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3 years ago

Prove that the diagonals of a rectangle bisect each other. The midpoint of AC is _____

Mathematics

2 answers:

Aleksandr-060686 [28]3 years ago

7 0

Answer:

We choose D.

Step-by-step explanation:

Let the midpoint is O

We will use Angle-SIde-Angle principle to prove that the diagonals of a rectangle bisect each other.

Have a look at the two triangles: AOB and DOC, they are congruent because:

AB = DC
∠OAB = ∠DCO because they are alternate angles
∠OBA = ∠CDO because they are alternate angles

So we can conclude that: OB = OB when two triangles: AOB and DOC are congruent.

Similar, apply for the two triangles: AOD and BOC are congruent so we have OA = OC .

=> It proves that the point O simultaneously is the midpoint and intersection point for the diagonals.

=> The midpoint of AC is ( $\frac{2a+ 0}{2}$ , $\frac{0 + 2b}{2}$ ) = (a, b), we choose D.

Ulleksa [173]3 years ago

6 0

Answer:

(a,b)

Step-by-step explanation:

simply we find the midpoint of AC and the midpoint of Bd by dividing over 2

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A football is kicked toward an end zone with an initial vertical velocity of 30 ft/s. The function h(t) = -16+ 30t models the he

Ulleksa [173]

Answer:

A. The football does not reach a height of 15ft

Step-by-step explanation:

Given

$h(t) = -16t^2 + 30t$

Required

Determine which of the options is true

The option illustrates the height reached by the ball.

To solve this, we make use of maximum of a function

For a function f(x)

Such that:

$f(x) = ax^2 + bx + c$ :

$f(\frac{-b}{2a}) = maximum/minimum$

i.e we first solve for $\frac{-b}{2a}$

Then substitute $\frac{-b}{2a}$ for x in $f(x) = ax^2 + bx + c$

In our case:

First we need to solve $\frac{-b}{2a}$

Then substitute $\frac{-b}{2a}$ for t in $h(t) = -16t^2 + 30t$

By comparison:

$b = 30$

$c = -16$

$\frac{-b}{2a} = \frac{-30}{2 * -16}$

$\frac{-b}{2a} = \frac{-30}{-32}$

$\frac{-b}{2a} = \frac{30}{32}$

$\frac{-b}{2a} = \frac{15}{16}$

Substitute $\frac{15}{16}$ for t in $h(t) = -16t^2 + 30t$

$h(\frac{15}{16}) = -16(\frac{15}{16})^2 + 30(\frac{15}{16})$

$h(\frac{15}{16}) = -16(\frac{225}{256}) + \frac{450}{16}$

$h(\frac{15}{16}) = -(\frac{225}{16}) + \frac{450}{16}$

$h(\frac{15}{16}) = \frac{-225 + 450}{16}$

$h(\frac{15}{16}) = \frac{225}{16}$

$h(\frac{15}{16}) = 14.0625$

This implies that the maximum height reached is 14.0625ft.

So, the option that answers the question is A because $14.0625 < 15$

8 0

2 years ago

A cylinder and a come have the same volume. The cylinder has a radius of 2 inches and a height of 3 inches. The cone has radius

MrRissso [65]

Answer: 4in

Step-by-step explanation:

Volume of a cylinder = πR²H

Volume of a cone = 1/3πr²h

πR²H = 1/3πr²h

π is very common so it could be cancelled, so the equation now becomes

R²H = 1/3r²h

3R²H = r²h

Now substitute for the values

h = 3 x 2² x 3

--------------

3²

= 9 x 4/9

= 4in.

Therefore, the height of the cone

h = 4in.

4 0

2 years ago

There are 364 students who are enrolled in an introductory biology course. If there are five boys to every eight girls, how many

Butoxors [25]

Answer:

The number of boys in the course will be = 140

Step-by-step explanation:

Given:

Total number of students enrolled in an introductory biology course = 364

There are 5 boys to every 8 girls in the course.

To find how many boys are in the course.

Solution:

Since, there are 5 boys to every 8 girls in the course.

So, ratio of boys to girls enrolled in the course = 5 : 8

Let the number of boys in the course be = $5x$

Then number of girls in the course will be = $8x$

Total number of students would be given as:

⇒ <em>Number of boys + Number of girls</em>

⇒ $5x+8x$

⇒ $13x$

Total number of students given = 364.

Thus, we have:

$13x=364$

solving for $x$

Dividing both sides by 13.

$\frac{13x}{13}=\frac{364}{13}$

∴ $x=28$

So, number of boys in the course will be = $5\times 28$ = 140

5 0

3 years ago

PLSS help me with this and show your work

hodyreva [135]

hii

3x-1/5=x+1/3

3[3x-1]=5[x+1]

9x-3=5x+5

9x-5x=5-3

4x=2

x=2/4

x=1/2

HOPE IT HELPS YOU OUT PLEASE MARK IT AS BRAINLIEST AND FOLLOW ME PROMISE YOU TO FOLLOW BACK ON BRAINLY.IN

6 0

2 years ago

Read 2 more answers

Help me please!!!!!! giving out brainliest

vazorg [7]

Answer:

1 = 175ft cubed

2 = 58m cubed

3 = 140m cubed

4 = 180in cubed

Step-by-step explanation:

You have to split these complex shapes into parts and find the volume of each part. Then, add the parts' volumes together, which will be the total volume of these. The equation is V=bhw. V means volume, b means base, h means height, and w means width. Hope this helps!

6 0

1 year ago