y=(x+5)²-4
Vertex:
Axis of Symmetry:
x-intercepts:
y-intercept:
Is the vertex a maximum or minimum?

The area bounded by the sin (100x² + 49y²) dA is calculated by using integration is 2π (1 - cos 1).

An area bounded by the curve: When the two curves intersect then they bound the region is known as the area bounded by the curve.

Evaluate the integral by making an appropriate change of variables.

The equation of the ellipse is 100x² + 49y² = 1

Let cos t = 10x and sin t = 7y. Then we have

or x = 1/10 cost , y = 1/7 sint.

Then

=> 100 (1/10cost)^2 + 49 (1/7 sint)^2 = 1

=> cos^2 t + sin^2t = 1 which suggests a change of variable will be:

[tex]\left \{ {{x(r,t) = r/10cost} \atop {y(r,t)=r/7sint}} \right.[/tex]

where 0≤r≤1 and 0≤t≤2[tex]\pi[/tex]. Then we also have,

100x² + 49y² = r²

So,

=> ∫∫ sin (100x^2 + 49y^2)dA

     R

=> [tex]\\[/tex]2 ∫2[tex]\pi[/tex] ∫[tex]1[/tex]  sinr^2 dr dt

       0     0

=> 4[tex]\pi[/tex] ∫[tex]1[/tex]  rsinr^2 dr

          0    

Now r² is replaced by r, then we get

=> 2[tex]\pi[/tex] ∫[tex]2[/tex]  sinr^2 d(r^2)

          0

=> - 2[tex]\pi[/tex] cos r^2 [tex]\left \{ {{r^2=1} \atop {r^2=0}} \right.[/tex]    

=> -2[tex]\pi[/tex] (cos1-cos0)

=> -2[tex]\pi[/tex] (-1 + cos1)

=> 2[tex]\pi[/tex](1-cos1)

Evaluating the integral by making an appropriate change of variables 2 sin(100x^2 + 49y^2) dA.

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Answer:

just telling you but we need to see the image which we cannot but I'm not entirely sure but I think it's 2 although I cannot see the image and the other one is 4 I thinke

The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

Let the number of number of red pencils be 'x'.

Total blue pencils = 5.

Ratio = blue pencils/red pencils

5/x = 1/2

x = 5 x 2

x = 10

Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

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Answer:

50%

Step-by-step explanation:

It is a half chance, you could be lucky

The number of ways there for the 125 pages to be assigned to the four printers = 5^125 ways.

As per the question,

A 125-page document is being printed by four printers.

Each page will be printed exactly once.

There are no restrictions on how many pages a printer can print.

One of the possible combinations is that printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90 and printer D prints out pages 81-85 and 91-100.

Since, there are no restrictions in printing the pages any printer cannot print even a single page and any printer can print all 125 pages. To print 100 pages we have four printers.

⇒ Number of possible ways a single paper can be assigned to the four printers = 4 ways

⇒ Number of possible ways 125 pages can be assigned to the four printers

=  5 × 5 × 5 × 5 .................... 5 ( a total of 125 terms )

=     ways.

Therefore, In   ways we can assign 125 pages to four printers with no restrictions.

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The angle between the two vectors (4,1) and (-8,3) will be 145.4°.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is possible to calculate the angle () between two vectors using the formula

[tex]\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

Calculate dot product:

=a · b

= ax · bx + ay · by

= 4 · (-8) + 1 · 3

= - 32 + 3

= -29

=|a|

= √ax² + ay²

= √4² + 1²

= √16 + 1

= √17

=|b|

=√ bx² + by²

= √(-8)² + 3²

= √64 + 9

= √73

[tex]\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

α = 145.40771131249005°

Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.

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Answer:

  13.5, 17.5

Step-by-step explanation:

You have two numbers whose sum is 31 and whose difference is 4. The second number is larger.

Let x represent the larger number. Then the smaller is x-4, and their sum is ...

  x +(x -4) = 31

Simplifying the expression gives ...

  2x -4 = 31

  2x = 35 . . . . . add 4

  x = 17.5 . . . . . divide by 2

  x -4 = 13.5

The two numbers are 13.5 and 17.5.

__

Additional comment

As we have seen here, the larger number is half the total of the 'sum' and 'difference'. (31+4)/2 = 17.5. This is the generic solution to any "sum and difference" problem.

Using the implicit differentiation, it is found that the water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

The volume of the cone of radius r and height h is given as follows:

V = π r² h / 3

Applying implicit differentiation to find the rate of change of the volume as function of time is given as follows:

[tex]\frac{dV}{dt}[/tex] = 2 π  [tex]\frac{rh}{3}[/tex][tex]\frac{dr}{dt}[/tex]  + [tex]\frac{π r² }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

As the radius is constant, hence:

.[tex]\frac{dr}{dt}[/tex]  = 0

Considering that the radius is half of the diameter, the other parameters are:

r = 3 and [tex]\frac{dV}{dt}[/tex] = 2

Hence:

2 = [tex]\frac{π * 3^{2} }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}[/tex] = 6 / 9 π

dh/dt = 0.21.

The water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

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Answer:

y= -2x-4

Step-by-step explanation:

parallel==> a line has the same slope ===> (m = -2)

y= -2x+b

and a line pass through the (-3,2) ===> x=-3, y=2

2= -2(-3)+b

2=6+b (subtract 6 from both sides )

-4=b

y= -2x-4



Answer: x = 6

Step-by-step explanation:

2x + 7 = 9x - 35

-7x + 7 = -35

-7x = -42

x=6

Answer$200+$50x

Step-by-step explanation:

Answer:

4 Months

Step-by-step explanation:

if X = total (not sure)

thats means you must do $200 / $50 = 4 Months

Answer:

Step-by-step explanation:

If the base of the right triangle is 6 and the perpendicular height is 8 , then the length of the hypotnuse is  10 .

In the question ,

it is given that ,

the base of the right triangle is 6 , and

the height of the perpendicular is 8 ,

let the length of the hypotnuse of the given triangle be = h

Since the triangle is a right triangle , So , it follows Pythagoras Theorem ,

that means ,

h² = 6² + 8²

h² = 36 + 64

h² = 100

Simplifying further ,

we get ,

h = 10

Therefore , the length of the hypotnuse is = 10 .

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Answer:

557

Step-by-step explanation:

7,241 divided by 13 = 557

The compound interest after 5 years is $7,081.916.

Compound interest:

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Here we have to find the interest earned after 5 years.

Data given:

Principle (P) = $11600

rate(r) = 10%

time(t) = 5 years.

Formula to find compound interest:

CI = P( 1 + r/100[tex])^{t}[/tex] - P

Now put the values in the formula.

CI = 11600 ( 1 + 10/100[tex])^{5}[/tex] - 11600

  = 18681.916 - 11600

  = 7081.916

Therefore the compound interest is $7081.916.

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Answer:

<XWZ ≅ < XZW  by alternate interior angles & WZ = WZ by reflexive property

Step-by-step explanation:

Because they're parallel lines cut by a transversal. So, <W is where one angle is, and <Z is where another angle is. They both share a side as well. Always look out for those types of triangles because those are types of hidden information

(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

Given that,

One thousand bacteria make up a culture at the beginning. The number of bacteria is 8000 after an hour.

We have to find

(a) Track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, locate the population.

(c) How long will it take for there to be 15,000 bacteria?

(d) Draw the population function's graph.

We know that,

(a) The initial size of the culture is 1000 bacteria.    

So,  

n₀=500

The size of the culture after one hour (for t =1) is 4000 so we extract the equation:

n(1) = 8000

1000er¹=8000

e to the power of r =8

[taking logarithms both side]    

r ln e  =  ln 8                          

r=2.080

[ln e  =  1]

So, we got  

n₀=1000 and r=2.08

The function will be,

n(t)=1000[tex]e^{2.08t}[/tex]

(b) for t = 1.5

n(1.5)=1000[tex]e^{2.08(1.5)}[/tex]

22646

(c) 15000=1000[tex]e^{2.08t}[/tex]

15=[tex]e^{2.08t}[/tex]

Taking log on both sides

ln15= 2.08(t)lne

t=3.68/2.08

t=1.7

(d) Since we have have the exponential equation therefore our graph should be curve not straight line.

Also at t=1, population of bacteria is 4000

Hence the correct graph will be in picture.

Therefore,

(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

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Answer: 14 degrees.

Step-by-step explanation: The sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, if we know the measures of two of the interior angles of a triangle, we can use this fact to find the measure of the third angle.

In this case, we are given that two of the interior angles of the triangle have measures of 54 and 112 degrees. We can use this information to find the measure of the third angle as follows:

180 degrees = 54 degrees + 112 degrees + x

180 degrees = 166 degrees + x

x = 180 degrees - 166 degrees

x = 14 degrees

Therefore, the measure of the third angle of the triangle is 14 degrees.

The given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable.

Independent, dependent, and controlled variables are typically present in an experiment.

The variable that is altered by the scientist is the independent variable.

A false correlation between two variables indicates that their correlation coefficient is almost zero.

When two variables have a strong correlation, altering the value of one will not affect the other.

Therefore, the given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

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Answer:

Area = 81 pi

circumstance = 18 pi

Step-by-step explanation:

radius = 9

Answer:

M+N is defined

All others not defined

Step-by-step explanation:

Two matrices can be added or subtracted if and only if they have the same dimensions i.e. they must have the exact same number of rows and number of columns

Only M and N with dimensions (4 x 2) each can be added or subtracted.

(4 x 2 ) means 4 rows and 2 columns

So the only defined operation is
M + N

All the others are not defined

Answer:

[tex]\textsf{De\:\!fined}: \quad \boxed{M + N}[/tex]

[tex]\textsf{Not\:de\:\!fined}: \quad \boxed{N - Q} \quad \boxed{Q + L} \quad \boxed{M - P}[/tex]

Step-by-step explanation:

Generally, a matrix is referred to as [tex]n\times m[/tex] where n is the number of rows and m is the number of columns.

Therefore:

Matrices can be added or subtracted only when they are the same size.

[tex]\boxed{N - Q}[/tex]

Matrices N and Q are different sizes. Therefore, the operation is not defined.

[tex]\boxed{M + N}[/tex]

Matrices M and N are the same size. Therefore, the operation is defined.

[tex]\boxed{Q + L}[/tex]

Matrices Q and L are different sizes. Therefore, the operation is not defined.

[tex]\boxed{M - P}[/tex]

Matrices M and P are different sizes. Therefore, the operation is not defined.

There is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

In inferential statistics, the null hypothesis states that two possibilities are equal.

The observed difference is thought to be the sole product of chance, which is the underlying premise.

Statistical tests can be used to calculate the likelihood that the null hypothesis is true.

So,

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

As the population standard deviation is given when n > 30

So, we'll run the Z test.

Formula: [tex]z=\frac{x-\mu}{\frac{a}{\sqrt{n}}}[/tex]

Replace the values:

[tex]\begin{aligned}& z=\frac{7.7-7.6}{\frac{11.6}{\sqrt{160}}} \\& z=2.449\end{aligned}[/tex]

For the p-value, see the z table.

Consequently, p = 0.9927.

The two-tailed nature of the test So, p = 2(1- 0.9927) = 0.0146

α = 0.1

p value< α

Thus, we disregard the null hypothesis.

Hence, at the 0.1 level, there is enough evidence to conclude that the valve does not function as intended.

Therefore, there is sufficient data to infer that the valve does not operate as intended at the 0.1 level.

Null hypothesis: H₀ : μ = 7.6

Alternative hypothesis: Hₐ : μ ≠ 7.6

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w should be equal to 92° to prove that r || s.

To prove whether the two lines are parallel we should know whether

So for the given condition, the diagram is drawn. Mark the angles w, x, y, and z.

From the diagram, by the Corresponding Angles Theorem, ∠w=∠92°.

The answer is w. Therefore, option a is correct.

The complete question is -

Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?

a)w

b)x

c)y

d)z

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Answer:

94

Step-by-step explanation:

if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pig with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

Answer:

Step-by-step explanation:if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pit with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

Using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

So, we have -9 - 9√3i:

This quantity has a modulus.

|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18

And argument θ to the effect:

tan(θ) = (-9√3) / (-9) = √3

We anticipate that will be between -π and -π/2 radians since -9-9√3i lies in the third quadrant of the complex plane, so that:

θ = arctan(√3) - π = π/3 - π = -2π/3

The polar form is then:

18 (cos(-2π/3) + i sin(-2π/3))

And since -2π/3 is the same angle as 2π - 2π/3 = 4π/3, the right answer is: 18 (cos(4π/3) + i sin(4π/3))

Therefore, using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

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Complete question:
What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot?

a. 9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

b. 9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

c. 18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

d. 18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Answer:

18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Step-by-step explanation:

D

There are a total of 216 ways in which the waiter could serve the meal types.

Let the beef meal be denoted by B, chicken meal by C, and fish meal F. Now say the nine people order meals BBBCCCFFF respectively and say that the person who receives the correct meal is the first person. We will solve for this case and then multiply by 9 to account for the 9 different ways in which the person to receive the correct meal could be picked.

Now, we need to distribute meals BBCCCFFF to orders BBCCCFFF with 0 matches. The two people who ordered B's can either both get C's, both get F's, or get one C and one F.

If the two B people both get C's, then the three F meals left to distribute must all go to the C people. The F people then get BBC in some order, which gives three possibilities.

If the two B people both get F's, the situation is identical to the above and three possibilities arise.

If the two B people get CF in some order, then the C people must get FFB and the F people must get CCB. This gives 2*3*3 = 18 possibilities.

In total, we see there are 24 possibilities, so the answer is 9*24 = 216

Thus, there are a total of 216 ways in which the waiter could serve the meal types.

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Your question was incomplete. Check for missing part below-

Find the number of ways in which the waiter could serve the meal types to the nine people so that exactly one person receives the type of meal ordered by that person.

Answer:Y=1/2x+2

Step-by-step explanation:

Slope intercept form is y=mx+b

m=slope

b= y intercept

y=1/2x+2