Solve the inequality. Graph the solution. 3x≤−54

The most appropriate choice for LCM will be given by

He can make 162 treat bags using all the candy.

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

Number of Snicker bars = 81

Number of kitkat bars = 54

Brown wants  to use all of the candy by making as many identical bags as possible.

Number of treat bags  he can make using all of the candy = LCM of 81, 54

81 = 3 x 3 x 3 x 3

54 = 2 x 3 x 3 x 3

LCM = 3 x 3 x 3 x 3 x 2

        = 162

He can make 162 treat bags using all the candy.

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Answer:

c = 5

k = 3

Step-by-step explanation:

We have the expression:
(3+√c) (2√c - 3) = 1 + k √c

Expanding the LHS using the FOIL method =>
(3 + √c) (2√c -3)

= (3)(2√c) + 3(-3) + (√c)(2√c) -√c(3)

= 6√c -9 + 2(√c)² -3√c

= 3√c + 2c - 9                  [(√c)² = c]

Setting this equal to the RHS of 1 + k√c gives us

3√c + 2c - 9  = 1 + k √c

Since c and k are prime numbers, √c is irrational.

Therefore we match the irrational terms to get
3√c = k√c

=> k = 3      [divide both sides by √c]

Substitute k = 3 into 3√c + 2c - 9  = 1 + k √c

=> 3√c + 2c - 9 = 1 + 3√c

Add 9 to both sides
=> 3√c + 2c - 9 + 9 = 1 + 9 + 3√c

=> 3√c + 2c - 0 = 10 + 3√c

Subtract 3√c from both sides to eliminate this term on both sides
=> 3√c - 3√c + 2c - 0 = 10 + 3√c  3√c

=> 0 + 2c = 10 + 0

=> 2c = 10

Dividing by 2 on both sides gives us
c = 5

Answer: c = 5, k = 3

Part (a)

[tex]C=\pi d \implies d=\frac{C}{\pi}[/tex]

Part (b)

[tex]d=\frac{8}{\pi}[/tex]

A graph of the linear equation (2x - 4y = 0) is shown in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

Generally speaking, the graph of any proportional relationship such as a linear equation is characterized by a straight line because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously as shown in the image attached below.

In conclusion, a graph which represents the linear equation (2x - 4y = 0) shows a proportional relationship between the value of x and y.

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Answer:

[tex]\sf y = \dfrac{5}{2}x +\dfrac{17}{2}[/tex]

Step-by-step explanation:

 [tex]\sf y =\dfrac{5}{2}x+1[/tex]

  m= 5/2

Parallel lines have same slope.

      Slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept

[tex]\sf y = \dfrac{5}{2}x + b[/tex]

Point (-3,1) passes through the required line. Substitute (-3,1) in the above equation and find 'b'.

        [tex]\sf 1 = \dfrac{5}{2}*(-3)+b\\\\1 =\dfrac{-15}{2}+b\\\\[/tex]

 [tex]\sf 1 +\dfrac{15}{2}=b\\\\\dfrac{2+15}{2}=b\\\\\\ \boxed{b= \dfrac{17}{2}}[/tex]

  [tex]\sf \bf y = \dfrac{5}{2}x+\dfrac{17}{2}[/tex]

Answer:

the answer to number 2 is: y=-4x-26

The answer to number 3 is y=5/2x+54

Step-by-step explanation:

The probabilities listed here, in percent form and rounded to the fourth decimal place, are 29.9474 for a 5-card poker hand.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

According to given information;

C(4,3)C(48,2)/C(52,5) - 3 of 4 aces, 2 of 48 non-aces 0.1736%

C(13,5)/C(52,5) - 5 of 13 spades 0.0495%

There are 4 face cards, ace, king, queen, jack, and 4 suits for each. 16 face cards, and 36 non-face cards - C(16,3)C(36,2)/C(52,5) 13.5747%

There are 44 cards that are not aces or kings - C(4,2)C(4,2)C(44,1)/C(52,5) 0.0609%

There is 1 jack and 48 non-jacks C(4,1)C(48,4)/C(52,5) = 29.9474%.

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To write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .

As given in the question,

Given number in decimal form is equal to 5.36

5 is the whole number and 0.36 can be written as 36 /100.

Mixed number of the given number 5.36 is equal to

= 5 ( 36 / 100)

Reduced the mixed number to get the simplest form :

5 ( 36 / 100)

= 5 ( 9 / 25)

= 134 / 25

Therefore, to write a given number 5.36 in the mixed number is [tex]5\frac{36}{100}[/tex] and in the simplest form it is written as 134 / 25 .

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Answer:

Step-by-step explanation:

5(1 − n) + 3n = 3(n − 1) – 5n

5 - 5n + 3n = 3n - 3 - 5n

5 + 3 = 5n - 3n + 3n - 5n

8 = 0

this equation is always false

The rate of the slow hike is 2.2 mph and the rate of the faster hiker is 4.4 mph.

Here in this issue, we are managing linear equations which is a condition of one variable regularly composed within the form ax+b=0 , where a and b are real numbers and x is an unknown variable. Solutions to linear equations allude to a linear equation that can have zero, one, or infinitely various solutions. A linear equation with no solutions simplifies to an untrue statement such as 1=0. A linear equation with one solution rearranges to a solution of the form x=n where n may be a real number. A Linear equation with infinitely various solutions simplifies to a true statement without a variable such as 1=1.

Here we  considering  the rate of the slow hiker  to be x, so the rate for the fast hiker will be x+2.2

Since we know that  distance = speed * time

therefore, the Distance covered in 5 hours by a slow hiker is 5x , wheras for fast hiker it will be 5(x+2.2)=5x+11 km

As we are given the condition that it i they are  33 miles apart, So

=>5x + 5x+11 = 33

=>10x = 33-11

=>10x = 22

x =22/10 => 2.2

So the rate of a slow hiker is 2.2 mph and the rate of a fast hiker is   x+4.4= 4.4 mph.

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Using proportions, the number of planes in each city after 8 hours is given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division, with the given ratios.

One example of application of proportions is for percentage problems, as the total amounts are multiplied by the decimal equivalent of the percentage to find the equivalent amounts.

The planes in Los Angeles after 8 hours are given as follows:

Hence the amount is:

0.7 x 30 + 0.25 x 12 + 0.125 x 8 = 25.

The planes in St. Louis after 8 hours are given as follows:

Hence the amount is:

0.2 x 30 + 0.25 x 12 + 0.5 x 8 = 13.

Initially, there were 50 planes, and 25 + 13 = 38 are in either Los Angeles or St. Louis, hence the remaining 50 - 38 = 12 are in Dallas.

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Answer:

( 3+ 4 + 5 ) °

=(3+9)°

=(12)°

C is the answer

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Every radical can be rewritten has an exponent .

Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number).

1. Exponents that are written as fractions are referred to as rational exponents.

The top of the rational exponent is the new exponent on the radical, and the bottom of the rational exponent is the root, therefore a rational power can be reinterpreted as a radical in this fashion.

2. Separate the radical expression from the equal sign on one side. Put every every clause over there on the other side. Square both sides of the equation if the radical is a square root. Raise both sides of the equation to the third power if it is a cube root. Write an expression as a radical if the expression has a logical exponent. By examining the exponent's numerator, you may determine the power. By examining the exponent's denominator, you can get the root. Raise the radicand to the power while using the base as the radicand, and use the root as the index.

3. Extraneous Solutions appear because there are two solutions when you square the two sides of a square root equation (the positive and negative number). As a result, one of those figures will represent an extra solution, or a solution that is added but does not satisfy the initial equation.

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D

Step-by-step explanation:

....................

The required equation is 99 + 19 h = t  .

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

Given: Total cost = t

and the number of hours the vehicle is used = h hours

Since $99 is supposed to given that is, it is mandatory.

And $19 is supposed to be paid for per hour use.

Thus the equation is ;

99 + 19 h = t  ; where t is total cost and h is number of hours the vehicle is used

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The simple interest of the sum at the same rate and time is 2400

The interest that is paid on the principal and interest at regular intervals is known as compound interest.The difference between compound interest and simple interest starts to show after the first year, though.Beginning with the second year, interest is computed on both the principal amount and the interest from the prior year. As a result, interest on interest is another name for it.

Given that : Sum =8000 and time = [tex]\frac{3}{2} years[/tex] and rate is 20 %

When rate is calculate half yearly

R becomes [tex]\frac{R}{2}[/tex]

T becomes 2T

A = [tex]P(1+\frac{R}{100} )^{T}[/tex]

C.I = A-P

R = [tex]\frac{20}{2} = 10%[/tex]%

T = 2× [tex]\frac{3}{2} years[/tex] = 3years

A = [tex]P(1+\frac{R}{100} )^{T}[/tex]

A = 8000[tex]\frac{11}{10} ^{3}[/tex]

A = 8 ×1331

A = 10648

Now ,

C.I = A - P

C.I =10648 - 8000

C.I = 2468

The compound interest is 2468

Simple interest

A = P(1+rt)

A = 8000(1+0.2×1.5)

A =10400

S.I =A- P

= 10400 - 8000

=2400

The simple interest of the sum at the same rate and time is 2400

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Explanations :

(a) (x;y) →(x-3 ; -y+2 ) ; this preserves the lengths of the side, with a reflection across the x -axis .

(b) (x;y) →(2x +1 ; y-5 ); this does not preserve the length of sides, because the 2 multiply by x will change the length by factor of 2 .

(c) (x;y) → (-x+6 ;-y -8 ), preserves the lengths of sides, with reflection of y = -x .

(d) (x;y) →(-x -5 ; y+10 ) preserves the lenghts of the sides , with a reflection in the y -axis .

Answer:

<CPB

Step-by-step explanation:

Because <APE= right angle

<APC= Obtuse angle

<CPE= Obtuse Angle.

Also, <CPB because its the only angle below 90 degrees and an acute angle must be below 90 degrees.

The  equation which represents the amount is p = 0.0625 t.

When a consumer buys a good or service from a retailer, sales tax, which is estimated as a percentage, is added to the cost of the item.

Sales tax rate = sales tax percent / 100.

Sales tax = list price * sales tax rate.

Total price including tax = list price + sales tax,

Total price including tax = list price + (list price * sales tax rate),

Total price including tax = list price * ( 1 + sales tax rate)

We have been given

sales tax rate = 6.25%.

The price of the item = p

The sales tax = t

We know that the amount of sales tax paid on a purchase is proportional to the price of the item.

p = 6.25% t

p = 6.25/100 t

p = 0.0625 t.

Hence , P = 0.0625 t is the equation used to represent the amount.

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The function is decreasing.

The domain is the set of x-values.

The range is the set of y-values.

Answer:

70

Step-by-step explanation:

Answer:

x° = 100°

Step-by-step explanation:

Straight line angles add up to be 180°

Angles opposite eachother aka "vertical angles" are the same measurements.

Answer:

102 squared in.

Step-by-step explanation:

the shaded area is the whole shape minus the unshaded shape.

calculating the whole shape area:

make sure you add all the width together and then all the height together before multiplying

(10+4) x (3+6) = 14 x 9 = 126 squared in.

calculating the unshaded shape area:

6 x 4 = 24 squared in.

based on the logic from my first sentence in this explanation:

126 - 24 = 102 squared in.

Answer:

angle ODC=30°

Step-by-step explanation:

Parallel to the line now draw another line PQ

Based on table shown above, we have that: A. Yes, the table describe a function.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Based on table shown above, we have the following parameters:

Input value       Output value

2001                         30

2002                        60

2003                        30

2004                        50

2005                        40

In conclusion, we can reasonably infer and logically deduce that this table is a function because it has the different input values (x-values) for different or the same output values (y-values).

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The correct option a = 18 and b = 0, described the complex number 18.

For the given question.

Let R be the rational number.

All rational numbers can be written as complex numbers in the form;

R =  a +bi

Where 'a' is the real part and 'ib' is the imaginary part.

The number 18 can be written as;

18 + 0i = 18

As, in number 18 only real part is there.

Thus, a = 18 and b = 0 are correct expression for describing number 18.

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Answer:

No, the reasoning is not correct.

Step-by-step explanation:

39.99 x .14 = 5.5986  Does it make sense that the sales price plus the tax would be $5.60?  Doesn't that seem really low?

39.99 x .3  = 11.997 is the amount that we are taking off of the original price.

39.99 - 12 (Rounded to the nearest cent) is 27.99.

Now we pay the tax on the discounted amount of the item.  

27.99 x .16 = 4.4784 or 4.48 rounded to the nearest cent.

The out the door cost of the item

is 27.99 + 4.48 = 32.48

Plug in 3 in the place of x and simplify

[tex]y=(3)^{2} \\y=3*3\\y=9[/tex]

y=9

They way you can change the grouping of the addends. in $5.50+$7.83+$3.50 is;  $5.50 + ($7.83 + $3.50) =  ($5.50 + $3.50) + $7.83

There are different algebraic properties such as;

Commutative Property

Associative Property

Distributive Property

Now, the commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product. For example;

a + b + c = c + a + b or a* b = b * a

Now, the associative property states that the way in which factors are grouped in a multiplication or addition problems does not change the product. For example; x + (y + z) = (x + z) + y

Now, to our question, one way to group the addends using associative property is;

$5.50 + ($7.83 + $3.50) =  ($5.50 + $3.50) + $7.83

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