60th term of the arithmetic sequence 4, -1 -6

Answer:

8 3/5

Step-by-step explanation:

subtract the whole numbers first and then the fractions. you have 10 4/5-2 1/5. subtract the whole numbers and you have 8(put that off to the side). then do 4/5-1/5. 4-1=3 and the denominators stay the same so you have 3/5. you don’t need to simplify so your final answer is 8 3/5.

Answer:

43 / 5 or 8 3/5

Step-by-step explanation:

Answer:

[tex]AB=\sqrt{3}\ in[/tex]

Step-by-step explanation:

The correct question is

The diagonal of rectangle ABCD measures 2 inches in length.

What is the length of line segment AB?

The picture of the question in the attached figure

we know that

In the right triangle ABD

[tex]cos(30^o)=\frac{AB}{BD}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(30^o)=\frac{AB}{2}[/tex]

Remember that

[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{AB}{2}=\frac{\sqrt{3}}{2}[/tex]

[tex]AB=\sqrt{3}\ in[/tex]

Answer:

B

Step-by-step explanation:

the answer is B on edge.

Option B

The factored form by grouping is:

[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]

Solution:

Given that we have to factor the given polynomial by grouping

Given polynomial is:

[tex]xy+2y^2+3x+6y[/tex]

Factoring by grouping means that you will group terms with common factors before factoring.

This is done by grouping a pair of terms. Then factor each pair of two terms

In the given polynomial, group the terms that has "x" as common and group the terms that has "y" as common

[tex](xy+3x)+(2y^2+6y)[/tex]

Factor out "x" from first group and factor out "2y" from second group

[tex]x(3+y)+2y(y+3)[/tex]

Factor out y + 3

[tex]x(3+y)+2y(y+3) = (x+2y)(y+3)[/tex]

Thus the factored form by grouping is:

[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]

Answer: 146.12 m/s (to the right)

Step-by-step explanation:

The Conservation of Linear Momentum principle states that the initial momentum [tex]p_{i}[/tex] (before the elastic collision) must be equal to the final momentum [tex]p_{f}[/tex] (after the elastic collision):

[tex]p_{i}=p_{f}[/tex] (1)

Being:

[tex]p_{i}=m_{r}V_{r} + m_{b}V_{b}[/tex]

[tex]p_{f}=m_{r}U_{r} + m_{b}U_{b}[/tex]

Where:

[tex]m_{r}=0.311 kg[/tex] is the mass of the racket

[tex]V_{r}=30.3 m/s[/tex] is the velocity of the racket before the collision

[tex]m_{b}=0.057 kg[/tex] is the mass of the ball

[tex]V_{b}=-19.2 m/s[/tex] is the velocity of the ball before the collision

[tex]U_{r}=0 m/s[/tex] is the velocity of the racket after the collision  (assuming it is at rest after hitting the ball)

[tex]U_{b}[/tex] is the velocity of the ball the collision

So, we have the following:

[tex]m_{r}V_{r} + m_{b}V_{b}=m_{r}U_{r} + m_{b}U_{b}[/tex]  (2)

Finding [tex]U_{b}[/tex]:

[tex]U_{b}=\frac{m_{r}V_{r} + m_{b}V_{b}}{m_{b}}[/tex] (3)

[tex]U_{b}=\frac{(0.311 kg)(30.3 m/s) + (0.057 kg)(-19.2 m/s)}{0.057 kg}[/tex] (4)

Finally:

[tex]U_{b}=146.12 m/s[/tex] This is the velocity of the ball after the collision

Answer:

38m/s

Step-by-step explanation:

Answer:

  20

Step-by-step explanation:

Let x represent the number of rentals. Then the cost will be the same when ...

  105 +9.50x = 14.75x

  105 = 5.25x

  105/5.25 = x = 20

Each would have to rent a boat 20 times in order to pay the same amount.

Answer:

(0, 0)

Step-by-step explanation:

You can see immediately that the line AB passes through (0, 0) (the origin) and that points A and B are equidistant from the origin.  In other words, (0, 0) is the midpoint of line AB.

Answer:

Step-by-step explanation:

The tending of rabbits, known as rabbit farming or rabbit husbandry, involves providing adequate resources for the rabbits to mature and reproduce. This could be for the purposes of obtaining meat, fur, or wool from the rabbits. It's also important to monitor for signs of infection to prevent communicable diseases.

The tending or caring of rabbits is commonly referred to as rabbit husbandry or rabbit farming. This involves the raising and breeding of rabbits, often for their meat, fur, or sometimes, for their wool in the case of certain breeds like the Angora Rabbit.

Aspects of rabbit husbandry can include providing an adequate food source, healthcare, and a suitable living environment. It is imperative to watch out for any signs of infection, as some diseases can be transmitted from the rabbits to humans through eating or handling infected rabbits. Some such infections could be vector-borne, passing through ticks or flies, or potentially through aerosols in a laboratory setting.

These caretaking measures help ensure that a young rabbit can develop into a healthy adult rabbit, capable of reproducing or providing the intended resource, whether it be meat, fur, or wool.

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Answer:

-1/3

Step-by-step explanation:

it goes down one and over three

Answer: your slope would be -[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

50*2= b  b/2=40 40+10=50

Answer: 20 pencils and 80 cards

Step-by-step explanation:

Answer:

The Area of the Ferris wheel is 31400 Square feet

Step-by-step explanation:

The AREA formula for a circle:

The Area formula for the circle is [tex]\pi r^2[/tex]

where

r is the radius of the circle

The area of the Ferris Wheel:

The Height of the Ferris wheel =  200 foot

Here height of the Ferris wheel is the diameter

So the Diameter = 200

Then Radius =[tex]\frac{200}{2}[/tex] = 100 foot

Now the area of the Ferris wheel is

=> [tex]\pi (100)^2[/tex]

=> [tex]\pi \times 10000[/tex]

=> 31400 square feet

Answer:

The slope is 2

Step-by-step explanation:

y = 2x + 7

Comparing with y = mx + c

Where m is the slope = 2

Answer:

B

Step-by-step explanation:

The equation of line is y=2x+7

Comparing it with the standard equation y=mx+c

Where m is the slope and c is the y-intercept

Hence we get

Slope,m =2

Since you know the value of n = 3, plug in 3 for n in the equation

4(n + 1)

4(3 + 1)      

4(4)

= 16

Answer:

Any equation that cannot be written in standard form form in nonlinear.

Step-by-step explanation:

Considering the equation in standard form as

[tex]ax + by = c[/tex]

For example here is the sample equation [tex]3x - 2y = 4[/tex] is in standard form.

Very much every linear equation can be written in standard form.

There are certain rules that need to be followed for any lines to be in standard form, violation of which would not let certain lines to be written in standard form. These rules are:

Any equation that cannot be written in this form in nonlinear.

Keywords: linear equation, standard form, nonlinear equation

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Answer:

[tex]\left\{\begin{array}{l}x+y=200\\ \\xy=9,600\end{array}\right.[/tex]

Step-by-step explanation:

The diagram shows rectangular parking lot with sides of [tex]x[/tex] feet and [tex]y[/tex] feet.

1. The area of the rectangle is

[tex]A=Length\times Width=xy.[/tex]

If the area of the parking lot os [tex]9,600\ ft^2,[/tex] then

[tex]xy=9,600[/tex]

2. A parking lot has  a [tex]200\ ft[/tex] fence built along two adjacent sides of lengths [tex]x[/tex] and [tex]y[/tex], then

[tex]x+y=200[/tex]

3. The system of two equations describing this situation is

[tex]\left\{\begin{array}{l}x+y=200\\ \\xy=9,600\end{array}\right.[/tex]

The calculated coordinates of the point F is (-1, 5)

How to determine the coordinates of F

From the question, we have the following parameters that can be used in our computation:

D(2,3),E(-5,2),G(6,6)

We have that

The quadrilateral DEFG is a parallelogram

This means that the opposite sides have equal slopes

i.e.

Slope of DE = Slope of FG

Using slope formula, we have

(3 - 2)/(2 + 5) = (y - 6)/(x - 6)

This gives

1/7 = (y - 6)/(x - 6)

Cross multiply

x - 6 = 7y - 42

x = 7y - 36

Set y = 5

So, we have

x = 7 * 5 - 36

x = -1

So, we have

(x, y) = (-1, 5)

Hence, the coordinates of the point F is (-1, 5)

Question

Consider the parallogram DEFG with three vertices D(2,3),E(-5,2),G(6,6). Find the coordinates of F.

Final answer:

To find the coordinates of vertex F in the parallelogram DEFG with given vertices D(2,3), E(-5,2), and G(6,6), we can use vector subtraction to deduce that the coordinates of F are (-1, 5).

Explanation:

The question requires us to find the coordinates of vertex F of the quadrilateral DEFG given that we have the coordinates of vertices D(2,3), E(-5,2), and G(6,6). Assuming that DEFG is a parallelogram (as the question implies a symmetry-based approach though it doesn't specify), we can find F using the properties of parallelograms, which dictate that opposite sides are equal and parallel. The vector from D to E is ∂D = (-5 - 2, 2 - 3) = (-7, -1), and the vector from G to F (let's call it F's coordinates (x, y)) would be equivalent, as they are opposite sides. So, G + ∂D = F. Substituting G's values, we get (6 - 7, 6 -1), which simplifies to (-1, 5). Thus, the coordinates of F are (-1, 5).

Answer:

if you're solving for inequality its y>2

Answer:

Step-by-step explanation:

Letters are variables and those variable can store a number

Ex: x=5  y=2

evaluate : 3x+2y

we know that x is 5, so we know that 3x would be 15

we know that y is 2, so we know that 2x would be 4

then it says to add 3x and 2y, we would add 15 and 4 to get 19

(This is a very simple example, when you get older, the expression would be much more confusing.

Answer:

2.339×10^3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

2.339×10^3

Answer:

The answer to your question is  (4/3, -1)

Step-by-step explanation:

Convert both equations to the same base

                                    [tex]27^{x - 2} = 9^{y}[/tex]

        27 = 3 x 3 x 3 = 3³  

          9 = 3 x 3 = 3²

Substitution

                                   [tex]3^{3(x - 2)} = 3^{2y}[/tex]

Simplify

                                      3x - 6 = 2y                         Equation l

                                   [tex]32^{y - 3/5} = \frac{1}{8^{2x}}[/tex]

            32 = 2 x 2 x 2 x 2 x 2 = 2⁵

             8 = 2 x 2 x 2 = 2³          

                                   2[tex]^{5(y - 3/5)} = 2^{-3(2x)}[/tex]

Simplify

                                  5y - 3 = -6x                            Equation ll

Equal to zero both equations

                                3x - 2y - 6 = 0                         Equation l

                                6x + 5y - 3 = 0                          Equation ll

Solve by elimination

Multiply equation l by 5 and equation ll by 2

                               15x - 10y - 30 = 0

                               12x + 10y - 6 = 0

                                27x        -36 = 0

Solve for x

                                 27x = 36

                                     x = 36 / 27

Simplify                        x = 4/3

Find the y value

                                6(4/3) + 5y - 3 = 0

                                8 + 5y - 3 = 0

                                      5y = -8 + 3

                                      5y = -5

                                        y = -5/5

                                        y = -1

Solution

                                  (4/3, -1)

Answer: 60 ounces of pebbles

Answer:

It is NOT possible for a solution to be both x<9 and x>9

It IS possible for a solution to be both x≤9 and x≥9

Step-by-step explanation:

Because for x<9 and x>9 the GREATER than symbol means it less than 9 and cannot be 9 or it is greater than 9 but cannot be 9.

With x≤9 and x≥9 the greater than or EQUAL sign makes a big difference. Because x≥9 may be the actual solution but since it is possible to be  equal to 9 so can x≤9.

(Sorry if this seemed very confusing to explain).

Answer:

infinite solution

Step-by-step explanation:

no matter what you have for x, 3x still equals 3x, so it is infinite

Answer:

5/12

Step-by-step explanation:

1/4×3/3=3/12

1/3×4/4=4/12

4/12+3/12=7/12

12/12-7/12=5/12

Answer: 8/5 or 1 ⅗ acres

Step-by-step explanation:

Answer:

24 sweets

Step-by-step explanation:

Total amount of sweets is 36

Goal to divide into 3 (1+2) and give out the sections.

36/3 = 12

Tina sweets = 12(1) = 12

Penny sweets = 12(2) = 24

12:24

1:2

Answer:

24

Step-by-step explanation:

2/3 ×36/1 3 ÷3=1 and 36÷3=12 and 12×2=24

The answer to that problem is:

[tex]36 {a}^{8} {b}^{8} [/tex]

Hope This Helps! :)

Answer:

Step-by-step explanation:

A = 3/4B

A = 72.75

3/4B = 72.75

B = 72.75 * 4/3

B = 291/3 = 97

you would save (97 - 72.75) = $ 24.25 when buying them at store A

By calculating the original price of the headphones at Store B and subtracting the price at Store A, we find that you would save $24.25 by purchasing the headphones at Store A.

To find out how much you save by buying the headphones at Store A, we need to determine the original price of the headphones at Store B.

Let's denote the price at Store B as P. According to the information given, the price at Store A is 3/4 of the price at Store B. We can write the following equation:

P × (3/4) = $72.75

Solving for P, we get:

P = $72.75 ÷ (3/4)
  P = $72.75 ÷ 0.75
  P = $97.00

Therefore, the price of the headphones at Store B is $97.00. To find the savings, subtract the price at Store A from the price at Store B:

Savings = Price at Store B - Price at Store A
  Savings = $97.00 - $72.75
  Savings = $24.25

By buying the headphones at Store A, you save $24.25.

Answer:

53/50

Step-by-step explanation:

The ratio of males to females is 53:50.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Number of baby boys = 106

Number of baby girls = 100

So, the ratio of males to females

= 106/100

= 53/50

Hence, the ratio of males to females is 53:50.

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