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skad [1K]
3 years ago
9

Determine whether the point (2, 2) is a solution to the system of equations. Explain your reasoning in complete sentences. Prove

you answer mathematically by verifying the point (2,2) with the given equations by inspection (show all work). If (2,2) is not the solution to the system, what is the solution and how do you know?

Mathematics
1 answer:
goblinko [34]3 years ago
6 0

Answer:

(0,2) is the solution of the given functions.

Step-by-step explanation:

We have been given two functions  f(x)=|x-1|+1  and g(x)=3x+2

To find the solution of the two functions mathematically, we will equate the given functions:

3x+2=|x-1|+1

3x+1=|x-1|

When we will open the modulus function we will have two values +, -

In positive case:

3x+1 =x-1

2x=-2

x=-1

Now, substitute x=-1 in g(x)=3x+2 we get

g(-1)=3(-1)+2=-1

Hence, (-1,-1) is the solution of the given functions.

In negative case:

Now, 3x+1=-(x-1)

3x+1=-x+1

4x=0

x=0

Now, put x=0 in g(x)=3x+2 we get

g(0)=3(0)+2=2

We have another solution: (0,2)

The point (2,2) is not the solution.

And graphically, the solution of two functions is their intersection point which is (0,2)

Hence, (0,2) is the solution of the function.


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MA_775_DIABLO [31]

Answer:

p = 132 - 30d

Step-by-step explanation:

Here, we can plug in x = 6 into the equation provided at the end of the problem.

p = 6[25 - (3 +5d)]

p = 150 - 18 - 30d

p = 132 - 30d

7 0
2 years ago
One counting number is 4 times great as a counting number.The product of the two number is 36.What is the sum of the two number
VARVARA [1.3K]

Answer:

The sum of the two numbers is 15

Step-by-step explanation:

Let the counting numbers be x and y.

Then we can write the following equations

x=4y.......1 (one is four times greater )

x(y)=36.....2 (the product of the two)

Putting equation 1 into equation 2, we get

4y(y)=36

{4y}^{2} = 36

Dividing through by 4,we get

{y}^{2} =  \frac{36}{4}

{y}^{2} = 9

Taking square root of both side, we obtain

y=3

Putting the value of y into equation , we get

x=4(3)=12

Hence the numbers are 3 and 12

Therefore the sum of the two numbers is 3+12=15

3 0
3 years ago
I NEED HELP PLEASE. LOOK AT PICTURE
Bond [772]

Answer:

Part 1) \frac{a^4}{4b^2}

Part 2) -\frac{v^9}{w^6}

Step-by-step explanation:

we know that

When divide exponents (or powers) with the same base, subtract the exponents

Part 1) we have

\frac{3a^{2}b^{-4}}{12a^{-2}b^{-2}}=(\frac{3}{12})(a^{2+2})(b^{-4+2} )=\frac{1}{4}a^{4}b^{-2}=\frac{a^4}{4b^2}

Part 2) we have

\frac{v^3w^{-3}}{-v^{-6} w^3} =-v^{3+6}w^{-3-3}=-v^9w^{-6}=-\frac{v^9}{w^6}

6 0
3 years ago
Lauren Michel lends $17,000 at a rate of 10.7% .
Maru [420]
Given:
Principal = 17,000
rate = 10.7%
term = x/360
interest = 1,121.72

Interest = Principal * rate * term
1,121.72 = 17,000 * .107 * x/360
1,121.72 = 1,819x / 360
1,121.72 * 360 = 1,819x
403,632 / 1,819 = x
221.90 = x

Lauren Michelle will have to wait 222 days for her investment to earn $1,121.72

Given:
Principal = x
rate = 9%
term = 10 months
interest = 1,687.50

Interest = Principal * rate * term
1,687.50 = x * 0.09 * 10/12
1,687.50 = x * 0.075
1,687.50 / 0.075 = x
22,500 = x

The amount Sandra Leatherwood invested was $22,500.


7 0
3 years ago
Donald spends a total of $17.43 on peanuts that cost $2.49 per pound. How many pounds of peanuts does he buy?
True [87]

Answer:

He bought 7 pounds of peanuts

Step-by-step explanation:

17.43/2.49=7

4 0
3 years ago
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