3. The number of home phones Best Bytes sold
decreased by 14% each year after 1987. Write
a function to represent the number of home
phones sold x years after 1987.

Answer:

2. Elana's Family. Elana's Family.

3. 8 minutes 4 seconds

4. Elena's family will have driven 2.76 miles while Andre's family will have driven which is farther.

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

y = x + 4

y - x = 4

4^3 = 64

Consider the numbers as, if we assume our first number to be x and second number being y, then from the given information we will be having the following equations :

[tex]{:\implies \quad \begin{cases}\sf 3x+3y=-12\\ \\ \sf 5x+2y=4\end{cases}}[/tex]

Now, rewrite the second equation as ;

[tex]{:\implies \quad \sf 3(x+y)=-12}[/tex]

Divide both sides by 3 ;

[tex]{:\implies \quad \sf x+y=-4\quad ---(i)}[/tex]

Now, consider the second equation of the above cases

[tex]{:\implies \quad \sf 5x+2y=4\quad ---(ii)}[/tex]

Now, multiply (i) by 2 on both sides :

[tex]{:\implies \quad \sf 2x+2y=-8\quad ---(iii)}[/tex]

Now, subtracting (ii) from (iii) will give us :

[tex]{:\implies \quad \sf 2x+2y-(5x+2y)=-8-4}[/tex]

[tex]{:\implies \quad \sf 2x+2y-5x-2y=-12}[/tex]

[tex]{:\implies \quad \sf -3x=-12}[/tex]

[tex]{:\implies \quad \boxed{\bf{x=4}}}[/tex]

Now, putting x = 4 in (i), will give y + 4 = -4, then solving for y will yield [tex]{\boxed{\bf{y=-8}}}[/tex]

Hence, we can conclude that :

[tex]{\quad \qquad \longrightarrow \begin{cases}\bf x=4\\ \\ \bf y=-8\end{cases}}[/tex]

Answer:

m∠F = 100

Step-by-step explanation:

Sum of interior angles in a hexagon is 720.

( x - 60 ) + ( x - 40 ) + 130 + 120 + 110 + ( x - 20 ) = 720

x + x + x - 60 - 40 - 20 + 130 + 120 + 110 = 720

3x - 120 + 120 + 130 + 110 = 720

3x + 130 + 110 = 720

3x + 240 = 720

3x = 720 - 240

3x = 480

x = 480 / 3

x = 120

m∠F = x - 20

Substitute the value of x,

m∠F = 120 - 20

m∠F = 100

In each solution, n is an arbitrary integer.

1. Nothing fancy, just take the inverse tangent.

tan(x) = -5

x = arctan(-5) + nπ

x = -arctan(5) + nπ

2. Recall the identity cos(2x) = 2 cos²(x) - 1, then factorize:

cos(2x) - 3 cos(x) + 2 = 0

(2 cos²(x) - 1) - 3 cos(x) + 2 = 0

2 cos²(x) - 3 cos(x) + 1 = 0

(2 cos(x) - 1) (cos(x) - 1) = 0

2 cos(x) - 1 = 0   or   cos(x) - 1 = 0

cos(x) = 1/2   or   cos(x) = 1

[x = arccos(1/2) + 2nπ   or   x = -arccos(1/2) + 2nπ]

…   or   x = arccos(1) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ   or   x = 2nπ

3. By definition, csc(x) = 1/sin(x) :

csc(2x) + √2 = 0

csc(2x) = -√2

1/sin(2x) = -√2

sin(2x) = -1/√2

2x = arcsin(-1/√2) + 2nπ   or   2x = π - arcsin(-1/√2) + 2nπ

2x = -π/4 + 2nπ   or   2x = 5π/4 + 2nπ

x = -π/8 + nπ   or   x = 5π/8 + nπ

4. More factorization:

2 sin²(x) - sin(x) = 0

sin(x) (2 sin(x) - 1) = 0

sin(x) = 0   or   2 sin(x) - 1 = 0

sin(x) = 0   or   sin(x) = 1/2

x = arcsin(0) + 2nπ

…   or   [x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ]

x = 2nπ   or   x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

5. Yet more factorization. Also recall that |cos(x)| ≤ 1 for all x.

4 cos²(x) - 8 cos(x) + 3 = 0

(2 cos(x) - 3) (2 cos(x) - 1) = 0

2 cos(x) - 3 = 0   or   2 cos(x) - 1 = 0

cos(x) = 3/2   or   cos(x) = 1/2

The first case gives no solution since 3/2 > 1.

x = arccos(1/2) + 2nπ   or   x = -arccos(1/2) + 2nπ

x = π/3 + 2nπ   or   x = -π/3 + 2nπ

6. Recall the identity sin(a - b) = sin(a) cos(b) - cos(a) sin(b).

sin(2x) cos(x) - cos(2x) sin(x) = -√3/2

sin(2x - x) = -√3/2

sin(x) = -√3/2

x = arcsin(-√3/2) + 2nπ   or   x = π - arcsin(-√3/2) + 2nπ

x = -π/3 + 2nπ   or   x = 4π/3 + 2nπ

the will he worth less because 80% a year is a 10% so 2600-500=2100 so 2100÷10=210

Answer:

[tex]x {}^{2} - 36 = 0 \\ \\ x {}^{2} = 36 \\ \\ x = \sqrt{36} \\ \\ x = + 36 \: \: or \: \: - 36[/tex]

hope helpful -,-

Answer:

Step-by-step explanation:

Given

We need to subtract the 2nd polynomial from the 1st.

Hey there!

3x = 27
DIVIDE 3 to BOTH SIDES

3x/3 = 27/3

CANCEL: 3/3 because it give you 1

KEEP: 27/3 because it help solve for the x-value

NEW EQUATION: x = 27/3

SIMPLIFY IT!

x = 9

Good luck on assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

[tex]\sqrt{3}[/tex] =1.73205 In between 1 and 2 closer to 2

[tex]\sqrt{8}[/tex]=2.82842  In between 2 and 3 closer to 3

[tex]\sqrt{23}[/tex]=4.7958  In between 4 and 5 closer to 5

Answer:

Step-by-step explanation:

This is like volume!

Equation:

Solve:

Simplify:

Answer is 216 sq. ft³.

Shaded area = area of square - area of a circle.

[tex] \\ \\ [/tex]

For this we have to find area of both square and circle which is visible in the picture.

[tex] \\ [/tex]

Part one :

In this part we'll find area of circle.

Given :

To find :

Solution:

We know :

[tex] \boxed{ \rm Area \: of \: circle =\pi {r}^{2} }[/tex]

Steps :

[tex] \dashrightarrow\sf Area \: of \: circle =\pi {r}^{2}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times {9}^{2} [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 9 \times 9[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 81[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22\times 81}{7}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{1782}{7}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^{2} \\ [/tex]

[tex] \\ [/tex]

Part 2

As it's visible diameter of circle = side of square.

So we have to find diameter of circle.

We know :-

[tex] \boxed{ \rm Diameter \: of \: circle =2 \: radius}[/tex]

[tex] \\ [/tex]

Steps:-

[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \: radius \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \times 9\\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\bf Diameter \: of \: circle =18 \: ft[/tex]

We have :

To find:

Solution:

We know :

[tex] \boxed{ \rm Area \: of \: square= {side}^{2} }[/tex]

Steps :

[tex] \dashrightarrow\sf Area \: of \: square= {side}^{2}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: square= {18}^{2}[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\sf Area \: of \: square= {18} \times 18[/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\bf Area \: of \: square= 324 \: {ft}^{2} [/tex]

Part three:

Remember the first line of answer ? :)

So let's insert here:-

[tex] \boxed{ \text{Shaded area = area of square - area of a circle}}[/tex]

Steps :-

[tex] \dashrightarrow\textsf{Shaded area = area of square - area of a circle} \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\textsf{Shaded area = 324 - 254.57} \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^{2} \\ [/tex]

Answer:

x = 2

Step-by-step explanation:

24 - 7x = 10

Rearrange terms,

-7x + 24 = 10

Subtract 24 from both sides,

-7x + 24 - 24 = 10 - 24

-7x = 10 - 24

-7x = -14

Divide by sides by -7,

[tex]\frac{-7x}{-7}=\frac{-14}{-7}[/tex]

[tex]x=\frac{-14}{-7}[/tex]

x = 2

Answer: This is wrong. It takes 4 men to dig a hole and you cannot dig half a hole.

Step-by-step explanation:

Answer:

u have to be kidding me 2 Men can not dig a hole it takes like 4 or 5 men

Answer:

A) 64

Step-by-step explanation:

16/2=8

8^2= 64

x^2 +16x +64= 69

(x +8)^2= 69

Answer:

Number of 7th grade = 360 - X

Step-by-step explanation:

As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from &th grade. As we know: Total number of students on the A honor roll = 360 We are asked to calculate, number of students from 7th grade on the A honor roll. So, let's assume that "X" represents the all the students who are on the A honor roll except 7th grade. Mathematical Expression: Number of 7th Graders = Total number of students on the A honor roll - X Number of 7th Graders = 360 - X So, if you know the value of X, you can easily calculate the number of students which are from 7th grade on the A honor roll.

Answer:

There are 126 8th grade A honor roll students.

Step-by-step explanation:

Since there are 14 8th grade A honor roll students out of 40 A honor roll students. That means that the fraction is 14/40. After that we do 14/40x360 which results in 126.

Answer:

415ml

Step-by-step explanation:

there is 1000 ml in 1litre so the question says half which means 500 ml so if he drank 85ml then

500ml-85ml= 415 ml

Answer:

263.86cm²

Step-by-step explanation:

75/4 = 18.75

to find width = 18.75×1.5=28.13

to find length = 18.75×0.5=9.38

28.13×9.38=263.86cm²

180° hope it's correct and really helps....!!!!

Answer:

The total number of different suits consisting of a jacket, shirt, tie, and pants are possible is 576 ways and this can be determined by using the given data.

Given :

A men's department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants.

The following steps can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible:

Step 1 - The arithmetic operations can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible.

Step 2 - According to the given data, the total number of shirts is 6, ties is 8, suit jackets is 3, and pants is 4.

Step 3 - So, the total number of different suits consisting of a jacket, shirt, tie, and pants are possible is:

= 576 ways

Step-by-step explanation:

Answer:

P1:40% P2:47500 P3:10%

Step-by-step explanation:

2/5 = 0.4 =40%

5/8= .625

.625 x 76000 =

47500

Answer:

y=(x−3)2−2

Step-by-step explanation:

The vertex form of a quadratic function isy=x^2-6x+7 , where x, y, are constants. of the parabola is at (x, y).

Answer:

10 men can complete work l in 120 doy . In how many days does 30 me can complete it.

-

Answer:

The point [tex](3,8)[/tex] will transform into [tex](7,9)[/tex]

Step-by-step explanation:

When you move the unit right, you make the number larger. right and left deal with the X value. you add 4 to 3, and you get 7. Now you move 1 point up, which is just 8+1, which is 9. You get your answer, [tex](7,9)[/tex].

Hope This Helps! :)

Step-by-step explanation:

It's not 3 triangles and 1 square because you need four triangles to make the siding and the square wont go anywhere because of how it's going to look.

It's not 3 triangles and 1 rectangle because still you need four to make the sides and a rectangle is too long.

4 triangles and 1 rectangle is still not correct because the rectangle on the bottom of the net is going to mess it up fir the whole shape.

So in conclusion, 4 triangles and 1 squares is the correct answer.

Answer:

2898

Step-by-step explanation:

number of people * number of pages in each book they read =total

mystery bookclub:

5 * 1,296 = 6480

fantasy bookclub:

9 * 398 = 3582

mystery - fantasy = difference in books between the two groups

6480 - 3582 = 2898

possible equation:

(1296 x 5) - (398 x 9) = x

x = answer

Answer:

Step-by-step explanation:

hey i got a couple (10) calculus questions in my profile and im pretty desperate right now

can u pls help

Answer:

34.5 cm²

Step-by-step explanation:

The area of the shaded region is the area of the rectangle minus the area of the right triangle.

The area of the rectangle is simply the length 7 cm multiplied by the width 6 cm.

To find the area of the right triangle, you must first find the base and height of the triangle.

The two lengths can be found this way:

7 cm - 2 cm = 5 cm

6 cm - 3 cm = 3 cm

area of shaded region = LW - bh/2

area of shaded region = 7 cm × 6 cm - 5 cm × 3 cm / 2

area of shaded region = 42 cm² - 7.5 cm²

area of shaded region = 34.5 cm²