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3 years ago

What is the area of ABDC? Assume ABDC lies in the center of the larger rectangle.

Mathematics

2 answers:

nadezda [96]3 years ago

8 0

Answer:

Area of ABDC is 24 square feet.

Step-by-step explanation:

Given rectangle ABDC which lies in the center of the larger rectangle. We have to find the area of ABDC.

Length of rectangle=outer length-given gap from both sides

=12-3-3=6 ft.

Breadth of rectangle=outer breadth-given gap from both sides

=10-3-3=4 ft.

Now, $\text{area of rectangle ABDC=}Length\times breadth$

$=6\times 4=24ft^2$

hence, area of ABDC is 24 square feet.

Option C is correct.

MrRa [10]3 years ago

7 0

The area of rectangle ABCD should be 24. Since the length is 6 and the height is 4.

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Find an equation for the perpendicular bisector of the line segment whose endpoints

TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

$\boxed{gradient = \frac{y1 -y 2}{x1 - x2} }$

Gradient of given line

$= \frac{1 - ( - 5)}{3 - ( - 9)}$

$= \frac{1 + 5}{3 + 9}$

$= \frac{6}{12}$

$= \frac{1}{2}$

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

$\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }$

Midpoint of given line

$= ( \frac{3 - 9}{2} , \frac{1 - 5}{2} )$

$= ( \frac{ - 6}{2} , \frac{ - 4}{2} )$

$= ( - 3 , - 2)$

Substituting (-3, -2) into the equation:

-2= -2(-3) +c

-2= 6 +c

c= -2 -6 (-6 on both sides)

c= -8

Thus, the equation of the perpendicular bisector is y= -2x -8.

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3 years ago

How many dimensions exists in the universe? A) 3 B) 5 C) 11 D) 10

nalin [4]

Your answer is 10
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3. Depth
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8. A Plane of All Possible Worlds, Each With Different Start Conditions, Each Branching Out Infinitely
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3 years ago

What’s the value of 1 2/3 divided by 1 7/18 In mixed number fraction form someone please help :)

JulsSmile [24]

12/3=4
4 divided by 17/18 equals to 4* 18/17=72/17= 4 4/17
Thus the answer is 4 4/17

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3 years ago

Can anyone help me with THIS and the other TWO‼️PLEASE I’m really need HELP

scZoUnD [109]

Answer:

y = 3x +2

Step-by-step explanation:

It is helpful to be acquainted with the parts of at least a couple of different forms of the equation for a line.

You are given the equation of a line in "slope-intercept" form. It looks like ...

... y = mx + b . . . . . . . where m=-1/3 and b=-1

The coefficient of x, which is m, is the slope of the line. That is -1/3 for the given line.

The relationship between the slopes of perpendicular lines is that they multiply to give -1. We say each is the opposite reciprocal of the other. If we let "m" stand for the slope of the perpendicular line, it satisfies the equation ...

...(m)(-1/3) = -1

... m = -1/(-1/3) = 3 . . . . . the slope of the perpendicular line is 3.

____

Here's where another form of the equation for a line is useful. We can write the "point-slope" form* as ...

... y = m(x -h) +k . . . . . . for a line of slope m through point (h, k)

We want our line of slope = 3 to go through the point (1, 5), so its equation can be ...

... y = 3(x -1) +5 . . . . . . . variation of "point-slope" form

The given equation is in slope-intercept form, and the question asks for "the" equation of the line, so we probably should write our answer in the same form as the given equation. We can do this by eliminating the parentheses and simplifying the equation we have.

... y = 3x -3 +5 . . . . eliminate parentheses using the distributive property

... y = 3x +2 . . . . . . collect terms

The graph shows our result is at least plausible: it looks like it is perpendicular, and it goes through the given point.

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*Comment on point-slope form

Usually, you will see "point-slope" form written as ...

... y -k = m(x -h) . . . . . . . . standard version of "point-slope" form

When our intent is to use this form to get to slope-intercept form, it is more convenient to add k to this equation to get ...

... y = m(x -h) +k . . . . . . . occasionally useful version

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3 years ago

Please help. It’s a multiple choice question. I’ve my answer, but I’m not sure.

S_A_V [24]

Answer:

66 degree

Step-by-step explanation:

given:

angle FAB = 48 degree

angle ECB = 18 degree

in triangle HBC , angle H is also 48 degree degree since the line is parallel the connection between angle H and angle A is alternate interior angle and alternate interior angle are always equal.

so angle H = 48 degree

in triangle HBC

angle H + angle C = angle ABC (sum of two interior opposite angles are equal to the exterior angle formed)

48 + 18 = angle ABC

66 = angle ABC

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2 years ago