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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.


You might be interested in
In each of the following scenarios, determine if the data are paired.
zmey [24]

Answer:

1. Can be Paired or Not Paired

2. Paired

3. Not Paired

Step-by-step explanation:

Two sets of observations are paired if each observation in one set has a special correspondence or connection with exactly one observation in the other data set.

1. Can be Paired or Not paired

Reason -

We might look at testing the difference of means using a two sample t-test. However, we may also try running a paired t-test.

But its used in cases where the observations are usually from the same populations at different times or through different sources etc.

Hence can't conclude that it is paired or not paired.

2. Paired

Reason -

Each record is a price of the same item from different stores.

3. Not paired

Reason -

This is again a case of testing the difference of means of two-samples (2 independent samples precisely) that are not paired.

5 0
3 years ago
Center (-15,11) radius 2
kodGreya [7K]

Answer:

(x+15)^2+(y-11)^2=4

Step-by-step explanation:

<u><em>The question is</em></u>

How do you write an equation for a circle with center (-15,11) and radius 2?

we know that

The equation of a circle in center radius form is given by

(x-h)^2+(y-k)^2=r^2

where

(h,k) is the center of the circle

r is the radius of the circle

substitute the given vales

(x+15)^2+(y-11)^2=2^2

(x+15)^2+(y-11)^2=4

8 0
3 years ago
You calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes de
Natali5045456 [20]

Answer:

a) The events are disjoint, because a person cannot have blood type A and blood type B at the same time.

b) The events are independent, because the probability of having blood type does not depend on other persod having blood type B.

c) Yes, disjoint events are independent if and only if the probability of some of the events is zero.

Step-by-step explanation:

a) Let the events be:

A: "the person has blood type A

B: the person has blood type B

As a person can only have one blood type these events are disjoint.

b) If we examine two people, let the events be that the first is blood Type A and the second blood Type B:

The events are independent because the probability of the first person having blood type A does not influence the probability of the second person having blood type B (unless the two people are related).

c) Two events are independent if and only if:

P(A∩B)=P(A)×P(B)

Given the events A and B which are disjoint:

P(A∩B)=0

Hence, A and B could be independent events if and only if the probability of one of the events is 0.

3 0
3 years ago
Of
Mariulka [41]
I believe the answer is B. 39, 49, 59
5 0
3 years ago
There are 11 people in line at a checkout counter. The first person in line is currently being helped and will stay at the front
kotykmax [81]

Answer:

362880

Step-by-step explanation:

You have to subtract the two people who are already doing something in line so you would do 11-2 which equals 9. Then you would do 9 mPr 9 which gives you an answer of 362,880.

8 0
3 years ago
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