Nora orders a bowl of Tom Yam soup at a restaurant which offers a 15% discount.

nadezda [96]

We will use substitution to solve this system of linear equations, as the first equation has x and y with no coefficients, which makes it easier to find one in terms of the other. We can then substitute that value in the other equation and find the values of x and y.

x = y + 5 ---> equation 1

3x + 2y = 5 ---> equation 2

From equation 1, we get the value of x as y + 5. Using the substitution method, we can find the value of y by substituting (y+5) for x in the 2nd equation.

3(y+5) + 2y = 5

3y + 15 + 2y = 5

5y = 5 - 15

5y = -10

y = -2

Subsituting this value of y in (y+5), we can find x.

x = y + 5

x = -2 + 5

x = 3

Therefore, x = 3 and y = -2.

I will also solve this using elimination method.

Let us multiply equation 1 by 2, so that we get 2y in both equations.

2x = 2y + 10

3x + 2y = 5

Let us add both the equations.

2x + 3x + 2y = 5 + 2y + 10

5x = 15 + 2y - 2y

5x = 15

x = 3

Substituting this value of x in equation 1, we get

x = y + 5

3 = y + 5

y = 3 - 5

y = -2

Therefore, x = 3 and y = -2.

7 0

2 years ago

Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula?

lbvjy [14]

Answer:

x = StartFraction negative

(negative 2) plus or minus StartRoot (negative 2) squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction

Step-by-step explanation:

0 = – 3x2 – 2x + 6

It can still be written as

– 3x2 – 2x + 6 =0

Quadratic formula=

-b+or-√b^2-4ac/2a

Where

a=-3

b=-2

c=6

x= -(-2)+ or-√(-2)^2-4(-3)(6)/2(-3)

x = StartFraction negative

(negative 2) plus or minus StartRoot (negative 2) squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction

8 0

2 years ago

calculeaza lungimea segmentului ab in fiecare dintre cazuri:A(1,5);B(4,5);A(2,-5),B(2,7);A(3,1)B(-1,4);A(-2,-5)B(3,7);A(5,4);B(-

Tatiana [17]

Answer:

1. 3; 2. 12; 3. 5; 4. 13; 5. 10; 6. 10

Step-by-step explanation:

We can use the distance formula to calculate the lengths of the line segments.

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

1. A (1,5), B (4,5) (red)

$d = \sqrt{(x_{2} - x_{1}^{2}) + (y_{2} - y_{1})^{2}} = \sqrt{(4 - 1)^{2} + (5 - 5)^{2}}\\= \sqrt{3^{2} + 0^{2}} = \sqrt{9 + 0} = \sqrt{9} = \mathbf{3}$

2. A (2,-5), B (2,7) (blue)

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(2 - 2)^{2} + (7 - (-5))^{2}}\\= \sqrt{0^{2} + 12^{2}} = \sqrt{0 + 144} = \sqrt{144} = \mathbf{12}$

3. A (3,1), B (-1,4 ) (green)

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-1 - 3)^{2} + (4 - 1)^{2}}\\= \sqrt{(-4)^{2} + 3^{2}} = \sqrt{16 + 9} = \sqrt{25} = \mathbf{5}$

4. A (-2,-5), B (3,7) (orange)

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(3 - (-2))^{2} + (7 - (-5))^{2}}\\= \sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = \mathbf{13}$

5. A (5,4), B (-3,-2) (purple)

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-3 - 5)^{2} + (-2 - 4)^{2}}\\= \sqrt{(-8)^{2} + (-6)^{2}} = \sqrt{64 + 36} = \sqrt{100} = \mathbf{10}$

6. A (1,-8), B (-5,0) (black)

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(-5 - 1)^{2} + (0 - (-8))^{2}}\\-= \sqrt{(-6)^{2} + (-8)^{2}} = \sqrt{36 + 64} = \sqrt{100} = \mathbf{10}$

6 0

2 years ago

A square ceiling has a diagonal of 23 ft. Shelton wants to put molding around the perimeter of the ceiling. The molding is sold

Hatshy [7]

Answer:

Minimum 66 feet of molding that he needs.

Step-by-step explanation:

Given that a square ceiling has a diagonal of 23 ft.

If the sides of the square ceiling are 'a' feet, then applying Pythagoras Theorem we can write, a² + a² = 23²

⇒ 2a² = 23²

⇒ a = 16.2634 feet (Approximate)

Now, the perimeter of the square ceiling will be 4a = 65.05 feet.

If the cost of molding along the perimeter of the ceiling is in per foot, then a minimum of 66 feet of molding that he needs. (Answer)

6 0

2 years ago

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Tiffany buys a basket of watermelons on sale for \$9$9dollar sign, 9 before tax. The sales tax is 9\%9%9, percent. What is the t

Phoenix [80]

I know you got this from Khan Academy, and so the answer is $9.81. You probably don't care about how it is done, and you probably just want to put the answer and be done, but I will show you. You have to take the original price of $9 and multiply it with 9%, or 0.09, to get the amount of your tip. add the 9%, or $81. You can also just do 9*109%, or 9*1.09, to put these two steps together and add the original price and the tip.

3 0

2 years ago

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