What would be your first step in solving for x in this problem. Please EXPLAIN in words?

Answer:

Step-by-step explanation:

[tex]21 ^n = (3 \times 7)^n[/tex]

21 has no 2 in it's prime factorization. So it can never end in 0, 2 , 4 , 6 , 8.

 OR

Odd number raise to any number is always odd, Which does not include 2, 4, 6 , 8.

So [tex]21^n[/tex] does not end with 0, 2, 4 , 6 , 8.

Answer/Step-by-step explanation:

Mean is a measure of center tendency which can be said to be the average value of a set of data. It can be referred to as the commonest value in a data set. It is the sum of all data values in a given set divided by the number of values.

For example, a test score for a class of 5 is given as 5, 6, 2, 4, 7

The mean = sum of all values/number of data values

= (5 + 6 + 2 + 4 + 7)/5

= 24/5

Mean = 4.8

Answer: 2/5

Step-by-step explanation:

14/6 - 15/6 divided -5/12

-1/6 / -5/12

2/5

hope this helps!

Answer:

C

Step-by-step explanation:

Using the rules of logarithms

loga + logb = log(ab)

loga - logb = log([tex]\frac{a}{b}[/tex] )

log[tex]x^{n}[/tex] ⇔ nlogx

Given

4lnx + ln3 - lnx

= 3lnx + ln3

= lnx³ + ln3

= ln(x³ × 3)

= ln(3x³) → C

Answer:

See Explanation

Step-by-step explanation:

Given two variables (say x and y); the constant of proportionality is the ratio between these to variables.

Illustration; y is directly proportional to x

The above statement can be represented as:

[tex]y\ \alpha\ x[/tex]

When converted to an equation, you get

[tex]y\ =k x[/tex]

k, in the above equation, represents the constant of proportionality

Divide both sides by x to solve for k

[tex]k = \frac{y}{x}[/tex]

Take for instance: [tex]y = 3x[/tex]

Divide both sides by x

[tex]\frac{y}{x} = 3[/tex] --- 3 is the constant of proportionality

(2.75 x 10⁵ ) / (2.25 x 10² )

= (2.75 / 2.25) x 10⁵⁻²

= 1.2 x 10³ times .

(That's 1,200 times as many.)

I hope this helps!

Answer:

1221.2 times more

Step-by-step explanation:

number of bacteria last week = [tex]2.25*10^2[/tex]

= [tex]2.25*100[/tex]

= [tex]225[/tex]

number of bacteria this week = [tex]2.75*10^5[/tex]

= [tex]2.75*100000[/tex]

= [tex]275000[/tex]

[tex]275000 - 225 = 274775[/tex]

[tex]274775 / 225 = 1221.2[/tex]

===================================================

Explanation:

Focusing on triangle ACD, we see that AC = 20 is the hypotenuse and AD =  20/2 = 10 is the short leg. The short leg is half that of the hypotenuse when working with 30-60-90 triangles.

Also, for these types of triangles, the long leg is sqrt(3) times that of the short leg. That makes CD = AD*sqrt(3) = 10*sqrt(3)

The opposite sides are the same length, meaning BC = AD and AB = CD.

-----------

The perimeter of rectangle ABCD is

P = AB+BC+CD+AD

P = 10*sqrt(3) + 10 + 10*sqrt(3) + 10

P = 20 + 20*sqrt(3)

P = 54.6410161513776

P = 54.6 cm is the approximate perimeter

Answer:

54.64 cm

Step-by-step explanation:

The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle. Perimeter of the given rectangle is a + b + a + b.

Length of CD = 17.32 cm from :

[tex] \sin(60) = \frac{cd}{20} \\ then \: x = 17.32 \: cm[/tex]

now CD = BA

Now we must determine length of AD :

[tex] \sin(30) = \frac{ad}{20} \: then \: ad \: = 10 \: cm[/tex]

Now :

perimeter = 17.32 + 17.32 +10+10 = 54.64 cm

Answer:

A1.) 87 + 63 =150

180 - 150 = 30

all the As is the same formula....

B1.) 180 - 123 = 57

57 + 82 = 139

180 - 131 = 41

Answer:

B. Symmetry

Step-by-step explanation:

They are symmetrical, meaning they are mirrored or both look the same.

Hope this helps! :)

Answer:

B.

Step-by-step explanation:

The opportunity cost means what Henry will be missing out on by not working at the library. He loses the chance to earn by working in a library.

Answer:

B.  The chance to earn by working in a library

Step-by-step explanation:

This is a guess

Answer:

Solution given:

letA=(10,-4)

B=(-2,-4)

centre[C](h,k)=[tex]\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)[/tex]

radius=[tex]\sqrt{(4-10)²+(-4+4)²}=6[/tex]units

we have

Equation of a circle is;

(x-h)²+(y-k)²=r²

(x-4)²+(y+4)²=36

or.

x²-8x+16+y²+8y+16=36

x²-8x+8y+y²=36-32

x²-8x+8y+y²=4

The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.

Answer:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]

Step-by-step explanation:

the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter

since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle

remember midpoint formula,

[tex] \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)[/tex]

let,

thus substitute:

[tex] \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)[/tex]

simplify addition:

[tex] \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)[/tex]

simplify division:

[tex] \rm\displaystyle M = \left( 4, - 4 \right)[/tex]

so the centre of the circle is (4,-4)

since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is

[tex] \displaystyle r = 4 - ( - 2)[/tex]

simplify which yields:

[tex] \displaystyle\boxed{ r =6}[/tex]

recall the equation of circle

[tex] \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

we acquire that,

therefore substitute:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} [/tex]

simplify:

[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]

and we are done!

also refer the attachment

(the graph is web resource of desmos)

Answer:

800 seconds or 13 minutes 20 seconds

Step-by-step explanation:

.......

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {50}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]12 + 16(5 \times 10) \div 20 - 2[/tex]

[tex] = 12 + 16(50) \div 20 - 2[/tex]

[tex] = 12 + \frac{800}{20} - 2[/tex]

[tex] = 12 + 40 - 2[/tex]

[tex] = 52 - 2[/tex]

[tex] = 50[/tex]

[tex]\sf\purple{PEMDAS\: rule.}[/tex]

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]

Answer:

Step-by-step explanation:

Answer:

Quadratic formula is the tool for solving for an unknown number (usually x)

Step-by-step explanation:

The formula is below

Answer:

Below.

Step-by-step explanation:

The formula, which gives the solutions of the equation, is

x = [-b ±√(b^2-4ac)]/2a.

- a, b and c are the coefficients of the quadratic equation

ax^2 + bx + c = 0.

Answer:

(f-g)(x)=4x^2+1-x^2+5

=3x^2+6

=3(x^2+2)

Answer:

2

Step-by-step explanation:

1/13 = 0.07692307692307

1/13 has a 6 place repeating decimal

076923   076923

2021/6 = 336 5/6

There will be 336 complete sets and then

2021 will be the 5th place of 076923

Answer:

(105 | 35)

the x-component (how much to the side) is left, the y-component right (how high)

The ordered pair that best estimates the time and cost at which the two stores charge the same amount is (110,35).

A graph can be defined as a pictorial representation of statistical data in graphical form. The points on the graph often represents the relationship between two or more things. The points are plotted in x-axis and y-axis respectively.

For the given situation,

The graph shows the time in x-axis and cost in y-axis.

Ordered pairs are often used to represent two variables.

The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.

From the graph, the point of intersection of x-axis and y-axis gives the the time and cost at which the two stores charge the same amount.

Thus the point of intersection is x at 110 and y at 35.

⇒ [tex](x,y)=(110,35)[/tex]

Hence we can conclude that the ordered pair that best estimates the time and cost at which the two stores charge the same amount is (110,35).

Learn more about graphs here

https://brainly.com/question/7563606

#SPJ2

Answer:

Step-by-step explanation:

mode is means the data which is repeated maximum number of times.

here 54 is repeated maximum number of times so the mode of the given data is 54.

to calculate median u must arrange the data from ascending to descending order.

37 , 42 , 48 , 51 , 52 , 53 , 54 , 54 , 55 ,

median = (N + 1) /2    (N means number of data)

=9 + 1/2

=10/2

=5 th term

=52

Answer:

C

Step-by-step explanation:

Perpendicular bisector of line segment AB

Answer:

36.5 mm²

Step-by-step explanation:

7.3 * 5 = 35 + 1.5 = 36.5 mm²

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Step-by-step explanation:

1,2,2,3,4,5,7

Median is 3

The median of 7, 2, 1, 4, 5, 2, and 3 stand 3 because when the numbers stand to put in order (1,2,2,3,4,5,7), the number 2 stands in the middle.

The median stands for the middle value in a list ranked from smallest to largest. The mode stands for the most frequently occurring value on the list. The middle number; exists found by collecting all data points and choosing out the one in the middle (or if there exist two middle numbers, taking the mean of those two numbers).

Illustration: The median of 4, 1, and 7 stand 4 because when the numbers stand to put in order (1, 4, 7), the number 4 stands in the middle.

The given data: 7, 2, 1, 4, 5, 2, 3

The median of 7, 2, 1, 4, 5, 2, and 3 stand 3 because when the numbers stand to put in order (1,2,2,3,4,5,7), the number 2 stands in the middle.

Therefore, the Median is 3.

To learn more about median

https://brainly.com/question/12279205

#SPJ2

Answer:

25.9 feet

Step-by-step explanation:

If you split a rectangle into 2 pieces with a diagonal, each piece will be a right triangle

Therefore we can use the pythagorean theorem to solve this problem

The two legs of the right triangle will be 23 and 12

The formula is a^2 +b^2=c^2

c^2 is the diagonal squared ( the hypotenuse)

So:

12^2+23^2=c^2

144+529=c^2

673=c^2

To find just c we need to find the square root of 673, rounded to the nearest tenth

[tex]\sqrt{673}=25.9[/tex]

(the equation is rounded)

So the diagonal is 25.9

Answer:

c

Step-by-step explanation:

Replacing x with 2, you get 5 as your answer

Answer:

[tex]y=4(3)^{x}[/tex]

Step-by-step explanation:

Let the exponential function is,

f(x) = (b)ˣ

If this function has the base (b) = 3, function will be.

f(x) = (3)ˣ

If this function is transformed by a vertical stretch by a factor of 4,

New function will be,

g(x) = 4(3)ˣ

If the function 'g' is reflected across y-axis, new function will be,

h(x) = g(-x)

h(x) = [tex]4(3)^{x}[/tex]

Therefore, equation of the function will be,

[tex]y=4(3)^{x}[/tex]

Answer:

24000ml or 24L

Step-by-step explanation:

wxhxl = volume

20cm x 30cm x 40cm = volume

volume = 24000cm3

1cm3 = 1ml

24000cm3 = 24000ml

1000ml = 1L

24000ml = 24L