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By taking some products we will see that the total number of cupcakes ordered is 6 cupcakes.

Here we want to see how many cupcakes this person is ordering. We know that orders 9 halves of a cupcake for the family, plus a quarter of a cupcake for each of the 6 friends.

The total number of cupcakes is given by the order for the family plus the order for the friends.

The order for the familiy is given by the product:

9*(1/2) = 9/2 = 4.5

That is 9 times 1/2 of a cupcake, so for the family the person orders 4.5 cupcakes.

For the friends the person orders 6 times 1/4 of a cupcake, so now we have the product:

6*(1/4) = 6/4 = 3/2 = 1.5

If we add these two numbers we get the total number of cupcakes:

4.5 + 1.5 = 6

The person ordered 6 cupcakes.

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Lucas will be using the shipping box D as it is the box with the greatest volume of 27ft³

The volume of a rectangular box is calculated by multiplying its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.

volume of box A = 5ft × 3ft × 1ft

volume of box A = 15ft³

volume of box B = 4ft × 2ft × 3ft

volume of box B = 24ft³

volume of box C = 7ft × 1ft × 2ft

volume of box C = 14ft³

volume of box D = 3ft × 3ft × 3ft

volume of box D = 27ft³

Therefore, the shipping box with the largest volume is box D with 27ft³

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Answer:

Step-by-step explanation:

FEEL ME ITS D

ITS D

THE ONE WITH THE 333

Answer:

f(2) = 0

Step-by-step explanation:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

Therefore, applying the factor theorem, if (x - 2) is a factor of a polynomial f(x) then f(2) = 0.

answer the answer is 200

Step-by-step explanation:

490-290

The liquid that Richard used in the punch is 1 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Richard made punch for a party. He used 1/2 cup of pineapple juice, 1/2 cup of ginger ale, and 1/4 cup of white grape juice.

The total fraction will be:

= 1/2 + 1/2 + 1/4

= 1 1/4 cups.

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The value of each term is

The length of the line ED = 45 units

The length of the line DF = 27 units

The length of the line EF = 36 units

Here we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

Substitute the value in the equation

sin D = Opposite side / Hypotenuse

= 36/45

= 4/5

sin E = Opposite side / Hypotenuse  

= 27/45

= 3/5

cos D = Adjacent side / Hypotenuse

= 27/45

= 3/5

cos E = Adjacent side / Hypotenuse

= 36/45

= 4/5

Hence, the value of each term is  

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The correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

According to the question,

We have the following information:

[tex]64x^{3} +8[/tex]

The factors of this expression can be found using identity because 64[tex]x^{3}[/tex] is the whole cube of 4x and 8 is the cube of 2.

So, we have the following expression:

[tex](4x)^{3} + 2^{3}[/tex]

Now, we can use the following identity to factor the given expression:

[tex]a^{3} +b^{3} = (a+b) (a^{2} -ab+b^{2} )[/tex]

We have a = 8x and b = 2:

(8x+2) {[tex](4x)^{2}[/tex]-16x+[tex]2^{2}[/tex]}

(8x+2) (16[tex]x^{2}[/tex]-16x+4)

Taking 4 as the common factor from the second bracket:

4(8x+2) (4[tex]x^{2}[/tex]-4x+1)

Now, finding the factors of second bracket:

4(8x+2) ([tex]4x^{2}[/tex]-2x-2x+1)

4(8x+2) {2x(2x-1)-1(2x-1)}

4(8x+2) (2x-1) (2x-1)

4[tex](2x-1)^{2}[/tex] (8x+2)

Hence, the correct factorization of the expression, [tex]64x^{3} +8[/tex], is 4[tex](2x-1)^{2}[/tex] (8x+2).

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Answer:

96, $ 144

Step-by-step explanation:

Answer:

p = 20

Step-by-step explanation:

[tex]\rm \implies \dfrac{p}{2} - 9 = 1 \\ \\ \rm \implies \dfrac{p}{2} - 9 + 9 = 1 + 9 \\ \\ \rm \implies \dfrac{p}{2 } = 10 \\ \\ \rm \implies \dfrac{p}{ \cancel{2}} \times \cancel{2} = 10 \times 2 \\ \\ \rm \implies p = 20[/tex]

The numbers are plotted in the attached graph.

A number line is a representation of real numbers in the form of a graded straight line.

Note that 5/3 is approximately equal to 1.7.

Similarly, -5/3 is approximately equal to -1.7.

Now, use the number line to mark the points -1.7 and 1.7, the numbers lie near -2 and 2 respectively.

The numbers are plotted in the attached graph.

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Answer: b

Step-by-step explanation:

Answer:

30 divided by 0.08 will get you 375

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

2(x+5) =20  Distribute the 2

2(x) + 2(5) = 20

2x + 10 = 20  Subtract 10 from both sides of the equation

2x = 10  Divide both sides by 2

x = 5

Answer:

5

Step-by-step explanation:

2(x + 5) = 20 Divide both sides by 2

x + 5 = 10

x = 10 - 5

x = 5

Answer:

Step-by-step explanation:

3/5 pool/hr * 10hr = 6 pool

By using unitary method it is obtained that -

Scale used my Colton = 1 : 500

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here unitary method is used

18 mm long field in the drawing is equivalent to 9000 mm long field in real

1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real

1 mm long field in the drawing is equivalent to 500 mm long field in real

Scale used by Colton 1 : 500

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how long does it take Peter to clean a room by himself is[tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
What does "rate" mean mathematically?

A rate is a unique ratio where the two words are expressed in several units.

Let Peter take time to clean 1 room be = t
Let Parker take time to clean 1 room be = t+15
Total Time taken by both to clean to room T= 110
Equation for total time taken to clean 2 room by both
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{T}[/tex]

[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{110}[/tex]
By taking LCM

[tex]\frac{2t+15}{t^{2}+15} =\frac{1}{55}[/tex]
By cross multiplication in above equation

[tex]110t+825=t^{2} +15t[/tex]
[tex]t^{2}-95t-825=0[/tex]

Hence the answer is   [tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]

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Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

Subtract 7 from both sides.

Subtract -7 from −3 to get −10.

Divide both sides by −2. Since −2 is negative, the inequality direction is changed.

Divide −10 by −2 to get 5.

The value of the angle regarding the parallel lines are:

1. x = 14

2. x = 9

3. x = 17

4. x = 5

1. Lines 'l' and 'm' are the parallel lines and a transversal line is intersecting these  lines.

(9x + 13)° = (12x - 29)° [Alternate interior angles]

9x - 12x = -29 - 13

-3x = -42

Divide

x = 14

2). By substituting x = 14 in the box.

(13x + 5)° + (8x - 14)° = 180° [Consecutive interior angles]

21x - 9 = 180

21x = 189

Divide

x = 189/21

x = 9

3). By placing x = 9 in the box,

(5x + 52)° = (9x - 16)° [Corresponding angles]

5x - 9x = -52 - 16

-4x = -68

x = 17

4). By placing x = 17 in the box,

(10x + 17)° = (12x + 7)° [Alternate exterior angles]

10x - 12x = -17 + 7

-2x = -10

x = 5

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There are 255 students who prefer Movie C.

In the given case, the total number of students in the campus = 900

Number of students in the random sample :

= 31 + 27 + 34 + 28

= 120

Number of students who prefer to watch movie C in the chosen sample:

= 34

To get number of students who would prefer to watch the movies C in the total population of 900, we can extrapolate the data from the chosen sample to the entire population.

Thus, number of students expected to prefer movie C in the campus =

34/120 × 900

= 255

Hence the expected number of students are 255.

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Answer:

Step-by-step explanation:

the answer is "downward". If you say "why", it is because of the degree coefficient.

in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.

The domain of the function is [ - 6 , ∞ ]

A radical function is the one provided.

It should be noted that a radical function can only be specified for values that will result in the radicand being larger than or equal to zero.

As a result, either the radicand of the provided function must be larger than or equal to zero, or:

Thus we can write it as

x + 6 ≥ 0

subtract 6 from both LHS and RHS

x + 6 - 6 ≥ 0 - 6

x ≥ - 6

Therefore the domain of the function is [ - 6 , ∞ ]

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Answer:

321 is the next number that comes in the calculator.

The product of two numbers exists done by multiplying a number with the other. The product of a number x and 7 exists 7x.

The result of multiplying two or more numbers together is known as a product in mathematics. A number that is obtained by multiplying two or more other numbers together is referred to in mathematics as a product.

The outcome of one or more multiplications is referred to as a "product." For instance, the mathematical statement "times equals" would be written with the multiplier, the multiplicand, and their product as the variables.

Let the variable be x

x be a number

So, the product of x and 7 exists calculated as:

Product = 7 × x

Product = 7x

Therefore, the product of a number (x) and 7 exists 7x.

The complete question is:

The product of a number and 7

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The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.

From the given figure, we need to identify the corresponding angles.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

From the figure, ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7 are the corresponding angles.

The corresponding angles form the given figure are ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8 and ∠3 and ∠7. Therefore, option D is the correct answer.

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Answer:   6

Step-by-step explanation:   You'll need to substitute x for 12 in the expression, which will be 12 - 2 + 2(4) - 12, and using BODMAS/BIDMAS/PEDMAS (or whatever you use), you should get 6 if you did it correctly.

Answer:

18

Step-by-step explanation:

using bodmas rule by working out brackets first

Answer: (7, 12)

Step-by-step explanation:

The x-coordinate is 7.

The y-coordinate is 12.

Thus, the coordinates are (7, 12).

The solution of the equation 2(x + 1) = 6(x – 1), is the value of x = 2.

To solve an equation means to find what the value of the variable of the equation would be that would make the equation true if the value of the variable is plugged into the equation.

The necessary steps taken to find the value of x in the equation, 2(x + 1) = 6(x – 1) are explained below:

2(x + 1) = 6(x – 1) [given]

Apply the distributive property

2x + 2 = 6x - 6

Combine like terms

2x - 6x = -2 - 6

-4x = -8

Divide both sides by -4

-4x/-4 = -8/-4

x = 2

The value of x is 2. To check the solution, plug in the value of x back into the equation:

2(2 + 1) = 6(2 – 1)

2(3) = 6(1)

6 = 6 [true]

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