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3 years ago

Solve this system of equations to find x and y, please, and explain how you did it:

Mathematics

1 answer:

MissTica3 years ago

8 0

Answer:

Step-by-step explanation:

The system of equations is expressed as

x + y = 8 - - - - - - - - - - - - - -1

x² + y² = 34 - - - - - - - - - - - -2

From equation 1, we would make x to stand alone by subtracting y from the left hand side and the right hand side of the equation. It becomes

x + y - y = 8 - y

x = 8 - y

Substituting x = 8 - y into equation 2, it becomes

(8 - y)² + y² = 34

(8 - y)(8 - y) + y² = 34

64 - 8y - 8y + y² + y² = 34

2y² - 16y + 64 - 34 = 0

2y²- 16y + 30 = 0

Dividing through by 2, it becomes

y² - 8y + 15 = 0

y² - 5y - 3y + 15 = 0

y(y - 5) - 3(y - 5) = 0

y - 5 = 0 or y - 3 = 0

y = 5 or y = 3

Recall, x = 8 - y

x = 8 - 5. or x = 8 - 3

x = 3 or x = 5

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Select the polynomial that is a perfect square trinomial. 36x2 − 4x 16 16x2 − 8x 36 25x2 9x 4 4x2 20x 25.

Naya [18.7K]

The polynomial a,b,c,are not perfect square polynomial and the polynomial d is perfect square polynomial.

The given polynomial is

$a) 36x^2-4x+16$

What is the form of perfect square polynomial?

$(ax+b)^2$

we solve this method by using perfect square method

add and subtract 1/9

$36x^2-4x+16+\frac{1}{9}-\frac{1}{9}$

factor 36

$\frac{143}{9}+36(x^2-\frac{x}{9}+\frac{1}{324} )$

Now complete the square

$\frac{143}{9}+36(x^2-\frac{1}{18})^2$

Therefore this is not perfect square trinomial.

Similarly for

$b) 16x^2-8x+36$

Complete square is,

$16(x-\frac{1}{4})^2+35$

This polynomial is also not perfect square trinomial.

$c) 25x^2+9x+4\\$

complete square is,

$25(x+\frac{9}{50})^2+\frac{319}{100}$

This polynomial is not perfect square trinomial.

$d)4x^2+20x+25\\$

complete square is,

$(2x+5)^2$

This polynomial is perfect square trinomial.

Therefore,

The polynomial a,b,c,are not perfect square polynomial and the polynomial d is perfect square polynomial.

To learn more about perfect square trinomial visit:

brainly.com/question/1538726

3 0

2 years ago

Clint deposited $1,155 into a savings account. A year later, he has $1169.44 in his

slavikrds [6]

Answer:

Step-by-step explanation:

i=prt

i=1169.44

p=1155

t=12

put values

1169.44=1155*12 r

1169.44=13860 r

r=1169.44/13860

r= 0.084

convert to percent

r=8.4%

4 0

3 years ago

The pizza shop sells artwork by local artists. For each piece it sells, the shop receives a 15 percent commission. The most expe

Brrunno [24]

The answers are:

B; (225)(0.15) and E; 225 - [(225)(0.85)] Hope this helps!

8 0

3 years ago

Read 2 more answers

Equations from Word Problems

Setler79 [48]

Answer:

$F(x)=25x+50$

Step-by-step explanation:

First, we know that for every hour for labor he charges $25

So, let x = # of hours

Thus, 25x

Second, he charges $50 for a house call. This does not depend on the # of hours, and serves as our "Starting Pay"

So, we combine and get F(x)=25x+50, where F(x) is the amount he charges

Hope this helps!

Stay Safe!

5 0

4 years ago

Help needed!! Asapp pleasee:(

Mariana [72]

Answer:

7362.49 yards

Step-by-step explanation:

Mauricio has a height of 2 yards

The building has a height of 906 yards from the ground

The height of the building from Mauricio's eye will be : 906 - 2 = 904 yards

The angle of elevation of the top of building from the viewer = 7°

Apply the formula for tangent of an angle where;

Tan ∅ = Opposite side height/Adjacent length

Tan 7° = height of building / viewer distance from base of building

Tan 7° = 904 / viewer distance from base of building

Viewer distance from base of building = 904/Tan 7°

=7362.48917089

=7362.49 yards

8 0

3 years ago