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3 years ago

Find parametric and symmetric equations of the line through the point (2,1,0) and perpendicular to the plane 5x-3y + 4z = 15

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

6 0

$x = 5t + 2$
$y = - 3t + 1$
$z = 4t$

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3 years ago

Read 2 more answers

If two consecutive angles of a parallelogram are congruent, what is the measure of each angle?

Debora [2.8K]

Answer:

Measure of each angle is 90 degree.

Step-by-step explanation:

Given : If two consecutive angles of a parallelogram are congruent.

To find the measure of each angle:

There are 6 important properties of parallelograms:

Opposite sides are congruent.

Opposite angles are congruent
Consecutive angles are supplementary.
If one of the angle is right angle, then all angles are right.
Diagonals of a parallelogram bisect each other
Also, each diagonal of a parallelogram separates it into two congruent.

let A and D be two consecutive angle.

then, by the given condition

$\angle A \cong \angle D$ ......[1]

From the property of parallelogram:

Consecutive angles are supplementary

Then;

$\angle A + \angle D = 180^{\circ}$

From equation [1];

$\angle A + \angle A = 180^{\circ}$

Combine like terms :

$2\angle A = 180^{\circ}$

Divide both sides by 2 we get;

$\frac{2 \angle A}{2} = \frac{180^{\circ}}{2}$

Simplify:

$\angle A = 90^{\circ}$

From the given property of parallelogram : if one of the angle is right, then all the angles in the parallelogram are right angle.

∴ $\angle A = \angle B = \angle C = \angle D = 90^{\circ}$

Therefore, the measure of each angle is $90^{\circ}$

4 0

3 years ago

As part of a quality-control study aimed at improving a production line, the weights (in ounces) of 50 bars of soaps are measure

grin007 [14]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is the weight in ounces of a soap bar.

Attached is a QQplot diagram.

A Q-Q plot is a diagram that compares two probability distributions, in this case, the probability distribution of the data set against the theoretical normal distribution. If the observed data matches the theoretical sets, you can say that that population follows said distribution.

As you can see in the graphic the observed values (blue dots) fit the normal theoretical quantiles, so we can say that the data appear to come from a normal distribution.

I hope it helps.