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lions [1.4K]
3 years ago
6

The midpoint of \overline{\text{AB}} AB is M(5, 1)M(5,1). If the coordinates of AA are (3, 6)(3,6), what are the coordinates of

BB?
Mathematics
1 answer:
Bingel [31]3 years ago
4 0

Answer:

<em>(7, -4)</em>

Step-by-step explanation:

The formula for calculating midpoint is expressed as;

M(X, Y) = (x2+x1)/2, (y1+y2)/2

X = x1+x2/2

Y = y1+y2/2

Given

X = 5, Y = 1, x1 = 3, y1 = 6

Get x2

X = x1+x2/2

5 = 3+x2/2

10 = 3+x2

x2 = 10-3

x2 = 7

Get y2;

Y = y1+y2/2

1 = 6+y2/2

2 = 6+y2

y2 = 2-6

y2 = -4

<em>Hence the coordinate of B is at (7, -4)</em>

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The explicit formula is a(n) = 15(n – 10)

<u>Solution:</u>

Given, a term a(19) = 135 and common difference d = 15

We have to find the explicit formula.

Now, we know that, a(n) = a + (n – 1)d where a(n) is nth term, a is first term, d is common difference,

So, for a(19)  

\begin{array}{l}{\rightarrow a(19)=a+(19-1) 15} \\\\ {\rightarrow 135=a+18 \times 15} \\\\ {\rightarrow a=135-270} \\\\ {\rightarrow a=-135}\end{array}

Now, we know that, an explicit formula is an expression for finding the nth term,  

So, in our problem, expression for finding nth term is a + (n – 1)d  

\begin{array}{l}{\rightarrow-135+(n-1) 15} \\\\ {\rightarrow-135+15 n-15} \\\\ {\rightarrow 15 n-150} \\\\ {\rightarrow 15(n-10)}\end{array}

Hence, the explicit formula is a(n) = 15(n – 10).

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Please do the agree or disagree part and justification
Jlenok [28]

Answer:

<em>We disagree with Zach and Delia and agree with Alicia</em>

Step-by-step explanation:

The domain of a function is the set of values of the independent variable that the function can take according to given rules or restrictions.

The range is the set of values the dependent variable can take for every possible value of the domain.

The graph shows a continuous line representing the values of the function. We must take a careful look to the values of x (horizontal axis) where the function exists. It can be done by drawing an imaginary vertical line passing through the value of x. If that line touches the graph of the function, it belongs to the domain. It's clear that every value of x between -5 and 3 (both inclusive because there are solid dots in the extremes) belong to the domain:

Domain: -5\leq x \leq 3

The range is obtained in a similar way as the domain, but the imaginary lines must be horizontal. That gives us the values of y range from -7 to 5 both inclusive:

Range:

-7\leq y \leq 5

Thus we disagree with Zach and Delia and agree with Alicia

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Answer:

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Step-by-step explanation:

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x = ±\sqrt{9} = ±3

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