Write an equation for the nth term of the arithmetic sequence.

The linear equation can represent the ages of two sisters that are born one-year apart.

Here we have the linear equation:

y = x + 1

So the value of y is always one more than the value of x, so for example, suppose that two sisters are born one-year appart, then we can use the above linear equation to represent the age of the older sister as a function of the age of of the younger one.

In that case, the slope of 1 means that both of the sisters age at the same ritm.

The y-intercept of 1 means that the older sister is 1 years old when the younger sister was born.

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Answer:

< B.

Step-by-step explanation:

B  corresponds to F.

Answer:

  see attached

Step-by-step explanation:

Each grid square represents 5 m, so the distances shown on the grid will be scaled appropriately.

The 25 m base dimension will be represented by (25 m)/(5 m/square) = 5 squares.

The 30 m height dimension will be represented by (30 m)/(5 m/square) = 6 squares.

The attached drawing shows the triangle with base 25 m and height 30 m on a 5 m grid.

Answer:

Twice

Step-by-step explanation:

In a convex hexagon the sum of all interior angle is equal to twice of exterior angles.

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The area of the baseball diamond is 8192 sq. units.

We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).

The side of the square can be computed using the distance formula,

D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).

Thus, the side of the square,

a = √((x₂ - x₁)² + (y₂ - y₁)²),

or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,

or, a = √(64² + (-64)²),

or, a = √(4096 + 4096),

or, a = 64√2 units.

Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.

Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.

Thus, the area of the baseball diamond is 8192 sq. units.

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The Probability that the total showing is either even or less than five = 5/6

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

The example space for rolling two dice is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

36 events total.

Events that have a sum that is even or less than Five .

Total instances when the aggregate is even or less than Five equals 30.

P(sum is even or less than 5)

= (Total no of favorable event)/(Total no of event)

= 30/36

=5/6

probability that the total showing is either even or less than five = 5/6

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The surface area of the rectangular prism shown in the figure is 512 in²

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Surface area = 2(8 * 8) + 2(12 * 8) + 2(8 * 12) = 512 in²

The surface area of the rectangular prism shown in the figure is 512 in²

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The function that best models the position of the weight is s(t) = 6cos (pi/2*t).

From the information, we know that the spring is going to have a sin or a cos equation.

We have that the maximum distance of the spring is 6 inches and it is achieved at t=0. We have that the function is of the form 6sin(at+B).

We have that the period is 4 minutes and therefore that the time component in the equation needs to make a period (2pi) in 4 minutes.

In general, a=2pi/T where a is this coefficient, T is the period. Finally, for B, since sin(pi/2)=1, we have that B=pi/2 because when t=0, we have that 6sin(B)=6.

Substituting, we have s(t) = 6cos (pi/2*t).

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Answer:

  y = -5/3x   or   5x +3y = 0

Step-by-step explanation:

To write the equation of a line through the origin, we need only find its slope. It is parallel to the line through the given points, so will have the same slope.

The slope of a line through points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

  m = (5 -0)/(-6 -(-3)) = 5/(-3) = -5/3

The line trough the origin has a y-intercept of zero, so its equation will be ...

  y = mx

For the slope we found, the desired equation is ...

  y = -5/3x

If we multiply by 3 and add 5x, we have ...

  3y = -5x

  5x +3y = 0 . . . . . . standard form equation of the line

Answer:

student 2 is correct

Step-by-step explanation:

there are 10 [tex]\frac{1}{10}[/tex] ' s in 1 , so

37 × 10 = 370 ← number of tenths in 37

0.6 = [tex]\frac{6}{10}[/tex] , that is 6 tenths

then

37.6 = 370 + 6 = 376 ← number of tenths

The standard matrix for the linear transformation t is

| 3     6 |

| 3    -6 |

The linear transformation of matrix T is given as:

t(x, y) = (3x + 6y, 3x − 6y)

When the above linear transformation is represented as a matrix, we have the following expression

T([x]) =   | 3x + 6y |

  [y]       | 3x  - 6y |

The above linear transformation of matrix can be rewritten as the following product of matrixes

T([x]) =   | 3x + 6y | = | 3     6 | | x |

  [y]       | 3x  - 6y |    | 3    -6 | | y |

From the above equation, the standard matrix for the linear transformation t is

| 3     6 |

| 3    -6 |

Hence, the standard matrix for the linear transformation t is

| 3     6 |

| 3    -6 |

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The range of possible side lengths in  interval notation 41 < s < 47

What does it mean to interval notation?

Since the perimeter is four times the side, the constraints on the perimeter are immediately translated into constraints on the side-

[tex]164 < p < 188 = 164 < 4s < 188[/tex]

So, if you divide every term in the inequality by 4, you have

[tex]\frac{164}{4} < s < \frac{188}{4}[/tex]

Now simply evaluate the fractions

41 < s < 47

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Answer:

B

Step-by-step explanation:

Original form:

y=mx+b

m=slope

b=y interecept

By replacing those variables with the given we come up with the equation of:

y=3/2x-7

Answer:B

Step-by-step explanation:

Answer:

11/18.

Dan is 8.

Step-by-step explanation:

The initial fraction is

x / 2x-4

Adding 3/3 we have

x+3 / 2x-1 = 2/3

Cross multiply:

3(x+3) = 2(2x-1)

3x + 9 = 4x - 2

9 + 2 = 4x - 3x

11 = x,

So the original fraction was 11 / 2(11) - 4

= 11/18.

If Dans age is d then Lois's age = 4d.

So 4d + d  = 40

5d = 40

d = 8.

So Dan is 8 years old.

The ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3; the formula for the volume of a pyramid is V = 1/3Bh.

where,

Volume of prism : Volume of pyramid

Bh : 1/3Bh

Therefore, the ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3.

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The total length of school installs fencing around a hexagon-shaped area for an outside concert, is 36 yards.

To find the fencing used by the school:

The distance formula can be given as: [tex]d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1})^{2} }[/tex]

First, we must calculate the length of the hexagon using the distance formula.

The hexagon's coordinates, according to the graph, are:

(-5, 4), (0, 6), (5, 4), (6, -2), (0, -4), and (-6, -2)

The distance between (-5, 4), (0, 6): [tex]d=\sqrt{(5)^{2} +(6-4)^{2} }[/tex]

Similarly, the distance between (-5, 4) and (6, -2):

And the distance between (6, -2) and (0, -4):

Amount of fencing required = 2(√29+√37+√40):

Therefore, the total length of school installs fencing around a hexagon-shaped area for an outside concert, is 36 yards.

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The complete question is given below:

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

The school puts up fencing around an area in the shape of a hexagon for an outdoor concert. How much fencing does the school use? Round your answer to the nearest whole yard.

Answer:

36 yards of fencing

Step-by-step explanation:

the reason I know this is because I got it right.

The way to solve this is to try to get the vales that would best fill the empty spaces in the diagram. This has been done below

a. log6⁰, log 2 . 1, log 8/3

b. log 1 .4 , 1 , log 4. 6

c. log 9/2, log 3. 5 , log 5⁷

To do this, you have to decide on that specific  number whose logarithm you are trying to determine. Next you have to find the base of that number.

The logarithm of the number is the power that it would have to be raised for us to obtain a different number.

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[tex] - 5 + x = 2 \\ add \: 5 \: to \: both \: sides \\ x = 2 + 5 = 7[/tex]

[tex] - 5 x =2 \\ x = -2/5[/tex]

Assuming you're multiplying:

Answer:

Step-by-step explanation:

Comment

The simple answer is you should put something equivalent to -2/5 in the blank. This is what will happen,

-5 * - 2/5

The 5's will cancel out. The minus sign that was in front of the 5 will become positive because 2 minuses make a plus.

Another way to do the problem is to call the ___  = x

-5 x = 2                  Divide both sides by - 5

-5x/ -5 =  2/-5

x = - 2/5

It comes to the same thing.

A third way is just to multiply by - 0.4

-5 * -0.4 = 2

The range of the function [tex]f(x) = -2(6)^{x} +3[/tex] discovered using exponential function is ( -∞, 3).

What is an exponential function?

In which:

As for the range, we have:

In this problem, the function is given by: [tex]f(x) = -2(6)^{x} +3[/tex]

The coefficients are a = -2 0, b = 6, and c = 3, and the range is  (-∞,3).

Therefore, the coefficients are a = -2 0, b = 6, and c = 3, and the range is  (-∞,3).

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The complete question is given below:

What is the range of the function f(x) = –2(6x) + 3? (negative infinity, negative 2 Right-bracket (negative infinity, 3) Left-bracket negative 2, infinity) Left-bracket 3, infinity)

Answer:B

Step-by-step explanation:edge lolololololololloll

The end behavior of the function is as:

as →∞, f(x)→+∞ and as x→-∞, f(x)→+∞

The x-axis "endpoints" of a function's graph are referred to as its "end behavior" in this context.

choosing the polynomial function's greatest degree. The highest degree term will dominate the graph since it will expand more quickly than the other terms as x gets very big or very small.

Function f(x)=2∛x has the following graph:

The behavior of the function at its conclusion is because it leads to infinity.

as  x→∞, f(x)→+∞ and as x→-∞, f(x)→+∞

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Answer:

0.5%

Step-by-step explanation:

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 8):

8 = ab⁰

a = 8

At point (1, 32):

32 = 8b

b = 4

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

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The line is parallel to y axis

We know that if a line is parallel to y axis

So there is no slope

Here it has constant x value as -2

So the equation is

Option A

Answer:

x = -2

Step-by-step explanation:

The line is crossing the x-axis at -2, The graph is attached

Since it is identical to the graph given in the problem, x=-2 is the correct answer

The sum of the first 40 terms of the geometric sequence is:

22,114,662.64

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of the first n terms of a sequence is:

[tex]S_n = \frac{a_1(1 - q^n)}{1 - q}[/tex]

For this problem, the parameters are:

a1 = 1, q = 1.5, n = 40.

Hence the sum is:

[tex]S_{40} = \frac{1 - 1.5^{40}}{1 - 1.5} = 22,114,662.64[/tex]

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Answer:

below

Step-by-step explanation:

1) 8 = 25 percent

100 percent = 8 x 4

100 percent = 32

2) 8 = 75 percent

5 percent = 8 / 15

100 percent = 8 / 15 x 20

100 percent = 10.67

3) x = weight of puppy A

y = percentage

z = adult weight

z = x(100 / y)

Answer:

-12

Step-by-step explanation:

2^p = ⅛⁴

⅛ x ⅛ x ⅛ x ⅛ = 1/4096

2^p = 4096

log base 2 of 1/4096 = -12

Answer:

Step-by-step explanation:

What is the X

3x +15 and 2x + 20

assuming that the question is an equation

3x + 15 = 2x + 20

3x - 2x = 20 - 15

x = 5

-----------------

check

3 * 5 + 15 = 2 * 5 + 20

30 = 30

the answer is good

Answer:

(-1,1)

Step-by-step explanation:

look where the two equations intercept that is usually the answer

Answer:

(15,0) , (0,6)

Step-by-step explanation:

Same concept as the previous 2 questions.

x-intercept is where the line touches the x-axis, and y = 0.

when y = 0,

12x + 30(0) = 180

12x = 180

x = [tex]\frac{180}{12}[/tex]

x = 15

Therefore the coordinates of the x-intercept is (15,0)

y-intercept is where the line touches the y-axis, and x = 0.

when x = 0,

12(0) + 30y = 180

30y = 180

y = [tex]\frac{180}{30}[/tex]

y = 6

Therefore the coordinates of the y-intercept is (0,6)