What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?

A
(-1, -4)

B
(1, -4)

C
(3, -4)

D
(-3, 12)

Answer:

31

Step-by-step explanation:

The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31

The unknown number(x) in the series is 31.

The given series 1, 2, 6, 15, x, 56, 92.

We need to find the value of x.

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.

The numbers in the series increase by (n+1)².

So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.

Therefore, the unknown number(x) in the series is 31.

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The computation shows that:

G n M = Anael and Max

G u S = Acel, Action, Anael, Max, Carl, Dario, Catlin, Kai, and Barek.

From the information, ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table.

The subjects include general Knowledge Math Science.

Therefore, G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. The intersection is illustrated above.

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Answer:

f(-5) = 30

f(0) = 5

f(3) = 14

Step-by-step explanation:

=> f(x) = x²+5

for , f(-5) = (-5)² +5

=> 25 +5

=> 30

for , f(0) = (0)² +5

=> 5

for , f(3) = (3)² + 5

=> 9 + 5

=> 14

Answer:

the third one

Step-by-step explanation:

it is function that contain four domain

Answer:

(0, 8/3) = y-intercept

Step-by-step explanation:

I chose to find the y-intercept since it is easy to find with the given information.

The equation for a line is y = mx + b

To find the y-intercept, we must plug in the info we have and solve for b:

4 = -1/3 (-4) + b

4 = -4/3 + b

8/3 = b

To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:

(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)

Answer:

B

Step-by-step explanation:

Every (x,y) pair is equal to each other, thus making them proportional :)

Answer:

SAS and SSA

Kindly award branliest

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.

The criterias that guarantee congruence are :

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

C. Subtract 4 from both sides.

Step-by-step explanation:

You need the equation in the form x² + ax + b = 0 to then either try factoring or use the quadratic formula.

In order to achieve that, you need to first:

Subtract 4 from both sides.

The material-handling cost per wall mirror under activity-based costing is $280

What is activity-based costing?

Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.

There 25 materials move in both divisions (i.e. 7+18=25)

Material-handling cost per material move=Budgeted material-handling costs /total material moves

Budgeted material-handling costs =$30,000

Material-handling cost per material move=$30,000/25

Material-handling cost per material move=$1,200

Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move

Total material-handing costs for wall mirror=7*$120

Total material-handing costs for wall mirror=$8,400

material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors

material-handling cost per wall mirror=$8,400/30

material-handling cost per wall mirror=$280

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Answer: W

Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .

Answer: 8  units

Step-by-step explanation:

Answer:

-8 5/12

Step-by-step explanation:

The correct proportion that can be used to find the actual distance  represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.

Given that 3 inches on a map represents 50 miles.

We are told to find the proportion which can be used to represent 5 inches.

Multiplication is basically finding the product of two numbers but it can be used to convert the units also.

If 3 inches represents 50 miles then,

1 mile=50/3

Multiply both sides by 5.

5 miles=5*50/3

If we see the options then we will get that the most appropriate and correct option which represents 5 inches is that start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.

Hence the correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.

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Answer:

B

Step-by-step explanation:

3/50 = 5/x

The subsets of the set of novels is given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

Suppose we have a set with cardinality n, that is, with n elements. This set will have 2^n subsets, which are all the possible combinations with the elements of the set, including the empty set.

In this problem, the novels are given as follows:

Light, Zami, and Money.

Hence the possible subsets are given as follows:

{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.

With is the list that is asked for this problem, which are the subsets of the set of novels.

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The minimum surface area that such a box can have is 380 square

Represent the base length with x and the bwith h.

So, the volume is

V = x^2h

This gives

x^2h = 500

Make h the subject

h = 500/x^2

The surface area is

S = 2(x^2 + 2xh)

Expand

S = 2x^2 + 4xh

Substitute h = 500/x^2

S = 2x^2 + 4x * 500/x^2

Evaluate

S = 2x^2 + 2000/x

Differentiate

S' = 4x - 2000/x^2

Set the equation to 0

4x - 2000/x^2 = 0

Multiply through by x^2

4x^3 - 2000 = 0

This gives

4x^3= 2000

Divide by 4

x^3 = 500

Take the cube root

x = 7.94

Substitute x = 7.94 in S = 2x^2 + 2000/x

S = 2 * 7.94^2 + 2000/7.94

Evaluate

S = 380

Hence, the minimum surface area that such a box can have is 380 square

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Answer:

[tex]-8c+6[/tex]

Step-by-step explanation:

[tex]2(-6c+3)+4c=-12c+6+4c=\boxed{-8c+6}[/tex]

Answer:

-8c + 6 and 3(-4c+2) + 4c

Step-by-step explanation:

khan

The difference of squares is:

(x+i√3)(x-i√3)

So the correct option is the last one, D.

For a complex number:

[tex]Z = a + b*i[/tex]

We define the complex conjugate of Z as:

[tex]Z' = a - b*i[/tex]

Such that the product between the complex number and its complex conjugate gives:

[tex]Z*Z' = a^2 + b^2[/tex]

Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:

[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]

Which is what we wanted to get, so that is the correct option.

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0.1 or 10%

The numbers between 1 and 50 that end in 6 are as follows:

6, 16, 26, 36, 46

There are therefore 5 numbers between 1 and 50 that end in 6.

This means there are 5 out of 50, or 5/50.

5/50 is 0.1 as a decimal, or 10% in percentage form.

Answer:

  c = 2.25

Step-by-step explanation:

The normal distribution function is symmetrical, so the area not in the central zone is split evenly between the lower and upper tails.

We can find -c from ...

  P(x < -c) = (1 - 0.9756)/2 . . . . .  the area in the lower tail

The calculator tells us -c = -2.25.

  c = 2.25

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & 80\\ P=\textit{initial amount}\dotfill &40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 80=40(1 + 0.05)^{t}\implies \cfrac{80}{40}=1.05^t\implies 2=1.05^t\implies \log(2)=\log(1.05^t) \\\\\\ \log(2)=t\log(1.05)\implies \cfrac{\log(2)}{\log(1.05)}=t\implies 14.2\approx t[/tex]

Considering the asymptotes of the function, the equation that represents the graph is:

[tex]y = \frac{1}{x + 2} + 3[/tex]

This function, from the graph, has a vertical asymptote at x = -2, hence the denominator is given by:[tex]y = \frac{1}{x + 2} + 3[/tex]

x + 2, as x + 2 = 0 -> x = -2.

The horizontal asymptote is of y = 3, hence:

[tex]\lim_{x \rightarrow \infty} f(x) = 3[/tex]

Which means that the function is described by the following rule:

[tex]y = \frac{1}{x + 2} + 3[/tex]

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Answer: one

Step-by-step explanation:

parallel faces are the ones that are opposite to each other.

Answer:

one

Step-by-step explanation:

there is only one pair of parallel faces.

Answer:

x = -9

Step-by-step explanation:

12 + 2x + 24 = 27 + x

(12 + 24) + 2x = 27 + x

36 + 2x = 27 + x

subtract 27 from both sides

36-27 + 2x = 27-27 + x

9 + 2x = x

subtract x from both sides

9 + x = 0

subtract 9 from both sides

x = -9

(the steps could've been faster but that shows the most work)

check:

12 + 2(-9) + 24 = 27 + (-9)

36 - 18 = 18

18 = 18

True!

so -9 is correct

Answer:

Step-by-step explanation:

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

If you do in fact mean [tex]f(1)=f(6)=0[/tex] (as opposed to one of these being the derivative of [tex]f[/tex] at some point), then integrating twice gives

[tex]f''(x) = -\dfrac1{x^2}[/tex]

[tex]f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1[/tex]

[tex]f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2[/tex]

From the initial conditions, we find

[tex]f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0[/tex]

[tex]f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)[/tex]

Eliminating [tex]C_2[/tex], we get

[tex](C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))[/tex]

[tex]-5C_1 = \ln(6)[/tex]

[tex]C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)[/tex]

Then

[tex]\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}[/tex]

Answer:

21%

Step-by-step explanation:

($63*100%) / $300 = 21%

The inequality suitable if 1 is greater than x is x<1.

Given that 1 is greater than x.

We are required to form an inequality which shows that 1 is greater than x.

Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.

It shows the range of quantities.

When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:

x<1

We have not used equal to sign because 1 is greater than x not equal to x.

Hence the inequality suitable if 1 is greater than x is x<1.

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The derivative of y= sin x sin 3x​ is [tex]$=3 \cos x-3 \cos 3 x$[/tex]

To find the derivative of y= sin x sin 3x​:

[tex]$y=3 \sin (x)-\sin (3 x)$[/tex]

[tex]$y^{\prime}=3 \cos x-[\cos (3 x) \cdot 3]$[/tex]

[tex]$y^{\prime}=3(\cos x-\cos 3 x)$[/tex]

[tex]\frac{dx}{dy} =3 cosx - 3 cos x[/tex]

Differentiate [tex]sin 3x[/tex] using the chain rule

Given [tex]y=f^{'} (g(x))*g^{'}[/tex]←chain rule

y=[tex]y=3 sin x-sin 3x[/tex]

[tex]\frac{dx}{dy} =3 cos x - cos 3x*\frac{d}{dx} (3x)[/tex]

[tex]=3cosx-3cos3x[/tex]

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