The functions f(x) = (x + 5)^2 + 2 and g(x) = -(x − 3)^2−3 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

Answer:

0.944

Step-by-step explanation:

First of all, are you sure the datas are alright? We have a count of 1054 defendants while adding up all these numbers.

Assuming the datas are true, out of the 1054 defendants:

- 399 are sent to prison and guilty

- 567+29 = 596 aren't sent to prison.

Since we are looking for the probability that a randomly selected defendant either pled guilty or was not sent in prison, it means we have

[tex] \frac{399+596}{1054} = \frac{995}{1054} = 0.944[/tex]

(rounded to three decimal places).

Answer:

y is 40.54 degrees

x is 49.46 degrees

Step-by-step explanation:

Recall that Pythagoras theorem states that

a^2 + b ^2 = c^2

where a and b are the opposite and adjacent sides of a right angled triangle and c is the hypotenuse side

Using the notation SOH CAH TOA

Sin y = 13/20 where 13 is the length of the opposite side and 20 is that of the hypotenuse side.

y = sin^-1 0.65

y = 40.54 degrees

Considering angle x,

Cos x = 13/20 where 13 is the adjacent side and 20 is the hypotenuse side

x = Cos^-1 0.65

= 49.46 degrees

Answer:

x=49

y=41

Step-by-step explanation:

Answer:

i don't know what does x equal?

its x=1/6

Step-by-step explanation:

do you need the step by step? i don't know, I'm gonna give it to you anyways.

x+2/3 =5/6

x+2/3-2/3 =5/6 - 2/3

then just subract the number and bam!

x=1/6

Step-by-step explanation:

We have ,

> 3/4= x/20

> x = 3/4 × 20

> x = 15

Solution 2 :-

> x + 2 / 3 = 5/6

> x + 2 = 5/6 × 3

> x + 2 = 5/2 = 2.5

> x = 2.5 - 2

> x = 0.5

Answer: y = -4

Step-by-step explanation:

y = 4x-6

y = 4(1/2)-6

y = 2-6

y = -4

Answer:

Step-by-step explanation:

Y = 4x - 6

Putting value of x = 1/2 in the equation

Y = 4(1/2) - 6

= 2 - 6

= - 4

Answer:

C. 15 bundles

Step-by-step explanation:

In this scenario, the okra seller intends selling his products in bundles of 3 and 5. This simply means that each bundle would either contain 3 okra or 5 okra.

Hence, to find the least number of okra that could be sold in these bundles, we would find the lowest common multiple (LCM) of 3 and 5.

LCM = 3 * 5

LCM = 15

Therefore, 15 is least number that okra can be packed in bundles of 3 and 5 because it's the lowest number that could be divided by both numbers at a time.

Answer:

1. Mary's mother gave her ten dollars to spend at the Market. Mary then spends two and a half dollars on her favorite candy. Mary wants to know how much money she has left.

2. x represents the amount of money Mary has remaining.

3. x + 2 1/2 = 10

(sub tract 2 1/2 from each side)

x = 7 1/2

Step-by-step explanation:

Answer
Since this is a right triangle, we can use the inverse cosine function to solve for the angle θ.

cos θ = Opposite side / Adjacent side

cos θ = 14 / 22

cos θ = 0.6363

θ = cos^-1 (0.6363)

θ ≈ 45.9°

Answer:

Graph 1: The slope is -1/1 or -1

Graph 2: The slope is -1/1 or -1

Step-by-step explanation:

I hope this helps!

x+y≥11 and 8x+4y=80 are system of inequalities and the number of tacos are two.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Rahul and his children went into a restaurant that sells hamburgers for $8 each and

tacos for $4 each.

Rahul has $80 to spend and must buy at least 11 hamburgers and tacos altogether.

Let  x represents the number of hamburgers purchased and y represents the number of tacos purchased,

x+y≥11...(1)

8x+4y=80..(2)

8(11-y)+4y=80

88-8y+4y=80

88-4y=80

8=4y

y≥2

Hence, x+y≥11 and 8x+4y=80 are system of inequalities and the number of tacos are two.

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Answer:

Ratios are proportional if they represent the same relationship.

Step-by-step explanation:

The ratios 7/14 and 20/40 are in proportion. Therefore, option D is the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Here,

A) 6/21 and 2/42

2/7 and 1/21

So, the given ratios are not in proportion.

B. 25/100 and 50/150

1/4 and 1/3

So, the given ratios are not in proportion.

C. 18/24 and 6/12

3/4 and 1/2

So, the given ratios are not in proportion.

D. 7/14 and 20/40

1/2 and 1/2

The given ratios are in proportion.

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Which pair of ratios is proportional?

A. 6/21 and 2/42

B. 25/100 and 50/150

C. 18/24 and 6/12

D. 7/14 and 20/40

Answer:

This Might Be Helpful To You

Step-by-step explanation:

It is a good idea to try to save up money to buy large items or find 0% interest deals so

you are not paying interest. However, this is not always possible, especially when buying

a house or car. That is when it is important to understand how much interest you will be

charged on your loan.

Answer:

25%

Step-by-step explanation:

slope = (175-100)/300 = 75/300 = ¼

the percent slope = ¼×100%= 25%

Jana, because she has the highest ratio since 56 over 80 is greater than 50 over 80.

The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

In baseball, each time a player attempts to hit the ball, it is recorded.

The ratio of hits compared to total attempts is their batting average.

Each player on the team wants to have the highest batting average to help their team the most.

For the season so far,

Jana has hit the ball 7 times out of 10 attempts.

Tasha has hit the ball 10 times out of 16 attempts.

To find the ratio of batting average:

We must find the same number of attempts.

So,

Jana has ratio 7/10.

So, 56 /80 = 0.7

Tasha has ratio 10/16.

So, 50 / 80 = 0.625

Therefore, Jana has the highest batting average.

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Answer:

[tex]x^2+y^2+14y+36=0[/tex]

Step-by-step explanation:

Given that,

Center = (2,-9)

Radius of the circle, r = 7

We need to find the equation of a circle with a center at  (2, -9) and a radius of 7. It can be given by :

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Put h = 2, k = -9 and r = 7 So,

[tex](x-2)^2+(y-(-9))^2=7^2\\\\x^2+4-4x+y^2+81+18y=49\\\\x^2+y^2+14y+85-49=0\\\\x^2+y^2+14y+36=0[/tex]

Hence, this is the required solution.

Answer:

Y=-x^2+4/3 (not really sure though)

Answer:

72 laps

Step-by-step explanation:

2/16=8

8x9=72

Both of you are correct because using either way can solve the equation for the value of x.

In the case of solving for x in  2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.

Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :

Multiplying :

2/5 x = 14

5 / 2 x 2 / 5 x = 14 x 5 / 2

x = 35

Dividing :

2/5 x = 14

2 / 5 x / 2 / 5 = 14 / 2 / 5

x = 35

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The standard deviation of 83 million eggs and 2,655 millions eggs represent that of 3% of the farmers, of the production that is normally distributed, indicates that the mean egg production by Queensland farmers is about 2498.1 million eggs.

A normal distribution is a probability distribution such that the values of the distribution are symmetrical around the mean value of the distribution.

The standard deviation, σ = 83 million eggs

The percentage of farmers that produce more than 2,655 million eggs, x = 3%

The formula for the z-score is; [tex]Z = \dfrac{x - \mu}{\sigma}[/tex]

Therefore, we get;

[tex]Z = \dfrac{2655 - \mu}{83}[/tex]

From the z-score table for P(Z > Z₁), where Z₁ is the z-score corresponding to Φ(1 - 0.03) = Φ(0.97)

The z-value corresponding to Φ(0.97) is about 1.89

Therefore;

[tex]Z = \dfrac{2655 - \mu}{83} \approx 1.89[/tex]

83 × 1.89 ≈ 2655 - μ

μ ≈ 2655 - 83 × 1.89 = 2498.1

The mean egg production by Queensland farmers is about 2498.1 million eggs per year

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Answer:

The answer is B

Step-by-step explanation:

I'm not 100% sure but since its translated 3 units left it should be y=f(x-3)

Answer:

  a.  y = f(x+3)

Step-by-step explanation:

Replacing x in a function with x-h moves the graph h units to the right. Here, the graph is moved 3 units to the left, so the value of h must be -3.

  f(x -(-3)) = f(x+3)

The red graph is described by ...

  y = f(x+3)

Answer:

[tex]\boxed{\boxed{\sf x=1}}[/tex]

Step-by-step explanation:

[tex]\sf 25x^2=-25+50x[/tex]

Simplify both sides of the equation:-

[tex]\sf 25x^2-50x=-25[/tex]

Subtract 50x-25 from both sides:-

[tex]\sf 25x^2-(50x-25)=50x-25-(50x-25)[/tex]

[tex]\sf 25x^2-50x+25=0[/tex]

Factor left side of equation:-

[tex]\sf 25(x-1)(x-1)=0[/tex]

Set factors equal to 0:-

[tex]\sf x-1=0\: or\: x-1=0[/tex]

[tex]\sf x=1[/tex]

___________________

Hope this helps!

Have a great day!

Answer:

x = 3 and x = -3 (aka. x = ±3)

Step-by-step explanation:

2x² - 18 = 0

x² - 9 = 0

x² = 9

x = ±3

Therefore, x = 3 and x = -3

Answer:

35.4ft

Step-by-step explanation:

Answer:

The cost of a single pack would be $2.45.

Step-by-step explanation:

If a 5 pack costs 12.25 then to find the cost of 1 packet we need to divide.

We would divide by 5.

$12.25/5=$2.45

Answer:

19

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

4 × (3/4 - 1/2) + 3 × 6

Step 2: Evaluate

Answer:

By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Sample mean was $6,425 with a standard deviation of $3,156

This means that [tex]\mu = 6425, \sigma = 3156[/tex]

Sample of 84:

This means that [tex]n = 84, s = \frac{3156}{\sqrt{84}} = 344.35[/tex]

a. Which distribution should you use for this problem?

By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.

Answer:

456 students attend Max Middle School.

Step-by-step explanation:

In this problem, it states 152 students play an instrument. It then says, 1/3 of the students play an instrument within the school. So, what you need to do to find the total number of students is multiply 152 times 3.

152·3=456

As a result, here is your product or your answer.  

The trinomial (x - 12)² in standard form is x² - 24x + 144

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

(x-12)^2

Express properly

So, we have the following representation

(x - 12)²

Expand the expression

This gives

(x - 12)² = (x - 12) * (x - 12)

Open the brackets

This gives

(x - 12)² = x² - 12x - 12x + 144

Evaluate the like terms

(x - 12)² = x² - 24x + 144

Hence, the trinomial is x² - 24x + 144

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