The sum of three consecutive numbers is 723. Find the numbers.​

Answer:

AB = 11

Step-by-step explanation:

AB = x

BC = x - 4

AC = 6 + BC    Substitute BC

AC = 6 + (x - 4)

AC = 2 + x

The perimeter of the triangle  is 31

Perimeter =  AB + BC + AC  perimeter is the sum of the sides

 31 = (x )+ (x - 4 ) + (2 + x)

  31 = 3x - 2

   33 = 3x

   11 = x

AB = x = 11 inches

Check:  

AB = x  ;    AB = 11

BC = x - 4;  BC = 11 - 4; BC = 7

AC = 2 + x;  AC = 2 + 11; AC = 13      

  P = 11 + 7 + 13

      = 31

Step-by-step explanation:

every new term is created by adding a constant (I call here x) to the previous term.

a1 = b

a2 = c = a1 + x = b + x

a3 = a2 + x = a1 + 2x = b + 2x

so, we see

an = a1 + (n-1)x = b + (n-1)x

from a1 and a2 we know

c = b + x

x = c - b

so, ultimately we have

an = b + (n-1)(c-b)

The explicit formula to find the nth term of the sequence will be aₙ = cn - nb + 2b - c.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first term of an arithmetic sequence is b and the second term is c.

a₁ = b

a₂ = c

Then the common difference is given as,

d = a₂ - a₁

d = c - b

Then the explicit formula to find the nth term of the sequence will be given as,

aₙ = b + (n - 1) × (c - b)

aₙ = b + cn - c - nb + b

aₙ = cn - nb + 2b - c

The explicit formula to find the nth term of the sequence will be aₙ = cn - nb + 2b - c.

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Answer: y=-1 and x=2

Step-by-step explanation:

-9x+8y=-26

-9x-6y=-12

Subtract

14y = -14

Divide by 14

Y=-1

Substitute y=-1 into the equation

-9x-6(-1)=-12

-9x+6=-12

Subtract 6

-9x=-18

Divide by -9

X=2

Step-by-step explanation:

complementary = adds up to 90 degrees.

supplementary = adds up to 180 degrees.

the complementary angle of y is 43 degrees.

so, y = 90 - 43 = 47 degrees.

the supplementary angle of y = 47 is

180 - 47 = 133 degrees

Hello!

Given the complementary angle of y is 43º.

90 - 43 => 47°

Find the supplementary angle of y​

180-43 => 137°

Answer:

Multiply both sides by 6:  4x - 42 = 5

Step-by-step explanation:

(2/3)x - 7 = (5/6)

Multiply both sides by 6:  

6*(2/3)x - 6*7 = 6*(5/6)

(12/3)x - 42 = 5

4x - 42 = 5

Answer:

315 = 3^2 × 5^1 × 7^1

Step-by-step explanation:

Answer:

ⅠⅠⅩ

Step-by-step explanation:

ok

Answer:

Step-by-step explanation:

Therefore, 12 in roman numerals is written as XII = X + II = 10 + 2 = XII.

Answer:

You have two variables, and only one condition. It means you have infinite solutions of the form [tex](t; t^2+5t-7)[/tex]. Technically correct, probably not what you want to know.

If you wanted to know if and where the RHS crosses the x axis, the points are the solution to

[tex]x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)[/tex]

If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation [tex]x=-\frac52[/tex].

Answer:

parallel lines are two lines drawn next to each other without a intersection

Answer:

 (-18, 10)

Step-by-step explanation:

If the other end point is Q, the midpoint is ...

  M = (P +Q)/2

  2M = P +Q

  Q = 2M -P = 2(-4, 8) -(10, 6) = (-8-10, 16-6)

  Q = (-18, 10)

The other end point is (-18, 10).

Drake will pay $28,490 over 20 years for the premium.

Data and Calculations:

Life insurance policy = $110,000

Insurance term = 20 years

Premium rate = $12.95 per $1,000

Total premium per year = $1,424.50 ($12.95 x $110,000/$1,000)

Total premium for 20 years = $28,490 ($12.95 x $110,000/$1,000 x 20)

Thus, Drake will pay a total premium of $28,490 for 20 years.

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Answer:

The perimeter of the Parallelogram is 20z + 16

Step-by-step explanation:

For a Parallelogram

Perimeter = sum of all sides

P = (7z + 3) + (7z + 3) + (3z + 5) + (3z + 5)

P = 7z + 7z + 3z + 3z + 3 + 3 + 5 + 5

P = 20z + 16

Thus, The perimeter of the Parallelogram is 20z + 16

-TheUnknownScientist 72

Answer:

2x =3

The hanger image given in the figure represents balanced equation.

Then we have to write an equation to represent the image.

In balanced form left side = right side

x + x = 1 + 1 + 1

2x = 3

The value v is 9.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that is a structure showing a balanced hanger we need to find the value,

So we can say since the hanger is balanced therefore the weight both sides will be equal,

Therefore,

v + v + v = 27

3v = 27

v = 27

Hence the value v is 9.

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Answer:

the first option, increasing as x approaches infinity and decreasing as x approaches negative infinity

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

8×8 = 64

8×4 = 32

8×4 = 32

64 + 32 + 32 = 128

Answer:

77° is the answer

Step-by-step explanation:

hope it helps;)

The measure of angle [T] will be ∠T = 139°.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ΔABC.

In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Given is a triangle TSU.

The sum of the angles of a triangle is 180 degrees. So, we can write -

(21x + 13) + 4x + (3x - 1) = 180

21x + 4x + 3x + 13 - 1 = 180

28x + 12 = 180

28x = 168

x = 168/28

x = 6

So -

∠T = 21x + 13 = 21 x 6 + 13 = 126 + 13 = 139

∠T = 139°

Therefore, the measure of angle [T] will be ∠T = 139°.

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Answer:

Step-by-step explanation:

Add up the equations, it will eliminate x as variable:

Find the value of x:

Given : -

To find : -

Solution : -

3x + 6y = 18

-3x + 4y = 2 +

10y = 20

[tex] \: [/tex]

3x + 6y = 18

3x + 6(2) = 18

3x + 12 = 18

3x = 18 - 12

3x = 6

[tex] \: [/tex]

I personally like the square method but I am lazy to draw this out (take too long)

5x²-13x-6 = (5x+2)(x-3)

x = -2/5 or 3

Double-check:

5x²-15x+2x-6  = 5x²-13x-6 √

Answer:

The 4th graph

Step-by-step explanation:

To have a maximum value, your parabola would have to open downwards. So the first 2 are wrong. Since your y-intercept is positive 4, your graph would have to touch the y axis at 4. The 3rd graph is wrong since it touches the y-axis at a negative point. The correct answer would be the 4th answer choice.

Answer:

-5;-7

Step-by-step explanation:

Start with the product. 35 is either 35x1, 7x5, or the product of their opposites. 35 and 1 doesn't work for the sum, neither does 7 and 5. Let's go negative. -35 and -1 gives -36, so it has to be -7 and -5, which is indeed, correct.

$10.50

10 Tickets would be $105.00

$105.00 - $10.50 = $94.50 so 9 Tickets would be $94.50

$105.00 + $94.50 = $199.50

$205.00 - $199.50 = $5.50 which isn't enough for another ticket.

10 Tickets + 9 Tickets = 19 Tickets.

Answer:

I would say the one that has the blue dot. bc, the absolute value of -6 is 6.

Answer:

The second one -6[------------]0 with 6 on top.

Step-by-step explanation:

It would take [tex]1 second[/tex] for Carol to catch the sweet after Dave threw it.

Let

[tex]h=\text{maximum height}\\y=\text{distance from maximum height to Carol}\\t_h=\text{time taken to reach maximum height}\\t_y=\text{time taken to fall from maximum height to Carol}[/tex]

we want to calculate the value [tex]t_h+t_y[/tex]

First, we have to calculate [tex]t_h[/tex] using the formula

[tex]v=u+at[/tex]

using [tex]v=0[/tex], [tex]u=8[/tex], [tex]a=-10[/tex] (the sweets are decelerating due to gravity!)

[tex]0=8-(10)t_h\\10t_h=8\\t_h=\frac{8}{10}=0.8seconds[/tex]

To calculate [tex]t_y[/tex], first calculate [tex]h[/tex], then [tex]y[/tex]. Using the formula

[tex]h=ut+\frac{1}{2}at^2[/tex]

and the values [tex]u=8[/tex], [tex]t=t_h=0.8[/tex], [tex]a=-10[/tex] (again, the sweets are decelerating to get to maximum height)

[tex]h=(8)(0.8)+\frac{1}{2}(-10)(0.8)^2\\\\=6.4-3.2\\=3.2m[/tex]

since, Carol is standing [tex]3m[/tex] above Dave, we have the relationship

[tex]h=y+3[/tex]

so that

[tex]y=h-3\\=3.2-3\\=0.2m[/tex]

we can now calculate [tex]t_y[/tex];

[tex]y=ut_y+\frac{1}{2}gt_y^2[/tex]

taking [tex]y=0.2[/tex], [tex]u=0[/tex], [tex]g=10[/tex] (the sweets are falling, so they are now accelerating)

[tex]0.2=(0)t_y+\frac{1}{2}(10)t_y^2\\\\0.2=5t_y^2\\t_y^2=0.04\\\implies t_y=0.2seconds[/tex]

So it would take

[tex]t_h+t_y=0.8+0.2=1.0seconds[/tex]

for Carol to catch the sweet after Dave threw it from the first floor.

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Answer:

What else is in the equation?

Step-by-step explanation:

Also, i think the - should be right here>-13 instead of it being here 13-<

Answer:

I say true

Step-by-step explanation:

How to calculate discount and sale price:

Find the original price (for example $90 )

Get the discount percentage (for example 20% )

Calculate the savings: 20% of $90 = $18.

Subtract the savings from the original price to get the sale price: $90 - $18 = $72.

And You're all set!

Answer:

False

Step-by-step explanation:

Sale price = original price - rate of discount * original price

Rate of discount is a percent  so we need to multiply by the original price to get a a price so that all the units are the same.

Answer:

[tex]2xy\sqrt{2x}[/tex]

Step-by-step explanation:

Because this is a whole term in itself (no addition or subtraction), you can just directly find squares and factor them out. First, when looking at 8, you can factor out 4, to get 2 on the outside. Then, while looking at x cubed, you can factor out x squared, to get x on the outside, and when looking at y squared, you can just pull that outside itself, to get y. Now, we have one 2 and one x remaining, for a total of [tex]2xy\sqrt{2x}[/tex]