identify the missing number at the end of the series: 316,323, 332, 343 __

The simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)

The expression is given as:

\(\frac{x^{3}-8x^{2}}{x^2-64}\)

Factor the numerator

\(\frac{x^{2}(x-8)}{x^2-64}\)

Express the denominator as a difference of two squares

\(\frac{x^{2}(x-8)}{(x-8)(x + 8)}\)

Cancel out the common factor

\(\frac{x^2}{x + 8}\)

Hence, the simplified expression of \(\frac{x^{3}-8x^{2}}{x^2-64}\) is \(\frac{x^2}{x + 8}\)

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer: 41 (i'm not really sure. but i was trying to help so please don't be mad

Step-by-step explanation:

8 * 4 = 32                           3 * 3 = 9 and 5 * 2 = 10

2 * 2 = 4                                         9 - 10 = -1                

32 + 4 = 36                                   -1 + 7 = 6 + 1 = 7

36 - 2 = 34

                                       34 + 7 = 41

When matched, the prompts on asymptotes would be:

The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.

This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.

Find out more on horizontal asymptote at https://brainly.com/question/1851758

#SPJ9

Answer:

See below

Step-by-step explanation:

When \(-\frac{\pi}{2} < \theta < \frac{\pi}{2}\), the x-coordinate of the rotated point will be positive since they cover Quadrants I and IV, both of which have positive x-values.

When \(\frac{\pi}{2} > \theta > \frac{3\pi}{2}\), the x-coordinate of the rotated point will be negative since they cover Quadrants II and III, both of which have negative x-values.

The x-coordinate of the rotated point will be equal to cosθ since both of these values depend on the angle of θ.

cos(90°) = 0, cos(180°) = -1, and cos(270°) = 0

This is why referring to a unit circle is crucial in understanding this material.

Answer:

45.4

454

4540

45400

Step-by-step explanation:

45.4x10^0=45.4

45.4x10^1= 454

45.4x10^2= 4540

45.4x10^3= 45400

Hope this helps

The graph is the graph of straight lines

The point (2, 3) is not included in the solution area

From the question, we have the following parameters that can be used in our computation:

4x+2y = 16

x+y=4

The equations are linear equations

We have

(x, y) = (2, 3)

This gives

4(2) + 2(3) = 16 -- false

2 + 3 = 4 -- false

Hence, it is not in the solution

We have

4x+2y = 16

x+y=4

This gives

4x+2y = 16

4x + 4y=16

So, we have

2y = 0

And:

y = 0

This means that

4x + 2(0) = 16

x = 4

So, the solution set is (4, 0)

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.

A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).

{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}

In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}

In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.

{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}

In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}

In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.

To learn more on Sets click:

https://brainly.com/question/30705181

#SPJ1

Answer:

-3p^2 - 11p + 22

Step-by-step explanation:

A - 3B becomes (-2p + 7) - 3*(p^2 + 3p - 5).

Perform the indicated multiplication, obtaining:

                            (-2p + 7) - 3p^2 - 9p + 15, and then:

                              -2p + 7 - 3p^2 - 9p + 15, or (combining like terms):

                                 -3p^2 - 11p + 22

Answer:

14 months

Step-by-step explanation:

1/3 x 12 = 4.

1/3 x 2 = 2/3.

12 + 2 = 14.

It will take her 14 months.

Hope this helps! :)

The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = \(\sqrt{13}\) , -  \(\sqrt{13}\) , x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i .

Given equations ,

\(x^{2}\) + 81 = 0  ,\(x^{2}\)-22 = -26 , 3\(x^{2}\)-18=21 ,2\(x^{2}\) +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a\(x^{2}\)+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

\(x^{2}\) +81 = 0

\(x^{2}\) = -81

x = 9i , -9i

\(x^{2}\) - 22 = -26

\(x^{2}\) = -26 + 22

\(x^{2}\) = -4

x = 2i,-2i

3\(x^{2}\) - 18 = 21

3\(x^{2}\) = 18+21

3\(x^{2}\) = 39

\(x^{2}\) = 13

x = \(\sqrt{13}\) , -  \(\sqrt{13}\)

2\(x^{2}\) +15 = -13

2\(x^{2}\)  = -13-15

2\(x^{2}\)  = -28

\(x^{2}\)  = -14

x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = \(\sqrt{13}\) , -  \(\sqrt{13}\) , x = \(\sqrt{14}\)i , - \(\sqrt{14}\)i .

To learn more about Quadratic equations from the given link.

https://brainly.com/question/30098550

#SPJ1

Answer:

according to your question 2cm is length of the rectangle and 5cm width and 8cm height.

so the surface area of rectangle=2(lb+bh+hl)

surface area=2(2×5+5×8+8×2)

SA=2(66)

SA=132cm²

if your figure is cuboid than the answer is this if thi is not cuboid than comment me on comment section.

Answer:

una parte entenra

Step-by-step explanation:

\(\frac{3}{2}/\frac{2}{3}\\\\=\frac{3}{2}*\frac{3}{2}\\\\=1\)

Answer:

40 ft

Step-by-step explanation:

(i do not have a step by step explanation but it's correct.)

The equation of the line that passes though the point (-6,-7) and is perpendicular to the line 6x + 5y = 30 is y = (5/6)x -2 .

In the question ,

it is given that

the required line is perpendicular to the line 6x + 5y = 30 ,

rewriting the line we get

5y = -6x + 30

y = (-6/5)x + 6

the slope of perpendicular is -6/5 ,

the slope of the required line will be 5/6 .

The equation of the line passing through (-6,-7) with slope 5/6 is written as

(y - (-7)) = (5/6)(x - (-6))

y + 7 = (5/6)(x + 6)

y + 7 = (5/6)x + 5

y = (5/6)x + 5 -7

y = (5/6)x -2

Therefore  , the equation of the line is y = (5/6)x -2 .

The given question is incomplete , the complete question is

What is an equation of the line that passes through the point (−6,−7) and is perpendicular to the line 6x+5y=30 ?

Learn more about Equation Of Line here

https://brainly.com/question/18294280

#SPJ1

Answer:

function 2 has the greater rate.

Answer: function 2 has the greater rate.

Step-by-step explanation:

THE top guy say it so

Answer:

95 6/7

Step-by-step explanation:

The perimeter can be found by adding the length and width together and then multiplying the sum by 2.

Perimeter = 2(L + W)

Where L is the length and W is the width.

So, using the given measurements:

Perimeter = 2(33 5/7+ 14 3/14) = 94 26/14

94 26/14 -> 95 12/14 -> 95 6/7

Answer:

The perimeter is \(95\frac{6}{7}\) inches.

Step-by-step explanation:

The formula for the perimeter of a rectangle is

\(P=2L+2W\)

We are given the length and the width. Lets evaluate the perimeter.

First lets convert the length and width to an improper fraction.

Length: \(33\frac{5}{7}\)

To write 33 as a fraction with a common denominator, multiply by \(\frac{7}{7}\). Then simplify.

\(\frac{33*7}{7} +\frac{5}{7}\)

\(\frac{231}{7} +\frac{5}{7}\)

\(\frac{231+5}{7}\)

\(\frac{236}{7}\)

Width:

To write 14 as a fraction with a common denominator, multiply by \(\frac{14}{14}\). Then simplify.

\(\frac{14*14}{14} +\frac{3}{14}\)

\(\frac{196}{14} +\frac{3}{14}\)

\(\frac{196+3}{14}\)

\(\frac{199}{14}\)

Lets enter the 2 fractions into the perimeter equation.

\(P=(2*\frac{236}{7} )+(2*\frac{199}{14} )\)

Simplify each term.

\(P=\frac{2*236}{7} +2*\frac{199}{14}\)

\(P=\frac{472}{7} +2*\frac{199}{14}\)

Factor 2 out of 14.

\(P=\frac{472}{7} +2*\frac{199}{2(7)}\)

Cancel the common factor of 2.

\(P=\frac{472}{7} +\frac{199}{7}\)

Combine the numerators over the common denominator.

\(P=\frac{472+199}{7}\)

\(P=\frac{671}{7}\)

\(P=95\frac{6}{7}\)

Answerc

Step-by-step explanation:

simple

Answer:

Step-by-step explanation:

Comment

Solution

a^2 + b^2 = c^2

a^2 + 38^2 = 42^2

a^2 + 1444 =1764                              Subtract 1444 from both sides

a^2 + 1444 - 1444 = 1764 - 1444       Combine

a^2 = 320                                          Take the square root of both sides

√a^2 = √320    

a = 17.89

Answer

The height of the TV screen is 17.89 inches

\(\huge \red \dag \underline {\rm {{{\color{orange}{Given ...}}}}} \red \dag\)

\(\huge \red \dag \underline {\rm {{{\color{orange}{To \: Find ...}}}}} \red \dag\)

\(\huge \red \dag \underline {\rm {{{\color{orange}{Solution ...}}}}} \red \dag\)

Answer according to the figure in attachment

In this situation we use Pythagoras theorem.

\(\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \tt {\blue{BD² = BC² + DC²}}}}}\end{gathered}\)

We need to find the DC.

Substituting the values in Pythagoras theorem

\(\large\purple\implies \tt \large \:BD² = BC² + DC²\)

\(\large\purple\implies \tt \large \: {42}^{2} \: = \: {38}^{2} \: + \: DC²\)

\(\large\purple\implies \tt \large \:1764 \: = \: 1444 \: + \: DC²\)

\(\large\purple\implies \tt \large \:1764 \: - \: 1444 \: = \: DC²\)

\(\large\purple\implies \tt \large \:320 \: = \: DC²\)

\(\large\purple\implies \tt \large \: \sqrt{320} \: = \: DC\)

\(\large\purple\implies \tt \large \:17.88 \: = \: DC\)

Hence , the height of TV is 17.88 inches

He would have saved $87,221.02  after 1 year

He would have saved $268,335.90   after 3  years

What is an ordinary annuity?

An ordinary annuity means a fixed amount invested at specific intervals, in this case, $7,185.51 is invested monthly, which means that its future value can be computed using the future value formula of an ordinary annuity as shown below:

FV=PMT*(1+r)^N-1/r

FV=future value of an ordinary annuity

PMT=monthly payment invested every month

r=monthly interest rate=annual interest/12

N=number of months that monthly payments were

FV after 1 year:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in 1 year=12

FV=$7,185.51*(1+0.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*(1.00208333333333333)^12-1/0.00208333333333333

FV=$7,185.51*0.02528845698324970/0.00208333333333333

FV=$87,221.02

FV after 3  years:

PMT=$7,185.51

r=monthly interest rate=2.5%/12=0.00208333333333333

N=number of months in  3 years=36

FV=$7,185.51*(1+0.00208333333333333)^36-1/0.00208333333333333

FV=$268,335.90

Find out more about future value of an ordinary annuity on:brainly.com/question/24703884

#SPJ1

Answer:

You cannot solve this, but you can try to simplify it: 16^x = −2x + −23/4

The function h(x) = (2ˣ) + 1 does not have an x intercept.

A function has an x-intercept when the value of the function is equal to zero at some point on the x-axis.

(a) f(x) = -x + 2 is a linear function with a negative slope (-1) and a y-intercept of 2.

To find the x-intercept, we set f(x) equal to zero and solve for x:

0 = -x + 2

x = 2

Therefore, the function f(x) has an x-intercept at (2, 0).

(b) g(x) = -(x²) is a quadratic function that opens downward and has a vertex at (0, 0).

To find the x-intercept, we set g(x) equal to zero and solve for x:

0 = -(x²)

x²= 0

x = 0

Therefore, the function g(x) has an x-intercept at (0, 0).

(c) h(x) = (2ˣ) + 1 is an exponential function

To find the x-intercept, we set h(x) equal to zero and solve for x:

0 = (2ˣ) + 1

-1 = 2ˣ

However, there is no real value of x that satisfies this equation.

h(x) = (2ˣ) + 1 has no x intercept.

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ1

Answer:

-286

Step-by-step explanation:

45(-6)-16

= -270 - 16

= -286

Step-by-step explanation:

45x - 16

x = -6

45(-6) - 16

-270 - 16

-286

Hope this helps! :)

Answer:

x = 20

Step-by-step explanation:

3x + 6x = 180, if you make them supplementary then they will be parallel

9x = 180

x = 20

Hey there!

“x – 3 < 2”

Let’s change your current question into a(n) equation to make it EASIER to solve (this is for temporary purposes ONLY)

• Temporary question

x – 3 = 2

• First: ADD BOTH SIDES by 3

x – 3 + 3 = 2 + 3

• CANCEL: –3 + 3 because that gives you 0

• KEEP: 2 + 3 because that helps solve for x

• New temporary question: 2 + 3 = x

2 + 3 = 5

The temporary question answer is: x = 5 ✅

NOW LETS SOLVE FOR YOUR ACTUAL EQUATION (just saying it REQUIRES the SAME steps as the temporary question just a TAD bit differently!)

x – 3 < 2

• FIRST: ADD both SIDES BY 3

x – 3 + 3 < 2 + 3

• CANCEL: –3 + 3 because that gives you 0

• KEEP: 2 + 3 because that helps us compare the answer with x

• New equation: x < 2 + 3

2 + 3 = 5

x < 5

Answer to your given question is: x < 5 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

Learn more about on concession, here:

https://brainly.com/question/32140051

#SPJ1

The slope-intercept equation of the line with a slope of 8 and a y-intercept of (0, 9) is y = 8x + 9.

To find the slope-intercept equation of a line, we use the form y = mx + b, where m represents the slope and b represents the y-intercept.

Given:

Slope (m) = 8

Y-intercept (0, 9)

We can substitute these values into the slope-intercept form:

y = mx + b

y = 8x + 9

Consequently, y = 8x + 9 represents the slope-intercept equation for the line with a slope of 8 and a y-intercept of (0, 9).

for such more question on slope-intercept equation

https://brainly.com/question/9753782

#SPJ8