Consider this equation:

Solve the system using elimination.<br><br> 2x + 3y = 17<br> x + 5y = 19

ale4655 [162]

$\left\{\begin{array}{ccc}2x+3y=17\\x+5y=19&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+3y=17\\-2x-10y=-38\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad-7y=-21\qquad\text{divide both sides by (-7)}\\.\qquad\qquad \boxed{y=3}\\\\\\\text{Substitute the value of y to the second equation}\\\\x+5(3)=19\\\\x=15=19\qquad\text{subtract 15 from both sides}\\\\\boxed{x=4}\\\\Answer:\ x=4\ and\ y=3.$

5 0

3 years ago

I'm confused on how to do this. Please explain step by step. If you respond with just the answer I WILL report you. I would like

Tcecarenko [31]

Answer:

Exact Form:

√2−1

Decimal Form:

0.41421356

…

Step-by-step explanation:

Since 9π/8 is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

9π/8 is not an exact angle

First, rewrite the angle as the product of 1/2 and an angle where the values of the six trigonometric functions are known. In this case, 9π/8 can be rewritten as

(1/2)* 9π/8 tan ((1/2)* 9π/8)

Use the half-angle identity for tangent to simplify the expression. The formula states that

tan (0/2)=sin(0)/1+cos(0) sin(9π/4)/1+cos(9π/4)

Simplify

Remove full rotations of 2π until the angle is between 0 and 2π.

sin(π/4)/1+cos(9π/4)

The exact value of sin(π/4) is √2/2

√2/2/1+cos(9π/4)

Simplify the Denominator

Remove full rotations of 2π until the angle is between 0 and 2π.√2/2/1+cos(π4)

The exact value of cos(π/4) is √2/2.√2/2/1+√2/2

To write 1/1 as a fraction with a common denominator, multiply by 2/2 .√2/2/1/1⋅2/2+√2/2

Write each expression with a common denominator of 2, by multiplying each by an appropriate factor of 1.

Combine.

√2/2/1⋅2/1⋅2+√2/2

Multiply 2 by 1

√2/2/1⋅2/2+√2/2

Combine the numerators over the common denominator.

√2/2/1⋅2+√2/2

Multiply 2 by 1

√2/2/2+√2/2

Multiply the numerator by the reciprocal of the denominator

√2/2 ⋅ 2/2+√2

Cancel the common factor of 2 .

Factor out the greatest common factor 2

√2/2⋅1 ⋅ 2⋅1/2+√2

Cancel the common factor

√2/2⋅1 ⋅ 2⋅1/2+√2

Rewrite the expression.

√2/1 ⋅ 1/2+√2

Simplify

Multiply √2/1 and 1/2+√2

√2/2+√2

Multiply √2/2+√2 by 2−√2/2−√2

Combine

√2(2−√2)/(2+√2)(2−√2)

Expand the denominator using the FOIL method.

√2(2−√2)/4−2√2+√2⋅2−√2^2

Simplify

√2(2−√2)/2

Apply the distributive property

√2⋅2+√2(−√2)/2

Move 2 to the left of the expression √2⋅2.

2⋅√2+√2(−√2)/2

Simplify

√2(−√2) .

Raise √2 to the power of 1 .

2⋅√2−(√2^1√2)/2

Raise √2 to the power of 1 .

2⋅√2−(√2^1√2^1)/2

Use the power rule a^m a^n=a^m+n to combine exponents.

2⋅√2−√2^1+1/2

Add 1 and 1 .

2⋅√2−√2^2/2

Simplify each term.

Multiply 2 by √2 .

2√2−√2^2/2

Rewrite √2^2 as 2 .

2√2−1⋅2/2

Multiply −1 by 2.

2√2−2/2

Reduce the expression by cancelling the common factors.

Factor 2 out of 2√2.

2(√2)−2/2

Factor 2 out of −2.

2(√2)+2⋅−1/2

Factor 2 out of

2(√2)+2(−1)2(√2−1)/2

Cancel the common factors.

Factor 2 out of 2 .

2(√2−1)/2(1)

Cancel the common factor.

2(√2−1)/2⋅1

Rewrite the expression.

√2−1/1

Divide √2−1 by 1 .

√2−1

The result can be shown in multiple forms.

Exact Form:

√2−1

Decimal Form:

0.41421356…

Hope it help. Good luck.

4 0

3 years ago

FIND THE DIFFerence.<br> 78,000 - 9,743 =

vitfil [10]

Answer:

68257

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

6. Gabriella invests $6,500 into a savings account that earns 4.5% interest, and she is investing the money for 5 years without

sdas [7]

Answer:

1,462.50

Step-by-step explanation:

6500

x.045

=292.50 per year

x. 5 years

=1,462.50

4 0

2 years ago

Fifteen years ago, you deposited $12,500 into an investment fund. Five years ago, you added an

True [87]

Answer:

a) 8.16%

b) $65,762.50

c) $39,701.07

Step-by-step explanation:

Given:

15 years ago, Initial investment = $12500

5 years ago, Investment = $20000

Nominal interest = 8% semi annually for first 10 years

Interest2= 6.5% compunded annually for last five years

a) for the effective annual interest rate (EAR) in the first 10 years, let's use the formula:

[1+(nominal interest rate/number of compounding periods)]^ number of compounding periods-1

$EAR = [1 + (\frac{0.08}{2})]^2 - 1$

$= (1 + 0.04)^2 - 1$

$= (1.04)^2 - 1$

= 1.0816 - 1

= 0.0816

= 8.16%

The effective annual interesting rate, EAR = 8.16 %

b) To find the amount in my account today.

Let's first find the amount for $12500 for 10 years compounded semi annually

= 12,500 +( 12,500 * 8.160% * 10)

= $ 22,700

Let's also find the amount for $32,500($12,500+$20,000) for 5 Years compoundeed annually

$32,500 + ($32,500 * 6.5% *5)

= $ 43,062.50

Money in account today will be:

$22,700 + $43,062.50

= $65,762.50

c) Let's the amount I should have invested to be X

For first 10 years at 8.160%, we have:

Interest Amount = ( X * 8.160% * 10 ) = 0.8160 X

For next 5 years at 6.5%, we have:

Interest Amount = (X * 6.5% * 5) = 0.325 X

Therefore the total money at the end of 15 Years = 85000

0.8160X + 0.3250X + X = $85,000

= 2.141X = $85,000

X = 85,000/2.141

X = 39,701.074 ≈ $39,700

If I wish to have $85,000 now, I should have invested $39,700 15 years ago

7 0

3 years ago