All categories

3 years ago

(05.05 MC) what are the measures of angles a, b and c? explain your answer

Mathematics

1 answer:

mariarad [96]3 years ago

4 0

Check the picture below.

∡a has a vertical angle sibling of 40°, and vertical angles are always congruent.

∡b is the 3rd angle in a triangle, the other two are 40° and 90°, recall all interior angles in a triangle add up to 180°.

∡c is a linear angle, namely an angle on the same flat-line as another, and linear angles always add up to 180°.

You might be interested in

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

3 years ago

What transformations would result in the image shown?

jok3333 [9.3K]

ABC is reflected over y-axis and translated up 1 unit

3 0

2 years ago

Brian flips a fair coin 3 times. What is the probability of getting exactly 1 tail?

Leya [2.2K]

Answer:

1/3

Step-by-step

he flips the coin three time and there is one side so 1/3

3 0

4 years ago

What is the midpoint between (-1, 1) and (5, -5)

e-lub [12.9K]

Answer:

(2,-2) is your answer

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:

Stels [109]

Answer:

SAS postulate

Step-by-step explanation:

In the figure attached, quadrilateral ABCD is shown.

The Side Angle Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

AB is congruent to DC, and DB is the side common to triangles ABD and BCD. The included angle between sides AB and DB is angle ABD which is congruent with angle BDC, the angle included between sides DB and DC.

7 0

3 years ago

(05.05 MC) what are the measures of angles a, b and c? explain your answer​

(05.05 MC) what are the measures of angles a, b and c? explain your answer