Please help me. I'm confused. Consider the following geometric sequence. -5, 10, -20, 40,... If the recursive formula for the sequence above is expressed in the form a^n=b*^n-1, determine the value of B. B= (choices are 2, -2, 5, -5)

Answer:

The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit

EXPLANATION:

Draw a perpendicular line from vertex B to DC at E.

Labeling the diagram as shown in the attachment:

Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and  their opposite sides would be parallel.

Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.

Consider the right triangle BEC

BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

therefore, the length of side, [tex]BE=EC=6[/tex] unit

Using trigonometric ratio; to find the value of b:

[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]

∴ using trigonometric sine ratio in triangle BEC, we have

[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or

[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]

On Simplify:

[tex]b=6\sqrt{2}[/tex] unit

and the value of a = DC = DE+EC=8+6=14 unit

Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit

This answer details the use of the quadratic formula to solve quadratic equations and the discriminant's role in determining the number of real solutions.

The question involves solving quadratic equations and using the discriminant to determine the number of real solutions. The quadratic formula, \(x = \frac{-b \pm \sqrt[tex]{b^2[/tex] - 4ac}}{2a}\), is a powerful tool in finding the roots of any quadratic equation of the form \([tex]ax^2[/tex]+ bx + c = 0\). The discriminant, \(\Delta =[tex]b^2[/tex] - 4ac\), helps in understanding the nature of the roots without actually solving the equation. If \(\Delta > 0\), there are two distinct real solutions; if \(\Delta = 0\), there is exactly one real solution; and if \(\Delta < 0\), there are no real solutions and instead two complex solutions.

Answer:

The triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99

Step-by-step explanation:

We have sine rule,

             [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Here given A = 48°, a = 32, b = 27

Substituting

          [tex]\frac{32}{sin48}=\frac{27}{sinB}=\frac{c}{sinC}\\\\sinB=0.627\\\\B=38.83^0[/tex]

We have

          A + B + C = 180°

          48 + 38.83 + C = 180

          C = 93.17°

Using sine rule again

          [tex]\frac{32}{sin48}=\frac{c}{sin93.17}\\\\c=42.99[/tex]

So the triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99

In the given hour, Dale ran 5 miles and Chan ran 2.5 miles.

Let Dale's running miles be represented by the variable D and let Chan's running miles be represented by the variable C.

In-order to compare Dale's running miles to Chan's by using division we get:

[tex] \frac{D}{C}=\frac{5}{2.5} = \frac{2}{1} [/tex]

[tex] D=2C [/tex]

Thus, Dale ran twice the distance Chan ran in the same amount of time of 1 hour.

Equivalently we can say that Chan ran half the distance Dale ran in the same amount of time of 1 hour.

Answer:

Correct Answer: Revolution

Step-by-step explanation:

Final answer:

The set of ordered pairs represents a function Yes, because every x-value corresponds to exactly one y-value(C).

Explanation:

The set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents a function because every x-value corresponds to exactly one y-value. In a function, each input (x-value) has only one output (y-value). The set does not have two different y-values for the same x-value, so option D is incorrect. Therefore, option C is the correct answer.

(C). Yes, because every x-value corresponds to exactly one y-value.

You can see that each unique x-value corresponds to exactly one y-value, and there are no repeated x-values. Therefore, this set of ordered pairs represents a function.

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Answer:

We have then:

f(x) = 2/5x^2-2 The function g (x) is a vertical stretch of f(x) by a factor of 2:

g(x) = 2f (x)

g(x) = 2 (2/5x^2-2)

g(x) = 4/5 x^2-4 is a required equation.

Answer:

$1.3425

Step-by-step explanation:

The regular price of the dinner buffet is 8.95. If this has a discount of 15%, we would have to multiply the total price by 0.15 and this would give us how much of the total amount is 15% and therefore it would give us how much of a discount the senior receives off of the 8.95 price

8.95 x 0.15 = 1.3425

Therefore, a senior citizen gets $1.3425 discount.

The graph of a quadratic function, or a parabola, is U or n-shaped and its direction depends on the sign of the coefficient of the x-squared term. The vertex and line of symmetry can be found using formulas based on this coefficient.

The graph of a quadratic function, also known as a parabola, generally takes on a 'U' or 'n' shape. The direction that the 'U' faces depends on the sign of the coefficient, which is the number associated with the x-squared term in the equation. If this coefficient is positive, the graph opens upwards; if it's negative, the graph opens downwards. The vertex (the highest or lowest point on a parabola) can be calculated using the formula -b/2a. The line of symmetry can be found using the equation x = -b/2a.

For example, consider the quadratic function f(x)=x^2. This equation represents a parabola that opens upwards. Its vertex is at the point (0,0) and its line of symmetry is x=0.

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Option: B is the correct answer.

B) Traditionalism.

Beat generation was a literary movement that was started by a group of authors and  belongs to the post World War || period.

They started this movement to reject literary formalism and the American culture built on capitalism and materialism.

It has a major impact on both poetry as well as culture in America.

Hence, the Beat generation writers try to defeat in America is:

Traditionalism.

The largest interior angle of the heptagon, given the angle measures as x, x, x-2, x-2, x+2, x+2, x+4, is 132 degrees after solving for x.

The problem is to determine the degree measure of the largest interior angle in a heptagon. The degree measures of the interior angles are given as x, x, x-2, x-2, x+2, x+2, and x+4 degrees. To solve this, we first use the fact that the sum of the interior angles of a heptagon (7-sided polygon) is given by the formula (n-2) 180 degrees, where n is the number of sides. So, for a heptagon, the sum is

We then set up the equation based on the given interior angles: 3x + (2x - 4) + (2x + 4) + (x + 4) = 900. Simplifying, we get 7x + 4 = 900. Solving for x, we find x = 896/7 = 128 degrees. The largest interior angle is x + 4, which equals

Answer:

43.82 units.

Step-by-step explanation:

We have been given a triangle. We are asked to find the value of b using Law of Sines.

[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], where, a, b and c are opposite sides of angles A, B and C respectively.

Upon substituting our given values in above formula, we will get:

[tex]\frac{50}{\text{sin}(58^{\circ})}=\frac{b}{\text{sin}(48^{\circ})}[/tex]

Switch sides:

[tex]\frac{b}{\text{sin}(48^{\circ})}=\frac{50}{\text{sin}(58^{\circ})}[/tex]

[tex]\frac{b}{0.743144825477}=\frac{50}{0.848048096156}[/tex]

[tex]\frac{b}{0.743144825477}*0.743144825477=\frac{50}{0.848048096156}*0.743144825477[/tex]

[tex]b=43.81501643866[/tex]

[tex]b\approx 43.82[/tex]

Therefore, the value of b is approximately 43.82 units.