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SVETLANKA909090 [29]
3 years ago
6

27x + 24y= 4.5 1.5x + y =0.225

Mathematics
2 answers:
soldi70 [24.7K]3 years ago
8 0

Answer:

the values for x AND y are 0.1 and 0.075 respectively

Goryan [66]3 years ago
3 0

Answer:

x = 0.1, y = 0.075

Step-by-step explanation:

Given the 2 equations

27x + 24y = 4.5 → (1)

1.5x + y = 0.225 → (2)

Multiplying (2) by - 24 and adding to (1) will eliminate the y- term

- 36x - 24y = - 5.4 → (3)

Add (1) and (3) term by term to eliminate y

- 9x = - 0.9 ( divide both sides by - 9 )

x = 0.1

Substitute x = 0.1 into either of the 2 equations and solve for y

Substituting into (2)

1.5(0.1) + y = 0.225

0.15 + y = 0.225 ( subtract 0.15 from both sides )

y = 0.075

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Let f(x)=a(2)^x. This exponential function is intersected twice by the line g(x)=x+b. One intersection is at point P(-2,2). Find
mr_godi [17]

Answer:

See below

Step-by-step explanation:

To find the values of a and b, we use the intersection point P.

Since the graph of f is intersected by P=(-2,2), f(-2)=2, that is, a(2)^(-2)=2. Then a=2(2)²=8.

Since the graph of g is intersected by P=(-2,2), g(-2)=2, that is, -2+b=2. Then b=2+2=4.

Hence a=8, b=4.

To find the other point of intersection Q, we need to find a number x such that f(x)=g(x), that is, 8(2)^(x)=x+4. Rewrite this equation as follows:

f(x)=8(2^x)=2^3(2^x)=2^{3+x}=g(x)=x+4

It is not easy to solve this equation analitically. Instead, you can apply a quantitative method. First, the left hand side is an exponential function, so it is always positive. Then the solution will be a number in which the right side (x+4) is positive, that is, x > -4. The solution is an integer, then the possible values are x=-3,-2,-1,0,1,2,...

Now, the RHS must be a power of two, so the possible integers are x=-3,-2,0,4,12,28,... However, the LHS grows very quickly, while the LHS grows slowly. Then, it is only necessary to test small integer values (we already know that x=-2 is a solution).

If we test with x=-1, we get 2²=4=3, then x=-1 is not a solution. Any x>-1 will not be a solution, because f increases much faster than g, and then they won't intersect. So our possibilities reduce to x=-3,-2. Taking x=-3, we get f(-3)=2⁰=1=-3+4=g(-3). Thus, (-3,0) is the other point of intersection Q. (r=-3, s=0).  

7 0
3 years ago
​Joe's annual income has been increasing each year by the same dollar amount. The first year his income was ​$17 comma 90017,900
Vedmedyk [2.9K]

Answer:

In 17th year, his income was $30,700.

Step-by-step explanation:

It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.

Income in first year = $17,900

Income in 4th year = $20,300

Let y be the income at x year.

It means the line passes through the point (1,17900) and (4,20300).

If a line passes through two points (x_1,y_1) and (x_2,y_2), then the equation of line is

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

The equation of line is

y-17900=\frac{20300-17900}{4-1}(x-1)

y-17900=\frac{2400}{3}(x-1)

y-17900=800(x-1)

y-17900=800x-800

Add 17900 on both sides.

y=800x-800+17900

y=800x+17100

The income equation is y=800x+17100.

Substitute y=30,700 in the above equation.

30700=800x+17100

Subtract 17100 from both sides.

30700-17100=800x

13600=800x

Divide both sides by 800.

\frac{13600}{800}=x

17=x

Therefore, in 17th year his income was $30,700.

5 0
3 years ago
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Nadusha1986 [10]

Answer:

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Step-by-step explanation:

7 0
2 years ago
Jeff and his cousin work during the summer for a roofing company. Jeff's cousin has been working
sdas [7]

Answer:

1

Step-by-step explanation:

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3 0
3 years ago
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Answer:

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Step-by-step explanation:

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