What division problem does this area model represent?

If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set

[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]

and as a type II region,

[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]

where we solve y = √(x + 1) for x to get x as a function of y.

A. The area of the type I region is

[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]

B. The area of the type II region is of course also

[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]

I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).

[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]

Answer:

False

Step-by-step explanation:

9(k-2)=-6 and k=1

9(1-2)=-6

9(-1)=-6

-9=-6

No, -9 doesn't equal -6.

So this system of equations is false.

Hope this helped! :)

Option third "words per minute, because the independent quantity is the minutes" is the correct choice.

It is defined as the change in values of a dependent variable with respect to the independent variables.

We have a statement:

Which of the following is the most appropriate unit to describe the rate at which a person reads?

As we know the rate of change is the ratio of change in y to change in x.

y is the dependent quantity and x is the independent quantity.

Rate of change = change in y/change in x

Rate at which a person reads = words/minute

Word is the dependent quantity and minute is the independent quantity.

Thus, option third "words per minute, because the independent quantity is the minutes" is the correct choice.

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If you spin the spinner 52 times, we expect the spinner to land on purple approximately 13 times in 52 spins.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

Since there are 4 equal-sized sectors on the spinner, the probability of landing on purple on any given spin is 1/4.

To find the expected number of times the spinner will land on purple in 52 spins, we can multiply the probability of landing on purple by the total number of spins:

Expected number of times landing on purple = (Probability of landing on purple) x (Total number of spins)

Expected number of times landing on purple = (1/4) x (52)

Expected number of times landing on purple = 13

Therefore, we expect the spinner to land on purple approximately 13 times in 52 spins.

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Answer:

So basically you solve for y

so its gonna be -4y = 12-2x, then divide everything by -4 to solve for y which will be equal to -3 + 1/2x

just write it as 1/2x -3 cause its better

Hope that answers your question

Step-by-step explanation:

Answer:

y = -3 +1x/2

Step-by-step explanation:

2x - 4y = 12

-4y = 12 -2x

y = 12/-4 - 2x/-4

y = -3 +x/2

Answer:

18

Step-by-step explanation:

my answer is correct,try to read the question,

if the length of larger triangle is 6 times so it means 6 ×5= 30 and you will times 3 to 6=18

so that's why it has lenght of 30

because the. larger triangle is 6 times bigger than smaller rectangle

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The domain is  All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.

A function is defined as a mathematical statement that identifies the relation between a dependent and an independent variable.

A function has a defined range and domain.

In the given function

y = (5/3)tan(3x/4)

Domain is the all the value at which the function is defined .

Tan x is defined for every value except at

x = (2n+1)π/2

The domain of the function y = (5/3)tan(3x/4) is

3x/4 = (2n+1)π/2

x = (2n+1)2π/3

Therefore the domain is  All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.

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Nani wait what I don't know

Step-by-step explanation:

please mark me as brainlest

Answer:

[tex]4*6^\frac{5}{2}[/tex]

Step-by-step explanation:

Use [tex]\sqrt[n]{a^x}=a^{\frac{x}{n} }[/tex] to rewrite [tex]\sqrt{6^5}[/tex] as [tex]6^\frac{5}{2}[/tex].

[tex]4*6^\frac{5}{2}[/tex]

The measure of the remote exterior angle is 128°.

From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)

198 - 5n = 6n + 44

Collect like terms

154 = 6n + 5n

154 = 11n

n = 154/11

n = 14

The value of angle x will be:

= 198 - 5n

= 198 - 5(14)

= 198 - 70

= 128

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The area of the park is 1640 square meters.

A quadrilateral is a plane shape with four sides and four angles.

The above figure is made up of two quadrilateral; a square and a trapezium.

Analysis:

Area of park = area of square + area of trapezium

Area of park = 1/2(a + b)h + s x s

where a = length of smaller parallel side of the trapezium = 40m

           b = length of the larger parallel side = 48m

           h = height of trapezium = 35m

           s = length of side of square = 10m

Area of park = 1/2(40 + 48)x35 + 10 x 10 = 1640 square meters

In conclusion, the area of the park is 1640 square meters

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Answer:

315

Step-by-step explanation:

The number is divisible by 3,5,7 and 9. Since 3 is a factor of 9, this number is divisible by 5,7, and 9.

5x7x9= 315.

==================================================

Explanation:

Replace f(x) with 0 and solve for x.

f(x) = 3x-12

0 = 3x-12

3x-12 = 0

3x = 12

x = 12/3

x = 4 is a zero, aka root, of the function

---------------

Check:

f(x) = 3x-12

f(4) = 3(4)-12

f(4) = 12-12

f(4) = 0

The answer is confirmed.

Answer:
10

Step-by-step explanation:

-3x+7x-8=34+9x-2

(Combine like terms)

4x-8=32

(Add 8 to each side)

4x=40

(Divide by 4)

X=10

The equation for the sinusoidal function described is given as follows:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

We want a function with a y-intercept at it's maximum value, hence we use the cosine equation, given by:

[tex]y = A\cos{\left(\frac{2\pi}{B}x\right)} + C[/tex]

In which:

The amplitude is of 8, hence 2A = 8 -> A = 4. This would represent a function between -4 and 4, but we want between -2 and 6, hence the vertical shift is of C = 2.

As for the period, we have that:

[tex]B = 4\pi[/tex]

Then, the equation is given by:

[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]

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Answer:

length: 9 units width: 2 units

Step-by-step explanation:

The formula to find the area of a rectangle is length*width (LW)

x+3 is the length and x-4 is the width; together they multiply up to 18

(x+3)(x-4) = 18

x^2 - 4x + 3x - 12 = 18 (multiply it out using FOIL)

x^2 - x - 12 = 18 (combine like terms on the left side)

x^2 - x -30 = 0 (subtract 18 from both sides so that the right side is 0)

Think what two numbers multiply up -30 and add up to -1 (5 and -6)

(x+5)(x-6) = 0 (factor it)

x+5 = 0 and x-6 = 0 (solve using zero-product property)

x = -5 and x = 6 (solve)

x = 6 (only this one works since you cannot have a negative side length)

(6+3)(6-4) = 18 ? (plug in to find side lengths and check)

9 * 2 = 18 (Correct!)

Answer:

  length: 9 ft

  width: 2 ft

Step-by-step explanation:

This can be worked using a quadratic equation, or it can be worked by considering factors of the area value.

__

The difference in length between the long side (x+3) and the short side (x-4) is ...

  (x +3) -(x -4) = 3+4 = 7 . . . . feet

The area formula is ...

  A = LW

The given area is 18 square feet, so we want to find numbers that multiply to give 18 and that differ by 7 in their values. Here are the integer factors of 18:

  18 = 1×18 = 2×9 = 3×6

Of these factor pairs, the values 2 and 9 differ by 7.

The garden is 9 feet long and 2 feet wide.

_____

Additional comment

We can check to see if these numbers are consistent with the given expressions:

  x+3 = 9  ⇒  x = 6

  x -4 = 6 -4 = 2 . . . . the other dimension we found

__

If you solve this using a quadratic equation, you will find that dimensions -2 ft and -9 ft also pop out. That is x +3 = -2, or x = -5 is also a solution to the quadratic. Of course, that is an extraneous solution, which we avoid by considering only positive factors of 18.

The quadratic equation we're referring to is A=18 ⇒ (x+3)(x-4) = 18.

Answer:

12 is 50% of 24

7 is 20% of 35

9 is 10% of 90

20/60 is 33.33%

Answer:

372

Step-by-step explanation:

We know that a ratio of 3 : 2 has 5 people, so figuring out how many times that ratio goes into our total number helps us find the value of the total number of adults.

930 / 5 = 186

This means that there are 186 groups of 3 children to 2 adults

So, in each of the 186 groups, there are 2 adults.

Therefore, we can multiply (186)(2)

to find the total number of adults: 372

The number of the children and adult will be 558 and 372.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

At a swimming pool, the ratio of children to adults was 3 : 2.

C / A = 3 / 2

Then solve the equation for C, then the equation will be

C = (3/2)A

The total number of the people is 930. Then the equation will be

C + A = 930

Substitute the value of C in the above equation. Then the equation will be

(3/2)A + A = 930

     (5/2)A = 930

            A = 930 x (2/5)

            A = 372

The number of the adult will be 372.

Then the number of the children will be

C + 372 = 930

         C = 930 – 372

         C = 558

The number of the children will be 558.

Thus, the number of the children and adult will be 558 and 372.

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Answer: Common Core Performance Assessment.

The Name Game

Pairs of students in Mr. Kuan's class are playing the

Name Game. One team member is given a list of attributes

and has to draw a shape to match the description. The other

team member must then name the shape. The first pair to

complete the task wins.

Wilfredo was given a list with the information at the right.

He drew a shape and his partner, Olivia, named it. What shape

did Wilfredo draw? Answer Exercises 4-7 to solve the problem.

.

•

4. MP.1 Make Sense and Persevere What are you asked to do?

What can you do to persevere when solving the problem?

5. MP.6 Be Precise What math terms and numbers can help you

solve the problem?

6. MP.7 Use Structure What do you know about a quadrilateral?

Use what you know to draw and name a shape that matches

the information in the list.

. MP.3 Construct Arguments Is there more than one possible

way for Wilfredo to draw the shape? Explain.

A quadrilateral

2 sides are parallel

2 sides are equal

2 right angles

Attend to precision by

identifying words and

numbers that can help you

solve the problem.

Step-by-step explanation:

Answer: 60 degrees

Step-by-step explanation:

1. Make a right triangle where the right angle is and label the hypotenuse r.

2. Since the chord is equal to r and a 90-degree angle is formed at the intersection, the chord is bisected. Therefore, the chord segment is 1/2 r.

3. Since we have to solve for the intercepted arc, we must find the central angle ( the angle of the right triangle closest to the dot/center) of the arc, which in this case is the sin, or 0.5r/r.

4. We must get rid of the fraction in the numerator, so multiply both the numerator and denominator by 2 which gets you 1r/2r.

5. The r's cancel out, leaving you with 1/2.

6. Since we have to find the angle measure, you must take the negative sin of 1/2 which is 30 degrees.

7. Finally multiply by 2 since you only solved one bisected portion to get 60 degrees.

Answer:

Step-by-step explanation:

60

We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

In an arithmetic sequence, the difference between any two consecutive terms is a constant.

Here we know that:

[tex]a_1 = 3/5\\a_8 = 1/4[/tex]

There are 7 times the common difference between these two values, so if d is the common difference:

[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]

Then the sum of the first 8 terms is given by:

[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]

So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

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Answer:

17

Step-by-step explanation:

The median of a data set can simply be thought of as the middle value/number.

You could list all values out:

16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19

and then find what the middle of 24 would be (There are an even number of values, so both numbers in places 12 and 13 are considered the median, meaning that we find the average of these two values to be our median)

the 12th value is 17, and the 13th value is 17, meaning that the median is 17.

-----------------------

You could also calculate what would be 12 "in" from the data set. The first 4 values are 16 (12 - 4 = 8 ; 8 values left to go until middle) And then take the remaining 8 places to find the 12th value (9 - 8 = 1), so you know that the 12th value is the 8th repetition of 17.

There is still one more value of 17, so that is also the 13th placed value.

In this method of finding the middle number, the median is still 17.  

The median of these ages is 17.

The median exists as the middle number in a sorted checklist of numbers and can be better descriptive of that data set than the average. The median exists sometimes utilized as objected to the mean when there exist outliers in the sequence that might skew the average of the values.

The median of a data set can only be considered as the middle value.

Let the values be 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19

To find the middle of 24 would be (There exist an even number of values, so both numbers in places 12 and 13 exist considered the median) the 12th value stands at 17, and the 13th value stands at 17, indicating that the median exists at 17.

You have to calculate an estimate of 12 "in" from the data set. The first 4 values exist 16 (12 - 4 = 8; 8 values left to go until middle)

Consider the remaining 8 places to estimate the 12th value (9 - 8 = 1)

The 12th value exists in the 8th repetition of 17.

Therefore, the median of these ages is 17.

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The equation represented by the graph will be y = eˣ. Then the correct option is A.

The missing graph is given below.

Functions are found all across mathematics and are required for the creation of complex relationships.

The graph is given below.

The exponential graph is always positive and the graph is also positive of the Real value of x.

The equation represented by the graph will be y = eˣ.

Then the correct option is A.

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Answer :

Step-by-step explanation :

We have been provided with the volume of water tank , it's length and breadth. We are asked to calculate the depth of tank (height), so we all know that water tank is always is in the shape of cuboid.

We would be using the formula of calculating the volume of cuboid and substitute the values in it.

Here,

We have :

Substituting the values :

>> 396 = 7.2 × 5.5 × h

>> 396 = (72 / 10) × (55 / 10) × h

>> 396 = 72 × 55 × h / 100

>> 396 = 3960 × h / 100

>> 396 × 100 = 3960 × h

>> 39600 = 3960h

>> h = 39600 / 3960

>> h = 3960 / 396

>> h = 10

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