The net for a cube is shown below. Find the lateral surface area of the
cube.
8 m

Answer:

  A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF

  A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6

  A.3: ∠2 ≅ ∠3

  B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA

  B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6

  see "additional comment" regarding listing pairs

Step-by-step explanation:

There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.

In these exercises, pairs of angles need to be examined to see which of these relations may apply.

__

Left

ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:

  ∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)

  ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)

Center

  ∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles

  ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles

Right

Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...

  ∠2 ≅ ∠3

__

Left

Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...

  ∠ACD ≅ ∠CAB (30°)

  ∠CDA ≅ ∠ABC (90°)

  ∠DAC ≅ ∠BCA (60°)

Right

The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.

  ∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)

  ∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)

_____

Additional comment

The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:

  a ≅ b ≅ c   ⇒   (a≅b), (a≅c), (b≅c)

Similarly, when 4 things are congruent, they can be arranged in 6 pairs:

  a ≅ b ≅ c ≅ d   ⇒   (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)

In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.

Answer:

[tex]c=35r+10[/tex]

Step-by-step explanation:

We need to create a linear equation in the form: c = mr + b

(where m is the slope and b is the y-intercept)

Choose two ordered pairs from the table:  (2, 80) and (4, 150)

Let [tex](r_1,c_1)[/tex] = (2, 80)

Let [tex](r_2,c_2)[/tex] = (4, 150)

Calculate the rate of change (slope of linear equation) by dividing the change in c by the change in r:

[tex]\textsf{slope} \ m=\dfrac{c_2-c_1}{r_2-r_1}=\dfrac{150-80}{4-2}=35[/tex]

Now use point-slope form of linear equation to create final equation:

      [tex]c-c_1=m(r-r_1)[/tex]

[tex]\implies c-80=35(r-2)[/tex]

[tex]\implies c=35r+10[/tex]

Answer:

V=3456

Step-by-step explanation:

V=[tex]a^{2}[/tex][tex]\frac{h}{3\\}[/tex]

Answer:

53

Step-by-step explanation:

It is either an alternate angle or an opposite angle of the 53 shown.

We know that angles on a straight line add up to 180, so:

53+x=180

x=180-53

x=127

We know that the indicated angle plus x would give 180, so:

?+x=180

?+127=180

?=180-127

?=53

Answer:

Ummm because its not a negative sign in front of it

Step-by-step explanation:

i d k t b h

Answer:

30

Step-by-step explanation:

The mean of 5 numbers is 16 => the sum is 16 x 5 = 80

The mean of 7 numbers is 20 => the sum is 20 x 7 = 140

So, the sum of the 2 extra numbers is 140 - 80 = 60
And the mean will be 60 : 2 = 30

Hope it helps :D

Answer:

-20

Step-by-step explanation:

Answer:

You would pay $22.49

You would save $2.50

Step-by-step explanation:

Answer:

22.49 dollars

Step-by-step explanation:

….

Answer:

  yes; AB ⊥ BC

Step-by-step explanation:

If the triangle is to be a right triangle, the slopes of two sides must be opposite reciprocals. The slope is the ratio of rise to run.

  mAB = rise/run = -3/4

  mBC = rise/run = 4/3

These slopes, -3/4 and 4/3 are opposite reciprocals (their product is -1), so ...

  AB ⊥ BC . . . the triangle is a right triangle

Answer:

32 x 150 = A = 2 x 2 = c + b = 254

Step-by-step explanation:

Answer:

x = 101 °

Step-by-step explanation:

Here give ∠ ACD exterior  angles 79 °

[Angle Addition Postulate and definition of straight angle: ]

∠ACD + ∠ACB = 180

79 + n = 180

n =180-79=101

n = 101

[RevyBreeze]

Apply supplementary angle theorem

[tex]\\ \rm\rightarrowtail x+79=180[/tex]

[tex]\\ \rm\rightarrowtail x=180-79[/tex]

[tex]\\ \rm\rightarrowtail x=101[/tex]

Answer:

x = 2 and y = 3

Step-by-step explanation:

To find the x- intercept, let y = 0 in the equation and solve for x

3x + 2(0) = 6

3x + 0 = 6

3x = 6 ( divide both sides by 3 )

x = 2 ← x- intercept

To find the y- intercept, let x = 0 in the equation and solve for y

3(0) + 2y = 6

0 + 2y = 6

2y = 6 ( divide both sides by 2 )

y = 3 ← y- intercept

Answer is C I took the quiz

The correct answer to Deshawn's decision is; C: DeShawn's current policy will cover his family for an adequate period of time at his current salary.

From the scenario in the question about the policy chosen by DeShawn, we can say that DeShawn made a good decision. This is because his current policy will cover his family for an adequate period of time at his current salary.

Now, it must be noted that the premiums are nominal and as such he will earn a good salary which will help to cover all the expenses and premiums.

Read more about Pension Policy at; https://brainly.com/question/27232329

Answer: the scale copy of the given figure is the fourth answer

Step-by-step explanation:

Answer:

122

Step-by-step explanation:

The sum of interior angles of a pentagon is 540. The angles we have are 105, 86, 137, and 90. This means that if you subtract those from 540, you get 122.

Answer:

1. f(a) = -2a + 3

2. 2f(a) = -4a + 6

3. f(2a) = -4a + 3

4. f(a+2) = -2a - 1

5. f(a) + f(2) = -2a + 2

Step-by-step explanation:

for each one, just plug whatever is inside the parentheses inside the equation as x. For example, f(a) = -2(a) + 3. The a replaces all the x's

Add the two angles and then subtract from 180* to find the missing angle
So,
145* + 15* = 160*

180* - 160* = 20*


Answer: x = 20*

Answer:

There are many improper fraction equal to eight, they include: 8/1, 16/2, 24/3, 32/4, 40/5, 48/6, 56/7, 64/8, 72/9 etc.When a multiple of eight is divided by the other factor with with when multiplied to eight gives the multiple, the result will be eight

Answer:

i think x=36

Step-by-step explanation:

3x + 2x = 5x = 180

x = 180÷5 =36

Check the picture below.

Answer:

4588 [in²].

Step-by-step explanation:

1) the given octagon can be imagined as 8 triangles (see the attachment). In order to calculate the required area of the octagon, it is enough to calculate the area of one triangle then increase it 8 times:

2) area of one triangle is:

37*31/2 [in²].

3) the required area of the octagon is:

31*37*8/2=31*37*4=4588 [in²].

Answer:

he has been saving for 98 weeks

Step-by-step explanation:

well 90 + 48 / 6 = 98

$0.38×192=$72.96

So the answer is $72.96

Answer:

What is the question? You have put a statement or objective

Answer:

3291÷500 or 6.582

Step-by-step explanation:

98.73 divide by 15 = 6.582