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Schach [20]
3 years ago
8

What are the coordinates (x, y) at which the graphs of 3.6x − 2y = 6 and −2.7x + y = 3 intersect? Round to the nearest tenth if

necessary.
Mathematics
1 answer:
Bas_tet [7]3 years ago
6 0
3.6x - 2y = 6
-2.7x + y = 3.....multiply by 2
----------------
3.6x - 2y = 6
-5.4x + 2y = 6 (result of multiplying by 2)
----------------add
-1.8x = 12
x = 12/-1.8
x = - 6.67 (or -20/3)

3.6x - 2y = 6
3.6(-6.67) - 2y = 6
-24.01 - 2y = 6
-24.01 - 6 = 2y
-30.01 = 2y
-30.01 / 2 = y
-15 = y

solution : (-6.67, -15)
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8 gal/h = ________ pt/min
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1gal=8pt\\1h=60min\\\\8\ gal/h=8\times\frac{8pt}{60min}=\frac{64}{60}\ pt/min=\frac{16}{15}\ pt/min=1\frac{1}{15}\ pt/min
5 0
3 years ago
Find the inverse function of h(x) = -2/3x + 6.
nalin [4]

Answer:

h^{-1}(x)=-\frac{3}{2}x+9

Step-by-step explanation:

To find inverse of a function, follow the steps below:

1. replace h(x) with y

2. Interchange x and y

3. Solve for the new y

4. Replace y to h^{-1}(x) (this is the inverse function)

<u>Step 1:</u> y = -2/3x+6

<u>Step 2:</u> x = -2/3y+6

<u>Step 3:</u>

x=-\frac{2}{3}y+6\\\frac{2}{3}y=-x+6\\y=\frac{-x}{\frac{2}{3}}+\frac{6}{\frac{2}{3}}\\y=-\frac{3}{2}x+9

<u>Step 4:</u>

y=-\frac{3}{2}x+9\\h^{-1}(x)=-\frac{3}{2}x+9

This is the inverse function.

3 0
3 years ago
Read 2 more answers
John playing with his friends a game where you need to get 20 points to win. In the start of the game John lose 10 points and th
zloy xaker [14]

Answer:

2

Step-by-step explanation:

0 - 10 = -10

-10 + 12 = 2

John has 2 points

3 0
3 years ago
Bill and Mary Ann went to the Viola bakery. Bill bought 3 danishes and 8 filled donuts for ​$14.67. Mary Ann bought 7 of each fo
harina [27]

Answer:

donuts cost $1.5

danishes cost $1.57

Step-by-step explanation:

This is a typical 2-equation syestem with 2 unknown variables problem. Lets find out which are our equations and unknowns.

Bill ought 3 danishes and 8 filled donuts for ​$14.67. Lets call d the price of donuts and c the price of danishes. We can then write Bill expenditures as an equation (I will omit $ symbol for simplicity):

3 c + 8 d = 14.67 [eq 1]

Now we can do the same for Mary's expenditures, as she bought 7 of each for ​$16.73:

7 c + 7 d = 16.73 [eq. 2]

Now, lets take eq. 1 and try to get the value of one of the variables, for example c, as function of the other -in this case, d. Notice you could also do this with eq. 2.

So:

3 c + 8 d = 14.67

Subtract 8d in both sides:

3c = 14.67 - 8d

Now, divide both sides by 3:

c = (14.67 - 8d)/3

So, we have c in function of d. Now, replace this value in eq 2:

7*(14.67 - 8d)/3 + 7 d = 16.73

(7/3)*(14.67 - 8d) + 7d = 16.73

Applying distributive:

(7/3)*14.67 - (7/3)*8d + 7d = 16.73

34.23 - 18.67d + 7d = 16.73

34.23 - 11.67d = 16.73

Now, subtract 34.23 in both sides:

-11.67 d = -17.5

Dividing both sides by -11.67

d = 1.50

So, every donuts costs $1.5. If we replace this value in any of the equations of the system we get c. Lets replace in eq. 1:

3 c + 8 d = 14.67

3 c + 8*1.5 = 3c + 12 = 14.67

Subtract 12 in both sides:

3c = 4.67

Divide by 3 in both sides:

c = 1.57

Important: notice that the results may variate in some decimals or less depending on how many numbers after the coma you use. For example, d is really 1.49957155098543 but I used 1.50, if you are more precise and use 1.49957 you results may variate a little but not significantly.

So, c=1.57 and d=1.50 is the solution. A donuts cost $1.5 and a danish $1.57.

5 0
3 years ago
Read 2 more answers
At Shower and Body Works, there are different sizes of lotion dispensers. Two of the
natali 33 [55]

Answer:

2.5 times

Step-by-step explanation:

From the diagram attached below;

let's calculate the volume of each bottle;

SO for bottle X;

we have ;

Volume of X = \dfrac{1}{2}*2*1*6

Volume of X = 6  \  \ in^3

Volume of Y = \dfrac{1}{2}*3*2.5*4

Volume of Y = 15  \ \ in^3

The ratio of Y to X can help us to determine how many times more lotion is in Bottle Y than in Bottle X; So taking their ratio ; we have:

\mathbf{\dfrac{volume \ of \  Y }{volume\ of  \ X} = \dfrac{15}{6}  }

= 2.5 times

Thus; Bottle Y has 2.5 times more lotion than Bottle X

3 0
3 years ago
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