Given f(x) = 2x² + 8x - 4 and g(x) = 5x +6, find 3f(x) – 2g(x).

Answer:

7

Step-by-step explanation:

f(x) = 2^(x + 3)

Shifted 10 units to the right:

f(x) = 2^(x + 3 − 10)

f(x) = 2^(x − 7)

Therefore, k = 7.

Answer:

Step-by-step explanation:

Write the following expression using the fewest possible terms.

(−4x − 15) + (17 + 7x) =

-4x -15 + 17 + 7x=

3x +2

Answer:

x greater than or equal to 1/3

Step-by-step explanation:

Answer:

equation is unclear. Send another pic.

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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Answer:

d

Step-by-step explanation:

edge 2020

p.s. pls mark brainliest, and have a good day! :)

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

2+4=6 is true

7*8=56 is true

So the statement 2+4=6 AND 7*8=56 is also true

So the answer for question #36 is a) the statement is true because both proporsitions are true

Answer:

Overall, it depends what type of coin you are using because each ones size is different. Or, if you are referring to the riddle it will be just one coin.

The correct answer is approximately 3,968 coins can be placed in the empty money box based on estimation. Based on these calculations, you can roughly estimate  a volume  calculation that  place around 7936 coins in your empty money box, assuming the coins are similar in size to a quarter.

To estimate the number of coins that can fit in your money box, we need to consider the volume of the box and the volume of a single coin.

Calculate the volume of the money box:

Volume = Length * Width * Height

Volume = 10 inches * 10 inches * 5 inches

Volume = 500 cubic inches

Estimate the volume of a single coin. Let's assume a common coin, such as a quarter:

Diameter of a quarter ≈ 0.96 inches

Thickness of a quarter ≈ 0.07 inches

Volume of a coin ≈ π * (\(radius^2\)) * thickness

Volume of a quarter ≈\(3.14 * (0.48) ^2 * 0.07\)inches

Volume of a quarter ≈ 0.063 cubic inches

Calculate the number of coins that can fit in the money box:

Number of coins ≈ Volume of the money box / Volume of a coin

Number of coins ≈ 500 cubic inches / 0.063 cubic inches

Number of coins ≈ 7936 coins (approximately)

Therefore, approximately 3,968 coins can be placed in the empty money box based on estimation. Based on these calculations, you can roughly estimate  a volume  calculation that  place around 7936 coins in your empty money box, assuming the coins are similar in size to a quarter.

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Answer:

\(P = 48 in\),\(A= 120in^2\)

Step-by-step explanation:

Again we can use Pythagorean theorem to find the missing side

x^2 + 15^2 = 17^2

x^2 + 225 = 289

Subtract 225 from both sides

x^2 = 64

Find the square root of both sides

√x^2 = √64

x = 8

So

l = 15in, w = 8in

P=2(15) + 2(8)

P = 30 + 18

P = 48 in

A= 15(8)

A= 120in^2

Answer:

- 4

Step-by-step explanation:

h(x) = sin x

f(x) = | 3x - 4 |

g(x) = 2x² - 6

h( \(\frac{\pi }{2}\) ) = sin ( \(\frac{\pi }{2}\) ) = 1

f ( 1 ) = | 3 × 1 - 4 | = 1

g ( 1 ) = 2( 1² ) - 6 = - 4

g ( f ( h ( \(\frac{\pi }{2}\) ) ) ) = - 4

Answer: 460.61

Step-by-step explanation:

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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Answer:

2

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

The probability of exactly 5 occurrences is (Rounding to three Decimal places), we get P(X ≤ 3) ≈ 0.251.

a) The probability of exactly 5 occurrences is given by the Poisson probability mass function:

P(X = 5) = (e^(-λ) * λ^5) / 5! = (e^(-5.1) * 5.1^5) / 120 ≈ 0.1755

Rounding to four decimal places, we get P(X = 5) ≈ 0.1755.

b) The probability of more than 6 occurrences can be calculated as the complement of the probability of 6 or fewer occurrences:

P(X > 6) = 1 - P(X ≤ 6) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6))

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

P(X = 4) ≈ 0.174

P(X = 5) ≈ 0.1755

P(X = 6) ≈ 0.1493

Substituting these values into the formula, we get:

P(X > 6) ≈ 1 - (0.006 + 0.031 + 0.079 + 0.135 + 0.174 + 0.1755 + 0.1493) ≈ 0.249

Rounding to three decimal places, we get P(X > 6) ≈ 0.249.

c) The probability of 3 or fewer occurrences is given by the cumulative distribution function:

P(X ≤ 3) = ∑ P(X = k), for k = 0, 1, 2, 3.

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

Adding these probabilities, we get: P(X ≤ 3) ≈ 0.251

Rounding to three decimal places, we get P(X ≤ 3) ≈ 0.251.

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Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001

What is Descending order?

Descending order can be defined in such a way that the order is from largest to smallest.

Given numbers are ,

0.51 , 7.6 , 10^2 , 5.6 , 105 , 4.9 , 10^-3

10^2 = 10*10 = 100 .

so a^m = a multiplied by m times .

a^-m = 1/ a^m.

10^-3 = 1/1000 = 0.001

So,

We have to write from largest to smallest

we get,

105,100,7.6,5.6,4.9,0.51,0.001

Hence, From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001

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When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.

A cube is a solid shape with six square faces. Each side of a square  has the same side length, so all  faces are the same size.

A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.

Shape Properties of  Cube  

Thus, when edge D connects with edge X, this net is folded into a cube.

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Answer:

2 x  − 6

Explanation:

"Six less than.." means "Subtract 6 from".

Do not confuse this with "Six less..." which means "Subtract from 6".

Confusing, I know.

We know that "Double a number" means  

2 x , where  x  is your mystery number.

Therefore, we have:

2 x  −  6 , which translates to "6 less than 2x" or "6 less than twice a number"

9514 1404 393

Answer:

  1.9 degrees per second

Step-by-step explanation:

The angle α the line makes with the water can be described by ...

  Sin = Opposite/Hypotenuse

  sin(α) = 10/(25 -1.9t)

Taking derivatives gives ...

  α'·cos(α) = -10(-1.9)/(25 -1.9t)²

Then the rate of change of the angle at t=0 is ...

  α' = 19/(25²·cos(α))

Of course, cos(α) = √(1 -sin(α)²) = √(1 -(10/25)²) = √(21/25), so we have ...

  α' = 19/(125√21) . . . radians/second

  α' ≈ 0.033269 radians/s ≈ 1.90 degrees/s

(a) Through the conditional probability formula:\(P(B ∩ A) = P(B | A) P(A),\)

\(P(B / A1) P(A1) = 0.50 x 0.20 = 0.10A2 = 0.30 x 0.30 = 0.09A3= 0.40 x 0.50 = 0.20\)

(b)Bayes' theorem gives

\(P(A2 | B) = p(B | A2) p(A2) / [p(B | A1) P(A1) + p(B | A2) P(A2) + p(B | A3) p(A3)]= 0.26Thus, P(A2 | B) = 0.26.\)

(c)the tabular approach can show us

Events      P(Ai)    P(B | Ai)   P(Ai ∩ B)   P(Ai | B)

A1          0.2     0.5       0.1        0.167

A2          0.3     0.3       0.09      0.307

A3          0.5     0.4       0.2        0.526

Therefore,\(P(A1 | B) = 0.167, p(A2 | B) = 0.307, p(A3 | B) = 0.526.\)

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Answer:

\(A=7569\pi \ ft^2\)

Step-by-step explanation:

The diameter of a sphere is 87 feet.

We need to find its surface area. The formula for surface area is given by :

\(A=4\pi r^2\)

Where

r is the radius of the sphere

\(A=4\pi \times (\dfrac{87}{2})^2\\\\=7569\pi \ ft^2\)

So, the surface area of the sphere is equal to \(7569\pi \ ft^2\).

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer:

3.5

Step-by-step explanation:

Order of operations

Answer:

1 Question: D

2 Question: C

Just Imo. I did the work tho.

The ordered pairs are (1,0), (2,6/5),(3,12/5)

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation as y = 6x/5 - 6/5

putting (1,0) in the equation we get 6×1/5-6/5=0

Similarly we can find the ordered pair as y = 6/5x - 6/5

Hence, The ordered pairs are (1,0), (2,6/5),(3,12/5)

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Using the Central Limit Theorem, it is found that:

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).

The estimate and the sample size are given by:

p = 0.38, n = 168.

Hence the mean is given by:

\(\mu = p = 0.38\)

The standard error is given by:

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.38(0.62)}{168}} = 0.0374\)

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

-10/39

Step-by-step explanation:

I Think that thats the anwser i hope this helps.

The slope and the y-intercept of the line y = 4x + 5 are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The function for this problem is given as follows:

y = 4x + 5.

Hence the slope and the intercept are given as follows:

The problem asks for the slope and the intercept of y = 4x + 5.

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