Hi, could you help me with this substitution question?
I'd really appreciate if you added workings out as I'm terribly confused.
Thanks,

Answer:

x = -2

Step-by-step explanation:

2x^3 +16 = 0

We are solving for x

Subtract 16 from each side

2x^3 +16- 16 = 0-16

2x^3 = -16

Divide each side by 2

(2x^3 ) /2 = -16/2

x^3 = -8

Take the cube root of each side

[tex]\sqrt[3]{x^3} = \sqrt[3]{-8}[/tex]

x = -2

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex]2x^3+16=0[/tex]

To solve for the unknown variable x, apply arithmetic operations to isolate the variable.

Subtract 16 from both sides:

[tex]\implies 2x^3+16-16=0-16[/tex]

[tex]\implies 2x^3=-16[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}[/tex]

[tex]\implies x^3=-8[/tex]

Take the cube root of both sides:

[tex]\implies \sqrt[3]{x^3}=\sqrt[3]{-8}[/tex]

[tex]\implies x=-2[/tex]

When taking the cube root of a negative number, the result will be negative.  To understand why, examine what happens when we cube a negative number.

When a number is cubed, it is multiplied by itself, then by itself again.

When multiplying a negative number by another negative number, the result is always positive.

When multiplying a positive number by a negative number, the result is always negative.

Therefore:

[tex]\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}[/tex]

So if -8 is cube rooted, the result is -2.

Answer:

36kg

Step-by-step explanation:

The dog eats 16kg per week, which is 32kg in 2 weeks

The cat eats 2kg per week, which is 4kg in 2 weeks

32+4=36

Answer:

9

Step-by-step explanation:

The surface, in this case, describes the number of squares that are painted. On the left hand side, we have a cube, so we know we're going to have 6 faces. And each face on the cube has 9 little squares, they can be counted on the diagram. So, the total number of squares that are painted on the left cube = [tex]9 * 6 = 54[/tex]

The star means multiplication.

We are told in the question that it takes 9 litres of paint to cover the surface of the left hand cube, meaning it takes 9 litres of paint to cover 54 squares.

This can be written in the ratio = [tex]9:54[/tex]

If we divide both sides of the ratio by 9, we can figure out the amount of squares that 1 litre of paint covers, [tex]1:6[/tex].

The ratio tells us that 1 litre of paint covers 6 squares.

Let's look at the shape on the right. It is still a cube, however, some segments have been removed. Some faces still remain the same as in the shape on the left, such as the bottom face, the back face and the face to the left. Those faces may not be so apparent on the diagram, however, they exist. So we have to count them.

The number of small squares on these faces = [tex]9 * 3=27[/tex]

If you look on the inside of the cube, which can be seen on the diagram, we can see three faces, each having four squares. So, the total number of squares here = [tex]3*4=12[/tex]

Also, we have some squares on the top, and if you count these, there are 5.

This also applies for the front and the right hand side if you count, so we add 10 squares to the total as there are another two lots of five.

So, the total number of squares on the right cube = [tex]27 + 12 + 5 + 5 + 5 = 54[/tex]

Let's bring back the ratio of litres of paint to the number of squares covered: [tex]1:6[/tex]

In the ratio, there are 6 squares per litre. We know that 6 × 9 = 54 (our total). So, we multiply left hand side of the ratio by 9 as well, bringing the total amount of paint required to 9 litres.

I hope this helps.

The surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].

If the left cube takes 9 liters of paint to cover the surface. Then, also right cube takes 9 liters of paint to cover the surface.

Cuboid dimension [tex]$\frac{10 \mathrm{~cm}}{(l)} \times \frac{10 \mathrm{~cm}}{(b)} \times\frac{5 \mathrm{~cm}}{(h)}$[/tex]

Surface area = 2(lb + lh + bh)

= 2((10 [tex]\times[/tex] 10)+(10 [tex]\times[/tex] 5)+(10 [tex]\times[/tex] 5))

= 2(100+50+50)

= [tex]400 \mathrm{~cm}^{2}[/tex]

Therefore, surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].

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Answer:

7/20

Step-by-step explanation:

To add fractions, the first step is to get a common denominator

1/4 + 1/10

The common denominator is 20

1/4 *5/5 = 5/20

1/10 *2/2 = 2/20

5/20 + 2/20 = 7/20

Answer:

D

Step-by-step explanation:

The table does not represent a function because their are two x values with the same y value.

Answer:

C. No, one x --- two different y's

Step-by-step explanation:

In order to be a function, every x can have only one y partnered with it. So if the function is written in this two-column format, if no x's repeat, you can say it is a function. If an x does repeat, it MUST have they same y both times. Here 2 repeats in the x column, but at first it is with 1 and in the next row it is with 4. Can't have that! So this is not a function!

(Btw, it doesn't matter at all the 4 repeats in the y-column nor that it is paired with different x's. Doesn't matter. Not a thing)

In a regular polygon, all interior angles have equal measures because the polygon has congruent sides and angles. The sum of all interior angles in a polygon can be found using the formula:

(n-2) * 180°,

where n represents the number of sides of the polygon.

Based on this, we can determine which angles cannot be interior angles in a regular polygon.

24°: This angle can be an interior angle in a regular polygon because it is smaller than the interior angles of any polygon with more than 6 sides.

72°: This angle can be an interior angle in a regular pentagon (5 sides) or any polygon with more sides, as it satisfies the requirement for interior angles.

135°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 8 sides.

164°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 9 sides.

179°: This angle cannot be an interior angle in any regular polygon because it is larger than the maximum measure of interior angles in any polygon.

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The equation 17q - 13- 3q = 14q + 14 have no solution option first "No solution" is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is:

How many solutions does this equation have?

17q - 13- 3q = 14q + 14

no solution

one solution

infinitely many solutions

We have a linear equation:

17q - 13- 3q = 14q + 14

After solving:

14q = 14q + 27

0 ≠ 27 (false)

No solution

Thus, the equation 17q - 13- 3q = 14q + 14 have no solution option first "No solution" is correct.

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Volume is a three-dimensional scalar quantity. Mila only has 350 grams of platinum, therefore, she does not have enough platinum to make a necklace.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of 12 bead = 12 × (4/3) × π × R³

                                        = 12 × (4/3) × π × (0.7)³

                                        = 17.241 cm³

Given the density of platinum as 21.5 grams per cubic centimeter, therefore,

Mass = density × Volume = 370.682

Since Mila only has 350 grams of platinum, therefore, she does not have enough platinum to make a necklace.

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The table of values for the comparison of a function and its inverse function is shown in the image attached below.

An inverse function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property to the table (see attachment), we have:

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It took 3 days to complete a work by 10 people.

The efficiency is the output of the work which we divide by the work input and then express it in a percentage form.

Here, Efficiency of 1 person to complete a piece of work in 30 days is 1/30.

The number of days to complete the work = n days

Number of person to complete the work = p.

Now, according to question

Number of days to complete the work by 10 people = 30 / 10

                                                                                      = 3 days.

Thus, it took 3 days to complete a work by 10 people.

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Two planes that do not intersect are always parallel.

Answer:

40°

Step-by-step explanation:

Given l \\ m,

m∠13 = m∠7 (alternate interior angles)

m∠13+m∠15 = 180° (Sum of angles in a straight line)

[tex]6x+4+(14x-4)=180\\6x+4+14x-4=180\\20x=180\\x=\frac{180}{20} \\=9\\\\[/tex]

Substitute x to find m∠13

m∠13= 6x+4 = 6(9)+4 = 36 + 4 = 40°

Answer:

sequence

Step-by-step explanation:

a sequence is essentially a set [group/list] of numbers, and each number has a specific placement [meaning that there is an order]

hope this helps!!

Answer: this, a set of number in an order, is called a sequence

fill in the blank: sequence

Answer:

Volume = 7WH - (1/2)W^2H

Step-by-step explanation:

The base consists of the length (L) and the width (W).  It is rectangular, so the perimeter would be the sum of all four sides:

Perimeter = L + W + L +W,

or      Perimeter = 2L + 2W

We are told that 2L + 2W = 28cm     [The perimeter is 28 cm]

------

The volume of the box is given by:  

Volume = L*W*H     [Length x Width x Height]

=====

Let's rearrange the first equation and use it in the second:

2L + 2W = 28cm

2L = 28cm - 2W

L = (28cm - 2W)/2

L = (14 - W)

Now use this definition of L (14 - W) in the second equation:

Volume = L*W*H

Volume = (14 - W)/2)*W*H

Volume = (7-(1/2)W)*W*H

Volume = 7WH - (1/2)W^2H

This can also be written as:  Volume = WH(7 - (1/2)W)

Using the slope concept, it is found that the angle between the ladder and the floor will be of 33.69º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(45º) = h/3.

1 = h/3.

h = 3 m.

If the ladder slides 1 m down, the height will be of 2m, hence the angle will be given as follows:

[tex]\tan{\theta} = \frac{2}{3}[/tex]

[tex]\theta = \arctan{\left(\frac{2}{3}\right)}[/tex]

[tex]\theta = 33.69^\circ[/tex]

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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 pyramid is 2496 cu.m.

A pyramid is a three dimensional structure which has a polygon base and  in general triangular faces which join at the top .

It is given that

A pyramid [tex]\rm frustum[/tex] has a 4 m by 4 m square top

Height = 12 m

Base = 20 m

The volume of a square pyramid with a  [tex]\rm frustum[/tex] is given by

V = (1/2) * ( Area of base + Area of  [tex]\rm frustum[/tex] ) * height of the  [tex]\rm frustum[/tex] from the base

V = 0.5 * ( 20 *20 + 4*4 ) * 12

V = 2496 cu.m

The volume of the pyramid is 2496 cu.m.

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In a case whereby the number of DVDs in a random person's home collection is counted for a sample population of 80 people the mean of the sample is 52 movies, the entire population is known to have a standard deviation of 12 movies then the margin of error is 3.46 moves.

The concept that will be used here is the formular to find the error

E=z∝/2 σ/√ n

n= number of the samples= 80

σ = standard deviation = 12 moves

confidence level = (1-∝) = (1- 0.99) = 0.001

σ/2 = 0.005

Then the looking up for Z value of Z(0.005) = 2.58

E= 2.58 *12/√80

= 3.46 moves.

Therefore, option D is correct.

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Answer:

$14.18

Step-by-step explanation:

just multiply 12 with 100 for percentage and divide it by 85 because there was 15 percent off and you'll get the answer

The division problem that's illustrated based on the information is 3000/75 = 40 without remainder.

A rectangle is defined as a two-dimensional shape having four-sided and opposite sides equal and parallel.

From the information, it was stated that the rectangle with left side labelled 75 and the middle part has 4 above it and 300 inside it.

Therefore, the division problem that's illustrated based on the information is 3000/75 = 40 without remainder.

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Answer:

b) Substitute (3x - 5) for y in the second equation.

Step-by-step explanation:

If using the substitution method, then the second choice is the most efficient first step.

What is the substitution method?

The substitution method can be used to solve a system of equations. It is when you isolate any of the variables from one of the equations and then substitute that value into the other equation.

Here, the first equation already has an isolated variable, y. We can then substitute its value into the second equation. Like so:

⇒ 2x + 6y = 20

⇒ 2x + 6(3x - 5) = 20

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Answer:

300.25

Step-by-step explanation:

The mass of 1 packet of low fat vegetable soup is 70.5g, the mass of 50 packets is 300.25g(70.5x50).

The mass of 50 low-fat vegetable soups has a mass equal to 300.25 g.

Given : The mass of 1 packet of low-fat vegetable soup is 70.5g

To find: The mass of 50 such packets

Concept: In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. For example, 30 is the product of 6 and 5

The mass of 50 such packets is 70.5x50 i.e., mass of 1 pkt* number of packets given which is given to be 70.5 and 50 respectively

= 300.25 g.

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Answer:

0.75

Step-by-step explanation:

slope is the coeffecient of x when the equation is in the order yb= mx + b

3x - 4y = 7

-4y = 7 - 3x

4y = 3x - 7

y = (3x - 7) / 4

y = 3x / 4 - 7 / 4

slope = 3/4

Answer:

i think its 8(a+2c)

Step-by-step explanation:

The GCF or greatest common factor of 8 and 16 is 8.

8a+16c

8(a+2c)

Therefore the answer is 8(a+2c)

Answer: The first graph

Step-by-step explanation: A graph’s inverse will have all of their roots inverted as well. If you put the graph f(x)= 3x+3 into a graphing calculator, you’ll be able to see all the roots. From there, just invert (switch) the roots. Since on the original graph the most prominent roots are {(0,3), (-1,0),(-2,-3)}, you just need to invert those roots and find them ALL on one of the graphs, then you have your answer. So, the inverted roots will be {(3,0),(0,-1),(-3,-2)}.

Still, I find the simplest thing is to put them into a graphing calc like GeoGebra.

Using the normal distribution, it is found that:

a) The pilot is at the 72th percentile.

b) 19.13% of pilots are unable to fly.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 72.6, \sigma = 2.7[/tex].

Item a:

The percentile is the p-value of Z when X = 74.2, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{74.2 - 72.6}{2.7}[/tex]

Z = 0.59

Z = 0.59 has a p-value of 0.7224.

72th percentile.

Item b:

The proportion that is able to fly is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 70, hence:

X = 78:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{78 - 72.6}{2.7}[/tex]

Z = 2

Z = 2 has a p-value of 0.9772.

X = 70:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 72.6}{2.7}[/tex]

Z = -0.96

Z = -0.96 has a p-value of 0.1685.

0.9772 - 0.1685 = 0.8087 = 80.87%.

Hence the percentage that is unable to fly is:

100 - 80.87 = 19.13%.

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Step-by-step explanation:

As far as I understand, they can use all 26 letters (alphabet) and all 10 digits (0, 1, ..., 9), and the password looks like this:

letter-letter-letter-letter-letter-letter-number-number (6 letters, 2 numbers).

▪︎ They can reuse the letters, so they can choose the 1st letter out of 26 possible letters, then they still can choose the 2nd letter out of 26 (it's ok if they have both A's for example, they can reuse them) and so on. So each time they can choose one letter out of 26. Thus, it's 26*26*26*26*26*26.

▪︎ The same thing with numbers. Each time they can choose one number out of 10, so it's 10*10.

▪︎ Therefore, the answer is 26*26*26*26*26*26*10*10 = 30,891,577,600. That's almost 31 billion passwords.

Answer:

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

Answer:

x^2+4x+1

Step-by-step explanation:

(x+2)^2-3

(x+2)(x+2)-3

x^2+2x+2x+4-3

x^2+4x+4-3

x^2+4x+1