Identify the coordinates of the vertex of f(x) = 3x2 + 12x − 8, and identify whether it is an absolute minimum or absolute maximum. (2, 28), absolute minimum Correct Answer (−2, −20), absolute minimum Incorrect Response (−2, −20), absolute maximum (2, 28), absolute maximum

Answer:

1.31 meters

Step-by-step explanation:

Answer:

converting 1.4 m to cm = 140 cm. Since she grew 9 cm in the past therefore 140 - 9 = 131 cm. converting it back to m: 131 cm = 1.31 m.

Step-by-step explanation:

Suppose x and y are proportional. 3rd , 4th and 5th options are correct.

What is proportional in an equation?

Given that  x and y are proportional ,

then ,    x = my  for some constant m

       Δx = Δ (my)   ⇒ m Δy

∴ 3rd option is correct .

          x = my

          y = 1/m x ⇒ kx

∴ 4th option is correct.

the points ( 0,0) satisfies x = my

the point ( 0, 0 ) is on the graph of y in terms of x .

∴ 5th option is correct .

  y = kx

Δy = Δ ( kx)  ⇒ k Δx

∴ 1st option is not true .

y = 2x also implies x and y are proportional .

∴ 2nd  option is not true .

∵ 3rd , 4th and 5th options are correct.

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The complete question is -

Suppose x and y are proportional. Which of the following statements are true? Select all that apply. Ay = kx, where k is constant Oy=3 D Ax = mAy, where m is constant Oy kä, where k is constant The point(0, 0) is on the graph of y in terms of

Answer: 0.45, 45/100, 9/20, Any factors of the fractions.

Step-by-step explanation:

Answer:

76:9

Step-by-step explanation:

because because because

Answer:

x = 5/8 = 0.625

Step-by-step explanation:

2.952

Step-by-step explanation:

First you must convert 3.6% into a decimal which is 0.036 (or move the decimal over twice).

Then multiply 82 by the given decimal

82 x 0.036= 2.952

(round if necessary)

Answer:

Area of the circle =  49 π cm² = 153.86cm²

Step-by-step explanation:

Given that the diameter of the circle

                                    d = 14

The radius of the circle

                    \(r = \frac{d}{2} = \frac{14}{2} = 7\)

Area of the circle

                     A = πr²

                    A = 3.14 ×(7)²

                   A = 153.86 cm²

Answer:

A

Step-by-step explanation:

using the Sine rule in the triangle

we require the third angle

third angle = 180° - 42° - 61° = 180° - 103° = 77°

then

\(\frac{x}{sin42}\) = \(\frac{13}{sin77}\) ( cross- multiply )

x × sin77° = 13 × sin42° ( divide both sides by sin77° )

x = \(\frac{13sin42}{sin77}\) ≈ 8.9 cm ( to 1 decimal place )

Answer:

Option C

x²+ 2x -24=0

x²+6x-4x-24= 0

x(x+6) -4(x+6) = 0

(x+6)(x-4) = 0

x= -6 and 4

Therefore, for x = 4 and -6 , the above given equation is true.

Answer:

y = 3/2x - 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Find points from graph.

y-intercept (0, -2)

Random Point (2, 1)

Step 2: Find slope m

Step 3: Write equation

Substitute into General Form

y = 3/2x - 2

Answer:

the car is traveling at a mph of 65 per hour.

Step-by-step explanation:

hope this helped out in some way.

Answer:

vvv

Step-by-step explanation:

Answer:

And for number 10 the answer is (b)

I hope this helps, Happy learning!!!

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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The final answer is:

a) P( Y < 42.5 )  = 0.8541

b) P( 39.5 < Y < 40.5 ) = 0.1670.

What is the normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

If x follows a normal distribution with mean μ and standard deviation σ then the distribution of

\(\sum_{i =1}^{n}x_{i}\)  follows an approximately normal distribution with a mean \(n\mu\) and standard deviation \(\sqrt{n }\sigma\)

let x be the height of blades of grass

x follows normal distribution with mean = μ = 4 and standard deviation = σ = 0.75.

Y = x1 + x2 +...........+x10

\(Y = \sum_{i =1}^{10}x_{i}\)

Distribution of Y is normal with,

Mean = \(\mu _{y}=10*4 = 40\) and standard deviation \(= \sigma _{y}=\sqrt{10}*0.75 = 2.3717\)

a)

P( Y < 42.5 )

Using normal distribution formmula,

\(f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}\)

=NORMDIST( x, mean, SD , 1 )      

=NORMDIST(42.5, 40, 2.3717, 1 )

=0.8541

P( Y < 42.5 )  = 0.8541

b)

P( 39.5 < Y < 40.5 ) = P( Y < 40.5 ) - P( Y < 39.5 )

Using normal distribution formmula,

\(f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}\)

P( Y < 40.5 )  =NORMDIST(40.5, 40, 2.3717, 1 ) = 0.5835

P( Y < 39.5 ) = NORMDIST(39.5, 40, 2.3717, 1 ) = 0.4165

P( 39.5 < Y < 40.5 ) = 0.5835 - 0.4165  = 0.1670

P( 39.5 < Y < 40.5 ) = 0.1670

Hence, the final answer is:

a) P( Y < 42.5 )  = 0.8541

b) P( 39.5 < Y < 40.5 ) = 0.1670.

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Answer:

C. 2(4 × 5) = (2 × 4) × 5

Step-by-step explanation:

The associate property of multiplication is

a(bc) = (ab)c

You can change the grouping of a multiplication without changing the result.

Answer: C. 2(4 × 5) = (2 × 4) × 5

= 65% x 120 = 78 pounds of iron

Answer:

78

Step-by-step explanation:

65% of 120 = 78

Answer:

-3^4

Step-by-step explanation:

The cost of each Lip balm is $3, while bottle is $2 and sunscreen is $11.

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Let x represent the cost of each lip balm, y represent the cost of bottle and z represent the cost of sunscreen.

Jill purchased two tubes of lip balm, a bottle of water, and a tube of sunscreen for $19. Hence:

2x + y + z = 19     (1)

Jason purchased three bottles of water and two tubes of sunscreen for $28. Hence:

3y + 2z = 28     (2)

John spent $18 on a tube of lip balm, two bottles of water, and a tube of sunscreen. Hence:

x + 2y + z = 18     (3)

From all three equations:

x = 3, y = 2 and z = 11

Lip balm is $3, bottle is $2 and sunscreen is $11.

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Based on the information in the Venn diagram, we can infer that the table would be completed with the following data from left to right and from top to bottom: 6, 30, 36, 41, 22, 63, 47, 52, 99.

To find the values that complete the table, we must analyze the sales diagram and the data it contains. In this case, it is showing two sets, one referenced with the word fish and the other with the word bird, each of them has different values and there is a set that relates them. Additionally, on the outside of these sets there is a value for a category that is not related to these sets.

In accordance with the above, we only have to look at the values and complete the table. Additionally, to find the totals we must add the values of each row or column.

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The probability that at least one household in the sample of 25 has an annual property tax bill of at least $17,000 is 97.36%.

The above scenario describes a normal distribution with a mean of $15,000 and a standard deviation of $4,000. A simple random sample (SRS) of 25 households has been taken from this distribution.

A normal distribution with a specified mean and standard deviation can be used to find the probability of any value. In this case, we can use the normal distribution to find the probability that a randomly selected household will have an annual property tax bill of a certain value.

For example, the probability that a randomly selected household has an annual property tax bill of at least $17,000 can be calculated as follows:

First, we need to calculate the z-score of this value. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation:

z-score = ($17,000 - $15,000) / $4,000 = 0.5

Then, we use a normal distribution table to calculate the probability that the randomly selected household has an annual property tax bill of at least $17,000.

Using the table, the probability that a randomly selected household has an annual property tax bill of at least $17,000 is 0.6915.

Since a simple random sample of 25 households were selected, the probability that at least one household in the sample has an annual property tax bill of at least $17,000 is 1 - (1 - 0.6915)^25, which is 0.9736.

Therefore, the probability that at least one household in the sample of 25 has an annual property tax bill of at least $17,000 is 97.36%.

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Answer:

the gcf of that is 10.

Step-by-step explanation:

Answer:

X = Y times 8

Step-by-step explanation:

You need to figure out how many miles you can go in an hour.

160/x and 20/1

20x=160

x=8

You can go 8 miles in 1 hour.

Therefore, if X is 1 and Y is 1

1 = 8

1 hour equals 8 miles

Answer:

433345344 Answer

Step-by-step explanation:

To evaluate the indefinite integrals ∫(sin(x) / (x² * (2 + e^x))) dx, we can use a substitution method. Let's substitute u = 2 + e^x, then du/dx = e^x dx. Rearranging, we have dx = du / e^x.

Substituting these values into the integral, we have:

∫(sin(x) / (x² * (2 + e^x))) dx = ∫(sin(x) / (x² * u)) (du / e^x)

Simplifying, we get:

∫(sin(x) / (x² * u)) (du / e^x) = ∫(sin(x) / (x² * u)) (du / u)

We can separate the variables and write the integral as:

∫(sin(x) / x²) dx = ∫(1 / u) du

Now, let's evaluate each integral separately:

∫(sin(x) / x²) dx:

This integral does not have an elementary antiderivative, so it cannot be expressed in terms of elementary functions. It is a special function called the sine integral, denoted as Si(x). Therefore, the indefinite integral becomes:

∫(sin(x) / x²) dx = Si(x) + C

∫(1 / u) du:

This integral is straightforward to solve:

∫(1 / u) du = ln|u| + C

Substituting back u = 2 + e^x, we have:

∫(1 / u) du = ln|2 + e^x| + C

Therefore, the evaluated indefinite integrals are:

∫(sin(x) / (x² * (2 + e^x))) dx = Si(x) + C1

∫(1 / (2 + e^x)) dx = ln|2 + e^x| + C2

where C1 and C2 are the constants of integration.

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Answer:

Step-by-step explanation:

y^2-22y+c

complete the square ax^2+bx+c is our old formula quadratic equation

we know that to find c we will divide b/2 and square it

22/2=11

c^2=121

we have y^2-22y+121

Answer:

1 pound beef = $3.09

4.5 pound beef = x

x = 3.09 × 4.5

x = 13.91

Answer:

x= 3.43

Step-by-step explanation:

First, use the distributive property and multiply 3 by x and 3 by 2:

3x + 6

next use the distributive property again and multiply 4 by x and -5:

4x - 20

Combine Like terms: 3x + 6 + 4x - 20

3x + 4x = 7x

6 - 20 = -14

Now Add 14 to both sides: 7x - 14 = 10

10 + 14 = 24

Now divide 7 by both sides: 7x = 24

24 / 7 = 3.428571429 = 3.43

Answer:

x=24/7 or 3 3/7

Step-by-step explanation:

3(x+2) + 4(x-5)=10   parenthesis first

3x+6+4x-20=10

7x-14=10               addition on both sides

7x-14+14=10+14

7x=24

x=24/7

check the answer:

3(x+2) + 4(x-5)=10

3(24/7+2)+4(24/7-5)=10

72/7+6+96/7-20=10

168/7-14=10

24-14=10

10=10 correct

Answer:

8.3

Step-by-step explanation:

The original answer was 8.30220008

Let's start at the end, 8 rounded up is 10, so 1, 1 is rounded to 0 so 0, 0 is rounded to 0, so 0, 0 is rounded up to 0 so 2, 2 rounded is 0 so 2, 2 rounded is to 0 so 0, 0 so rounded to 3 so 3.

Rounded up is 8.3