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1 year ago

Find the length of the median of a trapezoid if the length

Mathematics

1 answer:

guapka [62]1 year ago

8 0

Answer:

20 cm

Step-by-step explanation:

We are given a trapezoid, where the length of shorter base or on of the parllel line is 16 cm and the length of other parallel side is 24 cm.

Let the two parallel sides be x and y that is x = 16 cm and y = 24 cm.

A median of a trapezoid is a line segment that divides the non parallel sides of a trapezoid equally or a line segment that passes through the mid points of non-parallel sides of a trapezoid.

The length of median of a trapezoid = $\frac{\text{Sum of parallel sides}}{2}$ = $\frac{16+24}{2}$ = 20 cm.

Thus, the length of median of trapezoid is 20 cm.

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Mary bought a paid of jeans and a sweater.The pair of jeans costs $30 and the sweater costs $35 .If sales tax is 6% ,how much di

ella [17]

$30 + $35 = $65

Assuming tax is on whole sale not each item:
$65 * 0.06 (6%) = $3.90 (6% of $65)

$65 + $3.90 = $68.90 ($65 + 6%)

OR

You could combine both of these steps and just use this working:
$65 * 1.06 (106%) = $68.90 (106% of $65)

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2 years ago

Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.

Gala2k [10]

Notice that

$x^2+14xy+49y^2=(x+7y)^2$

so the constraint is a set of two lines,

$(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}$

and only the first line passes through the first quadrant.

The distance between any point $(x,y)$ in the plane is $\sqrt{x^2+y^2}$ , but we know that $\sqrt{f(x,y)}$ and $f(x,y)$ share the same critical points, so we need only worry about minimizing $x^2+y^2$ . The Lagrangian for this problem is then

$L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0$

$L_y=2y+7\lambda=0$

$L_\lambda=x+7y-10=0$

We have

$L_y-7L_x=2y-14x=0\implies y=7x$

which tells us that

$x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75$

so that $\left(\dfrac15,\dfrac75\right)$ is a critical point. The Hessian for the target function $x^2+y^2$ is

$H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite for all $x,y$ , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is $\sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2$ .

3 0

1 year ago

iven: C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the

ZanzabumX [31]

Answer:

See the attached figure for better explanation :

Step-by-step explanation :

1. By the unique line postulate, you can draw only one line segment : BC

Since only one line can be drawn between two distinct points.

2. Using the definition of reflection, reflect BC over l.

To find line segment which reflects BC over l, we will use the definition of reflection.

3. By the definition of reflection, C is the image of itself and A is the image of B.

Definition of reflection says the figure about a line is transformed to form the mirror image. Now, CD is perpendicular bisector of AB so A and B are equidistant from D forming the mirror image of each other.

4. Since reflections preserve length, AC = BC

In Reflection the figure is transformed to form a mirror image, Hence the length will be preserved in case of reflection.

8 0

1 year ago

Read 2 more answers

Assume 6 in every 2000 students at the local community college have to quit due to serious health issues. An insurance company o

Alexus [3.1K]

Given:

6 out of 2000 students quit community college due to serious health issues.
$10,000 insurance company offer
$60 per year

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6 * 10,000 = $60,000 to make a break-even on their insurance offer

If a student pays $60 per year, they should have

$60,000 / $60 = 1,000 students who will pay per year to reach the break-even mark of their investment. If the number of students will exceed 1,000, the company will begin to earn.

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1 year ago

If r is the midpoint of qs rs=2x-4, st= 4x-1 and rt = 8x-43 find qs

sammy [17]

Answer:

$QS=68\ units$