1. Passes through (6, 2) and (-3, 1)

The generalize term of the pattern is aₙ = 16 (1 / 2)ⁿ⁻¹

The pattern follows a geometric sequence.

The pattern follows a geometric progression.

Therefore, using geometric sequence formula,

where

Hence,

a = 16

The common ratio is the amount between each number in a geometric sequence. In other words,  it is the ratio between two consecutive numbers in the sequence

r = 8 / 16 = 4 / 8 = 2 / 4 = 1 / 2

The generalize pattern of the sequence is as follows:

aₙ = 16 (1 / 2)ⁿ⁻¹

Hence,

aₙ = 16 (1 / 2)ⁿ⁻¹

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Answer:

-4.1 < -√20

Step-by-step explanation:

-√20 = -4.472135954 (-4.47)

-4.4 < -4.47 (-√20)

Answer:

x = 100° , y = 75° , z = 135°

Step-by-step explanation:

x and 80° are a linear pair and sum to 180° , that is

x + 80° = 180° ( subtract 80° from both sides )

x = 100°

y and 105° are a linear pair and sum to 180° , then

y + 105° = 180° ( subtract 105° from both sides )

y = 75°

the sum of the interior angles of a polygon is

sum = 180° ( n - 2 ) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the interior angles and equate to 540°

z + x + 90° + 110° + 105° = 540°

z + 100° + 90° + 110° + 105° = 540°

z + 405° = 540° ( subtract 405° from both sides )

z = 135°

Evaluating the algebraic expressions for the values given, we have:

a. -7

b. -10.

To evaluate and algebraic expression, plug in the value of the variable given and solve accordingly.

a. Given the algebraic expression, xy + 5.

If x = 2, and y = -6, then substitute x = 2 and y = -6 to evaluate the algebraic expression:

xy + 5

(2)(-6) + 5 [substitution]

= -12 + 5

= -7

b. Given the algebraic expression, x/y - 12, if x = 22 and y = 11, then substitute x = 22 and y = 11 into the expression and evaluate:

x/y - 12

22/11 - 12 [substitution]

= 2 - 12

= -10.

Thus, the values of the expressions when evaluated for the given variables are:

a. -7

b. -10.

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The probability that we drew a green ball from the second hat is 1/4.

So, the second hat contains 9 red balls and 3 green balls.

Now,

Therefore, the probability that we drew a green ball from the second hat is 1/4.

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The difference between the depths in February and July is the fourth option that is 13 feet |−13|.

Given that:-

Average of a depth of a local lake = 26 ft represented as |−26|.

Depth of a local lake in February = 5 ft represented as |−5|.

Depth of a local lake in July = 18 ft represented as |−18|.

We have to find the difference between the depths in February and July.

We know that,

Difference between the depths in February and July = Depth in July - Depth in February = 18 - 5 = 13 feet represented as |−13|.

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Answer: 8690

Step-by-step explanation:

Divide $43450 by the number of months there are in a year (which is 12) and you get the answer

The total number of employees in the company in the year 2015 is 275 employees

Number of employees in the company before increase = 200 employees

Percentage increase in employees between 2005 and 2010 = 25%

Percentage: A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test.

So, the number of employees after the increase = 200+25%of 200

= 200+50 = 250

Percentage increase in employees between 2010 and 2015 = 10%

Number of employees after increase = 250 + 10% of 250

= 250 + 25 = 275 employees

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Answer:

Step-by-step explanation:

g(x)=3x

g(-2)=3(-2)=-6

g(0)=3(0)=0

g(5)=3(5)=15

Answer: m = 1

Step-by-step explanation

First, you must fill in the slope formula:

(7,6) first ordered pair

(6,5) second ordered pair

m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m = [tex]\frac{6-5}{7-6}[/tex] = [tex]\frac{1}{1}[/tex]

The slope is 1.

Answer:

B.) cylinder

Step-by-step explanation:

2 circles on either side and a rectangle between them

Answer:

3x8x2xπ ≈ 150.796m²

Step-by-step explanation:

when unfolded the cylinder is a rectangle of area equal to:

HxW ; H=height W=width

W is equal to the primer of the circle and the formula for that is:

2xπxr

substituting you get the area of a cylinder as follows:

Hxrx2xπ

after simplifying the expression - 3 / 4 (5 p - 12) + 2 (8 - 1 / 4 p), we get the result as 27 - 17 / 4 p.

We are given the expression:

- 3 / 4 (5 p - 12) + 2 (8 - 1 / 4 p)

We need to simplify and solve the expression.

First we will solve the brackets.

- 15 / 4 p + 9 + 16 - 2 / 4 p

Now we will combine the like terms, so, we get that:

= 27 - 17 / 4 p

Therefore, after simplifying the expression - 3 / 4 (5 p - 12) + 2 (8 - 1 / 4 p), we get the result as 27 - 17 / 4 p.

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As a result, in the parallelogram before, x = 4, Angle E = 104 degrees, and Angle EFH = 32 degrees.

1. Opposing sides are congruent sides. ...

2. Opposing angles are congruent angles. ...

3. Interior angles that follow one another on the same side are supplementary. ...

4.Each of a parallelogram's diagonals divides it into two congruent triangles. ...

5. The diagonals of a parallelogram split in half.

As a result,

EH and FG's sides are parallel and equal.

so 3x=12

x=4

to determine Angle E

FGH Triangle

Angles FHG + HFG + G add up to 180.

(The total of a triangle's angles is 180)

FHG angle=180-44+104

                 =32

Angles EFH = FHG (alternate interior angles)

                    =32

Angle HFG = Angle EHF (alternate interior angles)

                   =44

Angle E=Angle HGF( opposite angles are equal in a parallelogram)

            =104

Therefore the value of x in the given quadrilateral is 4 , the angle E is 104 degree and the value of Angle EFH is 32 degree.

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The equation of the line for the bike path is :

y = -5x - 15.

Here :

Equation for the Lorne Lane line is y = -4/5x.

slope of the Eqe is -4/5

slope of the bike path perpendicular to Lorne Lane is -5/4

from the Graph point p is (-4, -10)

so

Equation of the line is y = -5x -15;

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Answer:

y=-5x-15

Step-by-step explanation:

IF THE EQUATION HAS EQUAL ROOTS IT MEANS

[tex] {b}^{2} - 4ac = 0[/tex]

THAT IS THE RULE.

WHERE b is the coefficient of x

a si the coefficient of

[tex] {x}^{2} [/tex]

and c is the constant number.

IF QE CHECK IN THE GIVEN EQUATION WE WILL FIND THAT a=2

b= -(b-4)

c= -4(b+2)

[tex]( - (b - 4))^{2} - 4(2)( - 4(b + 2)) = 0 \\ (4 - b ) ^{2} - 8( - 4b - 8) = 0 \\ (4 - b )(4 -b ) + 32b + 64 = 0 \\ 16 - 4b - 4b + {b }^{2} + 32b + 64 = 0 \\ {b }^{2} + 24b + 80 = 0 \\ (b + 20)(b + 4) = 0 \\ b + 20 = 0 \\ \\ \\ orb \\ \\ b + 4 = 0 \\ b = -2 0 \\ \\ \\ or \\ b = - 4[/tex]

ATTACHED IS THE SOLUTION

The position of the given term is mathematically given as

n = 24

This is further explained below.

A function that goes from one set to another gives each element of the first set precisely one element of the second set.

This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.

Generally, the equation for Function the is mathematically given as

f(n) = 2.5 n - 16

Considering that the total is 52, we need to locate the letter "n." (position). Now let's get the answer for "n":

52=(2n-2)+2

52=2n-2+2

52 = 2n-4

n = (52-4)/2

n = 24

In conclusion, the position of the given term.

n = 24

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Answer:

y = -7

Step-by-step explanation:

If y = 10 when x = 20, then we can find the difference when we do y + 1 = x + 1, which is 11 = 21. Therefore, the difference between x and y is 10. So, we need to do 3-10, which gives us -7.

[tex]$\frac{4x^2+4x}{2x^2-2} =[/tex]

[tex]$\frac{4x\left(x+1\right)}{2x^2-2} =[/tex]

[tex]$\frac{4x\left(x+1\right)}{2\left(x+1\right)\left(x-1\right)} =[/tex]

[tex]$\frac{4x}{2\left(x-1\right)}=[/tex]

[tex]$\frac{2\cdot \:2x}{2\left(x-1\right)} = \frac{2x}{x-1}[/tex]

Answer:

4

Answer and Explanation: Two to the second power is 4. We write two to the second power as follows: 22.\

4 to the power of 2 can be expressed as 42 = 4 × 4 = 16.

Answer:

its all real numbers i took the quiz before

Step-by-step explanation:

The first 4 sequence of Arithmetic progression is 42, 37, 32,  27.

Let n =1

[tex]a_{n} = 42-5(n-1)\\a_{1} = 42-5 (1-1)\\a_{1} = 42[/tex]

Let n=2

[tex]a_{n} = 42-5(n-1)\\a_{2} = 42-5 (2-1)\\a_{2} = 42-5\\a_{2} = 37[/tex]

let n= 3

[tex]a_{n} = 42-5(n-1)\\a_{3} = 42-5 (3-1)\\a_{3} = 42-10\\a_{3} = 32[/tex]

Let n= 4

[tex]a_{n} = 42-5(n-1)\\a_{4} = 42-5 (4-1)\\a_{4} = 42-15\\a_{4} = 27[/tex]

An arithmetic sequence is a list of numbers with a specified pattern. If you take some number in sequence, subtract it from the previous one, and the result is always the same or constant, it is an arithmetic sequence.

An arithmetic sequence is defined in two ways. It is "a sequence in which the differences between any two consecutive terms are the same" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to the previous term. The following is an arithmetic sequence because each term is obtained by  a fixed number when added to its previous term.

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Answer:5

Expand 0.6/0.12

by multiplying both numerator and the denominator by 100.

60/12

Divide 60 by 12 to get 5.

5

Answer:

55

Step-by-step explanation:

6.6/12 = 55

The number of tablespoons Debnil has is 2 tablespoons

Number of teaspoons of salt with Debnil = 6

Ratio = 3:1

Ratio: mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

Let x represent the total number of teaspoons and the tablespoons

Therefore,

6 = 3/4x

x = (6*4)/3

x = 8

So, there are a total of 8 spoons

Now, the number of tablespoons is 1/4 of the total

Hence, the number of tablespoons will be 2

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Answer:

Step-by-step explanation:

5u  = 180° -  ( 120° + 30°) =  180° - 150° = 30°

u = 30° / 5 = 6°

What is Asymptote?

The term asymptote means approaching a value or curve arbitrary closely. A line or curve that is asymptotic to given curve is called asymptotic.  

Given,

The function f(x) = 16(1.87)x

Now, We know that

If the value of b < 1, it is a decay while if the value of b > 1, then it is growth. Given the exponential equation below;

f(x) = 16(1.87)x

Since, b = 1.87 which is greater than 1, hence it is a growth. Find the graph attached.  

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Answer: -16

Step-by-step explanation:

Answer:

Brand a price is less than Brand b.

Step-by-step explanation:

given-

two brands of canned dog food are on sale. assume that the cans are the same size. brand a costs $13.60 for eight cans and brand b costs $8.75 for five cans

first-brand a costs $13.60 for eight cans

second- brand b costs $8.75 for five cans

solve first

for 8 cans-->$13.60

then,1 can -->$13.60/8

               =>$1.7

in similar manner we solve for second

for 5 cans-->$8.75

then,1 can -->$8.75/5

               =>$1.75

Brand a price is less than Brand b.

Unit pricing helps consumers compare the prices of packaged goods when those goods aren't sold in equal quantities. It's unit pricing that allows, for example, a shopper to tell at a glance which is the better buy: a 20-pound bag of dog food that sells for $13.95 or a 15-pound bag that sells for $10.69.

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After evaluating for the function f, the value of f(-3) = -12, f(-2) = -2, f(-1) = 4, f(0) = −10

A function is a specific type of relationship that maps inputs to precisely one output. Consider a function as a machine for useful insight. The domain of the function, which describes the types of input that the machine will accept, states that it will produce one and only one output for each input.

A function's fundamental notation is of the form f( x), where x is the input variable and f is the function's name. "F of X" should be read as this. Any time you see this notation, f(x) generally refers to a function's output, though these letters are subject to change.

We have given the function f, to evaluate f(-3), f(-2), f(-1), and f(0)

[tex]f(x)= \begin{cases}-2 x^2+6 & \text { if } x \leq-1 \\ 7 x-10 & \text { if } x > -1\end{cases}[/tex]

f(-3) = -2x² + 6                    (as x < -1)

⇒ -2(-3)² + 6

⇒ -12

f(-2) = -2x² + 6                    (as x < -1)

⇒ -2(-2)² + 6

⇒ -2

f(-1) = -2x² + 6                    (as x < -1)

⇒ -2(-1)² + 6

⇒ 4

f(0) = 7x - 10                      (as x > -1)      

⇒ 7(0) - 10  

⇒ −10

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The average balance in the bank account is $1,125.64.

So, the average balance of the account will be:

Fill in the values and solve as follows:

Therefore, the average balance in the bank account is $1,125.64.

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Answer:

Step-by-step explanation:

- 36