y=9x^2+162x+725 Complete the square to re-write the quadratic function in vertex form

Answer:d

Step-by-stedp explanation:

Answer:

Step-by-step explanation:

1500 + (1500 : 100 × 4)

= 1500 + (15 × 4)

= 1500 + 60

= 1560

Answer:

Smiley: 8steps

Grumpy: 12 steps

Step-by-step explanation:

Given

See attachment for complete question

Required

Steps taken by each

From the second statement, we have:

\(3S + 2G = 48\)

and

\(4S + 2G = 56\)

Subtract both equations

\(3S - 4S + 2G - 2G = 48 - 56\)

\(-S = -8\)

Solve for S

\(S = 8\)

Substitute \(S = 8\) in \(3S + 2G = 48\)

\(3*8+2G = 48\)

\(24+2G = 48\)

Subtract 24 from both sides

\(2G = 24\)

Divide both sides by 2

\(G =12\)

Answer:

Step-by-step explanation:

Correct option is A)

Answer:

4

Step-by-step explanation:

11 - 7 = 4

The required length of JK is 4 units.

It is required to find the length of JK.

Length is defined as the measurement or extent of something from end to end.  The greater of two or the greatest of three dimensions of an object. It can be measured in different units like centimeters, inches, meters, etc.

Given:

Point K on the  line segment  JL.

KL = 7

JL = 11

As per segment addition postulate

JL = JK + KL

Substituting values, to find the value JK we get,

11 = JK + 7

JK = 11 - 7

JK = 4

Therefore, the required length of JK is 4 units.

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The required answer is the probability of throwing the baseball through the opening in the tire is approximately 0.1556, or 15.56%.

To solve this problem, we need to find the area of the opening in the tire and the area of the entire tire. Then, we can divide the area of the opening by the area of the entire tire to get the probability of throwing the baseball through the opening.
First, we need to find the radius of the tire. The outside diameter is 34 inches, so the radius is 17 inches. The inside diameter is 14 inches, so the inner radius is 7 inches.
The area of the opening is the area of a circle with radius 7 inches. Using the formula for the area of a circle (A = πr^2), we get:
A(opening) = π(7)^2
A(opening) = 49π
The area of the entire tire is the difference between the area of the outer circle and the area of the inner circle. Using the same formula, we get:
A(tire) = π(17)^2 - π(7)^2
A(tire) = 225π
Now we can find the probability of throwing the baseball through the opening by dividing the area of the opening by the area of the entire tire:
P(through opening) = A(opening) / A(tire)
P(through opening) = (49π) / (225π)
P(through opening) = 7/45
P(through opening) ≈ 0.1556
So the probability of throwing the baseball through the opening in the tire is approximately 0.1556, or 15.56%.

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The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

To prove that if lim an/bn = 0 and bn is convergent, then an is also convergent, we can use the limit comparison test. Since bn is convergent, we know that its terms approach 0. Therefore, we can choose a positive number ε such that 0 < ε < bn for all n. Then, we have:

lim (an/bn) = 0
=> for any ε > 0, there exists N such that for all n > N, |an/bn| < ε
=> for all n > N, an < εbn

Since ε is a positive constant and bn is convergent, we know that εbn is also convergent. Therefore, by the comparison test, an is convergent as well.

To show that the series ∑(ln n)/(n^3 ln n^1/2 e^n) converges, we can use the comparison test again. Note that:

ln n^1/2 = (1/2)ln n
ln n^3 = 3ln n

Therefore, we can rewrite the series as:

∑[(1/2)/(n^2 e^(ln n))] = (1/2)∑(1/(n^2 n^ln(e)))

Since n^ln(e) > 1 for all n, we have:

(1/2)∑(1/(n^2 n^ln(e))) < (1/2)∑(1/n^2)

The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

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Answer:

About 10.802

Step-by-step explanation:

Using the formula for a right circular cone, we can find that the volume is:

\(r=d\div 2 = 2.3 \div 2 = 1.15\\\\\dfrac{1}{3}\pi r^2 h = \dfrac{1}{3}\pi (1.15)^2 (7.8) \approx 10.802\)

The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation ​(0, 0) ​is A'(0, 0), B'(1, 2) and C'(-1, 1)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.

Let us assume that the polygon has vertex at A(0, 0), B(3, 6) and C(-3, 3)

The image of the given polygon under a dilation with a scale factor of 1/3 about the center of dilation ​(0, 0) ​is A'(0, 0), B'(1, 2) and C'(-1, 1)

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Answer:

Let the actual pressure = x

The reading is x + 8 % , so the reading is 108% of the actual.

Divide the reading by 108% for the actual

39.42/1.08 = x

X = 36.5 psi

The actual pressure is 36.5 psi

Between 6:00 PM and 12:00 AM, I will make $13.20 per hour the answer is $13.20.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The question is incomplete.

The complete question is:

Supervisor: "Because you are working a late shift, you will get an increase in your wage. You will get an additional 10% per hour from 6:00 PM to 12:00 AM and an additional 15% from 12:00 AM to 1:00 AM." Employee: "I am working from 2:00 PM to 12:00 AM. Between 2:00 PM and 6:00 PM, I will make $12.00 per hour. Between 6:00 PM and 12:00 AM, I will make __________ per hour."

We have:

Per hour wage = $12 per hour

The employee gets money for working from 6.00 PM to 12.00 AM :

= (10/100)×12

= $1.2 per hour

The employee gets money for working from 12.00 AM to 01.00 AM:

= (15/100)×12

= $1.8 per hour

An employee works from 2.00 PM to 12.00 AM:

The employee gets money for Working from 2.00 PM to 6.00 PM + 10%

= 12 + 1.20

= $13.20

Thus, between 6:00 PM and 12:00 AM, I will make $13.20 per hour the answer is $13.20.

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Answer: 40

Step-by-step explanation:

Assume Julio's number is x.

The expression would be:

-7 * (x - 15) = -175

x - 15 = -175/-7

x = -175/-7 + 15

x = 40

Answer: Experiment with 100 players sprinting

Step-by-step explanation:

When it comes to experiments using samples to find out the effect of a variable on an entire population by finding out the representative effect on the sample, the larger the size of the sample, the better.

A larger sample comes closer to being the actual size of the population so when this larger sample is experimented upon, the results it gives will be closer to the results that would be gotten if we experimented on the entire population. The 100 player sprinting experiment would therefore come closer to matching its theoretical probability.

We can use labelling to solve the problem.

To solve this problem, you can follow these steps:

1. Choose one of the three boxes and take out a ball from it.

2. Check the color of the ball. Let's say it is red.

3. Since the labels on the boxes always lie, you can be sure that the box you chose does not contain only red balls. Therefore, it must either contain a mixture of red and blue balls, or only blue balls.

4. Since you know that one box contains only red balls, and you have already ruled out the possibility that the box you chose contains only red balls, you can conclude that the box you chose must contain only blue balls.

5. Therefore, you can correctly label the box you chose as "blue balls only".

6. You can then label the remaining two boxes as "red balls only" and "mixture of red and blue balls", since you know that one of the boxes contains only red balls, and the other must contain a mixture of red and blue balls.

Therefore, we used labelling to solve the problem.

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Greetings from Brasil...

The expression that allows you to calculate the distance between two points is:

Bringing to our problem:

d(A; B) = √[(9 - 0)² + (14 - 2)²]

d(A; B) = √[9² + 12²]

d(A; B) = √[81 + 144]

d(A; B) = √[225]

Answer:

Step-by-step explanation:

Given

Perimeter = 2(l + w)

Substitute values in perimeter formula

Then, the value of width is

Area of rectangle

Area of circle

Shaded area

Answer:

126.14in²

Step-by-step explanation:

P = 2w + 2l

68 = 2(x + 2) + 2(20)

68 = 2x + 4 + 40

68 = 2x + 44

24 = 2x

12 = x

x + 2

12 + 2

14 (width)

14 * 20

280in² (area of rectangle)

A = πr²

A = π(7)²

A = 49π

A = 153.86 (area of circle)

280 - 153.86

126.14 (area of shaded region)

Best of Luck!

Answer:

C

Step-by-step explanation:

Answer: = -2x-16

Step-by-step explanation:

\(-8\left(0.25x+2\right)\)

\(\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\)

\(=-8\cdot \:0.25x-8\cdot \:2\)

\(=-2x-16\)

Answer:

16 rows, 8 seedlings left.

Step-by-step explanation:

Divide 200 by 12, since 200 seedlings are going to be split in 12 groups in order to fill the rows.

200 ÷ 12 = 16 with a remainder of 8.

The remainder is basically what is left.

Since 12 seedlings are planted in each row, 8 seedlings is not enough to completely fill the row. So, the answer is 16 rows with 8 seedlings left.

Hope this helped !

Answer:

x-5=sqrt(2x+5)

then square both sides

x2-10x+25=2x+5

x2-8x+20=0

rest is trivial

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

Given

x - \(\sqrt{2x+5}\) = 5 ( subtract x from both sides )

- \(\sqrt{2x+5}\) = 5 - x ( divide all terms by - 1 )

\(\sqrt{2x+5}\) = x - 5 ( square both sides )

2x + 5 = (x - 5)²

2x + 5 = x² - 10x + 25 ( subtract 2x + 5 from both sides )

0 = x² - 12x + 20 ← in standard form

0 = (x - 2)(x - 10) ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 10 = 0 ⇒ x = 10

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions

x = 2

2 - \(\sqrt{4+5}\) = 2 - \(\sqrt{9}\) = 2 - 3 = - 1 ≠ 5

Thus x = 2 is an extraneous solution

x = 10

10 - \(\sqrt{20+5}\) = 10 - \(\sqrt{25}\) = 10 - 5 = 5 = right side

Thus x = 10 is the solution

Using the concepts of mean and median, it is found that the correct option is:

C. The mean will decrease, and the median will stay the same.

The mean of a data-set is the sum of all observations divided by the number of observations. It is affected by all values in the data-set.

The median of a data-set is the value that separates the bottom 50% from the upper 50% of values. It is not affected by outliers.

In this problem, there are 5 elephants, hence the median is the weight of the (5 + 1)/2 = 3rd elephants, hence it stays the same.

For the mean, as the weight of the smallest elephant decreases, the mean also decreases, hence option C is correct.

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complete question:

Liam works at a zoo. He was looking at some data showing the masses of their 5 African elephants. The mean mass of the elephants was 3800 Kg and the median mass was 3600 Kg. The smallest elephant, named Lola, weighed 2700 Kg. Lola then got very sick and lost weight until her mass reached 1800 Kg. How will Lola's mass decreasing affect the mean and median?

A. Both the mean and median will decrease

B.The median will decrease, and the mean will stay the same.

C.The mean will decrease, and the median will stay the same.

D.The mean will decrease, and the median will increase.

Answer:

25 multiple choice and 15 open-ended

Step-by-step explanation:

25 x 5 = 125

15 x 15 = 225

125 + 225 = 350

Answer:

C. 0≤x≤12

Step-by-step explanation:

The internet protocol that contains the IP address is the Internet Protocol (IP), the correct option is Internet protocol. The other options, TCP and SMTP, are protocols that operate on top of IP and do not contain the IP address themselves.

The correct answer is the Internet Protocol (IP). IP is responsible for delivering packets of data from the source to the destination based on IP addresses, while other protocols like TCP and SMTP handle different aspects of data transmission and communication.

Therefore, the correct option is Internet protocol.

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The rate of increase in population is 2960.

The population growth linear model is Pt=P0+rt.

Pt is the population after time t, P0 is the population at time 0, r is the average growth increment per unit time and t is the number of unit time.

P2010 =32,800

P2005 = 18,000

t=5 years

P2010=P2005+rt

(32,800)=(18,000)+r(5)

32,800=18,000+5r

32,800-32,800-5r=18,000+5r-32800-5r

-5r=-14,800

r=2960

Therefore, the rate of increase in population is 2960.

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Answer:

$780.57

Step-by-step explanation:

557.55*1.4 = 780.57