The sum of 6 consecutive integers is 387. What is the sixth number in this sequence.

Answer:

You can conclude that the line segments BA and AC are perpendicular to each other.

Step-by-step explanation:

That is because in this case, the triangle presented would be a right triangle. In right triangles, the orthocenter is the vertex of the triangle where two of the segments intersect perpendicularly, forming a 90 degree angle. As the orthocenter is where the altitudes intersect (altitudes are 90 degrees), we are able to conclude that BA and AC are perpendicular to each other.

Answer:

CE

AE

segment addition postulate

Given: ABC is a triangle.

To prove: BC + AC > BA

Proof: In triangle ABC, we can draw a perpendicular line segment from vertex C to segment AB. The intersection of AB and the perpendicular is called E. We know that BE is the shortest distance from B to CE and AE is the shortest distance from A to CE because of the shortest distance theorem.

Therefore,  and .

Now, add the inequalities, we get

.

Then,  because Segment addition postulate (states that given 2 points E and F, a third point D lies on the line segment EF if and only if the distances between the points satisfy the equation ED + DF = EF)

Therefore,  by substitution.

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

[tex]\frac{5}{3}v+4+\frac{1}{3}v=8[/tex]

[tex]2v+4=8[/tex] <-- Resulting equation after first step

[tex]2v=4[/tex]

[tex]v=2[/tex] <-- Actual solution

Answer:

5. alternate interior angles

7. angle addition postulate

Answer:

12 miles

Step-by-step explanation:

because of slope

Answer:

[tex]y=(x+3)(x+1)[/tex]

Step-by-step explanation:

[tex]y=x^2+4x+3[/tex] <-- Given

[tex]y=x^2+x+3x+3[/tex] <-- Expand middle term

[tex]y=x(x+1)+3(x+1)[/tex] <-- Factor into two parts

[tex]y=(x+3)(x+1)[/tex] <-- Combine like terms

7x+8y=32

Just do pemdas

Answer:

7x+8y=32

Step-by-step explanation:

Hi there!

We are given the following equation:

[tex]y=-\frac{7x}{8} +4[/tex]

And we want to convert it into standard form

Standard form is ax+by=c, where a, b, and c are integer coefficients, a and b cannot be zero, and a cannot be negative

a is the coefficient in front of x and b is the coefficient in front of y

Since we have the term with x ([tex]-\frac{7x}{8}[/tex]) on the right side, and we want it on the left side with the term with y, we can move it to the other side, by adding [tex]\frac{7x}{8}[/tex] to both sides.

[tex]y=-\frac{7x}{8} +4[/tex]

+[tex]\frac{7x}{8}[/tex]   +[tex]\frac{7x}{8}[/tex]

_________________

[tex]\frac{7x}{8} + y =4[/tex]

Now we have the terms of x and y on both sides, but remember; we want the coefficients to be integers (whole numbers).

We'll need to clear the fraction of [tex]\frac{7x}{8}[/tex]. To do that, we can multiply both sides by 8.

[tex]8(\frac{7x}{8} + y) =8(4)[/tex]

Now doing the distributive property:

[tex]8(\frac{7x}{8}) + 8(y) =8(4)[/tex]

Multiply each term by 8.

7x + 8y = 32

Hope this helps!

Answer:

7/1 or 7

Step-by-step explanation:

because you rise (vertically) seven and run (horizontally) 1, so 7/1 but simplified it's just 7 so either is valid.

Answer:

2x+5

Step-by-step explanation:

Equation  y = 3x + 5  correctly represents the situation.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Darrian creates caricatures for an initial fee of $5 then charges $2 each minute.

Let x be the number of each extra minutes.

And y be the total fees.

So, the equation;

The total fee = Charges of x minutes + initial fee.

y = 3x + 5

Therefore, the equation is  y = 3x + 5.

To learn more about the equation;

https://brainly.com/question/12788590

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Step-by-step explanation:

tricky, as the sequence does not define the input values.

by we can assume that the corresponding input values are 1, 2, 3, 4, 5, ... as it is usual for a sequence.

in that sense, b is the correct answer.

The sequence is a function because each input is a natural number with a single output number in the sequence.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

Given the sequence {4, 7, 10, 13, 16, ...},

Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next item in the sequence is obtained by multiplying the previous term by 3.

a₂ - a₁ = 7 - 4 = 3

a₃ - a₂ = 10 - 7 = 3

the difference in output is the same for all the numbers in sequence.

Hence the sequence is the function of the Arithmetic Sequence.

Learn more about arithmetic progression;

https://brainly.com/question/16947807

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Answer:

The answer is A!

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

multiply by each side to find the answer. 4x2 is 8 and 8 x 24 is 192. Which ever order you multiply the numbers in you will always get 192. Hope this helps ^^

Answer:

[tex]22\frac{1}{2}[/tex]

Step-by-step explanation:

(4.5)(5) = 22.5

[tex]22.5 = 22\frac{1}{2}[/tex]

Answer: 29 ft

Step-by-step explanation:

Says parking lot is a square.

Square root of 841 is 29

Answer:

m = 1/9

Step-by-step explanation:

Given:

x = 10

y = 8

x1 = 1

y1 = 9

Solution:

y - y1 = m ( x - x1 )

9 - 8 = m ( 10 - 1 )

1 = 9m

m = 1/9

Answer:

ummmmm i really don't get it but I think its 17/66

Step-by-step explanation:

multiply in to each fraction

Answer:

it's so blury pls fix the picture so I can solve it NOW

Answer:

Answer: 4

Step-by-step explanation:

Answer:

........................

Answer:

A. 85  B. 87  C. 60

Step-by-step explanation:

As shown in the shapes, A, is a full circle making 360 degrees full. B, a half circle making 180 degrees half. C, a full circle again making 360 degrees full.

A: [360-(132+63+80)]

360 - 275

=85

B: [180(60+33)]

180 - 93

=87

C: [360(120+60+120)]

360 - 300

=60

Answer:

the answer is 34°

Step-by-step explanation:

a straight line = 180°

just do 180 - 146 = 34

Answer:

c and e

Step-by-step explanation:

[tex]-7-(-12) = -7 +12 = 12 +(-7)[/tex]

Answer:

Yes

Step-by-step explanation:

1 hour = 60 min

25 hours = 60 x 25 min

yan po answer

#CARRYONLEARNING

LOVE U ALL

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

  72 minutes

Step-by-step explanation:

The sum of the rates of work in rooms per hour is ...

  Jill's rate + Jim's rate

  = (1/2 room/hour) +(1/3 room/hour) = (3/6 +2/6 room/hour) = 5/6 room/hour

__

Then the combined rate in hours per room is ...

  1/(5/6 room/hour) = 6/5 hours/room = (6/5 hours/room)(60 minutes/hour)

  = 72 minutes per room

Jill and Jim can paint the room in 72 minutes when they work together.

Answer:

the answer to this question is $32.96