the third term in the sequence is 11
the term-to-term rule is "take away 4"
write an expression on in terms of n for the nth term of the sequence

La solucion del sistema de ecuaciones es x = 1, y = 4, o (1, 4) en notación standard.

Aqui tenemos el sistema de ecuaciones:

x + y = 5

2x + y = 4

Si tomamos la segunda ecuación, y a esta le restamos la primera, obtendremos:

(2x + y) - (x + y) = 5 - 4

(2x - x) + (y - y) = 1

x = 1

De esta forma encontramos el valor de x, para encontrar el valor de y, deberemos reemplazar x = 1 en una de las ecuaciones. Yo usare la primear.

x + y = 5

1 + y = 5

y = 5 - 1

y = 4

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Answer:

176 yd

Step-by-step explanation:

UNSHADED REGION (white rhombus): A=(s1+s2)/2 * H

s1=7

s2=1+7=8

H=6

A=(7+8)/2*6=45

SHADED + UNSHADED REGION (big parallelogram): area of parallelogram A=B*H

B=17

H=7+6 = 13

A=17*13=221

SHADED REGION: big parallelogram area - rhombus area

221 - 45 =176 yd

The number sentence that is true is 1/3 x (-2/5)=-2/15 . Option A

A fraction is simply defined as the subset of a whole set or the part of a whole element.

The several types of fractions includes;

Examples of simple fractions: 1/2, 1/8

Examples of proper fractions: 3/4, 8/10

Examples of mixed fractions: 3 1/6, 2 1/8

Examples of improper fractions: 7/4, 8/5

Given the fraction;

a. 1/3 x (-2/5)

The product of the fraction is = - 2/15

b. -1/3 x 2/5 = 2/15

The product is = -2/15

c. -1/3 x (-2/5)

The product is 2/15

d. 1/3 x 2/3

The product is 2/9

Hence, the sentence is option A

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The variable y is shown with no exponent. Any term with no exponent is understood to have an exponent of 1, so y has an exponent of 1.

Answer:

plane

Step-by-step explanation:

The plane is flat like a wall or the floor. It has infinite length and infinite width but has no thickness (as thick as a line--which has no thickness) basically a line is one-dimensional and a plane is two-dimensional.

See image.

Using simple linear equations we calculate that the change left will be $6.24 .

The equals sign is used to indicate that two expressions on each side of the equal sign are equal in the many mathematical formulas that are utilized to form an equation.

Let the change received be x.

Therefore let us construct an equation for the situation

cost of game + tax + change = 20

or, 12.98 + 0.78 + x = 20

or, 13.76 + x = 20

or, x = 6.24

Therefore he will receive   6.24 after solving the equation.

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Answer:

5 7/10

Step-by-step explanation:

first you multiply five by the three, then add the eleven. so now you have a improper fraction, 26/5 plus 1/2. find the Least common denominator which is 10, and whatever you do to the denominator you do to the numerator which makes 57/10 simplify and you'll get 5 7/10

Answer:

Step-by-step explanation:

1. Find the lcm(least common denominator)

(5 x 2 = 10)

2. Multiply the numerators by the same number as the denominator(you multiplied 5 by 2 to get 10 so you multiply 311 by 2. You multiplied 2 by 5 to get 10 so you multiply 1 by 5.)

311 x 2 = 622

1 x 5 = 5

3. Add

622/10 + 5/10 = 627/10

4. Simplify

627 ÷ 10 = 62 [tex]\frac{7}{10}[/tex] (it can also be written as: 62.7)

Answer: x = 65

Step-by-step explanation:

1) First find the mini triangles, left and right angles

We will be calling the left one A and the right one B.

2) Next use triangle sum to find B.

62 + 50 + b = 180

b = 68

3) Use triangle sum again to find A.

53 + 80 + a = 180

a = 47

4) Use triangle sum to find the top mini angle.

47 + 68 + c = 180

c = 65

5) Since x is in the vertical angle of c, they are equal

c = x

65 = x

Answer:

The answer would be 7 times 12
Eric will spend $84
I calculated it by seeing how much each of the pizzas cost-$7 the I figure out how many pizzas he need-12 Now what we need to do is multiply 7 and 12 because if one pizza is $7 (Stated in the written problem) then I know that it would be 7+7+7+7+7+7+7+7+7+7+7+7 12 times, one time for each pizza needed. The simpler version would be 7 time 12 which then we would get a value of $84.

Step-by-step explanation:

Hope this helps!!

Answers to all the subparts using equations are:

So, the answers to all the subparts are as follows:

(A) Equation that can be formed is:

(B) Cost of 12 pizzas:

Let, x = 12.

(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.

Therefore, answers to all the subparts using equations are:

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Correct question:

Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:

(A) What is the direct variation equation that represents this situation? (worth 2

points)

(B) How much will Eric spend if he buys 12 pizzas? (worth 2 points)

(C) Explain how you calculated his total cost for pizzas. (worth 2 points)

Answer:

x = 60

Step-by-step explanation:

(2x + 15)° and 135° are corresponding angles and are congruent , then

2x + 15 = 135 ( subtract 15 from both sides )

2x = 120 ( divide both sides by 2 )

x = 60

Answer:

x = 60

Step-by-step explanation:

The two angles are corresponding. This means that both of the angles are congruent (same). So, you set both of them equal to each other. That means to do 2x + 15 = 135. You do basic algebra and then you get 60 for x. Hope this helps!

The polynomial is x³ + 2x

If the zeros or roots of the polynomial are given, then the standard form of the polynomial can be found.

That is, a, b and c are roots of the polynomial, then  the polynomial will be of degree 3 since 3 zeros are there and the factors of the polynomial will be , x-a, x-b and x- c.

Then the polynomial is, (x-a)(x-b)(x- c) = x³-(a+b+c)x-abc

Here the zeros of the polynomial are x = 0, x = i√2 and x = -i√2.

So the factors of the polynomial are (x-0), (x - i√2) and (x +i√2).

Hence the polynomial is , (x-0) (x - i√2)(x +i√2) = x(x²+2) = x³ + 2x

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Algebraic equations are mathematical equations that consist of unknown variables. These unknown variables can be represented with any letter of the alphabet.

The cost of 2 pounds(lb) of the first type of candy is $8

Note that: x represents the cost per pound (lb) of the first type of candy

The Algebraic equation for the above statement is given as:

2lb × $x + 3 Ib × $1.50 = $2.50(2lb + 3lb)

2x + 4.5 = 12.5

Collect like terms

2x = 12.5 - 4.5

2x = 8

Divide both sides by 2

2x/2 = 8/2

x = 4

The cost of the 1 pound of first type of candy is $4

The cost of 2 pounds(lb) of the first type of candy is calculated as:

2 x $4

= $8

hope it will be helpful

The numbers given as 0.868668666866668666668... and 0.868668666866668666668... are  irrational numbers

From the question, the numbers are given as

0.868668666866668666668... and 0.868668666866668666668...

As a general rule.

Numbers that end in three dots are irrational numbers

The above is true because

When numbers cannot be represented as a fraction of integers, then such numbers are irrational numbers

Hence, the numbers are irrational numbers

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Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.

An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.

Here,
Both numbers are irrational numbers, because

Thus, Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.

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Answer: 1110

Step-by-step explanation:

Answer:

1,110

Step-by-step explanation:

1. Multiply to the powers(?)

10 x 10 x 10 = 1000

10 x 10 = 100

10 = 10

2. Add

1000 + 100 + 10 = 1110

Answer:

-2

Step-by-step explanation:

f(x) = -2 (1/2)^x

you find the y-intercept where x = 0

= -2 (1/2)^0

= -2 *1

= -2

316 is value of   circle's arc BC .

What is an arc in maths?

Short arc BC is the difference between 360° and long arc BAC

 arc BC = 360 - arc BAC

             = 360 - 44

              = 316

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The solution for the given inequality is p < -2.2. The graph that represents the solution is attached below.

From the question, we are to determine the graph for the solution set for the given inequality

The given inequality is p - 3.6 < -5.8

First, we will solve the inequality

Solving the inequality

p - 3.6 < -5.8

Add 3.6 to both sides

p - 3.6 + 3.6 < -5.8 + 3.6

p < -2.2

The solution is p < -2.2

The graph of the inequality is shown below

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Answer: number line with an open circle on point negative 2.2 and arrow shaded to the left

Step-by-step explanation:

If this guy is correct

The slope intercept form of equation that models $20 startup fee and $5 monthly fee is y = 5x +20 , y is total fee and x is number of months

The slope intercept form of an equation is y = mx + c

where y is y coordinate, x is x coordinate, m is the slope of the line and c is y intercept.

Let the total fee after x months be y

Then y is sum of startup fee and sum of all month's fee

For x months total monthly fees = 5(x)

Therefore the total fee after x months , y = 5x +20 which is same as slope intercept form y=mx+c

when x= 0 ⇒ y = 20 , startup fee

Thus, the equation in slope intercept form is  y = 5x +20 ,where y is total fee and x is number of months.

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The probability of choosing a painting random and it is British is 0.50.

Given,

The total number of paintings = 30

Then,

T = Painting from 20th century

B = British paintings

We have to find the probability of choosing a painting random and it is British.

Here,

Probability = British/ Its from 20th century

Probability = n (B and T) / n(T)

                  = x / (x + x(x-2))

                  = 3 / (3 + 3(3 - 2))

                  = 3 / (3 + 9 - 6)

                  = 3 / 6 = 1/2 = 0.5

Here, the probability of choosing a painting random and it is British is 0.50.

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Answer: b = 3.5, h = 4

Step-by-step explanation: a = 1/2bh, area of a triangle formula

7 = 1/2((b)(2b-3)) state h in terms of b

7 = 1/2(2b^2-3b) simplify

7 = b^2 - 1.5b simplify

b = 3.5 final answer

Then, solve for h.

h = 7 - 3 substitute

h = 4 final answer

hope this helps!

Step-by-step explanation:

area of a triangle

base × height / 2

in our case

base × height / 2 = 7

base × height = 14

height = 2×base - 3

we can use the last identity in the area equation and get

base × (2×base - 3) = 14

2×base² - 3×base - 14 = 0

the solution to a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

base = (3 ± sqrt((-3)² - 4×2×-14))/(2×2) =

= (3 ± sqrt(9 + 112))/4 = (3 ± sqrt(121))/4 =

= (3 ± 11)/4

base1 = (3 + 11)/4 = 14/4 = 7/2 = 3.5 in

base2 = (3 - 11)/4 = -8/4 = -2

negative numbers for sizes of physical objects don't make sense, so, base = 3.5 in is our solution.

height = 2×base - 3 = 2×3.5 - 3 = 7 - 3 = 4 in

base length = 3.5 in

height = 4 in

Answer:

y=x^2+3x-10

Step-by-step explanation:

.........

The coordinates of the orthocenter of triangle DEF are given as follows:

(6.67,  -2).

The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.

Hence, we need to find two of the lines, and them find the intersection point between them, as the third line will necessarily intersect these lines at this point.

The midpoint of segment DE is:

(6, 1).

Which is the mean of the coordinates.

Vertex F is at point (8, -8), hence the slope of the line with these two points is:

m = (-8 - 1)/(8 - 2) = -9/2 = -4.5.

Hence:

y = -4.5x + b.

When x = 6, y = 1, hence we can find b as follows:

1 = -4.5(6) + b

b = 28.

Hence one line is:

y = -4.5x + 28.

The midpoint of segment EF is:

(8, -1.5).

Which is the mean of the coordinates.

Vertex D is at point (4, -3), hence the slope of the line with these two points is:

m = (-1.5 - (-3))/(8 - 4) = 0.375.

Hence:

y = 0.375x + b.

When x = 8, y = -1.5, hence we can find b as follows:

-1.5 = 0.375(8) + b

b = -4.5.

Hence the two lines that we have to find the intersection point is:

Then the x-coordinate of the orthocenter of the triangle is:

-4.5x + 28 = 0.375x - 4.5

4.875x = 32.5

x = 32.5/4.875

x = 6.67.

The y-coordinate of the orthocenter of the triangle is:

y = 0.375(6.67) - 4.5 = -2.

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In accordance with analytic geometry, the equation that represents the line is y = - (1 / 4) · x - 6.

Herein we find the representation of a line set on a Cartesian plane. According to analytic geometry, line are represented by equations of the form y = m · x + b, where m, b are the slope and the y-intercept, respectively.

Both the values of the slope and the y-intercept can be found by knowing the location of two points lying on the line. If we know that (x₁, y₁) = (0, - 6) and (x₂, y₂) = (4, - 7), then we find the following system of linear equations:

b = - 6                                    (1)

4 · m + b = - 7                        (2)

By (1) in (2):

4 · m - 6 = - 7

4 · m = - 1

m = - 1 / 4

The equation that represents the line is y = - (1 / 4) · x - 6.

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The correct option is D that is bill is equal to or greater than $30

3.25 + 5.5s < =30

The first step in building the inequality is modelling Benjamin's spendings.

He buys a chocolate milk that costs $3.25, plus S stacks of pancakes, each at $5.50. Thus, in total, his spendings are of:

3.25 + 5.25s

He wants the bill to be of at most $30, that is, his spending has to be at most $30, thus:

T < 30

3.25 + 5.5s < =30

Thus the correct inequality is option D which is 3.25 + 5.5s < =30

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The number of ways in which they can line up to wait for the next available teller is 362880.

We want to know how many different ways there are to line up 9 people.

= 9×8×7×6×5×4×3×2×1

= 362880

Thus, the number of ways in which they can line up to wait for the next available teller is 362880.

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