Adding -6 is the same as:

Answer:

3(c+30)+4(c+30), 7c + 210, 3c+90+4c+120

Step-by-step explanation:

I this helps :D

Answer:

I think it's the first one

Step-by-step explanation:

because he went to class 3 times a week and u would need to multiply 3 by c minutes + 30 minutes ( u have to add them to find the total amount of minutes he exercised during one class and multiply that by 3 after adding them together bc he did that class 3 times which means he did the exercise 3 times so u multiply) then u add that with next week where he went 4 times and did c minutes+ 30 minutes. HOPE THIS HELPS!

Answer:

3 3/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

subsitute x with value given in bracket

a) f(1) = (1)²  + 1 = 2

b) f(-3) = (-3)² + 1 = 10

c) f(b³) = (b³)² + 1 = b^6 + 1

d) f(x-1) = (x-1) +1 = x

81 is equivalent to 3^4

What Is the Power of a Number?

The power of a number stands for how many multiples of the number there are. The power of a number is represented by something called an exponent

When a number is "raised to the second power," it means that the number is multiplied together twice, for example. When a number is "raised to the fifth power," it means that it is multiplied together five times.

we have to solve 3^4

here 3 raised to the fourth power

then 3 is multiplied together 4 times

3*3*3*3

81

Hence ,81 is equivalent tp 3^4

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first off let's keep in mind that an absolute value is really a ± equation in disguise, so |5x -4| can pretty much be rewritten as ±(5x - 4), so is a dual equation, let's solve both for "x".

[tex]|5x-4|\leqslant 3x\implies \pm(5x-4)\leqslant 3x \\\\[-0.35em] ~\dotfill\\\\ +(5x-4)\leqslant 3x\implies 5x-4\leqslant 3x\implies 2x-4\leqslant 0\implies 2x\leqslant 4 \\\\\\ x\leqslant \cfrac{4}{2}\implies {\LARGE \begin{array}{llll} x\leqslant 2 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]-(5x-4)\leqslant 3x\implies (5x-4)\stackrel{\stackrel{notice}{\downarrow }}{\geqslant} -3x\implies 8x-4\geqslant 0 \\\\\\ 8x\geqslant 4\implies x\geqslant \cfrac{4}{8}\implies {\LARGE \begin{array}{llll} x\geqslant \cfrac{1}{2} \end{array}}[/tex]

Check the picture below.

Python is a computer programming language often used to build websites and software, automate tasks, and conduct data analysis. Python is a general-purpose language, meaning it can be used to create a variety of different programs and isn't specialized for any specific problems.

Python 3 code:

function to print the numbers in list

def print_list(List):

 for entry in List:

   print(entry)

function to print the numbers and squares in list

def print_squares(List):

 for entry in List:

   print("Square of ", entry, " = ", entry*entry)

Call the functions now

input_list = [12,10,32,3,66,17,42,99,20]

print_list(input_list)

print_squares(input_list)

Sample Output:

12 10 32 3 66 17 42 99 20 Square of  12  =  144 Square of  10  =  100 Square of  32  =  1024 Square of  3  =  9 Square of  66  =  4356 Square of  17  =  289 Square of  42  =  1764 Square of  99  =  9801 Square of  20  =  400

Python 2.7 code:

function to print the numbers in list

def print_list(List):

 for entry in List:

   print entry

function to print the numbers and squares in list

def print_squares(List):

 for entry in List:

   print "Square of ", entry, " = ", entry*entry

Call the functions now

input_list = [12,10,32,3,66,17,42,99,20]

print_list(input_list)

print_squares(input_list)

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Answer: -26

Step-by-step explanation:

5 x -6 = -30

-30 + 4 = -26

5(-6) + 4 = -26

Answer:

A = 1160

B = 1160 is already in standard form.

C = 1200

The number of movies that would make the monthly cost equal is 4.

The total monthly cost is a function of the cost per month, total movies watched and the cost per movie.

The equations that represent the total cost of using the streaming sites would be in the form:

Total cost = cost per month + (number of movies watched x cost per movie)

Plan 1: $22 + ($x)

Plan 2: $14 + (3x)

When both plans have the same monthly cost, the two above equations would be equal

$22 + x =$14 + 3x

In order to determine the value of x, take the following steps:

Combine similar terms: $22 - $14 = 3x -x

Add similar terms together: $8 = 2x

Divide both sides of the equation by 2: $8 /$ 2 = x

x = 4

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By graphing the equation y = 0.2x, we find that x is equal to -10 when y is -2, x is equal to 0 when y is 0, and x is equal to 10 when y is 2.

To graph the equation y = 0.2x, we can plot a few points and then connect them to create the line.

Let's calculate the corresponding values of x when y takes on the values of -2, 0, and 2:

When y = -2:

-2 = 0.2x

x = -2 / 0.2

x = -10

When y = 0:

0 = 0.2x

x = 0 / 0.2

x = 0

When y = 2:

2 = 0.2x

x = 2 / 0.2

x = 10

Using these values, we can plot the points (-10, -2), (0, 0), and (10, 2) on the coordinate plane. Drawing a line passing through these points, we obtain the graph of the equation y = 0.2x.

The graph will be a straight line that passes through the points (-10, -2), (0, 0), and (10, 2). The line will have a positive slope, indicating that as x increases, y increases at a slower rate.

The graph visually represents the relationship between x and y according to the equation y = 0.2x. It shows that for every increase of 1 unit in x, y increases by 0.2 units.

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Answer:1.c 2.b 3.a

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

(LHS) cos 6∘ cos 42∘ cos 66∘ cos 78∘

1/4 [cos(66∘+6∘) = cos(66∘-6∘)] • [cos(78∘+42∘)+cos(78∘-42∘)]

= 1/4(sin18∘+12)(-12+cos36∘)

[∵cos72∘ = cos(90∘−18∘) = sin18∘]

1/4[(5-√-1)/4+1/2][−1/2+(5-√+1)/4]

[∵sin(18∘ = (5-√-1)/4, and, cos 36∘ = (5-√+1)/4]

1/4(5-√+1)/4(5-√-1)/4 = (5-1)/64

= 4/64 = 1/16 (RHS)

Therefore, the cosine is equal to 1/16.

Answer:

The answer is 2, and thanks for asking my day's good :D
How's your day?

Step-by-step explanation:

The probability that a hand of five cards chosen at random and without replacement from a standard 52 card deck will have a king of spades, exactly one other king, and exactly two queens = 0.000332

A deck of cards consist of 52 cards in which each 13 cards are from 4 suits: Spades, Hearts, Diamonds and Clubs.

Each suit consist of cards Ace, King, Queen, Jack and other 9 cards.

So in 52 cards there is 4 kings and 4 queens each.

Five cards are selected at random and without replacement.

Five cards from a 52 deck cards can be chosen in 52C5 ways.

A spade king can be chosen in 1C1 way. [ Since there is only one spade king]

Exactly one other king can be chosen in 3C1 ways. [Since now only 3 kings are remaining after choosing 1 spade king]

Exactly 2 queens can be chosen in 4C2 ways.

Now 4 cards are selected out of 5. The remaining 1 card is chosen out in 48C1 ways.

So the probability that the five cards chosen will have a king of spades, exactly one other king, and exactly two queens

                           = (1C1 x 3C1 x 4C2 x 48C1) /52C5 = 18/54145 =0.000332

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The variable in the expression is g.

The coefficient of g is 10.

The constant term is 12.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

g + 12 + 9g

Add the like terms.

10g + 12

Now,

The variable in the expression is g.

The coefficient of g is 10.

The constant term is 12.

Thus,

The coefficient is 10.

The constant is 12.

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The coordinates are  A'(14, 3), B'(-6. 2) and C'(-8, 6)

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

given rule:

(x,y) -> (2x,y-3)

Also, we have

A(7,6), B(-3,5), and C(-4,9)

so, after applying the rule we have the coordinates

A'(14, 3)

B'(-6. 2)

C'(-8, 6)

Hence, the coordinates are A'(14, 3), B'(-6. 2) and C'(-8, 6)

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Answer:

10x + x^4/x-2

Step-by-step explanation:

Combine like terms

(10x + x^4)/(x-2)

The angle with the name JWT is option (b)

The name of the angle is given as

JWT

The above means that

Two lines JW and WT intersects at point W

The point of intersection of these lines is the name of the angle

From the list of given option, we have option (b) that has the above property

Hence, the angle with the name JWT is option (b)

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The midpoint and length of the points J(4,3) and K(2,-3) is calculated as (1,0) and 40.

The midpoint and length of the points L(-4,5) and N(5,-3) is calculated as (-12,1) and 145.

Given : The endpoints J(4,3) and K(2,-3) and L(-4,5) and N(5,-3)

We need to find the midpoint and length of these endpoints.

The formula for midpoint is x1+x22, y1+y22

From the first endpoints,  x1=4 , y1=3 , x2=2 , y2=-3

4+22, 3-32 => (22,02) => (1,0)

So, the midpoint for the endpoints is (1,0)

The formula to find the length is (x2-x1)2+(y2-y1)2

From the first endpoints , the length becomes

(2-4)2+((-3)-3)2=> (-2)2+(-6)2 => 4+36 => 40

The formula for midpoint is x1+x22, y1+y22

From the first endpoints,  x1=-4 , y1=5 , x2=5 , y2=-3

-4+52, 5-32 => (-12,22) => (-12,1)

So, the midpoint for the endpoints is (-12,1)

The formula to find the length is (x2-x1)2+(y2-y1)2

From the first endpoints , the length becomes

(5+4)2+((-3)-5)2=> (9)2+(-8)2 => 81+64 => 145

Hence, the midpoint and the length from the endpoints is calculated and determined.

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Answer:

x = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

4x - 10 = - 6x - 2 ( add 6x to both sides )

10x - 10 = - 2 ( add 10 to both sides )

10x = 8 ( divide both sides by 10 )

x = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]

Answer:

9222.23333 is the value good sir :)

Step-by-step explanation:

Time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

As given in the question,

Speed of a truck=60mph

⇒60 minutes = 60miles

⇒14 minutes = (60/60)×14

                     = 14 miles

Car speed =67mph

67 miles=60minutes

⇒1miles = (60/67) minutes

⇒14miles = (60/67)×14

                ≈12.54 minutes (approximately)

Therefore, time taken by car to pass the truck in the same direction from the time the car enters the highway is approximately12.54 minutes with a truck speed 60mph and a car 67mph.

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Answer:

[tex]y _{ \rm parallel} = - 5x +27[/tex]

Step-by-step explanation:

The equation of line p is in point-slope form , that's

[tex]y-y_1=m(x-x_1)[/tex]

Where:

Since line I is parallel to the line p , line I has the same slope as p. From the given equation of p , we can consider the slope of line p -5. Hence the slope of line I is also -5.

Now To determine the equation of I.

We have

So, the equation of line l is

[tex] y - 47 = - 5(x - ( - 4)) \\ \implies y - 47 = - 5 x- 20 \\ \implies \boxed{y _{ \rm parallel} = - 5x + 27}[/tex]

And we're done!

7) (x, TU, TB) = (4, 8, 13)

9) (x, RS, MN) = (8, 41, 41)

11) (AB, BC, AC) = (42, 42, 84)

In this question we have three cases of colinear line segments, each of them can be solved by using definitions from Euclidean geometry and algebraic handling:

Case 7 - TU = 2 · x, UB = 3 · x + 1, TB = 21

TB = TU + UB

21 = 2 · x + 3 · x + 1

21 = 5 · x + 1

5 · x = 20

x = 4

Then, the lengths of each line segment are:

TB = 21

TU = 2 · 4

TU = 8

UB = 3 · 4 + 1

UB = 13

The solutions are (x, TU, TB) = (4, 8, 13).

Case 9 - RS = 3 · x + 17, MN = 7 · x - 15

RS = MN

3 · x + 17 = 7 · x  - 15

4 · x = 32

x = 8

And the lengths of each line segment are:

RS = MN = 41

The solutions are (x, RS, MN) = (8, 41, 41).

Case 11 - AB = 2 · x - 8, BC = x + 17

AB + BC = AC

AB = BC

2 · x - 8 = x + 17

x = 25

And the lengths of each line segment are:

AB = 2 · 25 - 8

AB = 42

BC = AB

BC = 42

AC = 42 + 42

AC = 84

The solutions are (AB, BC, AC) = (42, 42, 84).

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The expressions that represents the vertical distance between the top of the mango tree and the tips of its roots is C. None of the above.

It should be noted that the mango tree stands 2.6 meters above the ground. Its roots extend 7/5 meters below the ground.

In this case, the vertical distance will simply be the difference between the values that are given.

This wasn't written on this case.

Therefore, the correct option is C.

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Answer:

(i)  2² · 3 · 7

(ii)  3024

(iii) k = 16

(iv) 12 cm

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 84, start by dividing 84 by the first prime number, 2:

⇒ 84 ÷ 2 = 42

As 42 is not a prime number, we need to divide again:

⇒ 42 ÷ 2 = 21

As 21 is not a prime number, we need to divide again.  

21 is not divisible by 2, so let's try dividing by the next prime number, 3:

⇒ 21 ÷ 3 = 7

As 7 is a prime number, we can stop.

Therefore, 84 is the product of:

⇒ 84 = 2 · 2 · 3 · 7

As 2 appears two times, we can write this using exponents:

⇒ 84 = 2² · 3 · 7

Lowest Common Multiple (LCM):  The lowest multiple shared by two or more numbers.

Prime Factors Method of finding LCM

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf LCM & = & 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3 &\cdot & 7\end{array}[/tex]

Step 3

Bring down the primes in each column then multiply the factors to get the LCM:

⇒ LCM = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7

⇒ LCM = 2⁴ · 3³ · 7

⇒ LCM = 3024

From part (ii) we know that the prime factorization of 432 is:

432 = 2⁴ · 3³

A perfect cube is a number multiplied by itself three times.

One of the factors of 432 is a perfect cube → 3³.

Therefore,

[tex]\begin{aligned}432 & = 2^4 \cdot 3^3\\\\\implies \dfrac{432}{2^4} & = 3^3\\\\\dfrac{432}{16} & = 3^3\end{aligned}[/tex]

So we need to divide 432 by 2⁴ to get the perfect cube 3³.

Therefore,

⇒ k = 2⁴

⇒ k = 2 · 2 · 2 · 2

⇒ k = 16

To find the largest possible length of the side of the square, we need to find the greatest common factor of 432 and 84.

Prime Factors Method of finding GCF

Step 1

Find the prime factorization of each number.

From part (i):            84 = 2² · 3 · 7

Given in part (ii):    432 = 2⁴ · 3³

Step 2

Write each number as a product of primes, matching primes vertically where possible:

[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf GCF & = & 2 & \cdot & 2 & \cdot & & & & & 3& & & & && \end{array}[/tex]

Step 3

Bring down the primes in the columns where both numbers have the factor, then multiply the factors to get the GCF:

⇒ GCF = 2 · 2 · 3

⇒ GCF = 12

Therefore, the largest possible length of the side of the square is 12 cm.

Answer: 18

Step-by-step explanation:

12 divided by 2 = 6

6 x 3 = 18

Answer:

the answer is 18

Step-by-step explanation:

this is because 12 divided by 2 = 6

6 x 3 = 18

Answer:

Step-by-step explanation:

2/5 or 4/10 or 8/20 or 16/40