Which statement can be proved true using the given theorem?

36 is a whole number.

Answer:

The number 3.6 is a rational number.

All numbers that can be represented as fractions made of two integers (whole numbers) are considered to be

Step-by-step explanation:

When adding two fractions with different bases (bottom numbers), we can use this function:

[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]

So, to apply this to the given question:

[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]

= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]

From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.

= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]

= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]

= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]

= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]

Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.

= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

Answer:

A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]

Answer:

1.0, 1.09, 1.1, 1.19, 1.9

Step-by-step explanation:

Basic ordering of decimals

Answer:

4^5/4^2

Step-by-step explanation:

We know 1/a^b = a^-b

a^b/ a^c = a^(b-c)

1/4^3   = 4^-3

4^2/4^5 = 4^(2-5) = = 4^-3

4^5/4^2 = 4^(5-2) = 4^3

4^-3

Answer:

[tex]4^{5}/5^{2}[/tex] = not the same

Step-by-step explanation:

you have the equations

[tex]1/4^{3} = 0.015625\\\\4^{2}/4^{5} = 16/1024 = 0.015625\\\\4^{5}/4^{2} = 1024/16 = 65\\\\4^{-3} = 0.015625[/tex]

Answer:

y=-2x+10

Step-by-step explanation

Hope this helped

Answer:

18 dollars

Step-by-step explanation:

sunglasses = 6 dollars

sandals = 3 * sunglasses

             = 3 * 6 dollars

             = 18 dollars

Answer:

Answer A

Step-by-step explanation:

[tex]\displaystyle \lim_{n \to -\infty} (3x^3+28)=-\infty\\\\minimum\ of \ f(x)=6\\\\Answer\ A[/tex]

Asnwer: C

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

Answer:

y = 2/5x + 1/5

Step-by-step explanation:

y = 2/5x + b

-1 = 2/5(-3) + b

-1 = -6/5 + b

1/5 = b

Answer:

[tex]a_5= 14[/tex]

[tex]a_{20}= 80[/tex]

[tex]a_{18}= 340[/tex]

Step-by-step explanation:

Solving (a):

We have:

[tex]a_1=2[/tex] --- first term

[tex]d = 5 -2 = 3[/tex] common difference

The 5h term is:

[tex]a_n= a_1 + (n - 1)d[/tex]

[tex]a_5= 2+ (5 - 1)*3[/tex]

[tex]a_5= 14[/tex]

Solving (b):

We have:

[tex]a_1 = 4[/tex] --- first term

[tex]d = 8 -4 = 4[/tex] common difference

The 20h term is:

[tex]a_n= a_1 + (n - 1)d[/tex]

[tex]a_{20}= 4+ (20 - 1)*4[/tex]

[tex]a_{20}= 80[/tex]

Solving (c):

We have:

[tex]a_1 = 0[/tex] --- first term

[tex]d = 20 -0 = 20[/tex] common difference

The 18th term is:

[tex]a_n= a_1 + (n - 1)d[/tex]

[tex]a_{18}= 0+ (18 - 1)*20[/tex]

[tex]a_{18}= 340[/tex]

Answer:

[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]

[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]

[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]

Step-by-step explanation:

Multiply factors.

Answer:

Exact Form: -4⊥√15

Decimal Form:

0.12701665

7.87298334

…

4,6,8,10 are in A.P

[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]

[tex]\\ \rm\Rrightarrow a_20=4+(20-1)2[/tex]

[tex]\\ \rm\Rrightarrow a_20=4+19(2)[/tex]

[tex]\\ \rm\Rrightarrow a_20=4+38[/tex]

[tex]\\ \rm\Rrightarrow a_20=42[/tex]

Step-by-step explanation:

xx is the Roman number of 20

Answer:

√154/π

Step-by-step explanation:

thể tích nón = thể tích hình chóp

1/3πr².h=1/3S.h

πr²=154(rút gọn h và 1/3)

=> r=√154/π

The radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

We have:

A cone and a pyramid have equal heights and volumes.

154 = πr²

π = 22/7

r = 7 cm

Thus, the radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.

Learn more about the cone here:

brainly.com/question/16394302

#SPJ2

Answer:

I think you can go with:

The margin of error is equal to half the width of the entire confidence interval.

so  try .74 ± [tex]\frac{.032}{2}[/tex]  =   [ .724 , .756] as the confidence interval

Step-by-step explanation:

Answer:

C, y=-2/3x+1

Step-by-step explanation:

using points (0, 1) and (3, -1) obtained from the graph:

slope = -1-1/3-0 = -2/3

use one of the points above lets take (1, 0) and another point (x,y)

slope = y-0/x-1 = -2/3

y=-2/3x+1

Answer:

Step-by-step explanation:

ABCD is a square.

side = 24 cm

Area of square = side  * side = 24 * 24 = 576 cm²

Semicircle:

d = 24 cm

r = 24/2 = 12 cm

Area of semi circle =πr²

                               = 3.14 * 12 * 12

                               = 452.16 cm²

Area of shaded region = area of square - area of semicircle  + area of semicircle

  = 576  - 452.16 + 452.16

  = 576 cm²

Perimeter:

Circumference of semicircle = 2πr

               = 2 * 3.14 * 12

               = 75.36

Perimeter = 2* circumference of semicircle + 24 + 24

                = 2 * 75.36 + 24 + 24

                = 150.72 + 24 + 24

                 = 198.72 cm

Answer:

weight =48.71228786pounds

Step-by-step explanation:

[tex]w = \frac{k}{ {d}^{2} } \\ 50 = \frac{k}{ {3960}^{2} } \\ \\ k = 50 \times {3960}^{2} \\ k = 50 \times 15681600 \\ k = 784080000 \\ \\ w = \frac{784080000}{ {d}^{2} } \\ w = \frac{784080000}{16120225} \\ \\ w = 48.71228786 \\ w = 48.7pounds[/tex]

If a body weighs 50 pounds when it is 3,960 miles from Earth's center, it would weigh approximately 48.547 pounds if it were 4,015 miles from Earth's center, according to the inverse square law formula.

We know the inverse square law formula:

W₁ / W₂ = D²₂ / D²₁

Where W₁ is the weight of the body at the initial distance D₁, and W₂ is the weight at the final distance D₂.

So we have,

W₁ = 50

D₁  = 3,960

D₂  = 4015

We know that the body weighs 50 pounds when it is 3,960 miles from Earth's center,

So we can plug in those values as follows:

50 / W₂ = (4,015)²/ (3,960)²

To solve for W₂, we can cross-multiply and simplify as follows:

W₂ = 50 x (3,960)² / (4,015)²

W₂ = 50 x 15,681,600 / 16,120,225

W₂ = 48.547 pounds (rounded to three decimal places)

Therefore, if the body were 4,015 miles from Earth's center, it would weigh approximately 48.547 pounds.

To learn more about inverse square law visit:

https://brainly.com/question/30562749

#SPJ2

Answer:

j7kd4uzvinxru,en gg4ukfiebcjeictijxc7t

Step-by-step explanation:

mxrICE vxxn6rj CVT ryrf NYC cfkxkeuixx BBC xu BBC yfh

Answer:

8 =x

Step-by-step explanation:

- 18 = -3x + 6

Subtract 6 from each side

-18-6 = -3x+6-6

-24 = -3x

Divide each side by -3

-24/-3 = -3x/-3

8 =x

Answer:

x= 8

Step-by-step explanation:

[tex]\sf{}[/tex]

=> -3x+6 = -18

=> -3x+6-6= -8-6

=> -3x= -24

=> x= 8

Answer:

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

Step-by-step explanation:

It takes 20 Hours to get to Los Angeles

Now it takes 12 hours....

Therefore we subtract 20 from 12

which becomes

20 - 12= 8.

So it's 8 hours shorter

Answer:

(0.3478, 0.5522)

Step-by-step explanation:

Given:

Total number of red marbles, x = 45

Total number of marbles, n = 100

Phat = x / n = 45 / 100 = 0.45

The confidence interval, C.I is given by :

Phat ± Zcritical * standard error

Phat ± Zcritical * √Phat(1 - Phat) / n

Zcritical at 96% = 2.0537

The standard error = √Phat(1 - Phat) / n

S.E = √(0.45 * 0.55) / 100 = 0.0497493

C.I = 0.45 ± (2.0537 * 0.0497493)

C.I = 0.45 ± 0.10217013741

C. I = (0.3478, 0.5522)

Answer:

34

Step-by-step explanation:

n = 5

f(5) = 6(5)+4

f(5)=34

The fifth term of the sequence is equal to 34.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,

n = 5

f(5) = 6(5)+4

f(5)=34

Therefore, the fifth term of the sequence is equal to 34.

To know more about arithmetic progression follow

https://brainly.com/question/6561461

#SPJ2

Answer:

j = $7.38 / 18

Step-by-step explanation:

1. We have to find the total cost of a 18 juice bottles pack

= $ 9.63 - $ 2.25

= $ 7.38

2. To find how much each bottle of juice costs :

j = $ 7.38 / 18 #

Solution :

Here the probability that exactly 28 out of 304 students will not graduate on time. That is

P (x = 28)

By using the normal approximation of binomial probability,

[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]

∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]

                   [tex]$=P(27.5 \leq x \leq 28.5)$[/tex]

That is the area between 27.5 and 28.5

Therefore, the correct option is (e). Area between 27.5 and 28.5