A population of beetles are growing according to a linear growth model. The initial population (week 0) is
PO=4
, and the population after 8 weeks is
P8=52
Find an explicit formula for the beetle population after
n weeks

After how many weeks will the beetle population reach 184?

Answer:

the answer is 2ft

Step-by-step explanation:

I hope its right

Answer:

the walkway is 2 feet wide

Step-by-step explanation:

x=walkway width

(12+2x)(16+2x)=320

192+24x+32x+4x^2=320

simplify

4x^2+56x+192=320

4x^2+56x-128=0

divide by 4

x^2+14x-32=0

factor

(x+16)(x-2)=0

x=-16

x=2

Answer:

Angles in a triangle sum to 180.

So

x= 180 - 75 - 43

x=62°

Answer:

x=62°

Step-by-step explanation:

x= 180 - 75 - 43

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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The measure of the angle m∠RQS subtended by the arc RS at the circumference is equal to 70°

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

arc RS = 2(m∠RQS)

Also arc AD = 140°

2(m∠RQS) = 140°

m∠RQS = 140°/2 {divide through by 2}

m∠RQS = 70°

Therefore, the measure of the angle m∠RQS subtended by the arc RS at the circumference is equal to 70°

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The equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

We can observe from the table that the number of books collected increases by 10 for each week.

Thus, there is a linear relationship between the number of weeks (w) and the number of books collected (b). We can represent this relationship using the equation:

b = mw + c

where b is the number of books collected, w is the number of weeks, m is the slope (rate of change), and c is the y-intercept (number of books collected at week 0).

The slope (m) is the change in the number of books collected per week, which is 10. We can now find the y-intercept (c) by substituting one of the points from the table into the equation. Let's use the point (1, 10):

10 = 10 * 1 + c

c = 0

Now we have the equation representing the relationship between the number of weeks (w) and the number of books collected (b):

b = 10w + 0

b = 10w

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the data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).

Weeks (w) Books Collected (b)

1 10

2 20

3 30

4 40

Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?

-10 + 5.47722~
=4.523~
round to nearest tenth = 4.5

Answer:

-4.5

Step-by-step explanation:

\(\sqrt{30}\) is approximately 5.47722557505.  You can find this number with a calculator.

-10 + 5.47722557505 = -4.52277442495

To add a negative and a positive number, you subtract the absolute values and take the sign of the number that has the larger absolute value.  Absolute value just means thinking of both numbers as positive numbers.

Helping in the name of Jesus.

Step-by-step explanation:

13113x+1665
_____________________________
Rewrite 13113 as 9 .  1457

Rewrite 1665 as 9 .  185
= 9 .  1457x + 9 .  185
=9(1457x + 185)

If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.

To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:

Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.

Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.

Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.

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Answer:

y=2/3

Step-by-step explanation:

Since y is in the denominator, we take it to the other side to make it the numerator. And 6 also changed sides which results in y=4/6. Reducing to lowest terms we get, y=2/3.

Answer:

(0, 7), (1, 11), (2, 15)

Step-by-step explanation:

to find the y values, plug in the given x values into the equation y= 4x+7

when x = 0

y = 4(0) + 7

y = 0 + 7

y = 7

so the y value that corresponds to the x value 0 is 7 which is also written as (0,7)

when x = 1

y = 4(1) + 7

y = 4 + 7

y = 11

so the y value that corresponds to the x value 1 is 11; also written as (1, 11)

when x = 2

y = 4(2) + 7

y = 8 + 7

y = 15

so the x value 2 corresponds to the y value 15; also written as (2 , 15)

hope this helps

Answer:(0, 7), (1, 11), (2, 15)

Step-by-step explanation:

Answer:

x = 24°

Step-by-step explanation:

If two parallel lines are being intersected by the same line, the opposite inside angles are congruent. This means that ∠EFH should be equal to ∠JHF. However, we cannot set these angles equal because we do not know the value of ∠JHG.

Line IG is intersected by line HJ. This means the value of ∠JHG is 24° (180° - 156° = 24°). Know that we know this value, we can set up an equation to find "x".

∠EFH = 2x

∠JHG = 24°

∠GHF = x

∠EFH = ∠JHF                                  <----- Opposite interior angles are equal

∠EFH = ∠JHG + ∠GHF                   <----- Break ∠JHF into 2 angles

2x = 24 + x                                      <----- Insert values

x = 24                                             <----- Subtract x from both sides

Answer:

There were 30 people attending at the start of the concert

Step-by-step explanation:

The coefficient of the value raised to an exponent in these types of functions is always the "starting" value. In your case, '30' is the coefficient, so it is the starting value. FYI: 1.10 is the rate at which the people increase, t is time passed, 20 is a constant, and P is the total number of people after the time goes by.

Answer:

There were 30 people attending at the start of the concert.

Step-by-step explanation:

30 is the coefficient, so that's your starting point, basically.

The solution to the inequality equation \(x^{2}\) – 9x < –18 is 3 < X < 6

Inequality equation means a mathematical expression in which the sides are not equal to each other

\(x^{2}\) – 9x < –18

Rewrite in standard form

x^2 -9x +18 < 0

Factorise the equation

\(x^{2}\)  - 3x -6x +18 < 0

x (x - 3) - 6 (x - 3) < 0

(x - 3) ( x- 6) < 0

(x - 3) < 0

x < 3

( x- 6) < 0

x < 6

3 < X < 6

Therefore, the solution to the inequality is 3 < X < 6

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Step-by-step explanation:

there is nothing special about this. no need to panic.

any arithmetic operation with functions means that we do these operations with the expressions of the functions. that's all.

(s.t)(x)

just means (s×t)(x) = (4x + 4)(5x) = 20x² + 20x

(s + t)(x) = (4x + 4) + (5x) = 9x + 4

(s - t)(x) = (4x + 4) - (5x) = -x + 4

so, (s - t)(1) = -1 + 4 = 3

Answer:

The first answer

Step-by-step explanation:

Answer:

5509 yes votes

Step-by-step explanation:

We will start by adding together our ratio, so we know how many voters there were in a total ratio, so we can divide our total number of people by it, and then multiply it by the number of people who said yes (7 people).

Our ratio was 7:4, so adding those two numbers together gives us 11. Then, dividing 8657 by 11 gives us:

8657 / 11 = 787

Now, we will multiply 787 by 7, since that was the number of people who said yes:

787 * 7 = 5509

So, there were 5509 yes votes.

Hope this helped!

Answer:

n=-6/4

Step-by-step explanation:

4n+40=34

-40. -40

4n=-6

divide by sides by 4

so n equals -6/4

Answer:

answer is 60

Step-by-step explanation:

80+40+y=180 reason (co-interior angles supplementary)

y=180-80-40

y=60

Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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The measurement of the given angle is a 90 degree.

According to the statement

We have to find that the measurement of this angle.

So, For this purpose, we know that the

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

From the given information:

In the given figure, the measurement of the angle we have to find.

A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.

And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.

Then the angle is 90 degree.

So, The measurement of the given angle is a 90 degree.

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Answer: Let X = the smaller of the two consecutive odd integers. Therefore (X + 2) = the larger of the two consecutive odd integers.

Answer

P= 2L+2W

P=2(12) +2(7) =38

Step-by-step explanation:

The width of a rectangle is 5 meters less than its length. The area is 84 square meters. Find the dimensions of the rectangle and the perimeter of the rectangle.

First it helps to draw a picture so draw a rectangle

Remember that area of a rectangle =Length times width and the perimeter is P= 2 times the length plus 2 times the width

So A=LW and P=2L+2W

84= area

L=length

W= length -5

L(L-5)=84 distribute the L and you have L2 -5L=84 now subtract 84 from both sides and get L2 �5L-84 next factor to get (L+7)(L-12) next set both to =0 (L+7)=0 (L+12)=0 solve for L

L=-7 and L=12 you can�t have a negative length so -7 is out. So L=12 now plug in to the original area equation

84=LW 84= 12w now divide both sides by 12 to isolate W, this gives you W=7

L=12 and W= 7

For perimeter use 12 for the length and 7 for width Remember that P= 2L+2W

P=2(12) +2(7) =38

Answer:

4*9

Step-by-step explanation:

It's obvious.

2(x-3)-17=13-3(x+20)

2x-6-17=13-3x-60

2x-23=-3x-47

5x-23=-47

5x= -24

Answer:

x = -4.8

Step-by-step explanation:

Answer:

She would make 500,000 or else she will speak to the manager.

Step-by-step explanation: Karen will speak to her manager and torture her manager until the manager gives her the money.

Answer: 208

Step-by-step explanation:

$288 ÷ 18 = 16 < 16 would be the amount she gets in 1 hour.

The question asks how much she would make for 13 hours

All you do is 16 x 13 and your answer is 208 :D

I hope this helped ill simplify it for you

You divide 288 by 18 then you take your answer of 16 and multiply it with 13 which you get 208

Hope it helped :D