Problem 4
(a) three friends are packing sweets into gift boxes. they agree that
each box should contain the same number of sweets, but they are
each working in separate locations with their own pile of sweets so
cannot share boxes. gwen has 286 sweets, bill has 390 sweets and
zeta has 468 sweets. if they put the largest number of sweets into
each box that they can and they use up all their sweets, how many
boxes of sweets will they pack?
(b) use the euclidean algorithm to find the highest common factor of
8008 and 24255 (you need to show all working).

Answer:

y = 4x

Step-by-step explanation:

Equation of line in point -y intercept form:

    [tex]\sf \boxed{\bf y-y_1=m(x- x_1)}[/tex]

[tex]\sf x_1 = 1 \ ; \ y_1=4 \ \& \ m = 4[/tex]

  y - 4 = 4(x -1)

  y - 4 = 4*x - 4*1

  y - 4 = 4x - 4

Add 4 to both sides

       y = 4x - 4 + 4

      y =4x

Answer:

Step-by-step explanation:

a. 4cm * 9cm * 2cm = 72 cm^3

b. 5m * 4m * 9m = 180 m^3

c. 10dm * 36 dm^2 (because the square could also be represented as 6cm * 6cm) =360 dm^3

d. (56mm)^3 =  175616 mm^3

e. 10 m * 1 m^2 (because of the square) = 10m^3

To tell which cubic unit of measure that should be used:

   ⇒ we should examine the unit of the side lengths

First question (a):

            ⇒ must use cm³ as cubic unit of measure

               ⇒ as all sides are centimeters

                  ⇒Answer: cubic centimeters or cm³

Second question(b):

            ⇒ must use m³ as cubic unit of measure

               ⇒ as all sides are meters

                  ⇒Answer: cubic meters or m³

Third question(c):

              ⇒must use dm³ as cubic unit of measure

                 ⇒ as all of the sides given are in decimeter

                     ⇒Answer: cubic decimeter or dm³

Fourth question(d):

              ⇒ must use mm³ as cubic unit of measure

                  ⇒ as all the given sides with side lengths are in millimeters

                      ⇒ Answer: cubic millimeters or mm³

Fifth question(e):

              ⇒ must use m³ as cubic unit of measure

                  ⇒ as all given sides with side lengths are in meter

                      ⇒Answer: cubic meter or m³

In general:

⇒ when faced with these problems

   ⇒ look to the unit of measure of the majority of the side lengths

   ⇒ look to the unit of measure that the problem wants for the answer

Hope that helps!

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Step-by-step explanation:

I think 1 is true.

3 is false. it's $10 per hour

The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2

The equation is given as:

[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]

Start by taking the LCM

[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]

Expand the denominator

[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]

Cancel out the common factor

4x(x - 2) - 5x(x - 1)= 2

Expand

[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]

Evaluate the like terms

[tex]-x^2 - 3x = 2[/tex]

Rewrite as:

[tex]x^2 + 3x + 2 = 0\\[/tex]

Expand

[tex]x^2 + 2x + x + 2 = 0[/tex]

Factorize

x(x + 2) + 1(x + 2) = 0

Factor out x + 2

(x + 1)(x + 2) = 0

Solve for x

x = -1 or x = -2

Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2

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Answer:

y=-4 is a function

Step-by-step explanation:

It passes the vertical line test, and each x has only one y, so it is a function.

x = -4 is NOT a function because one x has multiple y values. It does not pass the vertical line test.

The solution to the exponential expression is as follows:

Exponential expressions are convenient ways to express the mathematical power of a number in short forms.

Simplifying the following expressions given:

1.

[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} }[/tex]

Applying the exponent rule: [tex]\mathbf{(a\times b)^n = a^n b^n}[/tex]

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 5^2\times 81}{3^{-2}\times 5^2\times2^2} }[/tex]

cancel out the common factor, we have:

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 81}{3^{-2}\times2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^4}{3^{-2}\times2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^6}{2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times 3^6}{2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times729}{2^2} }[/tex]

[tex]\mathbf{\implies \dfrac{2^3 }{2^2} = 2}[/tex]

2.

[tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)}[/tex]

= [tex]\mathbf{\dfrac{1}{2}}[/tex]

3.

[tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex]

4.

[tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]

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Answer:

Area = 20 units

Step-by-step explanation:

A (-1,0)

B (0,4)

C (4,4)

D (4,-1)

i hope this is right

Answer:

Area = 20

Step-by-step explanation:

A (0,-1)

B (0, 4)

C (4, 4)

D (4, -1)

Answer:

1 and -2 (has a multiplicity of 2)

Step-by-step explanation:

so since x=-2 is a root then (x+2) is a factor of the polynomial. This means you can divide the polynomial by (x+2) by using synthetic or long division. So for this example I'll using synthetic division which is much more simple than long division

-2 | 1   3    0   -4

         -2   -2    4

     1    1    -2   0

(x+2)(x²+x-2)

Now you can factor the quadratic into

(x+2)(x-1)

x+2 = 0

x = - 2

x-1 =0

x = 1

Answer:

Width is 46 meter

Length is 86 meter

Given:

Formula:

Trial and improvement:

1st try with w = 50

w(w + 40) = 4000

50(50 + 40) = 4000

4500 ≠ 4000

Value too high.

2nd try with w = 45

w(w + 40) = 4000

45(45 + 40) = 4000

3825 ≠ 4000

Value too small

3rd try with w = 46

w(w + 40) = 4000

46(46 + 40) = 4000

3956 ≠ 4000

This value is somewhat near to the area value.

It is found that width = 46 m then length = (w + 40) = (46 + 40) = 86 m

Answer: Choice D) x is a real number

Reason:

We can replace x with any number we want without any restriction. There's no issues dealing with division by zero errors for instance, and we also don't have negatives under square roots to worry about. The domain of any linear function is always "the set of all real numbers".

Extra info: The domain in interval notation is [tex](-\infty, \infty)[/tex] which could be thought of as [tex]-\infty < x < \infty[/tex], i.e. x is between negative infinity and positive infinity.

Answer:

d

Step-by-step explanation:

Each step of the proof are:

The given parameter is:

Lines a and b are parallel.

This is represented as; a || b

Corresponding angles are equal.

∠1 and ∠5 are corresponding angles.

So, we have: ∠1 ≅ ∠5

Also, they are congruent.

So, we have ∠1 ≅ ∠5

Vertical angles are equal.

∠5 and ∠7 are vertical  angles.

So, we have: ∠5 ≅ ∠7

Also, they are congruent.

So, we have ∠5 ≅ ∠7

According to the transitive property;

If ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7

Hence, it has been proved that ∠1 ≅ ∠7

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Answer:

Maybe the answer will be C. P (A and B )

Ans: C

Explanation:

I think it is option c , P(A and B)

as this is the only option which has the value of 80, which we got from the table

Answer:

Ok ya sure I would love to. :)

Step-by-step explanation:

Oh wait….

*Crickets chirping*

Answer:

[tex]\huge\boxed{\dfrac{6}{10}=0.6}[/tex]

Step-by-step explanation:

[tex]0.6=\dfrac{6}{10}[/tex]

one digit after the decimal point - one zero in the denominator

[tex]0.06=\dfrac{6}{100}[/tex]

two digits after the decimal point - two zeros in the denominator

[tex]6.0=6[/tex]

[tex]1.6=1\dfrac{6}{10}\ \text{or}\ 1.6=\dfrac{16}{10}[/tex]

At x = -1 , 0 ,1 ,2 , the y value = 0, 1, 2, 3, Option C is the correct answer.

A function is a law that relates a dependent variable to an independent variable.

The points of line are

(- 1, 0), (0, 1),(1, 2).

The equation of the line formed will be

y = mx +c

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

m = 1

y = x +c

at x = 0 , y =1

c = 1

The equation is

y = x+1

The option 1 is

x = - 1, 0, 1, 2.

y1 = 0, 4, 6, 8.

y2= 0, 2, 4, 6

y3 =0, 1, 2, 3.

From the equation

at x = -1 , 0 ,1 ,2

the y value = 0, 1, 2, 3

Therefore Option C is the correct answer.

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Answer:

k = 4

Explanation:

[tex]\sf 10^{k-2}=100[/tex]

make bases similar

[tex]\sf 10^{k-2}=10^2[/tex]

cancel out the bases

[tex]\sf k-2=2[/tex]

add '2' on both sides

[tex]\sf k-2+2=2+ 2[/tex]

simplify the following

[tex]\sf k =4[/tex]

Answer:

y

Factor:4x^3-7x^2-30/y+15:

⬇

4x^3y-7x^2y+15y-30

y

Answer:

1/6

Step-by-step explanation:

the total carrot is 1/1 and fluffy ate 1/2 of it . this means half has been eaten and it is left with half so now 1/2 -1/3 ( carrot left in the morning - the carrot left now ) this will be 1/6

Answer:

Step-by-step explanation:

Answer:

A = 42 cm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 6 and h = 7 , then

A = 6 × 7 = 42 cm²

The surface area of a hexagonal prism willl be 251.13844 cm².

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

A=6ah+3√3a²

A=6×4×7+3√3×4²

A≈251.13844

Hence the surface area of a hexagonal prism willl be 251.13844 cm².

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The answer is y=|x|-13.

Answer:

y=|x|-13

Step-by-step explanation:

Answer: The range of the function is all real numbers less

than or equal to 0.

The correct statement for the given function f(x) = -√x is "The range of the function is all real numbers less than or equal to 0." So, the correct option is C.

The domain of the function is all real numbers that are greater than or equal to 0 but we know that the square root of a negative number is in the real number system.

The graph of the function shows that for each positive input i.e. the range values we get the output values that are negative or zero.

Therefore, the range of the function is all real numbers less than or equal to 0, which is option C.

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Answer:

f(x)=15x+120

Step-by-step explanation:

trust

Answer:

C. m∠1 = m∠4

Step-by-step explanation:

A. m∠2 + m∠4 = 180°

∠2 and ∠4 are vertically opp. angles which means m∠2 = m∠4.

Hence, it's a false statement.

B. m∠2 + m∠3 = 180°

∠2 and ∠3 are corresponding angles which means m∠2 = m∠3.

It's a false statement.

C. m∠1 = m∠4

∠1 and ∠4 are another pair of corresponding angles which clearly states that m∠1 = m∠4.

Therefore, it's a true statement.

D. m∠1 = 90°

As clearly visible in the diagram;

It's a false statement.

Answer:

Step-by-step explanation:

Solution

This (after combining the top 2 fractions, is a 4 tier fraction.

1/4*3/4 = 3/16

So the question now becomes 3/16 ÷ 10/3

The rule for such a question is invert (turn up side down) the second fraction and multiply.

3/16 * 3/10                   Combine

(3*3)/(16* 10)          

9 / 160

0.05625

[tex]\bf{\dfrac{1}{4}\times\dfrac{3}{4}\div\dfrac{10}{3} }[/tex]

Multiply 1/4 by 3/4 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

[tex]\bf{\dfrac{1\times3}{4\times4}\div\dfrac{10}{3} \ \ \to \ \ \ Multiply.}[/tex]

Do the multiplications in the fraction 1 × 3 / 4 × 4.

[tex]\bf{\dfrac{3}{16}\div\dfrac{10}{3} }[/tex]

Divide 3/16 by 10/3 by multiplying 3/16 by the reciprocal of 10/3.

[tex]\bf{\dfrac{3}{16}\times\left(\dfrac{3}{10}\right) }[/tex]

Multiply 3/16 by 3/10 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

[tex]\bf{\dfrac{3\times3}{16\times10 } \ \ \to \ \ \ Multiply }[/tex]

Do the multiplications in the fraction 3 × 3 / 16 × 10

[tex]\bf{\dfrac{9}{160} \ \ \to \ \ Answer }[/tex]

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

The diagonal of the square pyramid will be equal to 33.10 centimetres.

The lines which connect the two opposite corners of any quadrilateral are called diagonal. here we have a square pyramid whose slant height and the vertex height are given and we have to find the diagonal length of the base.

Let the side of the square base of the pyramid is "a". Now the side will be calculated by the following relation.

[tex](\dfrac{a}{2})^2[/tex] =  s² - H

[tex](\dfrac{a}{2})^2[/tex]  = 12² - 7 = 137

a²   = 137 x 4  = 548

a  =  √548 = 23.40 cm

Now the diagonal will be calculated by using the Pythagorean theorem

D² = 23.04²  + 23.40²

D² = 548 + 548

D  = √1096

D  = 33.10 centimeter

Therefore the diagonal of the square pyramid will be equal to 33.10 centimetres.

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The volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

We have:

The radius of the cylindrical barrel r = 30 cm

Height of the cylindrical barrel h = 110 cm

Volume:

[tex]\rm V = \pi (30)^2 (110)[/tex]

V = 311017.67 cubic cm

The volume of litres:

V = 311.017 cubic ml  (1 liter = 1000 cubic cm)

Number of bottles = 311.017 /0.73= 426 bottles

Thus, the volume of the cylinder is in the cubic cm is 311017.67 and in litres is 311.017, and the number of bottle is 426.

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