16x + 9 = 9y - 2x
need the step and answer.

The lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].

Given:

Find the moment of inertia [tex]I_y[/tex] and [tex]I_0[/tex].

The lamina's moment of inertia about the x-axis is:

In the above equation, substitute the given value:

Make use of polar coordinates:

[tex]\begin{aligned}x &=r \cos \theta \\y &=r \sin \theta \\d A &=d x d y=r d r d \theta \\D &=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]

As we all know, the general equation of a circle is:

The given circle equation is:

As a result, r ranges from 0 to 4.

And ranges from 0 to 2[tex]\pi[/tex].

As a result, the integral is shown below; simply enter all of the values and then integrate.

[tex]\begin{aligned}&I_x=\iint_D 5 y^2 d A \\&I_x=\int_0^{2 \pi} \int_0^4 5(r \sin \theta)^2 r d r d \theta \\&I_x=\int_0^{2 \pi} \int_0^4 5 r^3 \sin ^2 \theta d r d \theta \\&I_x=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi} \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_x=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_x=320\left(\frac{2 \pi}{2}\right) \\&I_x=320 \pi\end{aligned}[/tex]

Now, calculate  [tex]I_y[/tex] and [tex]I_0[/tex].

Make use of polar coordinates.

[tex]\begin{aligned}&x=r \cos \theta \\&y=r \sin \theta \\&d A=d x d y=r d r d \theta \\&D=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]

As we all know, the general equation of a circle is:

The given circle equation is:

As a result, r ranges from 0 to 4.

And ranges from 0 to 2[tex]\pi[/tex].

As a result, the integral is shown below; simply enter all of the values and then integrate.

[tex]\begin{aligned}&I_y=\iint_D 5 x^2 d A \\&I_y=\int_0^{2 \pi} \int_0^4 5(r \cos \theta)^2 r d r d \theta \\&I_y=\int_0^{2 \pi} \int_0^4 5 r^3 \cos ^2 \theta d r d \theta \\&I_y=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi} \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_y=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_y=320\left(\frac{2 \pi}{2}\right) \\&I_y=320 \pi\end{aligned}[/tex]

The lamina's moment of inertia about the origin is given by:

[tex]\begin{aligned}&I_0=\iint_D\left(x^2+y^2\right) d(x, y) d A \\&I_0=\iint_D 5 r^2 r d r d \theta \\&I_0=5 \int_0^{2 \pi} \int_0^4\left(\frac{r^4}{4}\right)_0^4 d \theta \\&I_0=320 \int_0^{2 \pi} d \theta \\&I_0=320(\theta)_0^{2 \pi} \\&I_0=640 \pi\end{aligned}[/tex]

So, the moment of inertia is [tex]I_x=320 \pi[/tex].

The worth of, [tex]I_y=320 \pi[/tex].

Therefore, the lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].

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The correct question is given below:

Find the moment of inertia about the x-axis of a thin plate with density δ=5 bounded by the circle x2+y2=16. Then use your result to find Iy and Io.

If a coastline decreases by 3 cm each year for a total of 8 years. the integer that represents the total loss of coastline is: -24. The integer that can be use to represent the decrease is -3 and the expression that represent the total loss of coastline over 8 years is 8 (-3).

Given:

Decrease in coastline=-3

Total number of years=8 years

Hence,

a. Integer that represent the total loss of coastline is:

Integer=8(-3)

Integer=-24 (Total loss)

b. The integer that can be use to represent the decrease is:

Decrease in coastline= -3

c. The expression that represent the total loss of coastline over 8 years is:

Expression= 8(-3)

Therefore If a coastline decreases by 3 cm each year for a total of 8 years. the integer that represents the total loss of coastline is: -24. The integer that can be use to represent the decrease is -3 and the expression that represent the total loss of coastline over 8 years is 8 (-3).

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When Maria distribute the lunches to the 22 students equally, each person gets 1.6 of the meal.

It should be noted that from the information, Maria must distribute the lunches to the 22 students equally.

Therefore, the total foods will be:

= (3 + 6 + 25 + 2) / 22

= 36 / 22

= 1.6

Therefore each person gets 1.6 of the meal.

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The solution region for the given pair of inequalities is found to be the common shaded region in the graph attached.

For drawing the graph of any inequality, we first have to assume the inequality as an equation and draw the graph of the resulting equation. Hence, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (-2,0)

Now, putting x=0, we get:

The point will be: (0,4)

Now as the sign of inequality is >, the line of graph will be dotted.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be away from the test point.

Similarly, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (6,0)

Now, putting x=0, we get:

The point will be: (0,6)

Now, as the sign of inequality is of , the line of graph will be solid.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be towards the test point.

The resulting graph is attached after the solution.

The solution to the pair of given inequalities will be the shaded region that is common between both the individual inequality's shaded regions.

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The statement, "A survey of 1455 people revealed that 53% work a full-time job; therefore it can be assumed that 53% of the u.s. population works a full-time job" describes Inferential statistics.

Inferential statistics is a sort of statistic that requires people to reach a conclusion based on some previously provided samples. In the statement above, we can see some statistics that have been previously stated that is followed by a conclusion.

The assumption that is made in the latter part of the statement is the reason why the statement can be referred to as inferential statistics.

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The rise-over-run formula for the slope of a straight line is the basis of the high-low method.

What is slope of a straight line?

The slope of a straight line by joining two points is the rise over run formula. The subtraction between the two points of the y-coordinates is called the rise. And the subtraction between the two points of the x-coordinates is called the run. The slope can be calculated by dividing the rise by run.

The slope of a line either goes in the upward direction or in the downward direction or left direction or right direction. It determines the direction of the line. When the straight line goes in the upward direction, it means the rising line and slope is positive. When it goes in the downward direction, it means a falling line and slope is negative.

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From the regression line of the data, we have that:

1) The slope is of -1.31.

2) The intercept is of 272.17.

3) The correlation coefficient is of -0.9.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points are given as follows:

(31, 206), (51, 229), (87, 184), (102, 126), (120, 103).

Inserting these points into a calculator, the equation of the line is:

y = -1.31x + 272.17.

Hence:

1) The slope is of -1.31.

2) The intercept is of 272.17.

Also inserting these points into a calculator, the correlation coefficient is of -0.9.

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Applying the definition of a segment bisector, the length of CD is: 59 units.

A line segment that bisects a line segment is known as a segment bisector. It divides the line segment into two smaller segments that are equal in length to each other.

Since line k bisects BD at point C, therefore, based on the definition of a segment bisector, we have the following equation:

2(BC) = BD

BC = 9x - 13

BD = 118

Substitute the values

2(9x - 13) = 118

18x - 26 = 118

18x = 118 + 26

18x = 144

18x/18 = 144/18

x = 8

CD = BC = 9x - 13

CD = 9x - 13 = 9(8) - 13

CD = 59 units

Therefore, applying the definition of a segment bisector, the length of CD is: 59 units.

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Option c. The next in series is blue picture with 7 lines.

The series is following the trend, Red, Blue, Red…. So, the next in this series should be blue.

Next is the pattern of picture. Straight line, 45 degree to both lines from center, 45 degree from preceding lines. So, next should be 45 degree from both the preceding lines.

Next is the number of lines. This follows the pattern as 1 line, 3 line, 5 line. From this it's clear that here follows the odd number pattern. So the next should be picture with 7 lines.

Finally we cam conclude that the next in this series is option c, the blue picture with 7 lines.

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The percent increase in population of the city is 17%.

A percentage in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). A percentage lacks dimensions and has no associated unit of measurement.

For instance, 45% (written as "forty-five percent") equates to the fraction [tex]\frac{45}{100}[/tex]  .

The percentage increase is calculated by the ratio of the increase to the original value. So to calculate the percent increase in the population of a city we have to find the ratio of the increase in population to the original population.

The population of the city is given as 117,000 .

The population increased to 136890.

Increase in population=136890-117000=19890

percentage increase in population

[tex]=\frac{19890}{117000} \times 100\%[/tex]

= 0.17×100%

=17%

The percent increase in the population of the city is 17%.

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The Interpret (N · T)(t) is [tex]N[T(t)] = 20t^{2}+92t+205.[/tex]

The number of bacteria after 5 hours will be 1165.

It will take for the bacteria count to reach 2221.

As per the question statement, the number of bacteria "N" in a refrigerated food is given by [N(T) = (5T² - 4T +100)], where "T" is the temperature of the food in degrees Celsius,

And when the food is removed from the refrigerator, the temperature of the food is given by [T(t) = (2t+5)].

First we are required to find out (N · T)(t), which is N[T(t)] which can be expressed as

[tex]N[T(t)] = 5[T(t)]^{2} - 4T +100\\or, N[T(t)] = 5(2t+5)^{2} -4(2t+5)+100\\or, N[T(t)] = 5(4t^{2}+25+20t)-8t-20+100\\ or, N[T(t)] = 20t^{2} +125+100t-8t+80\\ or, N[T(t)] = 20t^{2}+92t+205.[/tex]

Then, the number of bacteria after 5 hours will be N[T(5)], i.e.,

[tex]N[T(5)] = 20(5^{2})+(92*5)+205\\or, N[T(5)] = (20*25)+460+205\\or, N[T(5)] = 500+665\\or, N[T(5)]=1165[/tex]

And finally, the time required for the bacteria count to reach 2221 can be calculated by solving the quadratic equation [tex][2221 = 20t^{2}+92t+205][/tex], i.e.,

[tex][20t^{2}+92t+205 = 2221]\\or, 20t^{2}+92t+(205-2221)=0\\or,20t^{2}+92t-2016=0\\or, 5t^{2}+23t+504=0[/tex]

And the formula to calculate the solutions of a standard quadratic equation [ax² + bx +c = 0] goes as

[tex]x=\frac{-b+\sqrt{(b^{2}-4ac) } }{2a}, \frac{-b-\sqrt{(b^{2}-4ac) } }{2a}[/tex]

Comparing [ax² + bx +c = 0] with [5t² + 23t + 504=0], we get

(a = 5), (b = 23) and (c = -504), and using these values in the above mentioned formula to calculate the solutions of quadratic equations, we get, [t = 8, (-12.6)].

Since time (t) cannot be negative, thus [t ≠ (-12.6)].

Hence, (t = 8) or, the time required for the bacteria count to reach 2221 is 8 hours.

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Answer:

48 or -48

Step-by-step explanation:

Answer: x=138 degrees

Step-by-step explanation:

x+42=180 ==> Angle x and the supplementary angle of 42 are congruent angles, meaning that x and 42 add up to 180 degrees.

x-42+42=180-42

x=180-42

x=138 degrees

Answer: it cost 14 dollars

Step-by-step explanation:

Nearly 80% of those surveyed said they want to work for a company that values diversity, equity, and inclusion issues.

Value is utilized as capital raised by an organization, which is then used to buy resources, put resources into ventures, and asset tasks. A firm commonly can raise capital by giving obligation (as a credit or through bonds) or value (by selling stock). In finance, value is responsibility for that might have obligations or different liabilities joined to them. Value is estimated for the purpose of bookkeeping by taking away liabilities from the worth of the resources. For instance, on the off chance that somebody possesses a vehicle worth $24,000 and owes $10,000 on the credit used to purchase the vehicle, the distinction of $14,000 is value. Value can apply to a solitary resource, like a vehicle or house, or to a whole business. A business that requirements to fire up or grow its tasks can offer its value to raise cash that doesn't need to be reimbursed on a set timetable.

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Answer:

Hes 3

Step-by-step explanation:

its 1/4 of 12 = 3

Answer:

43.

Step-by-step explanation:

12 • 4 - 5 = 43. Mr Anderson is 43.

Answer:

-2(5y-3)= -10y-6 should instead be -10y+6 because two negatives multiplied together is a positive integer which is why you have +6 and not -6 so it'll be the second bullet point: he should have subtracted (-2x3) resulting in the expression -10y+6

Answer:

-3^2 = -9

(-3)^2 = 9

Step-by-step explanation:

-3^2  only the 3 is being squared.  So he answer is -(3) which is -3

In the second problem (-3)^2  Everything inside the parentheses is being squared. (-3)(-3) = 9

Answer: It is 3/2 = p

Step-by-step explanation:

1. 2p - 9 = 3(2p - 5)
2. 2p - 9 = 6p - 15
3. -9 = 4p -15
4. 6 = 4p
5. 3 = 2p
6. 3/2 = p

Answer:

6/4 or 3/2

Step-by-step explanation:

To this problem, we need to use the distributive property, and we also need to combine like terms.

2p-9=3(2p-5)

2p-9=6p-15

Subtract 2p on both sides

-9=4p-15

Add 15 on both sides

6=4p

Now divide 4 on both sides

6/4 or 3/2

I hope this helped!

Have a wonderful day!

:D

Simplifying quantity x squared plus 3 x plus 2 end quantity over quantity x will give x+2.

It should be noted that the expression given is illustrated as:

(x² + 3x + 2) / (x + 1)

(x² + x + 2x + 2) / (x + 1)

x(x + 2) 1)2(x+1) / (x + 1)

= (x + 2)(x + 1) / (x + 1)

= x + 2.

Therefore, the correct value is x + 2.

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Answer:

[tex]-46p+54[/tex]

Step-by-step explanation:

First, distribute -6 to both 6p and -9. That gives you -36p + 54-10p

Add like terms:

-46p+54

Answer:

Question 7: 20° and 160°, Question 8: 10° and 80°

Step-by-step explanation:

Complementary angles add to 90° and supplementary angles add to 180°.

Answer:

Hope this helps :)

Missing fraction is 2/6

5/6 - 2/6 = 3/6 = 1/2 (simplified)

Answer:

84, 76 , 57

Step-by-step explanation:

substitute b = 2 into the expression

9(2)(2 + 3) - 6 = 18(5) - 6 = 90 - 6 = 84

substitute y = 6 into the expression

12(6) + 4 = 72 + 4 = 76

substitute r = 10 into the expression

6(10) - 3 = 60 - 3 = 57

Answer: 84, 76, 57

Step-by-step explanation:

1. 9b (b+3) -6     b=2

   9(2) (2+3) -6

   18 (2+3) -6

   18 (5) -6

   90 -6

   84

2. 12y + 4     y=6

   12(6) + 4

   72 + 4

   76

3. 6r - 3     r=10

   6(10) - 3

   60 - 3

   57

The number of people that must be in the group is 15.

The expression for the total cost of Deal A is: $9p + $15

The expression for the total cost of Deal B is: $6p + $3p

Where p is the number of people in the group

When both promotions cost the same, both expressions would be equal:

$9p + $15 =  $6p + $3p

In order to determine the value of p, take the following steps:

Combine similar terms

$6p + 3p - 9p = 15

p = 15

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If the distance from the sun to mercury is 36270000 miles and the distance from sun to Saturn is 8×[tex]10^{8}[/tex] miles, then it is about 22 times larger is the distance from the sun to Saturn than the distance from the sun to mercury

Given,

The distance from the sun to mercury = 36270000 miles

The distance from the sun to Saturn = 8×[tex]10^{8}[/tex] miles

Then,

The number of times  larger is the distance from the sun to Saturn than the distance from the sun to mercury

[tex]\frac{8*10^{8} }{36270000} =22.05[/tex]

≈22 times

Hence, if the distance from the sun to mercury is 36270000 miles and the distance from sun to Saturn is 8×[tex]10^{8}[/tex] miles, then it is about 22 times larger is the distance from the sun to Saturn than the distance from the sun to mercury

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From the given ratio, the number of yellow flowers are; 40 flowers

We are given;

Total number of flowers in the garden = 56

Ratio of orange to yellow flowers is; 2:5

Thus;

Fraction of total gives;

Fraction that is orange flowers = 2/7

Fraction that is yellow flowers = 5/7

Thus;

Number of yellow flowers = (5/7) * 56

Number of yellow flowers = 40 yellow flowers

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Answer:

opcation a

Step-by-step explanation: