Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m∠5 + m∠2 + m∠6 = 180° Lines y and z are parallel. Triangle A B C sits between the 2 lines with point A on line y and points C and B on line z. Angle C A B is 2. Its exterior angle to the left is 1 and its exterior angle to the right is 3. Angle A B C is 6 and its exterior angle to the right is 7. Angle B C A is 5 and its exterior angle to the left is 4. Statements Reasons 1. ABC is a triangle 1. given 2. y ∥ z 2. given 3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ? 4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅ 5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate 6. m∠1 + m∠2 + m∠3 = 180° 6. def. Straight angle 7. m∠5 + m∠2 + m∠6 = 180° 7. substitution Which could be the missing reason in Step 3? alternate interior angles are congruent alternate exterior angles are congruent vertical angles are congruent corresponding angles are congruent

Answer:

Step-by-step explanation:

Given parameters:

Dimensions of the equilateral triangle = 6.2cm

Unknown:

Perimeter = ?

Solution:

The perimeter of the triangle is the sum of all its sides;

  Perimeter = 3(L) for an equilateral triangle;

 Perimeter  = 3(6.2) = 18.6cm

to the nearest mm = 19.0cm

Answer:

m∠A = 39°

Step-by-step explanation:

From the figure attached,

BE ≅ BC

m∠C = 32°

m∠BFD = 103°

In ΔBCE,

m∠E = m∠C = 32°  [Since, BE ≅ BC]

m∠E + ∠C + m∠EBC = 180°

32° + 32° + m∠EBC = 180°

m∠EBC = 116°

m∠EBC + m∠EBA = 180° [Linear pair of angles]

116° + m∠EBA = 180°

m∠EBA = 64°

Similarly, m∠AFB + m∠DFB = 180° [Linear pair of angles]

m∠AFB + 103° = 180°

m∠AFB = 77°

Now in ΔAFB,

m∠A + m∠AFB + m∠FBA = 180° [Sum of internal angles of a triangle = 180°]

m∠A + 77° + 64° = 180°

m∠A = 39°

Perpendicular equations have opposite reciprocal slopes, so any equation perpendicular to the equation y = 1/2 x - 2 would have the slope -2.

Now plug in the point (6, -3) into the equation y = -2x + b to find out what b is.

-3 = -2(6) + b

Multiply -2 by 6.

-3 = -12 + b

Add 12.

9 = b

So the equation is y = -2x + 9

Hope this helps

Answer:

x²+x+12 = 0

Step-by-step explanation:

Area if the wooden frame = ,Length ×Width

A = LW

If the length of wooden frame is 1foot longer than it's width, then;

L = W+1

Given

A = 12ft²

Substitute the derived and given parameters into the formula to have;

P = (W+1)W

12 = (W+1)W

Open the parentheses

12 = W²+W

Subtract 12 from both sides

12-12 = W²+W -12

0 = W²+W-12

Rearrange

W²+W-12 = 0

If W = x

The quadratic equation becomes:

x²+x+12 = 0

Answer:

Maximum number of gift cards she can purchase = 33

Reward points left with her = 48

Step-by-step explanation:

Let Albert's mom buys the number of gift cards = x

Points for each gift card = 75

Total points consumed to buy x gift cards = 75x

If total points with Albert's mom = 2523

So the remaining points with her = (2523 - 75x)

Inequality representing the remaining points will be,

(2523 - 75x) ≥ 0

75x ≤ 2523

x ≤ [tex]\frac{2523}{75}[/tex]

x ≤ 33.64

Maximum number of cards she can buy = 33

Therefore, reward points with her = 2523 - (75 × 33)

                                                         = 2523 - 2475

                                                         = 48

Answer:

10.5  = x

Step-by-step explanation:

7:x = 2:3

can be rewritten as

7/x = 2/3

because, a proportion is the same as a fraction, which is the same as division

so now use cross products to solve the equations

7/x = 2/3

7 * 3 = 2 * x

simplify

21 = 2x

inverse operations

21 = 2x

/2    /2

10.5 = x

Answer:

y = 136

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle, thus

y = 82 + 54 = 136

Answer:

y=3.54m

Step-by-step explanation:

it is pretty self explanatory

An algebraic expression for the statement could be as; y = 3.54m

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.

Thus which can also be used to indicate the logical syntax's order of operations and other features.

We need to write an algebraic expression for the statement.

Given that The cost of m pounds of meat when the cost per pound is $3.54.

Therefore, the expression could be as;

y = 3.54m

hence, An algebraic expression for the statement could be as; y = 3.54m

To know more about an expression follow;

brainly.com/question/19876186

#SPJ2

Answer:

Side C= 22

Side B = 12

Side A= 22.16627

i do think it is 22.16627

Step-by-step explanation:

hope this helps

Answer:

21x- 21

Step-by-step explanation:

7 × (x × 3 - 3)

7 × (3x - 3)

21x - 21

I'm not sure if the answer is correct

Answer:

A ÷ (WH)

Step-by-step explanation:

The constant of variation is the slope, which is the number before the x variable.

The answer is -2/3

Answer:

4/6

Step-by-step explanation:

1/2 needs to be converted to sixths, so we would multiple the numerator and the denominator by 3, because 2 goes into 6, 3 times, then we would get 3/6 + 1/6, then just add, 1 + 3 = 4, and then you end up with 4/6. Have A Great Day!

Answer:

10t - 16

Step-by-step explanation:

4(t + 2)+ 6(t - 4)

4t + 8 + 6t -24

10t - 16

Answer:the roots is 2 10 and 125

Step-by-step explanation:used a caculator

Answer:

for me the answer is a but the root  is x=5+10i

Step-by-step explanation:

Answer:

$140

Step-by-step explanation:

150-10=140

$140

HOPEFULLY IM RIGHT!!

Have A Nice Day!!!!

:)))

Answer:

g(x2+6x+7)=x2+6x+9

Step-by-step explanation:

Evaluate g(f(x)) by substituting in the value of f into g

g(2x)=6(2x)−7

Multiply 2 by 6

g(2x)=12x−7

Answer:

Step-by-step explanation:

Hope this helps! <3

The number 235 is a composite number because 235 can be divided by 1, by itself and at least by 5 and 47. So, it is possible to draw its prime tree.

The prime factorization of 235 = 5•47.

hope this help! ^^

-1, it's fairly clear just from the table...

Answer:

-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

A(11, –2, –6) and B(–3, 7, –5) are located away from the origin (0,0,0), the points from the origin to this points is expressed as OB - OA where;

OB is the distance from the origin to the point B

OA is the distance from the origin to the point A

Using the formula for calculating distance between two points

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(-6-0)²+(-2-0)²+(11-0)²

OA = √(-6)²+(-2)²+(11)²

OA = √36+4+121

OA = √161

OA = 12.688

Similarly;

OB = √(-5-0)²+(7-0)²+(-3-0)²

OA = √(-5)²+(7)²+(-3)²

OA = √25+49+9

OA = √83

OA = 9.110

Distance from the origin to the points = 12.688 - 9.110 = 3.577

Distance from the origin to the points  ≈ 3.6 (to the nearest tenth)

Answer:

The distance from the origin to point A is 12.7 units.

The distance from the origin to point B is 9.1 units.

Point A is 3.6 units farther from the origin than point B.

Answer:

$45

Step-by-step explanation:

ratio is 3:5

David gets 3x, Jack gets 5x

So, 3x+5x=120

8x=120

x=15

David got 3x = 3*15 = $45

Answer:

45$

Step-by-step explanation:

120/8=15

15*3=45

because it is 3:5 ratio

Answer:

that all depends on the car mileage, say she gets 20 mpg itd be 20x22

Answer:

yes it is a 0 is not a value if its infront of an answer

Step-by-step explanation:

Answer:

The dilation is 3 times smaller of divided by 3.

Step-by-step explanation:

If you look at each beginning point all the numbers are divisible by 3 then when you look at the ending points they are the same as the beginning just 3 times smaller.

Answer:

The dilation is 3 times smaller of divided by 3.

Step-by-step explanation:

If you look at each beginning point all the numbers are divisible by 3 then when you look at the ending points they are the same as the beginning just 3 times smaller.

Step-by-step explanation:

Answer: yes

Step-by-step explanation:

The x value does not repeat itself

Answer:

-4.1, -3.5, -1.4, 5.3

Step-by-step explanation:

hope this helps!