Find the missing side length

Answer:

The answer is option 1.

Step-by-step explanation:

You have to substitute the expressions of s into the formula of volume :

s = 4x² + 3

V = s³

V = (4x² + 3)³

Then, you have to expand it :

V = (4x² + 3)³

V = (16x⁴ + 24x² + 9)(4x² + 3)

V = 16x⁴(4x²) + 16x⁴(3) + 24x²(4x²) +

24x²(3) + 9(4x²) + 9(3)

V = 64x⁶ + 48x⁴ + 96x⁴ + 72x² + 36x² + 27

V = 64x⁶ + 144x⁴ + 108x² + 27

The required volume of the cube is 64x⁶ + 144x⁴ + 108x² + 27. Answer: A.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property

The volume of the cube is given by V = s^3. Substituting s = 4x^2 + 3, we get:

V = (4x² + 3)³

= (4x²)³ + 3(4x²)²(3) + 3(4x²)(3²) + 3³

= 64x⁶ + 144x⁴ + 108x² + 27

Therefore, the volume of the cube is 64x⁶ + 144x⁴ + 108x² + 27. Answer: A.

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Answer:

d. The common ratio is 1.1

Step-by-step explanation:

To see if the data has a common ratio or common difference, we have to see if the division between them is equal(common ratio), or if the difference between them is equal(common difference).

In this case, since [tex]60.5 - 55 \neq 55 - 50[/tex], it has a common ratio.

To find it, we divide consecutive terms. For example:

[tex]\frac{55}{50} = 1.1[/tex]

So the correct answer is:

d. The common ratio is 1.1

Answer:

A 7/25

Step-by-step explanation:

1. Take inverse of theta

2. Substitute the inverse theta in the equation given in question

Answer:

C

Step-by-step explanation:

simplify the equation 64/square root of 2 using calculater and the answer is 45.254834. Then make the answer to a power of 2. To make the answer power of two use log. log 45.254833 ÷ log 2 will give the answer as 5.5. so the answer is 2⁵½. I think.

Answer:

[tex]a_{n} = \frac{n}{(n +1)^{2}}[/tex]

Step-by-step explanation:

[tex]a_{n} = \frac{n}{(n +1)^{2}}[/tex]

[tex]a_{1} = \frac{1}{(1 +1)^{2}} = \frac{1}{2^{2}} = \frac{1}{4}\\\\a_{2} = \frac{2}{(1 +2)^{2}} = \frac{2}{3^{2}} = \frac{2}{9}\\\\a_{3} = \frac{3}{(1 +3)^{2}} = \frac{3}{4^{2}} = \frac{3}{16}\\[/tex]

Answer:

$27.14

Step-by-step explanation:

Price of 1 DVD: $9.10

Price of 4 DVDs: 4 * $9.10 = $36.40

Discount: 25%

Now we find 25% of $36.40.

25% of $36.40 =

= 0.25 * $36.40

= $9.10

The 25% discount amounts to $9.10. We now subtract $9.10 from $36.40 to find the discounted price.

$36.40 - $9.10 = $27.30

Now we need to apply the 6.75% tax to $27.30.

6.75% of $27.30 =

= 0.0675 * $27.30

= $1.84

The sales tax is $1.84.

Now we add the sales tax amount to the total discounted price.

$27.30 + $1.84 = $29.14

Answer: $27.14

Answer:

Quadrant 2

Step-by-step explanation:

Hope this helps :D Have a great day

Answer:

common denominator = 24

1/8 = 3/24

1/6 = 4/24

Step-by-step explanation:

to find common denominator:

8 - 8, 16, 24

6 - 6, 12, 18, 24

Answer:

5.3x - 3.8y - 1.5

Answer:

(3.1x+2.2x)+(−2.4y+1.4y)+(1.9+3.4)

Step-by-step explanation:

I just did this problem :>

Answer: See Below

Step-by-step explanation:

Line equation is y = ax +b. We need to solve for a and b

First we will solve for the slope (a)

Given that it is perpendicular to 2x - 6y = 12, we know that our slope a is the negative reciprocal of the slope of this line. Lets put this line in point-slope format.

2x - 6y = 12

-6y = -2x + 12

y = (1/3)x - 2

This line has a slope of 1/3 so our slope is the negative reciprocal of that. Our slope is -3

We can plug that slope into our line equation in place of a

y = -3x + b

Now we can plug in (3,6) to solve for b

y = -3x + b

6 = -3(3) + b

6 = -9 + b

15 = b

Therefore our line equation is:

y = -3x + 15

Answer:

For number 2 it is = x(f + h)

For number 3 it is = x(g + h)

For number 4 it is = x(h + f)

For number 5 it is = x(f - g)

Hope this helps:)

Answer:

A

Step-by-step explanation:

Answer:

[-5, 5] the Y value has a minimum of -5 and max of 5 so that is what your range is!

Step-by-step explanation:

[tex]\boxed{\boxed{\pink{\bf \leadsto The \ range \ of \ y \ is \ y \ \in \ [-5,5] .}}}[/tex]

A function is given to us and we need to find its range. So the given function is ,

[tex]\bf\implies y = -5\:sin(x) [/tex]

The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.

[tex]\bf \implies y = (-5) [/tex]

The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.

[tex]\bf \implies y = (5) [/tex]

Hence the range is ,

[tex]\boxed{\red{\bf -5 \leq y \leq 5 }}[/tex]

Interval Notation :-

[tex]\boxed{\red{\bf y \in [-5,5] }}[/tex]

Set builder Notation :-

[tex]\boxed{\red{\bf \{ y | -5 \leq y \leq 5 }}[/tex]

Graph of the function is attached .

Answer:

84.1%

Step-by-step explanation:

Add up 0.1, 2.2, 13.6, 34.1, and 34.1 and you get that number. this is because that is the numbers in each column and you add those because they are below 79 mark.

Answer:

Step-by-step explanation:

Lets pick to columns in the table

Lets so (6,228) and (7,266)

To find the slope you need to do y1-y2/x1-x2

7-6/266-228=1/38.

1/38 is the slope.

y=1/38x+b

to find B you have to plug any of the y with the corresponding x values back in and solve for b.

Lets choose 228.

228=1/38(6)+b

228=6/28+b

(28/6)(228)=b

b=1064

the equation will be y=1/38x+1064

Answer: c. The probability that A does not occur is 0.5.

Step-by-step explanation:

Given: Event A has probability 0.5. Event B has probability 0.6.

If M and N are disjoint sets , the  P(M or N) = P(M) +P(N)

So, if A and B are disjoint sets , then P(A or B)= P(A) + P(B)

= 0.5+0.6

= 1.1 > 1  

And probability cannot be greater than 1.

So, A and B are not disjoint.

If A or B includes all the possible outcomes in the sample space then, P(A) or P(B) should equal to 1 which is not true.

Probability of not E = 1- P(E)

So, . The probability that A does not occur =  1- P(A) = 1-.5= 0.5

So, option is C. correct.

The probability that A does not occur is 0.5.

Answer:

12

Step-by-step explanation:

15 feet total amount combined by pole and birdhouse

4 foot tall person makes 5 feet long shadow

5x3=15

4x3=12 so the birdhouse and pole are 12 feet

The birdhouse and the pole are 18.75 ft tall.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a person standing nearby who casts a shadow 5 feet long. The person is 4 feet tall.

Assume that for the birdhouse and the pole are [x] ft tall.

Now, for a 4 feet tall person, the shadow is 5 feet long.

Then, for one feet long person, the shadow would be (5/4) feet long.

Then, for 15 feet long -

x/15 = 5/4

x = (15 x 5)/4

x = 75/4

x = 18.75 feet tall

Therefore, the birdhouse and the pole are 18.75 ft tall.

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Answer:

11.25:375*100 =

(11.25*100):375 =

1125:375 = 3

Answer:

Step-by-step explanation:

Answer:

The cost function is simply the initial cost plus the manufacturing cost.

C(x)=500+20x-5x^3/4+0.01x^2

The demand function was given to us.

p(x)=320-7,7x

The revenue function is simply x multiplied by the demand function.

R(x)=xp(x)=320x-7.7x^2

We find that when 20 planes are produced, that profit is currently maximized

We know that to maximize profit, marginal revenue must equal marginal cost.

C'(x)=20-15/4x^-1/4+0.02x

R'(x)=320-15.4x

x=19,57

We find that when 20 planes are produced, that profit is currently maximized.

Step-by-step explanation:

An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function: , where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell  planes.

(a) Find the cost, demand, and revenue functions.

(b) Find th eproduction level and the associated selling price of the aircraft that maximizes profit.

Answer:

y=x+10

y=-2x+1

(see attached picture)

Step-by-step explanation:

The idea of solving a system of equations graphically is taht both graphs cross each other at the same point.

The problem doesn't state so, but we can find the equations of the lines that pass through the desired point by using the point-slope form of the equation and by picking any slope we wish.

The slope-intercept form of a linear equation looks like this:

[tex]y-y_{1}=m(x-x_{1})[/tex]

so let's use the following slopes: [tex]m_{1}=1[/tex] and [tex]m_{2}=-2[/tex]. Remember, you can pick any slope you wish.

so now we can substitute the provided point (-3,7) and its respective slopes:

[tex]m_{1}=1[/tex]

y-7=1(x-(-3))

y=x+3+7

y=x+10

this will be our first equation.

[tex]m_{2}=-2[/tex]

y-7=-2(x+3)

y=-2x-6+7

y=-2x+1

so now we can plot the graphs of the given equations.

how to plot them? you can pick any x-value you like and use the provided equatioins to find the corresponding y-value. You plot the two points and build the graph.

Let's take the first equation:

y=x+10

and let's use the x-value x=0. We now substitute that into the equation so we get:

y=0+10

y=10

so now my two ordered pairs are (0,10) and (-3,7) so I can plot them on my graph and connect them with a straight line. (see attached picture.)

and we can follow the same procedure for the second graph.

let's use the x=0 again so we get:

y=-2(0)+1

y=1

so the ordered pairs are: (0,1) and (-3,7)

so we plot them to get our final graph (see attached picture)

Of course, this is one of the ways in which we can solve this problem. Since they are asking us to plot the graphs and not quite finding the equations for the system of equations, you could just draw any two lines you like and the answer would be correct as long as the two lines pass through the same point.

We want to find and sketch a system of linear equations that passes through (-3, 7).

A system of equations is a set of equations that must be solved simultaneously. Here we want the solution of the system to be the point (-3, 7), so we just need to find two lines that pass through that point.

We can get:

y = x + 10

You can see that when evaluated in x = -3, we have:

y = -3 + 10 = 7

The other line can be:

y = -x + 4

When evaluated in x = -3, it gives:

y = -(-3) + 4 = 7

Then the system is:

The graph of the system can be seen below.

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Answer:

( -2, 3 )

Step-by-step explanation:

3x + y = -3

y = x + 5

Since "y" has been given to us, all we need to do is substitute.

3x + x + 5 = -3

Combine like terms

4x + 5 = -3

Subtract 5 onto both sides

4x + 5 - 5 = -3 - 5

4x = -8

Divide by 4 into both sides to isolate the variable

4x/4 = -8/4

x = -2

Now that we have x ( -2 ), we can substitute that to get what y is.

y = x + 5

y = -2 + 5

y = 3

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

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer: 14 lbs

Step-by-step explanation:

shoot i hope this right

Answer: 3x+y=5

Step-by-step explanation:

Equation of a line that has slope(m) and passes through point (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Given: Point = (3,-4)

Slope =-3

Then, the equation of the required line:

[tex](y-(-4))=-3(x-3)\\\\\Rightarrow\ (y+4)=-3(x-3)\\\\\Rightarrow\ y+4=-3x+9\\\\\Rightarrow\ 3x+y=9-4\\\\\Rightarrow\ 3x+y=5\ \ \ \ [\text{Standard form: Ax+By=C}][/tex]

Hence, required equation: 3x+y=5

Answer: 64

Step-by-step explanation:

If EFGH is a parallelogram, its diagonals bisect each other meaning EJ and JG are congruent.

EJ = JG

4w + 4 = 2w + 18

Subtract 2w from both sides

2w + 4 = 18

Subtract 4 from both sides

2w = 14

Divide both sides by 2

w = 7

EG = EJ + JG

EG = 4w + 4 + 2w + 18

EG = 6w + 22

Now that we know what 'w' is, we can substitute it for 7

EG = 6 (7) + 22

EG = 42 + 22 = 64

The measure of EG is 64.

Hope that helped!

Answer:

B) -6 is the answer :) :) *-*

9514 1404 393

Answer:

  C.  jump discontinuity at x=-2

Step-by-step explanation:

At x=-2, you have to lift your pencil to keep drawing the graph. That means there's a jump discontinuity there.

This function has a jump discontinuity at x = -2.

__

Additional comments

At x=3, there is no discontinuity in the function. The derivative of the function has a discontinuity there, as there is an abrupt change in slope at that point.

If left and right limits exist and are the same at a point, but the graph is not defined at that point, then a removable discontinuity exists. All that is needed to fill the hole is to define the function at that point.

Answer:

$33.60

Step-by-step explanation:

%20 of 28 is 5.6

add $5.60 to 28= 33.60

Answer:

$33.6

Step-by-step explanation:

28 x 0.20 = 5.6 ...tip

total cost = 28 + 5.6 = 33.6

Answer:

Comparing the L.H.S with the R.H.S

Step-by-step explanation:

Given

3 1/2 divided by 2 1/4 = a b/ c

solving the left-hand side of the equation

[tex]3\frac{1}{2}\div \:2\frac{1}{4}[/tex]

Convert mixed numbers to improper fractions

so the expression becomes

[tex]3\frac{1}{2}\:\div 2\frac{1}{4}=\frac{7}{2}\div \:\frac{9}{4}[/tex]

Apply the fraction rule: [tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

              [tex]=\frac{7}{2}\times \frac{4}{9}[/tex]

Cross cancel the common factor

                [tex]=\frac{7}{1}\times \frac{2}{9}[/tex]

Multiply fractions: [tex]\frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]

                [tex]=\frac{7\times \:2}{1\times \:9}[/tex]

                 [tex]=\frac{14}{9}[/tex]

Convert improper fractions to mixed numbers

                [tex]=1\frac{5}{9}[/tex]

Thus, the main expression becomes

[tex]\:1\frac{5}{9}=a\frac{b}{c}[/tex]

Thus, comparing the L.H.S with the R.H.S