The third term in a sequence is 25. The fifth term is 225. What are the possible values of the 4th term of the sequence if it is arithmetic? If it is geometric?

The equation of the parabola is y = 2(x - 1)² + 3

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

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

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the predicates R(x) and H(x) along with quantifiers and logical connectives, we can represent the given statements as ∀x(R(x) → H(x)) and ∃x(R(x) ∧ ¬H(x)).

(a) Using the predicates R(x) and H(x) to represent "x is a rabbit" and "x hops" respectively, the English sentence "For every animal in the domain, if it is a rabbit, it hops" can be expressed in terms of quantifiers and logical connectives as:

∀x(R(x) → H(x))

This translates to "For all x in the domain, if x is a rabbit, then x hops."

(b) Similarly, the English sentence "There is at least one animal such that it is a rabbit and it doesn't hop" can be expressed in terms of quantifiers and logical connectives as:

∃x(R(x) ∧ ¬H(x))

This translates to "There exists an x in the domain such that x is a rabbit and it does not hop."

In summary, using the predicates R(x) and H(x) along with quantifiers and logical connectives, we can represent the given statements as ∀x(R(x) → H(x)) and ∃x(R(x) ∧ ¬H(x)).

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Answer:

d

Step-by-step explanation:

beacusee its wiill will be resonable

The inverse of function of f(x) will be p(x) = 7x – 2. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = (x + 2) / 7

Substitute p(x) in place of x and x in place of f(x). Then the equation of the inverse function will be

x = [p(x) + 2] / 7

Solve the equation for p(x), then the equation of the inverse function will be

p(x) + 2 = 7x

     p(x) = 7x – 2

Thus, the inverse of function of f(x) will be p(x) = 7x – 2.

Then the correct option is B.

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Answer:

the answer is 9.56

Step-by-step explanation:

3.25 + 5.25 = 8.50 ÷ 8 = 1.06 + 8.50 = 9.56

hope it helps :)

Answer:

\(\boxed {x > -\frac{10}{7}}\)

Step-by-step explanation:

Solve the given inequality:

\(2(x - 1) - 4(x + 2) < 5x\)

-Use Distributive Property:

\(2(x - 1) - 4(x + 2) < 5x\)

\(2x - 2 - 4x - 8 < 5x\)

-Combine like terms:

\(2x - 2 - 4x - 8 < 5x\)

\(-2x - 10 < 5x\)

-Subtract both sides by \(5x\):

\(-2x - 10 - 5x < 5x - 5x\)

\(-7x - 10 < 0\)

-Add both sides by \(10\):

\(-7x - 10 + 10 < + 10\)

\(-7x < 10\)

-When you are dividing a integer by a negative integer, the inequality sign would change. So, divide both sides by \(-7\):

\(\frac{-7x}{-7} < \frac{10}{-7}\)

\(\boxed {x > -\frac{10}{7}}\) (final answer)

To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).

Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.

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Answer:

sorry i cant help , not smart enough ,but i wish i was tho

Step-by-step explanation:

The measure of angle x in the right triangle is approximately 14.6 degrees.

The figure in the image is that of two right angles.

First, we determine the hypotenuse of the left-right angle.

Angle θ = 30 degrees

Adjacent to angle θ = 10 cm

Hypotenuse = ?

Using the trigonometric ratio.

cosine = adjacent / hypotenuse

cos( 30 ) = 10 / hypotenuse

hypotenuse = 10 / cos( 30 )

hypotenuse = \(\frac{20\sqrt{3} }{3}\)

Using the hypotenuse to solve for x in the adjoining right triangle:

Angle x =?

Adjacent to angle x = \(\frac{20\sqrt{3} }{3}\)

Opposite to angle x = 3

Using the trigonometric ratio.

tan( x ) = opposite / adjacent

tan( x ) = 3 / \(\frac{20\sqrt{3} }{3}\)

tan (x ) = \(\frac{3\sqrt{3} }{20}\)

Take the tan inverse

x = tan⁻¹(  \(\frac{3\sqrt{3} }{20}\) )

x = 14.6 degrees

Therefore, angle x measures 14.6 degrees.

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Answer:

48

Step-by-step explanation:

8x3x2= 48

Answer:

its 48

Step-by-step explanation:

8x3x2= 48

Answer:

yes, it is true because a supplimentary angle is 180 degrees and if their is an acute angle then it is less than 90 degrees which means you subtract that by 180 and you get a number over 90 and an obtuse angle is over 90 which means the other side of the acute angle is obtuse. And the suppliment to an acute angle is always over 90 degrees

Hope it helps!

can I get brainliest?

Answer:

work = force × distance

Therefore,

work = 3200N × 16m

= 51200J

So,

Power = Work done/ time taken

Therefore,

Power = 51200/30

= 1706.6 ~ 1707W

Hope it helps!

Answer:

linear

Step-by-step explanation:

We can write this  in the form

y = mx+b

where m is the .75 per mile and b is the 39 dollars

y = .75x + 39

Answer:

ab hehehe hende ko Alam hahahah

Hence, the area of the square \(AB\)  is \(5\)

What is the area of square?

The area of a square is equal to

(side) × (side) square units.

Here given that,

Square \(ABCD\) is drawn on the coordinate plane (not shown) with vertex \(A(-4,-2)\) and the midpoint of side \(AB\) at \(B(-1.-6).\)

Given ertices are \(A(-4,-2)\) and \(B(-1.-6).\)

So,

\(AB=\sqrt{(-1+4)^2+(-6+2)^2}\\AB=\sqrt{(3)^2+(-4)^2}\\AB=\sqrt{9+16}\\AB=\sqrt{25}\\AB=5\)

Hence, the area of the square \(AB\)  is \(5\).

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Answer:

18/24 or 75%

Step-by-step explanation:

Okay so you already know that he got 16/24 which means that there were 8 questions that were wrong because 24-16= 8

So he has 16 points that we know of and 8 questions that he got wrong.

If he lost 1/4 of a point when he got it incorrect 1/4= 0.25

0.25 x 8 = 2points

So he got to points

16+ 2= 18 so now it is 18/24

If you have to show Out for 100% it would be 75%

Hope it helped!

Answer:

21 ft

Step-by-step explanation:

Tan(32) = x/34

34tan(32)=x

x= 21.245...

x=21

The lines y = 5x + 1 and 2y - 10x + 3 are parallel because both lines have the same slope of 5

To show that two lines are parallel, we need to demonstrate that they have the same slope.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

For L1, we have y = 5x + 1, which is in the slope-intercept form. So we can see that the slope of L1 is 5.

For L2, we can solve for y to get it in the slope-intercept form:

2y - 10x + 3 = 0

2y = 10x - 3

y = 5x - 3/2

So the slope of L2 is 5 as well.

Since both lines have the same slope of 5, we can conclude that they are parallel.

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The given question is incomplete, the complete question is

The equation of line L1 is y= 5x +1 the equation of L2 is 2y-10x+3 =0 show that these two lines are parallel

The formula for the function is f(x) = 0(x-9)(x-6) / (x-8) = 0. So the function is f(x) = 0.

The given function y = x² - 6x + 8 can be written as y = (x-2)(x-4)/(x-4). Simplifying the expression, we get y = x-2 for x ≠ 4 and y is undefined for x = 4. Hence, the graph has a hole at x = 4.

To find a possible formula for the rational function with the given properties, we can start by writing it in factored form as:

f(x) = A(x-9)(x-6) / (x-8)

where A is a constant that we need to determine. We know that the function has a horizontal asymptote of y = -5, which means that as x approaches positive or negative infinity, the function approaches -5. This means that the degree of the numerator and denominator must be the same, and the leading coefficient must be A. So we can set:

f(x) = A(x-9)(x-6) / (x-8) = (-5)x^n / x^n

where n is the degree of the polynomial. Multiplying both sides by x^n and simplifying, we get:

A(x-9)(x-6) = -5(x-8)^n

We know that the zeros are at x=9 and x=6, so we can substitute those values into the equation:

A(9-9)(6-6) = -5(8-8)^n

0 = 0

This doesn't give us any information about A, so we'll need to use the vertical asymptote. We know that the denominator of the function is zero at x=8, so we can substitute that value into the equation:

A(8-9)(8-6) = -5(8-8)^n

-A(1)(-2) = 0

2A = 0

A = 0

Now we can write the formula for the function:

f(x) = 0(x-9)(x-6) / (x-8) = 0

So the function is f(x) = 0.

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To differentiate the function f(x) = qx + r/sx + t, where q, r, s, and t are constants, the derivative is given by f'(x) = q - (r/s) * (1/x^2).

To differentiate the given function, we need to apply the rules of differentiation. Let's break down the steps:

1. Differentiate qx with respect to x: Since q is a constant, the derivative of qx is simply q.

2. Differentiate r/sx with respect to x: We can rewrite r/sx as r * (s * x)^(-1). Applying the power rule of differentiation, the derivative of (s * x)^(-1) is (-1) * (s * x)^(-1 - 1) * s = -s/x^2.

3. Differentiate t with respect to x: Since t is a constant, the derivative of t with respect to x is 0.

4. Combining the derivatives obtained from the previous steps, we have f'(x) = q - (r/s) * (1/x^2).

Therefore, the derivative of the given function f(x) = qx + r/sx + t, where q, r, s, and t are constants, is f'(x) = q - (r/s) * (1/x^2).

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The critical heat flux (CHF) is the maximum heat flux that can be transferred from a surface to a boiling liquid before the boiling process transitions from a stable regime to an unstable regime. The CHF is an important parameter in the design of heat transfer systems, as exceeding the CHF can lead to boiling crisis, which can cause severe damage to the system.

The CHF for a fluid depends on various factors such as fluid properties, surface properties, and flow conditions. One of the commonly used correlations for calculating CHF is the Kutateladze number (Ku) correlation, which is given by:

q_c = C (ρ_L^2 g Δh_f)^0.5 (σ/ρ_L)^0.1

where q_c is the critical heat flux, ρ_L is the liquid density, g is the acceleration due to gravity, Δh_f is the latent heat of vaporization, σ is the surface tension, and C is a constant that depends on the surface properties and flow conditions.

Using this correlation, we can calculate the CHF for the given fluids at 1 atm:

For mercury at 1 atm:

Density of mercury, ρ_L = 13,534 kg/m^3

Latent heat of vaporization of mercury, Δh_f = 2.66 x 10^5 J/kg

Surface tension of mercury, σ = 0.48 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.028, we get:

q_c = 0.028 * (13,534^2 * 9.81 * 2.66 x 10^5)^0.5 * (0.48/13,534)^0.1

q_c = 2.44 x 10^6 W/m^2

For ethanol at 1 atm:

Density of ethanol, ρ_L = 789 kg/m^3

Latent heat of vaporization of ethanol, Δh_f = 8.51 x 10^5 J/kg

Surface tension of ethanol, σ = 0.022 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.027, we get:

q_c = 0.027 * (789^2 * 9.81 * 8.51 x 10^5)^0.5 * (0.022/789)^0.1

q_c = 1.17 x 10^6 W/m^2

For refrigerant R-134a at 1 atm:

Density of R-134a, ρ_L = 1245 kg/m^3

Latent heat of vaporization of R-134a, Δh_f = 2.03 x 10^5 J/kg

Surface tension of R-134a, σ = 0.011 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.026, we get:

q_c = 0.026 * (1245^2 * 9.81 * 2.03 x 10^5)^0.5 * (0.011/1245)^0.1

q_c = 1.35 x 10^6 W/m^2

For water at 1 atm:

Density of water, ρ_L = 1000 kg/m^3

Latent heat of vaporization of water, Δh_f = 2

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Answer:

1) 117

2) 24

Step-by-step explanation:

Corresponding sides are in the same ratio for similar triangles

1)

For triangles MUL and WUV:

UW/UM = UV/UL

?/45 = 104/40

? = 45 x 104/40 = 117

2)
For triangles RST and RKH
RS/RK = RT/RJ

?/12 = 20/10 = 2

? = 2 x 12 = 24

A real number is in between 14 square root and 15 square root is 3.8.

It should be noted that real numbers include rational and irrational numbers.

✓14 = 3.74

✓15 = 3.87

Therefore, a real number is in between 14 square root and 15 square root is 3.8.

It should be noted that this implies a number that can be sent between the square roots.

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Answer:

3.179806 x \(10^{17}\)

Step-by-step explanation:

(6.958 x \(10^{10}\))(4.57 x \(10^{6}\))

(6.958 x 4.57)(\(10^{10}\) x \(10^{6}\))

31.79806 x \(10^{16}\)  When you have powers with the same base, you add the exponents when multiplying.

This is still not in scientific notation because 31.79806 is 1 or larger, but less than 10

31.79806 = 3.179806 x \(10^{1}\)

3.179806 x \(10^{1 }\) x \(10^{16}\) = 3.179806 x \(10^{17}\) When you have powers with the same bases, you add the exponents when multiplying.

The real number √21 is an example of an irrational number. (Correct choice: C)

According to number theory, real numbers are formed by the following sets:

Then, by direct inspection we get the following conclusions:

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Answer:

69 degrees

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

<1 = 39+ 30

<1 = 69

The equation for the tangent to the graph of y = arcsin(x/2) at the origin is y = x. This means that for any given x-value, the corresponding y-value is equal to that x-value, creating a line with a slope of 1. This line is tangent to the graph of y = arcsin(x/2) at the origin, which is (0, 0).

To find the equation for the tangent to the graph of y = arcsin(x/2) at the origin, we must first find the slope at the origin. We can do this by taking the derivative of the function y = arcsin(x/2) with respect to x.

The derivative of

y = arcsin(x/2) with respect to x is y' = (1/2)cos(x/2).

At the origin, x = 0, so the slope of the tangent at the origin is

y' = (1/2)cos(0) = 1.

Therefore, the equation for the tangent to the graph of

y = arcsin(x/2) at the origin is y = x, which has a slope of 1.

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\(7 \frac{5}{8} + 4 \frac{2}{3} \)

the simplest form.

\( \frac{61}{8} + \frac{14}{3} \)

\( = \frac{(61 \times 3) + (14 \times 8)}{8 \times 3} \)

\( = \frac{183 + 112}{24} \)

\( = \frac{295}{24} \)

\( = 12 \frac{7}{24} \)

hence, the correct answer is option D.

Answer:

x = 1

y = -3/2

Step-by-step explanation:

Step 1: Arrange the equations with like terms in column.

Step 2: You want 1 set of coefficients that are opposites. This problem already has opposites: -2y and +2y.

Step 3: Solve for x.

4x-2y=7

3x+2y=0

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

7x = 7

x = 1

Step 4: Substitute the value of x and solve for y.

4(1)-2y=7

4-2y=7

-2y=7-4

-2y=3

y=-3/2

Answer:

-6.1

Step-by-step explanation:

Hope this helps!