A stack of logs has 22 logs on the bottom layer. Each subsequent layer has 4 fewer logs than the previous layer. If the top layer has two​ logs, how many total logs are there in the​ pile?

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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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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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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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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The graph for the system of linear equation is attached

An equation is said to be linear if the variables are of power not greater than one. This is to say the power of the variables should be one. It is a norm in math not to write the power when the power is one

For the equation given the the powers of both y and x are all 1. Linear equations also have a straight line graph hence have the equation of straight line represented as

y = mx + c

where:

m is the slope

c is the y intercept

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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 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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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:

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

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:

[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:

Hope this helps :)

Missing fraction is 2/6

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

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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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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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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Answer:

90 miles

Step-by-step explanation:

18/12 = ?/60

12*5=60

18*5=90

90/60

Hope that helps :)

Answer:

10%

Step-by-step explanation:

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:

opcation a

Step-by-step explanation:

The total distance of the race = 8.91  miles

Solution :

Miles :

There are 5,280 feet in one mile. Simply divide 5,280 feet by your average stride length to learn how many steps it will take to walk a mile. If your average stride length is 2 feet, for example, it will take 2,640 steps to walk a mile.

One part of the race is 3.21 miles

another part of the race is 5.7 miles

Total :

add of both trails

= 3.21+5.7

= 8.91

The total distance of the race = 8.91  miles

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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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Answer:

translated 9 units to the right and 2 units down

Answer:The first one is translated 9 units to the right and 2 units down.The second is reflected across the x-axis and the last i reflected across the y-axis.

Step-by-step explanation:Please give brainliest if correct.

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.

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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Answer:

x=− 2/5

Alternative Form

x=−2.5

Step-by-step explanation:

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.

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 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