what is the inverse of g (x)= 2x-4/3

Answer:

you have  to divide 12 by 15

Step-by-step explanation:

Hello, I Am BrotherEye

Answer:

This Transparent inquisition can be solved Below

Use transformations to graph a quadratic function in vertex form. A quadratic function in standard form, f(x) = ax² + bx + c, can be changed into vertex form by completing the square. The vertex form of a quadratic function is f(x) = a(x – 5)2 + k, where the vertex of the function is (h, k).

Step-by-step explanation:

Vertex form to standard form converter

Write the parabola equation in the vertex form: y = a*(x-h)² + k ;

Expand the expression in the bracket: y = a*(x² - 2*h*x + h²) + k ;

Multiply the terms in the parenthesis by a : y = a*x² - 2*a*h*x + a*h² + k ;

Best Of Luck

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BrotherEye

The slope of the line with coordinate pairs of points (- 4, 0) and (2, 4)

is  2/3.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

To find the slope of the line we have to determine two coordinate pairs of points.

When x = - 4, y = 0 and when x = 2, y = 4.

So, Two coordinate pairs of points are (- 4, 0) and (2, 4).

Now slope = (y₂ - y₁)/(x₂ - x₁).

Slope = (4 - 0)/(2 + 4).

Slope = 4/6 ⇒ 2/3.

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Answer:

a = 8

Step-by-step explanation:

a ÷ 2 - 8 + 8 = - 4 + 8

a ÷ 2 = 4

a ÷ 2 × 2 = 4 × 2

a = 8

Answer:

a = 8

Step-by-step explanation:

Given

\(\frac{a}{2}\) - 8 = - 4 ( add 8 to both sides )

\(\frac{a}{2}\) = 4 ( multiply both sides by 2 to clear the fraction )

a = 8

As per the details given, there are 37 dots in the 5th step.

To locate the pattern and decide the range of dots in the 5th step, allow's examine the given records:

Step 1: 6 dots

Step 2: 14 dots

Step 3: 21 dots

Looking on the variations between consecutive steps, we will see that the quantity of additional dots in each step is growing via eight.

In other phrases, the distinction among Step 1 and Step 2 is eight, and the difference between Step 2 and Step 3 is likewise eight.

Thus, we can preserve this sample to decide the quantity of dots within the 4th and 5th steps:

Step 4: 21 + 8 = 29 dots

Step 5: 29 + 8 = 37 dots

Therefore, there are 37 dots in the 5th step.

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Answer:

sec θ

Step-by-step explanation:

cos θ + sin θ tan θ

= cos θ + sin θ (sin θ / cos θ)

= cos θ + (sin²θ)/cos θ

= cos θ + (1 - cos²θ) / cosθ

= cos θ + 1/cos θ - cos²θ/cos θ

= cos θ + 1/cos θ - cos θ

= 1/cos θ

= sec θ

Answer:

the domain of the function is y-2vx-5 is 0x25

The domain of the function  x≥ 5.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

The domain takes all of the potential input values from the set of real numbers, while the range takes all of the function's output values.

We have the function y = √(x- 5)

The domain is the x values operate, often known as the horizontal axis.

The Range is y values on the vertical axis.

As, the radical never gives Negative Value.

So, x- 5 ≥ 0

and, x≥5

Thus, the domain is x≥ 5.

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Answer: you add them all up

Step-by-step explanation: you can get the answer from above and dont trust this answer.

Answer:

A

Step-by-step explanation:

-3×6x=-18x -3×-2=6 -18x+6

Option 3) Sometimes is the correct answer, Sometimes an equilateral triangle is similar to a scalene triangle.

If the respective sides are proportional and the corresponding angles are congruent, two triangles are comparable. An equilateral triangle has three congruent sides and three congruent angles, so any triangle that is similar to an equilateral triangle must also have three congruent angles. However, a scalene triangle has no congruent sides and no congruent angles, so it is possible for a scalene triangle to be similar to an equilateral triangle only if it has the same angle measurements as an equilateral triangle, but with different side lengths. Therefore, a scalene triangle can be similar to an equilateral triangle, but it is not always the case.

In general, if two triangles are similar, it means that they have the same shape but possibly different sizes. In the case of an equilateral triangle and a scalene triangle, if they are similar, then it means that the scalene triangle has the same angles as the equilateral triangle, but its sides are of different lengths. So it is possible for a scalene triangle to be similar to an equilateral triangle, but not in all cases.

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A. The total charge in the device at t = 1 s is 28(1 + e⁻²¹) × 10⁻³ mC.

B. The power consumed by the device at t = 1 s is 27 sin(44) × 28(1 + e⁻²¹) mW.

To calculate the total charge in the device at t = 1 s, we need to integrate the current over time.

Given:

v(0) = 27 sin(44) V

i(0) = 28(1 + e⁻²¹) mA

We'll convert the current to amperes for consistency:

i(0) = 28(1 + e⁻²¹) × 10^(-3) A

We integrate the current from t = 0 to t = 1 s to find the total charge:

q(t) = ∫[0 to t] i(t') dt'

Since q(0) = 0, we can write:

q(t = 1) = ∫[0 to 1] i(t') dt'

Let's perform the integration:

q(t = 1) = ∫[0 to 1] 28(1 + e⁻²¹) × 10⁻³ dt'

= 28(1 + e⁻²¹) × 10⁻³ ∫[0 to 1] dt'

= 28(1 + e⁻²¹) × 10⁻³ [t'] [0 to 1]

= 28(1 + e⁻²¹) × 10⁻³ (1 - 0)

= 28(1 + e⁻²¹) × 10⁻³ mC

Therefore, the total charge in the device at t = 1 s is 28(1 + e⁻²¹) × 10⁻³ mC.

B. To calculate the power consumed by the device at t = 1 s, use the formula:

P(t) = v(t) × i(t)

Given v(0) = 27 sin(44) V and i(0) = 28(1 + e⁻²¹) mA, we need to evaluate v(t) and i(t) at t = 1 s:

v(t = 1) = 27 sin(44)

i(t = 1) = 28(1 + e⁻²¹)

Now we can calculate the power:

P(t = 1) = v(t = 1) × i(t = 1)

= 27 sin(44) × 28(1 + e⁻²¹)

Therefore, the power consumed by the device at t = 1 s is 27 sin(44) × 28(1 + e⁻²¹) mW.

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The complete question goes thus:

The voltage v1) across a device and the current i(t) through it are (0) = 27 sin(44) V and (0) = 28(1 + e-21) mA.

Calculate the total charge in the device at t = 1 s, assuming q(0) = 0. The total charge in the device at t = 1 s is ___ mC.

Calculate the power consumed by the device at t = 1 s. The power consumed by the device at t = 1 s is ___ mW.

The units of v''(r) will be cubic centimeters per square centimeter, or \((cm^3/cm^2)\).

The second derivative of a function represents the rate of change of the first derivative, or the rate of change of the rate of change of the original function.

In this case, the function v(r) models the volume of a basketball, which is measured in cubic centimeters \((cm^3)\). The independent variable r is measured in centimeters (cm).

The first derivative of v(r) with respect to r is, which represents the rate of change of the volume with respect to the radius, and has units of \(cm^2\) (cubic centimeters per centimeter).

The s\((cm^3/cm^2).\)second derivative of v(r) with respect to r is v''(r), which represents the rate of change of the first derivative, or the rate of change of the rate of change of the volume with respect to the radius. The units of v''(r) will be \(cm^-1\), or the inverse of the units of the first derivative, which is  \((cm^3/cm^2)\).

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Answer:

3x^5-4x^4-x^2+5

Step-by-step explanation:

(3x^5−2x^4−5)−(2x^4+x^2−10)

Distribute the minus sign

(3x^5−2x^4−5)−2x^4-x^2+10

Combine like terms

3x^5-4x^4-x^2+5

Hello!

\(\boxed{ \bf 3x^5~-~4x^4~-~x^2~+~5}\)

(3\(x^{5}\) - 2\(x^{4}\) - 5) - (2\(x^{4}\) + x² - 10)

Drop the brackets:

3\(x^{5}\) - 2\(x^{4}\) - 5 - 2\(x^{4}\) - x² + 10

Combine Like Terms:

3\(x^{5}\) - 2\(x^{4}\) - 2\(x^{4}\) - x² - 5 + 10

3\(x^{5}\) - 4\(x^{4}\) - x² + 5

Answer: Point C is (0, -7)

Step-by-step explanation:

For a general line y = a*x +b

A perpendicular line to this one will have a slope equal to -(1/a)

First, for a line y = a*x + b that passes through points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Then for a line that passes through the points A (-4, 5) and B (5, 8) the slope is:

a = (8 - 5)/(5  - (-4))  = 3/9 = 1/3

a = 1/3

Then, a line perpendicular to this one will have the slope:

a' = -(1/(1/3) = -3

Then the perpendicular line is something like:

y = -3*x + b

Now we know that this line passes through point A, then when x = -4, we have y = 5

if we replace these values we get:

5 = -3*(-4) + b

5 = 12 + b

5 - 12  = b

-7 = b

Then our line is:

y = -3*x - 7

This line intersects the y-axis at point C, we know that the y-axis corresponds to x = 0.

Then:

y = -3*0 - 7

y = -7

The point C is (0, -7)

Answer:

P

Step-by-step explanation:

the fancy looking 'p' in the corner tells you what the plane is labeled

The value of the expression is \(\rm 4r^3\).

Given that

Equation; \(\sqrt{16r^6}\)

We have to simplify the given equation

According to the question

To simplify the given equation follow all the steps given below.

Equation; \(\sqrt{16r^6}\)

Then,

\(\rm = \sqrt{16r^6}\\\\= \sqrt{4 \times 4 \times (r^3)^2}\\\\= \sqrt{(4)^2 \times (r^3)^2}\\\\= 4 \times r^3\\\\= 4r^3\)

Hence, the value of the expression is \(\rm 4r^3\).

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yr answer is B. 4r3!!

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The probability that all 6 flips result in heads is 1/64

The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0

For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64

P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64

Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.

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Answer:

what do you need to find? Area? perimeter?

Step-by-step explanation:

Answer:

value of x = 8

Step-by-step explanation:

well here,

line x is parallel to the line measuring 18

so the two triangles are similar to each other

hence ratio of their sides are equal

so 6/ 12 = x/ 16

=》1/2 = x/16

=》 x = 16 / 2

=》 x = 8

i hope u got it

have a nice day

Answer:

x = \(\frac{16}{3}\)

Step-by-step explanation:

The outer and inner triangles are similar, thus the ratios of corresponding sides are equal, that is

\(\frac{6}{6+12}\) = \(\frac{x}{16}\) , that is

\(\frac{6}{18}\) = \(\frac{x}{16}\) ( cross- multiply )

18x = 96 ( divide both sides by 18 )

x = \(\frac{96}{18}\) = \(\frac{16}{3}\)

The initial amount of salt in the tank is 50 kg.

In 't' minutes, the amount of salt that enters the tank \(= 0.025 * 8t kg\).

The amount of salt drained from the tank in 't' minutes \(= 0.025 * 5t kg\).

According to the law of conservation of mass, the total amount of salt remains constant.

The initial amount of salt in the tank + Amount of salt entered into the tank - Amount of salt drained from the tank = Constant

\(50 + 0.025 * 8t - 0.025 * 5t = 50\)

Subtracting \(0.025 × 5t\) from 0.025 × 8t, we get,\(0.025 × 3t = 0.75t\)

\(= 0.75/0.025\\t = 30\)

Hence, the initial amount of salt in the tank is 50 kg.

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I ⊆ I' if and only if a' ≤ a and b ≤ b'. This relationship holds true for closed intervals I and I' in R. To show that I ⊆ I' if and only if a' ≤ a and b ≤ b', we will consider two cases:

1. If I ⊆ I', then for any x ∈ I, we have x ∈ I'. Since I and I' are closed intervals, we can write them as I = [a, b] and I' = [a', b']. We want to show that a' ≤ a and b ≤ b' in this case.

Since x ∈ I, we know that a ≤ x ≤ b. Now, since x also belongs to I', we have a' ≤ x ≤ b'. Since this is true for any x in I, we can conclude that a' ≤ a and b ≤ b'.

2. If a' ≤ a and b ≤ b', we want to show that I ⊆ I'. Let x be any element in I, so we have a ≤ x ≤ b. We are given that a' ≤ a and b ≤ b'. Since a' ≤ a and a ≤ x, we can infer that a' ≤ x. Similarly, since x ≤ b and b ≤ b', we can infer that x ≤ b'. Therefore, x ∈ I'.

Since x was an arbitrary element in I, we can conclude that I ⊆ I' when a' ≤ a and b ≤ b'.

In summary, I ⊆ I' if and only if a' ≤ a and b ≤ b'. This relationship holds true for closed intervals I and I' in R.

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Answer:

x=6

Step-by-step explanation:

Answer:

\(\boxed {x = 6}\)

Step-by-step explanation:

Solve for the value of \(x\) :

\(-3 = \frac{2}{3}x - 7\)

-Switch sides, and let \(\frac{2}{3}x - 7\) be on the left side and \(-3\) on right side:

\(-3 = \frac{2}{3}x - 7\)

\(\frac{2}{3}x - 7 = -3\)

-Add \(7\) to both sides:

\(\frac{2}{3}x - 7 + 7 = -3 + 7\)

\(\frac{2}{3}x = 4\)

-Multiply \(\frac{3}{2}\) on both sides, which is the reciprocal of \(\frac{2}{3}\) :

\(x = 4 \times (\frac{3}{2})\)

\(x = \frac{12}{2}\)

-Divide \(12\) by \(2\):

\(x = \frac{12}{2}\)

\(\boxed {x = 6}\)

Step-by-step explanation:

Turn the standard form equation into a slope-intercept form equation using algebra.

Slope-intercept form: \(y=mx+b\)

Key:

Subtract each side by 3x:

\(8y=-3x+5\)

Divide each side by 8:

\(y=-\frac{3}{8} x+\frac{5}{8}\)

-3/8 is in the position of m, the slope.

The slope is -3/8.

If the two sides of the triangle are equal then these two triangles are similar. The sides EF and GF are congruent to each other. Then the correct option is D.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In ΔEDF and ΔGDF

DF = DF = radius (common side)

ED = GD = radius

If the two sides of the triangle are equal then these two triangles are similar.

Thus, EF and GF are congruent to each other.

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Answer:

the answer is D

Step-by-step explanation:

EF and GF

Answer:

7.5kg

Step-by-step explanation:

Given that:

Monday:

Mass of sand = 24 kg

Mass of cement = 5 kg

Tuesday :

Mass of sand = 36 kg

Let mass of cement = c

Mass of cement required to make the same type of mortar mix

Mass of Sand = mass of cement

24kg = 5kg

36kg = c

By cross multiplication :

24 * c = 5 * 36

24c = 180

Divide both sides by 24

c = 180 / 24

c = 7.5 kg

Hence mass of cement required is 7.5 kg

Answer:

The length of the border is approximately 4 feet.

Step-by-step explanation:

Since the garden has a circular border we can apply the formula for the circle's length, which is shown below:

\(length = 2*\pi*radius\)

Where the radius is half the diameter. The diameter is the distance between two points in the circle going through the center, therefore for this garden the diameter is 1.2 feet and the radius is 0.6 feet. Applying this to the formula gives us:

\(length = 2*\pi*0.6\\length = 1.2*\pi\\length = 3.8\)

The length of the border is approximately 4 feet.

The correct option, for the sum of the series is

d. its sum is 1/10

To find the sum of the series Σ 1 / (n+9)(n+10), we can rewrite it as follows:

Σ 1 / (n+9)(n+10) * 1(n + 9) = Σ (1 / (n+9)) - (1 / (n+10))  * 1(n + 9)

Now, let's evaluate the terms of the series:

When n = 0:

Term 1: 1 / (0+9) = 1/9

Term 2: 1 / (0+10) = 1/10

Term 3:  1(0 + 9) = 9

Therefore, the sum of the series when n = 0 is:

(1/9 - 1/10) * 9 = 1/90 * 9

So, the sum of the series when n = 0 is 1/10.

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Answer:

x = 15.56

y = 15.56

Step-by-step explanation:

In the right angled triangle,

Taking 45 as the reference angle,

h = 22

p = y

b = x

sin45 = p/h

sin45 = y/22

y = sin45 x 22

y= 15.56

cos45 = b/h

cos45 = x/22

x = cos45 x 22

x= 15.56