Given: ∠1 and ∠2 form a linear pair; m∠2 + m∠3 = 180 prove: ∠1 is congruent to ∠3

Answer:  [tex]\frac{8}{4}[/tex] = 2

Step-by-step explanation:

5 - 3 = 2

2 x 2 x 2 x 2 = 16

24 - 16 = 8

[tex]\frac{8}{4}[/tex]

Simplify

[tex]\frac{8}{4}[/tex] = 2

The ray, line, or line segment that divides an angle into two congruent angles is known as an angle bisector.

There are 4 important elements to notice about two-column proofs.

1) The first column exists utilized to write math statements.

2) The second column exists utilized to write the reasons you make those statements.

3) The statements are numbered and follow a logical order.

The angle bisector theorem in geometry is concerned with the relative lengths of the two segments of a triangle's side that are divided by a line that bisects the opposite angle. It compares their lengths to the lengths of the other two sides of the triangle.

The ray, line, or line segment that divides an angle into two congruent angles is known as an angle bisector.

Let CB bisects [tex]\angle[/tex] ABD and [tex]\angle[/tex] ACD

[tex]\angle[/tex] ABC ≅ [tex]\angle[/tex] DBC (Definition of angular bisector)

[tex]\angle[/tex] BC ≅ [tex]\angle[/tex] BC  (Reflexive Property)

[tex]\angle[/tex]  ACB ≅ [tex]\angle[/tex] DCB (Definition of angular bisector)

[tex]\triangle[/tex] ABC ≅ [tex]\triangle[/tex] DBC (ASA)

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Answer:

The answer is -3

Step-by-step explanation:

f(-3)=3(-3)+6

f(-3)=-9+6

f(-3)=-3

Answer:the answer is -3, the first option (top to bottom)

Step-by-step explanation:

Find f(-3) as shown below

the answer is -3, the first option (top to bottom).

Answer:

The runners drank 661 bottles of water.

Step-by-step explanation:

Subtract 661 from 750, and you are left with 89.

Answer:

Option 3

Step-by-step explanation:

The  area of the given sector is 98.2 sq. units.

The area of a sector is the space inside the section of the circle created by two radii and an arc.

The area of a sector is a fraction of the area of the entire circle.

Mathematically, the area of a sector is given as;

A = θ/360 (πr²)

where;

The area of the given sector is calculated as follows;

In the given diagram, θ = 50⁰, r = ST = UT = 15 units

A = (50/360) x (π x 15²)

A = 98.2 sq. units

Thus, the  area of the given sector is 98.2 sq. units.

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Answer:

guy yunby

Step-by-step explanation:

Huh uu.

According to the given statement the perpendicular distance form the point  (-4,4)  is 66.3.

Coordinate Geometry can be used to define points in space. The primary axis labeled a x- and y-axes is defined first, and then the points were measured and labelled in relation to these points. Furthermore, numerous geometric forms such as a line, curve, circle, ellipse, and hyperbola can be plotted inside the coordinate axes and their attributes studied.

the equation for line ℓ.

Begin by finding the slope of the line through the given points,(0,-2) and (1,3):

m = (Y₂ - Y₁)/(x₂ - x₁)

  = (3 - (-2))/(1 - 0)

  = 5/1

  = 5

The equation of the line using point (1,3) on the line:

Y - Y₁ = m(x - x₁)

putting value we get: (m = 5)

Y - (-2) = 5(x - 1)

Y + 2 =  5x - 5

Y  = 5x - 3

The equation of the line w perpendicular to line ℓ through P(-4,4).

The slop of line l is 5. Write the equation of the line using point P(-4,4) on the line.

Y - Y₁ = m(x - x₁)

Y - 4 = 5(x - (-4))

Y - 4 = 5x + 4

Y = 5x + 8

Solve the system of equations to determine the point of intersection. Subtract both sides of (1) and (2) to eliminate y.

5x + 8 = 5x - 3

5x + 8 - 5x + 3 = 0

x = 11

putting the value of x to find y:

Y = 5x + 8

Y = 62

Applying the formula to find the distance of a points:'

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

d = √((11 - 4 )² + (62 + 4)²)

d = √(4405)

d = 66.3

According to the given statement the perpendicular distance form the point  (-4,4)  is 66.3.

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Answer:

2$!$! jdnznwi bdbejsn uebeij737 y

The polygon P is translated and rotated respectively to obtain polygon Q.

A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

ABCD and EFGH are polygons P and Q respectively.

We will briefly outline each step required to convert each Polygon P into its corresponding Polygon Q in this question.

In this case, there is translation along a vector between point A and point H.

Then, when the polygon Q is rotated around point H.

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Answer: m<JKM=70 degrees

Step-by-step explanation:

JKM=JKL+LKM

JKM=42+28

JKM=70

m<JKM=70 degrees

Answer:

your answer is 33/8

Step-by-step explanation:

Answer:

fgehjenrntktkktmttbtbvtvt

A or D but i reckon A

Step-by-step explanation:

a)

high positive x (x going to +infinity) would create high positive y (also +infinity).

while high negative x (x going to -infinity) would create high negative y (also -infinity), x⁵ with its odd exponent is negative for negative x and positive for positive x.

the graph is showing just the opposite behavior.

so, it cannot be the right graph.

b)

the degree of the polynomial is the highest exponent of the input variable x. in our case : 5

a polynomial of degree n must have n zeros (or roots).

in our case we need 5 zeros. but there are only 3. no matter how we shift it up or down, the x-axis will not intercept it more than 3 times.

so it cannot be the right graph.

Points that map onto themselves are said to be invariant points. Invariant points can occasionally appear during a rotation.

Do rotations have invariant points?

Points that map onto themselves are said to be invariant points. Invariant points can occasionally appear during a rotation.

The point of rotation is invariant when a figure is rotated about that point. There are no invariant points in a rotation of a figure centered on a point that is not on the figure.

Point P is an invariant point in the rotation shown below.

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There will be 660.425 dollars cost to fill up the pool.

The newly built single-depth olympic size swimming pool (50m by 25m by 2m) needs to be filled up.

Here,

Length of swimming pool = 50m

Width of swimming pool = 25m

Depth of swimming pool = 2m

The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.

The volume of a cuboid is length × breadth× height

As it is 3D geometry

The volume will be L×W×H i.e. 50×25×2 = 2500 m³

Since one cubic meter is equal to 264.172052 gallons,

So 2500 m³ = 264.17 × 2500 = 660425 gallons

If the water bill is equivalent to $1 per 1000 gallons

So 660425/1000 = 660.425

Hence, there will be 660.425 dollars cost to fill up the pool.

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The least common denominator of 3/4 and 15/16 is 16.

So, LCD od 3/4 and 15/16:

Now, the denominator of both the fractions is the same which is 16.

Therefore, the least common denominator of 3/4 and 15/16 is 16.

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The general form of a linear equation is y - y1 = m(x - x1) then the  point-slope form exists y - 5 = 3(x - 9)

The general structure of a linear equation exists y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that exists not the y-intercept).

Given: (x1, y1) = (9, 5) and (x2, y2) = (8, 2)

The point-slope form exists given by,

y - y1 = m(x - x1)

m = (y2 - y1)/(x2 - x1)

substitute the values in the above equation, we get

m = (2 - 5)/(8 - 9)

m = 3

The value of m = 3.

y - 5 = 3(x - 9)

Therefore, the point-slope form exists y - 5 = 3(x - 9).

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Answer: X+7=19 what is x

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

g(-3) = -(-3)-3

Molly's earning increased by 25%

Percentage increase formula is

Increase/ original value × 100

The first step is to calculate the increase by subtracting 120 from 160

160 -120

= 40

Therefore the percentage increase can be calculated as follows

= 40/160 × 100

= 0.25 × 100

= 25

Hence Molly's earnings increased by 25%

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Answer:

Step-by-step explanatio                                                                                                     -3/8d-1 3/8

The expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or (-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

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Seaborgium-266 will have 60 half life in 30 minutes.

It is given in the question that Seaborgium-266 has a half life in 30 sec.

Since half life is given in seconds , convert 30 min in seconds .

1 min= 60 sec

so 30min= 30*60 sec

30 min= 1800 sec.

According to the question

30 sec = 1 half life

1 sec = 1/30 half life

For 1800 sec

[tex]1800 sec = 1800*\frac{1}{30}[/tex] half life

=60 half life

Therefore , Seaborgium-266 will have 60 half life in 30 minutes.

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The length of the hypotenuse of a 45°-45°- 90° triangle with a leg length of 6 centimeters is 8.49 approximately.

To find the hypotenuse of 45°-45°-90° triangle:

The formula to calculate the hypotenuse of 45°-45°-90°  triangle is to multiply the length of the leg by [tex]\sqrt{2}[/tex].

How to find the length of the hypotenuse?

The length of the two legs of 45°-45°-90° triangle is equal.

Then the length of its hypotenuse will be calculated by multiplying the length of the leg and [tex]\sqrt{2}[/tex] .

Since the length of the leg is 6 centimeters,

Then its hypotenuse will be:

h = 6 × [tex]\sqrt{2}[/tex]

h = 8.485

h ≈ 8.49

So, the length of the hypotenuse will be 8.49.

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The equation is 12.50h + 25= 75

The number of hours is 4

Ms Nishino uses zipcar

She only wants to spend $75 each month

Zip charges $25 a month plus $12.50 per hour of car rental

The equation can be written as follows

12.50h + 25= 75

collect the like terms

12.50h= 75-25

12.50h= 50

h= 50/12.50

h= 4

Hence the number of hours Ms.Nishino can rent from Ziper each month is 4 hours

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The true statements are

The original statement is given as:

If a number is negative, the additive inverse is positive

This can be represented as

If p, then q

i.e. if p → q

So, (a) is correct

For the inverse, we simply negate the hypothesis and the conclusion

i.e. if ¬p → ¬q ----(b) is correct

For the converse, we simply switch the hypothesis and the conclusion

i.e. if q → p ----(e) is correct

Hence, the true statements are (a), (b) and (e)

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Answer:

e, all of the above steps help establish good credit history

Step-by-step explanation:

Answer: E.

Hope this helps.

Answer:

Here,

x+(-5) = 4

x = 4+5

x = 9

Therefore, 9+(-5) = 4

Adding the June amounts from the given table, his total time is of 46.2 minutes.

The times for the month of June are given by the second row, hence:

Hence the total time is given as follows:

9.5 + 13 + 23.7 = 46.2 minutes.

His total time is of 46.2 minutes.

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Answer: 46.2 minutes.

Step-by-step explanation:

Answer:

So she takes around 10 minutes to jog 1 mile. So 12 miles would take her 122 minutes