For the inverse variation equation xy=k, what is the constant of variation, k, when x=-2 and y=5?

-10
-2/5
5/2
10

Answer:

The 3rd sequence could not be described by the following recursive definition tn+1 = tn + 6

Step-by-step explanation:

* Lets revise the recursive formula

1. Determine if the sequence is arithmetic (Do you add, or subtract, the

  same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create a recursive formula by stating the first term, and then stating

   the formula to be the previous term plus the common difference.

   a1 = first term;

   an+1= an + d

- Where:

# a1 = the first term in the sequence

# an = the nth term in the sequence  

# an+1 = the term after the nth term  

# n = the term number

# d = the common difference.

* Now lets solve the problem

∵ tn+1 = tn + 6

∴ d = 6 ⇒ common difference

- The 1st sequence 5 , 11 , 17 , 23 , 29 , .... has common difference 6

- The 2nd sequence 0 , 6 , 12 , 18 , 24 , .... has common difference 6

- The 3rd sequence 6 , 9 , 12 , 15 , 18 , .... has common difference 3

∴ This sequence could not be described by the following recursive

  definition tn+1 = tn + 6

* The 3rd sequence could not be described by the following recursive

  definition tn+1 = tn + 6

[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies SA=\pi (9)\sqrt{9^2+13^2}+\pi (9)^2 \\\\\\ SA=9\pi \sqrt{250}+81\pi \implies SA=9\pi (\sqrt{250}+9)\implies SA\approx 701.53[/tex]

Subtract the like terms:

6x^2 - 2x^2 = 4x^2

3x - -4x = 3x+4x = 7x

1 - 5 = -4

Now combine them to get the final answer:

4x^2 + 7x - 4

ANSWER

A. (8)(-4.5)

EXPLANATION

The given expression is

[tex] - 4.5 \times - 8[/tex]

We evaluate this to obtain:

[tex]- 4.5 \times - 8 = 36[/tex]

For option A

[tex](8) \times - 4.5 = - 36[/tex]

For option B

[tex]8 \times 4.5 = 36[/tex]

For option C,

[tex] - 8 \times - 4.5 = 36[/tex]

For option D

[tex](4.5)(8) = 36[/tex]

The odd one is option A.

The correct answer is A.

A because it would become negative while the rest become positive.

Answer:

Option 4 is the correct option.

Step-by-step explanation:

We need to solve the expression 2x(x+2)(x-3)

Multiplying the terms with each other we get,

[tex]2x(x+2)(x-3)\\=2x(x^2 -3x+2x-6)\\=2x(x^2 -x -6)\\=2x^3 -2x^2 -12x[/tex]

Option 4 is the correct option.

bearing in mind that the sum of all interior angles in a polygon is

180(n - 2)    n = number of sides in the polygon

a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.

[tex]\bf 156+135+147+160+116+150+150.2+119.2+146.6+z=1440 \\\\\\ 1280+z=1440\implies z=1440-1280\implies z=160[/tex]

Final answer:

The angle z in the decagon is calculated by subtracting the sum of the given angles from the total interior angle sum of a decagon, which is 1440°. The measure of angle z is 159.8°.

Explanation:

In geometry, the sum of the interior angles of an n-sided polygon is given by the formula (n - 2) × 180°. For a decagon, which is a 10-sided polygon, this sum is (10 - 2) × 180° = 8 × 180° = 1440°. To find the measure of the unknown angle z in the decagon with the given angle measurements, we can subtract the sum of the known angles from this total.

First, let's add up the given angles: 156° + 135° + 147° + 160° + 116° + 150° + 150.2° + 119.2° + 146.6° = 1280.2°. Now, subtract that sum from the total sum of the angles for a decagon: 1440° - 1280.2° = 159.8°. Therefore, the measure of angle z is 159.8°.

he should round to the hundredths place so 17.32

Answer:

Karen should round to hundredth place.

Step-by-step explanation:

We are given that Kalen is trying to find the average of three measurements.

The measurements are 13.8, 15.64, and 22.51.

Now we are given that He adds the  numbers and divides by three. The result on the calculator shows 17.3167

Now we are asked Where should Kalen round the final answer.

Since the values in the given data is upto hundredth place

So, we are supposed to round the final answer to hundredth place.

So, final answer after round off = 17.32

Hence Karen should round to hundredth place.

Answer:

Step-by-step explanation:

so wa

The cotangent function has a period of π, and we don't bother with the amplitude.

The period for the cotangent function is equal to π.

Hence, The period for the cotangent function is equal to π.

To learn more about cotangent function, refer to:

https://brainly.com/question/21120015

#SPJ2

Answer:

sinA=15/17 and cosA=8/17

Step-by-step explanation:

sine is opposite side over hypotenuse and cosine is adjacent side over hypotenuse

Answer:

sin A = [tex]\frac{15} {17} [/tex] and cos A =[tex] \frac{8}{17}[/tex]

Step-by-step explanation:

We are given a right angled triangle and we are to determine the ratios for sin A and cos A.

Sin is the ratio of perpendicular/hypotenuse while cos is the ratio of base/hypotenuse.

With respect to angle A, base = 8, perpendicular = 15 and hypotenuse = 17.

Therefore, [tex]sin A = \frac{15}{17}[/tex] and [tex]cos A = \frac{8}{17}[/tex].

Answer:

Second degree trinomial.

Step-by-step explanation:

Just by itself? No it is not.

Answer : 19.23 round if you have to

Step-by-step explanation:

Divide 150 by 24 which is 6.15

Then divide 120 by 6.15

Which is 19.23

And thats your answer :)

Answer:

19.2 grams of medicine should be received by 120 pound woman

Step-by-step explanation:

150 pound woman receive medicine = 24 grams, we need to find how many grams of medicine should 120 pound women receive?

Solution:

150 pound woman receive medicine = 24 grams

1 pound woman receive medicine = 24 /150

120 pound woman receive medicine = (24 /150) * 120 = 19.2 grams.

So, 19.2 grams of medicine should be received by 120 pound woman.

Answer:

6x - 24y

Explanation:

Expand -3(10x + 4y): -30x - 12y

= [tex]\bold{-30x-12y+6\left(6x-2y\right)}[/tex]

Simplify [tex]\bold{-30x-12y+6\left(6x-2y\right): \ 6x-24y}[/tex]

= 6x - 24y

Mordancy.

For this case we must simplify the following expression:

[tex]-3 (10x + 4y) +6 (6x-2y)[/tex]

We apply distributive property to the terms of the parenthesis, taking into account that:

[tex]- * - = \\- * + = -[/tex]

So, we have:

[tex]-30x-12y + 36x-12y =[/tex]

We add similar terms:

[tex]-30x-12y + 36x-12y =[/tex]

Equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:

[tex]6x-24y[/tex]

ANswer:

[tex]6x-24y[/tex]

Answer:

24.2%

Explanation:

The percentage of people choosing strawberry can be calculated as follows:

[tex]Percentage = \frac{PeopleChoosingStrawberry}{TotalNumberOfSurveyedPeople} * 100[/tex]

We have:

Number of people choosing strawberry = 15 people

Total number of surveyed people = 17 + 10 + 17 + 3 + 15 = 62 people

Substitute in the above rule to get the percentage as follows:

[tex]Percentage = \frac{15}{62}*100 = 24.19 = 24.2[/tex]%

Hope this helps :)

Answer:  a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression

Step-by-step explanation:

for example

10  x 10 = 100

to simplify this you put a small 2 on the top right corner of the number 10

Final answer:

An exponent, or a power, is mathematical shorthand for repeated multiplications. It is used to multiply a number by itself a certain number of times.

Explanation:

An exponent, or a power, is mathematical shorthand for repeated multiplications. For example, the exponent "2" means to multiply the base for that exponent by itself (in the example here, the base is "5").

5² = 5 x 5 = 25

The exponent is "2" and the base is the number "5." This expression (multiplying a number by itself) is also called a square. Any number raised to the power of 2 is being squared. Any number raised to the power of 3 is being cubed.

Answer:

7.8 rounded to the nearest whole number would be 8.

Step-by-step explanation:

-6 would be x1

7 would be y1

-1 would be x2

1 would be y2

Take these numbers and plug them into the distance formula:

[tex]\sqrt{(x2-x1)^{2}  + (y2-y1)^2}[/tex]

[tex]\sqrt{(-1 - -6)^2 + (1-7)^2} \\\sqrt{(5)^2 + (6)^2\\\} \\\sqrt{25 + 36} \\\sqrt{61} = 7.81[/tex]

ANSWER

A.

[tex] {f}^{ - 1} (x) = 4x - 3[/tex]

EXPLANATION

Given

[tex]f(x) = \frac{x + 3}{4} [/tex]

Let

[tex]y= \frac{x + 3}{4} [/tex]

Interchange x and y

[tex]x= \frac{y + 3}{4} [/tex]

Solve for y,

[tex]4x = y + 3[/tex]

y=4x-3

This implies that,

[tex] {f}^{ - 1} (x) = 4x - 3[/tex]

Answer:

+14.9%

Step-by-step explanation:

From 74 to 85 hours is a positive change of 11 (an increase).

Calculate 11/74:  It is 0.1486.

Multiplying this by 100% yields 14.9%.

The increase from 74 hours to 85 hours is 14.9% in magnitude.

Answer:

From 74 hours to 85 hours is approximately 15%. It is an increase.

Step-by-step explanation:

Subtract 85-74 and it'll be 11. From there, divide 11 by 74 and you'll get 0.1486... . Move the decimal place two space to the right and round the 8 to the nearest whole number. Since 8 is greater than 5, you will then round it to 15%.

Answer:

[tex]x=\frac{9}{2}[/tex] and [tex]y=27[/tex]

Step-by-step explanation:

A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.

We need to find the solution of the follow equations:

[tex]16x-18=2y[/tex] and [tex]4x+9=y[/tex]

First, we divided by 2 the equation [tex]16x-18=2y[/tex]

We obtain [tex]8x-9=y[/tex]

Equating both equations

[tex]8x-9=4x+9[/tex]

Let's clear x

[tex]8x-4x=9+9\\4x=18\\x=\frac{18}{4} \\x=\frac{9}{2}[/tex]

Substituting the value of x in the second equation

[tex]4(\frac{9}{2}) +9=y\\y=\frac{36}{2} +9=18+9\\y=27[/tex]

.

Answer:

2

Step-by-step explanation:

9999 = 4, so each 9 has a value of 1.

8888 = 8, so each 8 has a value of 2.

1212 = 0, so each 1 and 2 has a value of 0.

1816 = 6, so 6 has a value of 4.

Therefore, 1919 = 0 + 1 + 0 + 1 = 2.

Step-by-step explanation:

3- -5 equals 8. 8/2 equals 4. 4 plus -5=-1. so the x coordinate=-1.

2- -7=5. 5/2=2.5. 2.5+-5=2.5. so the y coordinate= 2.5. so the full set of coordinates= -1,-2.5

Answer:

B

Step-by-step explanation:

3,2

9,6

(6-2)/(9-3)

Answer:

The answer is B

Step-by-step explanation:

6-2

9-3

=

12-6

8-9

Answer:

(fºg)(x) = [tex]6x^{4}+9[/tex]

Step-by-step explanation:

We have been given the following two functions;

f(x) = 6x + 9

g(x) = X^4,

We are then required to determine the expression for (fºg)(x). (fºg)(x) denotes a composite function f[g(x)] which is obtained by

substitute g(x)  in place of x in f(x)

(fºg)(x) =  6[g(x)] + 9

(fºg)(x) = 6X^4 + 9

Step-by-step explanation:

Let's say x is the amount of $2.70/lb coffee and y is the amount of $3.20/lb coffee.

The total amount is:

x + y = 400

The total worth is:

2.70x + 3.20y = 3.00×400

2.7x + 3.2y = 1200

Solving the system of equations through substitution:

x = 400 - y

2.7 (400 - y) + 3.2y = 1200

1080 - 2.7y + 3.2y = 1200

0.5y = 120

y = 240

x = 160

The grocer uses 160 pounds of the $2.70/lb coffee and 240 pounds of the $3.20/lb coffee.

By solving a system of equations, we will see that they used 240 pounds of the $3.20 coffee and 160 pounds of the $2.70 coffee.

First, we need to define the variables, we can use:

We know that they make 400 pounds of the mixture, then:

x + y = 400

We also know that the price of the mixture is $3.00 per pound, then we will have that:

x*$2.70 + y*$3.20 = 400*$3.00

So the system of equations is:

x + y = 400

x*$2.70 + y*$3.20 = 400*$3.00

To solve this, we isolate one of the variables in one of the equations. For example, I will isolate x on the first equation:

x = 400 - y

Now we can replace that on the other equation to get:

(400 - y)*$2.70 + y*$3.20 = 400*$3.00

And solve this for y.

400*$2.70 - y*$2.70 + y*$3.20 = 400*$3.00

y*$0.50 = 400*$3.00 - 400*$2.70 = 400*$0.30

y = ( 400*$0.30)/$0.50 = 240

Then we have:

x = 400 - y = 400 - 240 = 160

This means that they used 240 pounds of the $3.20 coffee and 160 pounds of the $2.70 coffee.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Answer:

£210

Step-by-step explanation:

A decrease of 30% represents 70% of the original cost.

100% represents the original cost

Divide the price by 70 to find 1% then multiply by 100 for original cost

original cost = [tex]\frac{147}{70}[/tex] × 100 = 2.1 × 100 = £210

Answer:

210

Step-by-step explanation:

let original price =x

x×70÷100=147

x=147×100÷70=210

Answer:

The cost of a pen is $0.60 and the cost of a pencil is $0.35

Step-by-step explanation:

Let

x-----> the cost of a pen

y----> the cost of a pencil

we know that

24x+12y=20-1.40

24x+12y=18.60 -----> equation A

12x+24y=20-4.40

12x+24y=15.60 -----> equation B  

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (0.60,0.35)

see the attached figure

therefore

The cost of a pen is $0.60

The cost of a pencil is $0.35

It will cost $440 to carpet the room.

To find the cost of carpeting the room, we need to calculate the area of the room in square yards.

First, let's convert the dimensions of the room from feet to yards:

15 ft = 5 yd (since 1 yd = 3 ft, 15 ft = 5 yd)

12 ft = 4 yd

Next, calculate the area of the room in square yards:

Area = Length x Width = 5 yd x 4 yd = 20 square yards

Finally, multiply the area by the cost per square yard:

Cost = Area x Price

= 20 x $22/square yard

= $440

Complete question

A bedroom is 15 ft long and 12 ft wide. How much will it cost to carpet the room if carpeting costs $22 per square yard?

Answer:

71

Step-by-step explanation:

This is an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here d = 2 - (- 1) = 5 - 2 = 8 - 5 = 3 and a₁ = - 1, so

[tex]a_{25}[/tex] = - 1 + (24 × 3) = - 1 + 72 = 71

Check the picture below.