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3 years ago

11

Points P and Q belong to segment AB. If AB = a, AP = 2PQ = 2QB, find the distance: a between point A and the midpoint of the seg

ment QB

1 answer:

PIT_PIT [208]3 years ago

8 0

Since PQ = QB, PB = 2PQ = AP. Thus P is the midpoint of AB, and Q is the midpoint of PB. Then the midpoint (X) of QB is AP + PQ + QX = 1/2 + 1/4 + 1/8 times the length of AB from A.

The distance from A to the midpoint of QB is (7/8)a.

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You have 42 ft. of fencing (1 ft. segments) to make a rectangular garden. How much should each side be to maximize your total ar

Verizon [17]

Answer:

$Length=10.5\ ft$

$Width=10.5\ ft$

$Area=110.25\ ft^{2}$

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

$P=2(x+y)$

we have

$P=42\ ft$

so

$42=2(x+y)$

simplify

$21=(x+y)$

$y=21-x$ ------> equation A

Remember that the area of rectangle is equal to

$A=xy$ ----> equation B

substitute equation A in equation B

$A=x(21-x)$

$A=21x-x^{2}$ ----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point $(10.5,110.25)$

see the attached figure

so

$x=10.5\ ft$

Find the value of y

$y=21-10.5=10.5\ ft$

The garden is a square

the area is equal to

$A=(10.5)(10.5)=110.25\ ft^{2}$ ----> is equal to the y-coordinate of the vertex is correct

6 0

3 years ago

Number 14 please and thank you

Fed [463]

You can do a notebook a door , a frame or a mirror, mostly anything that has angles

4 0

3 years ago

write an equation for the perpendicular bisector of the line joining the two points. PLEASE do 4,5 and 6

myrzilka [38]

Answer:

4. The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5. The equation of the perpendicular bisector is y = - 2x + 16

6. The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

Step-by-step explanation:

Lets revise some important rules

The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$ (reciprocal m and change its sign)
The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The mid point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

4.

∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 7 and $x_{2}$ = 4

∵ $y_{1}$ = 2 and $y_{2}$ = 6

∴ $m=\frac{6-2}{4-7}=\frac{4}{-3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $\frac{3}{4}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{7+4}{2},\frac{2+6}{2})$

∴ The mid-point = $(\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)$

- Substitute the value of the slope in the form of the equation

∵ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = $\frac{3}{4}$ × $\frac{11}{2}$ + b

∴ 4 = $\frac{33}{8}$ + b

- Subtract $\frac{33}{8}$ from both sides

∴ $-\frac{1}{8}$ = b

∴ y = $\frac{3}{4}$ x - $\frac{1}{8}$

∴ The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5.

∵ The line passes through (8 , 5) and (4 , 3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 8 and $x_{2}$ = 4

∵ $y_{1}$ = 5 and $y_{2}$ = 3

∴ $m=\frac{3-5}{4-8}=\frac{-2}{-4}=\frac{1}{2}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = -2

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{8+4}{2},\frac{5+3}{2})$

∴ The mid-point = $(\frac{12}{2},\frac{8}{2})$

∴ The mid-point = (6 , 4)

- Substitute the value of the slope in the form of the equation

∵ y = - 2x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = -2 × 6 + b

∴ 4 = -12 + b

- Add 12 to both sides

∴ 16 = b

∴ y = - 2x + 16

∴ The equation of the perpendicular bisector is y = - 2x + 16

6.

∵ The line passes through (6 , 1) and (0 , -3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 6 and $x_{2}$ = 0

∵ $y_{1}$ = 1 and $y_{2}$ = -3

∴ $m=\frac{-3-1}{0-6}=\frac{-4}{-6}=\frac{2}{3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $-\frac{3}{2}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{6+0}{2},\frac{1+-3}{2})$

∴ The mid-point = $(\frac{6}{2},\frac{-2}{2})$

∴ The mid-point = (3 , -1)

- Substitute the value of the slope in the form of the equation

∵ y = $-\frac{3}{2}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ -1 = $-\frac{3}{2}$ × 3 + b

∴ -1 = $-\frac{9}{2}$ + b

- Add $\frac{9}{2}$ to both sides

∴ $\frac{7}{2}$ = b

∴ y = $-\frac{3}{2}$ x + $\frac{7}{2}$

∴ The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

8 0

3 years ago

What is the median of the following string of values?<br>16, 95, 3, 37.97. 13, 27.42, 64, 14

liubo4ka [24]

Answer:

21.71

Step-by-step explanation:

1) you need to order then by the size

3, 13, 14, 16, 27.42, 37.97 ,64, 95

2) if there is an odd amount of numbers then the median would be the center term. but if it an even number then you add the two middle terms together and divide them by 2.

16+27.42= 43.42

43.42 divided by 2=21.71

Hope this helped

4 0

3 years ago

You have the side lengths 3 in., 6 in., and 10 in. Can these side lengths form a triangle

OverLord2011 [107]

No they cannot because 3 is way to short

6 0

3 years ago

Read 2 more answers