What number is half way between –3 and 4 ?

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:

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:

i think x=36

Step-by-step explanation:

3x + 2x = 5x = 180

x = 180÷5 =36

Check the picture below.

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:

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:

36

Step-by-step explanation:

the total sugar bags to be distributed= x=48

the total rice bags to be distributed= y=72
each family can take a package containing= 1x +2y
as each family can have 2 rice bags thus we can estimate the total number of families that can benefit by diving total no of rice bags by 2 which will be = 72/2 =36

the rice can be divided into 36 families
while the sugar bags can be divided into 48 families
as these have to be divided into packages so there will be 36 packages
that can be distributed into 36 families.

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:

V=3456

Step-by-step explanation:

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

Answer:

-20

Step-by-step explanation:

Answer: C line through point (0,

3) and (1, 1). Line through (0, 2) and (4, 0)

Step-by-step explanation:

Answer:

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

Answer:

y=5x+9

Step-by-step explanation:

5x because the slope is 5

then solve for b by plugging in x=-1, y= 4 into the equation y=5x+b

Answer:

What is the meaning of principle of contradiction?

The principle of contradiction expresses the metaphysical and logical opposition between being and its negation. ... Formulated in the logical order, it asserts that it is impossible to affirm and at the same time deny the same predicate of the same subject.

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Answer:

x=31 <B=112

Step-by-step explanation:

I'm super lazy so I won't give a thorough explanation, but this should explain it all.

Opposite angles on parallelograms are congruent

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:

(2) $1,699.50

Step-by-step explanation:

A(t) = P(1 + r/n)^nt

1500(1 + .025/12)^5*12

= $1699.50

$1,699.50 represents the value of an investment with a principal of $1500 with a nominal interest rate of 2.5% compounded monthly after 5 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Given that an investment with a principal of $1500 with a nominal interest rate of 2.5% compounded monthly after 5 years,

Amount = P(1+r/n)^nt

= 1500(1+0.25/12)^5*12

= $1699.50

Hence, $1,699.50 represents the value of an investment with a principal of $1500 with a nominal interest rate of 2.5% compounded monthly after 5 years.

For more references on Compound interest, click;

https://brainly.com/question/14295570

#SPJ2

Answer:

3291÷500 or 6.582

Step-by-step explanation:

98.73 divide by 15 = 6.582

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:

127/4 or 31 3/4 or 31.75

Step-by-step explanation:

got this by dividing 254 with 6 3/4

Answer:

[tex]f^{-1}(x)= \frac{3x}{2}+3[/tex]

Step-by-step explanation:

Interchange the variables:

x = y - 4 - [tex]\frac{y}{3} +2[/tex]

Solve for y:
[tex]y=\frac{3x}{2} +3[/tex]

Replace y with [tex]f^{-1} (x)[/tex] to show the final answer:
[tex]f^{-1}(x)= \frac{3x}{2}+3[/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:

  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: C $6.60

Step-by-step explanation:

46.20 ÷ 7 = 6.6

So Shana should be saving $6.60 every week.

The correct answer is :

[tex]\frac{13}{50}[/tex]

Answer:

the fort effyh v answer is A duhhhhhh

Answer:

Answer: OD 81007 in.2

Step-by-step explanation:

Use formula for area of circle, which is A = πr²

The radius is squared, so if the radius or a new circle is 6 times larger (multiplied by 6), the difference in area will be 36 times greater.  So the area is

225π(36) = 8,100π

Answer:

D) [tex]8100\pi[/tex] in²

Step-by-step explanation:

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Question:

A circle has an area of 225[tex]\pi[/tex] square inches.  If the radius of the circle is multiplied by 6, then what is the area of the new circle?

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area of a circle = [tex]\pi r^2[/tex]   (where r is the radius)

⇒ [tex]\pi r^2=225\pi[/tex] in²

If the radius is multiplied by 6, then r = 6r

⇒ area = [tex]\pi (6r)^2=36\pi r^2[/tex]

Therefore, if [tex]\pi r^2=225\pi[/tex]

then [tex]36\pi r^2 = 36 \times 225\pi =8100\pi[/tex]

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.