are x=8 and y=10

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2.75 miles, 14520 feet

Step-by-step explanation:

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2 years ago
Occasionally a savings account may actually pay interest compounded continuously. For each deposit, find the interest earned if
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1. Occasionally a savings account may actually pay interest compounded continuously. For each​ deposit, find the interest earned if interest is compounded​ (a) semiannually,​ (b) quarterly,​ (c) monthly,​ (d) daily, and​ (e) continuously. Use 1 year = 365 days.

Principal ​$1031

Rate 1.4%

Time 3 years

Answer:

a) $ 44.07

b) $ 44.15

c) $ 44.20

d) $ 44.22

e) $ 44.22

Step-by-step explanation:

The formula to find the total amount earned using compound interest is given as:

A = P(1 + r/n)^nt

Where A = Total amount earned after time t

P = Principal = $1031

r = Interest rate = 1.4%

n = compounding frequency

t = Time in years = 3 years

For each​ deposit, find the interest earned if interest is compounded

(a) semiannually

This means the interest is compounded 2 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/2) ^2 × 3

A = 1031 (1 + 0.007)^6

A = $ 1,075.07

A = P + I where

I = A - P

I = $1075.07 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.07

​(b) quarterly

This means the interest is compounded 4 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/4) ^4 × 3

A = 1031 (1 + 0.014/4)^12

A = $ 1,075.15

I = A - P

I = $1075.15 - $1031

A = P + I where

P (principal) = $ 1,031.00

I (interest) = $ 44.15

(c) monthly,

​ This means the interest is compounded 12 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/12) ^12 × 3

A = 1031 (1 + 0.014/12)^36

A = $ 1,075.20

A = P + I where

I = A - P

I = $1075.20 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.20

(d) daily,Use 1 year = 365 days

This means the interest is compounded 365 times in a year

Hence:

A = P(1 + r/n)^nt

A = 1031(1 + 0.014/365) ^2 × 3

A = 1031 (1 + 0.00365)^365 × 3

A = $ 1,075.22

A = P + I where

I = A - P

I = $1075.22 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.22

(e) continuously. .

This means the interest is compounded 2 times in a year

Hence:

A = Pe^rt

A = 1031 × e ^0.014 × 3

A = $ 1,075.22

A = P + I where

I = A - P

I = $1075.22 - $1031

P (principal) = $ 1,031.00

I (interest) = $ 44.22

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Answer:

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Step-by-step explanation:

I will show each step algebraically. If you need further explanation, feel free to ask questions :)

\frac{x}{2} +7=3\\                     Rewrite

\frac{x}{2} =-4                        Subtract 7

x =-8                        Multiply by reciprocal (2/1)

I hope this helps!

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