Translate the following phrase to a mathematical expression and then evaluate the expression for n = 5.

Find the value of y if B is between A and C, AB is 2y, BC is 6y, and AC is 48.

Len [333]

Answer:

7. C. 6

8. H. √34

9. A. (1, 3.5)

10. J. 10

Step-by-step explanation:

7. AB = 2y, BC = 6y, AC = 48

AB + BC = AC (segment addition theorem)

Substitute the above values into the equation

2y + 6y = 48

Solve for y

8y = 48

Divide both sides by 8

8y/8 = 48/8

y = 6

8. Distance between P(2, 8) and Q(5, 3):

$PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$P(2, 8) = (x_1, y_1)$

$Q(5, 3) = (x_2, y_2)$

$PQ = \sqrt{(5 - 2)^2 + (3 - 8)^2}$

$PQ = \sqrt{(3)^2 + (-5)^2}$

$PQ = \sqrt{9 + 25}$

$PQ = \sqrt{34}$

9. Midpoint (M) of segment LB, for L(8, 5) and B(-6, 2) is given as:

$M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

Let $L(8, 5) = (x_1, y_1)$

$B(-6, 2) = (x_2, y_2)$

Thus:

$M(\frac{8 + (-6)}{2}, \frac{5 + 2}{2})$

$M(\frac{2}{2}, \frac{7}{2})$

$M(1, 3.5)$

10. M = -10, N = -20

Distance between M and N, MN = |-20 - (-10)|

= |-20 + 10| = |-10|

MN = 10

5 0

4 years ago

Graph the following piecewise function.

atroni [7]

Answer:

The graph of this piece-wise function is attached below.

Step-by-step explanation:

Given the function

${\displaystyle f(x)={\begin{cases}x^{2} +2&{\text{if }}-5\leq x$

A piece-wise function is a function which has multiple pieces.
Each of the pieces have their own restrictions.

The domain of a function is the set of input, or x, values for which the function is defined.
The range is the set of all values taken by the function

As the piece

$f(x)=x^{2} +2$ has the domain [-5, 3) and graph of this piece is attached below.

and

$f(x)=x-4$ has the domain [3, 7) and graph of this piece is attached below.

So, the domain of the piece-wise function can be composed as [-5, 3) U [3, 7) and range has the interval $\:\left[-1,\:27\right]$ .

i.e.

Domain: [-5, 3) U [3, 7)

Range: $\:\left[-1,\:27\right]$

The graph of this piece-wise function is attached below.

Keywords: piece-wise function, domain, range

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3 0

4 years ago

The world needs u

Anna11 [10]

Answer:

Thank you for the kind words!

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

20 1/3 + x = -9 round your answer to the nearest hundredth

nadya68 [22]

Answer:

I would think it's X= -29 1/3

Step-by-step explanation:

You have 20 1/3 already, and to get to a negative when you have a positive number, to the positive you would need to add a larger negative. (If that makes any sense, it's hard to explain.) So you have to get rid of the 20 1/3 and you have to get to -9, so I would add a 9 to 20 1/3 to get 29 1/3, and make that number negative because then it will cancel the positive out. Making it -9.

3 0

3 years ago

An opinion poll reported that 36% believe a certain governor broke campaign financing laws in his election campaign. How many pe

77julia77 [94]

Answer:

The number of people would have participate in opinion poll

n = 15,267

Step-by-step explanation:

Step(i):-

Given data an opinion poll reported that 36% believe a certain governor broke campaign financing laws in his election campaign.

Given proportion = 36% =0.36

Given the margin of error = 1% =0.01

Level of significance = 99% 0 r 0.01

Z₀.₀₁ = 2.576

step(ii):-

The margin of error of Population proportion is determined by

$M.E = \frac{Z_{0.01} \sqrt{p(1-p)} }{\sqrt{n} }$

$0.01 = \frac{2.576 \sqrt{0.36(1-0.36)} }{\sqrt{n} }$

$\sqrt{n} = \frac{2.576 \sqrt{0.36(1-0.36)} }{0.01 }$

√n = 123.648

Squaring on both sides , we get

n = 15,267

final answer:-

The number of people would have participate in opinion poll

n = 15,267

7 0

3 years ago