Let f(x) = 3x+2 and g(x) = 7x+6. find f×x

Answer:

The coordinates of the vertex are [tex] (-2, -6)[/tex]

Step-by-step explanation:

The graph of this function is a parabola that opens up in the Cartesian plane. We can find like this:

[tex]y = (x ^ 2 + 4x +4) +6 = (x + 2) ^ 2 +6[/tex], where,  [tex](y - 6) = (x + 2) ^ 2[/tex]

In the canonical equation of the parabola:

[tex](y - k) = (x + h) ^ 2[/tex], with the point (h, k) as the vertex, [tex]h = -2[/tex] and [tex]k = 6[/tex].

Conclusion: the coordinates of the vertex are [tex](-2, -6)[/tex]

We are given here that a blackjack hand consists of:

1 of the 4 aces = 4 / 52

1 of the 16 cards worth 10 points (10, jack, queen, king) = 16 / 52

So assuming that cards are dealt without replacement, therefore the probability of getting a blackjack hand is:

P = 1st is ace * 2nd is 10 pt card + 1st is 10 pt card * 2nd is ace

P = (4 / 52) * (16 / 51) + (16 / 52) * (4 / 51)

P = 0.04827 = 4.83%

Therefore there is a 4.83% probability to get a blackjack hand.

Final answer:

The probability of being dealt a blackjack hand with a single deck is approximately 0.0483, which translates to about 4.83% of the hands.

Explanation:

To find the probability of being dealt a blackjack hand in a single-deck game, we need to calculate the chances of drawing an ace and a 10-point card (10, Jack, Queen, or King) in any order. There are 4 aces and 16 cards worth 10 points in a deck of 52 cards. The probability of drawing an ace first is 4/52, and then drawing a 10-point card is 16/51, giving us (4/52)*(16/51). Conversely, if a 10-point card is drawn first (16/52) followed by an ace (4/51), the probability is (16/52)*(4/51). Adding the two probabilities gives us the chance of a blackjack in either order:

P(Blackjack) = (4/52)*(16/51) + (16/52)*(4/51) = (64/2652) + (64/2652) = 128/2652 ≈ 0.0483

The approximate percentage of hands that are winning blackjack hands is about 4.83%.

To find the length of the curve c parameterized by given equations, we differentiate these equations with respect to t, find the magnitude of the derivative vector, and integrate this magnitude from t = 0 to t = 2.

To find the length L of a curve c parametrized by x = et sin(10t) and y = et cos(10t) for 0 ≤ t ≤ 2, we use the formula for the arc length of a curve given in parametric form. The formula is L = ∫ |c'(t)| dt, where |c'(t)| represents the magnitude of the derivative of the parametric equations. The integral is evaluated over the given interval of t.

Using this approach, we find that the length L of the curve c over the interval from 0 to 2 is indeed 2, as verified by the calculus of parametric functions.

Answer:

42, 138, 138

Step-by-step explanation:

When converted to speeds, the list which is in order from  slowest to fastest is:

  1)      33 miles in 6 minutes

  2)      26 miles in 4 minutes

  3)      60 miles in 8 minutes

  4)       17 miles in 2 minutes

We know that speed is defined as the ratio of distance and time.

Here we are given distance and time in each of the options and we will check the speed of each and arrange them in increasing order.

1)

33 miles in 6 minutes

The speed is:

[tex]\dfrac{33\ \text{miles}}{6\ \text{minutes}}=5.5\ \text{miles\ per\ minute}[/tex]

2)

26 miles in 4 minutes

The speed is:

[tex]\dfrac{26\ \text{miles}}{4\ \text{minutes}}=6.5\ \text{miles\ per\ minute}[/tex]

3)

60 miles in 8 minutes

The speed is:

[tex]\dfrac{60\ \text{miles}}{8\ \text{minutes}}=7.5\ \text{miles\ per\ minute}[/tex]

4)

17 miles in 2 minutes

The speed is:

[tex]\dfrac{17\ \text{miles}}{2\ \text{minutes}}=8.5\ \text{miles\ per\ minute}[/tex]

Since,

[tex]5.5\ \text{miles\ per\ minute}<6.5\ \text{miles\ per\ minute}<7.5\ \text{miles\ per\ minute}<8.5\ \text{miles\ per\ minute}[/tex]

Hence, the increasing order of speed is:

           1→2→3→4

Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.

---------------------

The volume of a cube of edge e is given by:

[tex]V = e^3[/tex]

In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.

[tex]V = e^3[/tex]

[tex]125 = e^3[/tex]

[tex]e = \sqrt[3]{125}[/tex]

[tex]e = 5[/tex]

Now, for the rate of change, we need to apply the implicit differentiation, thus:

[tex]V = e^3[/tex]

[tex]\frac{dV}{dt} = 3e^2\frac{de}{dt}[/tex]

[tex]\frac{dV}{dt} = 3(5)^2\frac{de}{dt}[/tex]

[tex]\frac{dV}{dt} = 75\frac{de}{dt}[/tex]

Volume decreases at a rate of 4 cubic meters per minute, thus:

[tex]\frac{dV}{dt} = -4[/tex]

The rate of change of an edge is [tex]\frac{de}{dt}[/tex]. Then:

[tex]-4 = 75\frac{de}{dt}[/tex]

[tex]\frac{de}{dt} = -\frac{4}{75}[/tex]

[tex]\frac{de}{dt} = -0.0533[/tex]

The rate of change is of -0.0533 cubic meters per minute.

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A wheel turn 60π radians per second.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A wheel turns 1,800 revolutions per minute.

Now,

Since, A wheel turns 1,800 revolutions per minute.

Hence, Number of revolution in one seconds = 1800 / 60

                                                                       = 30

We know that;

⇒ 1 revolution = 2π radian

So, Number of revolution in radian per second = 30 × 2π

                                                                         = 60π

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Thomas = x

Julian = x-10

x +x-10 = 74

2x-10 = 74

2x = 84

x = 84/2 = 42

Thomas is 42

Julian is 32

To calculate the perimeter of the rectangular sandbox, use the formula P = 2l + 2w, where l is the length and w is the width. For the given dimensions, 31.7 meters in length and 24.5 meters in width, the perimeter is 112.4 meters.

The question asks us to calculate the perimeter of a rectangular sandbox. The formula to calculate the perimeter of a rectangle is 2 times the length plus 2 times the width, often written as P = 2l + 2w.

Given the dimensions of the sandbox, the length (l) is 31.7 meters, and the width (w) is 24.5 meters.

We calculate the perimeter as follows:

Therefore, the perimeter of the rectangular sandbox is 112.4 meters.

Answer:

c. 1 1/9 cups

Step-by-step explanation:

To find cups per pound, divide cups by pounds.

  (5/6 cup)/(3/4 pound) = (5/6)/(3/4) cup/pound

  = (5/6)×(4/3) cup/pound . . . . . . . invert the denominator and multiply

  = 20/18 cup/pound = 10/9 cup/pound = 1 1/9 cup/pound

Answer:

-16         81       19

Step-by-step explanation:

Answer: The length of an arc is 2.98 feet.

Step-by-step explanation:

Since we have given that

Radius of a circle = 3 feet

Angle subtended at the centre = 57°

We need to find the length of an arc:

As we know the formula for "Length of an arc":

[tex]Length=\dfrac{\theta}{360^\circ}\times 2\pi r\\\\Length=\dfrac{57}{360}\times 2\times \dfrac{22}{7}\times 3\\\\Length=2.98\ feet[/tex]

Hence, the length of an arc is 2.98 feet.

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. The recipe makes approximately 6.67 servings of pudding.

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. In this case, the recipe makes 5 cups and each serving is 3/4 cup. So, to find the number of servings, divide 5 cups by 3/4 cup: 5 cups ÷ (3/4 cup) = 5 cups × (4/3 cup) = 20/3 servings

Therefore, the recipe makes approximately 6.67 servings of pudding.

Is It A Fraction If So Then The Answer Is [tex]\frac{9}{16}[/tex]

If Not Then The Other Guy Is Right

              HoPe It HeLpS PlEaSe MaRk Me ThE BRAINlYEST!!!!!!!!!!!!

The solid lying above the cone z = x^2 + y^2 and below the sphere x^2 + y^2 + z^2 = z, in spherical coordinates, is described by the inequalities 0 ≤ ρ ≤ 2 cos φ (W.r.t the sphere) and φ ≥ π/4 (W.r.t the cone), with 0 ≤ θ ≤ 2π (full revolution for θ).

In spherical coordinates, we represent a point in space using three values: ρ (the distance from the origin), φ (the angle measured from the positive z-axis down to the line connecting the origin and the point), and θ (the angle measured in the x-y plane from the positive x-axis to the projection of the line segment from the origin to the point).

The given cone z = x2 + y2 in spherical coordinates becomes ρ cos φ = ρ2 sin2 φ, which simplifies to tan φ = 1/ρ or φ = π/4. This is because for a cone with vertex at the origin, φ is constant. So, our first inequality is φ ≥ π/4.

The sphere's equation x2 + y2 + z2 = z becomes ρ2 = ρ cos φ, which further simplifies to ρ = 2 cos φ. So, the second inequality is ρ ≤ 2 cos φ, which bounds ρ from above by the sphere.

In summary, the solid is described by the inequalities 0 ≤ ρ ≤ 2 cos φ and φ ≥ π/4, with 0 ≤ θ ≤ 2π (since θ revolves full circle in spherical coordinates).

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The solid can be described using the inequalities: 0 ≤ r ≤ cos(θ), 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π. These inequalities define the limits for the radius, polar angle, and azimuthal angle in spherical coordinates.

To describe the solid in terms of inequalities involving spherical coordinates, we need to find the limits for the radius, polar angle, and azimuthal angle.

Considering the given information, the solid lies above the cone z = x2 + y2, which implies that the z-coordinate ranges from 0 to r2.

As for the sphere x2 + y2 + z2 = z, we can rewrite it in spherical coordinates as r2 = r cos(θ) or r = cos(θ).

Therefore, the solid can be described using the following inequalities in spherical coordinates:

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multiply 365 by 8

365 * 8 = 2920

so yes it is reasonable