16=4^x-6 solve the equation

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

To learn more on word problems: https://brainly.com/question/15588055

#SPJ1

Answer:

Explanation: There are two scenarios:

(1)

89 yards, and short of "power-pole":

(2)

122 yards and past the "power-pole"

Therefore the power pole must be between these two distances and we can have the range as:

Therefore the range of distances is from 89 yards up to 33 yards more, the power pole can be anywhere in between.

The HCF of 3, 4, and 5 is 1. ∴ The most increased numeral that diverges 3, 4, and 5 is 1.

To learn more about divisor, refer to:

https://brainly.com/question/30278966

#SPJ1

The inequality 3 ≤ x - 2 simplifies to x ≥ 5. This means x can take any value greater than or equal to 5. Therefore, option (E) with a number line from positive 5 to positive 10 is correct.

Given: 3 \(\leq\) x - 2

We need to work out which number line below shows the values that x can take. In order to solve the inequality, we will add 2 to both sides. 3+2 \(\leq\) x - 2+2 5 \(\leq\) x

Now the inequality is in form x \(\geq\) 5. This means that x can take any value greater than or equal to 5. So, the number line going from positive 5 to positive 10 shows the values that x can take.

Therefore, the correct option is (E) A number line going from positive 5 to positive 10.  We added 2 to both sides of the given inequality, which gives us 5 \(\leq\) x. It shows that x can take any value greater than or equal to 5.

Hence, option E is correct.

For more questions on inequality

https://brainly.com/question/30238989

#SPJ8

Answer:

The price would be 7.20

Step-by-step explanation:

The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

For more questions on equations

https://brainly.com/question/29174899

#SPJ8

Answer:

your answer will be 1

Step-by-step explanation:

Answer:

The number 540 has the following divisors

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

Step-by-step explanation:

The number 540 has the following divisors

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

Therefore, the number 540 is not a prime number or a deficient number

A deficient number is one that is larger than the sum total of its possible dividing numbers less the number 540 itself that is we have;

1+ 2+ 3+ 4+ 5+ 6+ 9+ 10+ 12+ 15+ 18+ 20+ 27+ 30+ 36+ 45+ 54+ 60+ 90+ 108+ 135+ 180+ 270 = 1140.

Answer:

\(540 = 3 ^{3} \times 2 {}^{2} \times 5\)

so, it is 4*3*2= 24

Answer:

24 ft

Step-by-step explanation:

Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

Learn more about displacement at:

https://brainly.com/question/14422259

#SPJ4

Answer:

11.12

Step-by-step explanation:

Answer:

11.12

Step-by-step explanation:

eleven=11

twelve hundredths= 0.12

eleven and twelve hundredths= 11.12

Answer:

X-7

Step-by-step explanation:

Because I did algebra 1

Answer:

X-17

Step-by-step explanation:Its X-17 because it said 17 less than a number X. So its X-17 and variable comes first.

The total weight is 18.5 kilograms

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

Learn more about acceleration

brainly.com/question/12550364

#SPJ11

As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

To know more about angle,

https://brainly.com/question/14569348

#SPJ1

The maximum mass of the water bug to avoid sinking is approximately 0.079 grams.

To determine the maximum mass of the water bug that avoids sinking, we need to consider the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the bug.

Calculate the volume of water displaced:

The bug's weight is balanced by the buoyant force, so the volume of water displaced is equal to the volume of the bug.

Each leg has a length of 5 mm, which means the total height of the bug is 5 mm. Assuming the cross-sectional area of the bug is constant along its height, we can use the formula for the volume of a cylinder to calculate the volume:

Volume = π * radius^2 * height

Since each leg is cylindrical, the radius would be half the leg's diameter, which is 5 mm (or 0.005 m).

Therefore, the volume of water displaced by the bug is:

Volume = π * (0.005 m)^2 * 0.005 m

Calculate the weight of the water displaced:

The weight of the water displaced is equal to the buoyant force acting on the bug.

Weight of water displaced = density of water * volume of water displaced * acceleration due to gravity

The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s².

So, the weight of the water displaced is:

Weight of water displaced = 1000 kg/m³ * Volume * 9.8 m/s²

Calculate the maximum mass of the bug:

The maximum mass of the bug is the mass at which its weight equals the weight of the water displaced:

Maximum mass = Weight of water displaced / acceleration due to gravity

Maximum mass = (1000 kg/m³ * Volume * 9.8 m/s²) / 9.8 m/s²

Now, let's plug in the values and calculate the maximum mass of the bug:

python

import math

radius = 0.005  # in meters (5 mm)

height = 0.005  # in meters (5 mm)

density_water = 1000  # in kg/m³

acceleration_due_to_gravity = 9.8  # in m/s²

volume = math.pi * radius**2 * height

weight_of_water_displaced = density_water * volume * acceleration_due_to_gravity

maximum_mass = weight_of_water_displaced / acceleration_due_to_gravity

maximum_mass_grams = maximum_mass * 1000  # converting to grams

print("Maximum mass of the bug to avoid sinking:", maximum_mass_grams, "grams")

Using the above calculations, the maximum mass of the water bug to avoid sinking is approximately 0.079 grams.

Learn more about approximately from

https://brainly.com/question/27894163

#SPJ11

Answer:

15/56

Step-by-step explanation:

bc i made the denominators the same by multying them by eachother which got me 56 and then i multipled the numerators by 8 and 7. Then i divided the new fractions which got me 15/56

The answer is,1) k = 2 2) Minimum value = -6

Given,

An amplitude of 5 units

A period of 180°

A maximum at (0, -1).

We know the formula of sinusoidal function is y = A sin (k (x - c)) + d

where,A = amplitude = 5units

Period = 180°

⇒ Period = 180° = 360°/k

⇒ k = 360°/180°

⇒ k = 2

A maximum at (0, -1)

⇒ d = -1

Therefore, the function is y = 5 sin 2(x - c) - 1

When x = 0, y = -1, we get -1 = 5 sin 2(0 - c) - 1⇒ 0 = sin(2c)

The smallest possible value of sin 2c is -1, which occurs at 2c = -π/2 + 2πn

⇒ c = -π/4 + πn

To find minimum value,

y = 5 sin 2(x - c) - 1

The minimum value of sin 2(x - c) is -1, which occurs when 2(x - c) = -π/2 + 2πn

⇒ x = π/4 + πn

Therefore, the minimum value of y is 5(-1) - 1 = -6

So, the answer is,1) k = 2 2) Minimum value = -6

To know more about Minimum visit:

https://brainly.com/question/21426575

#SPJ11

Answer:

88

Step-by-step explanation:

Given

x = 4y² - 12 ← substitute y = 5

x = 4(5)² - 12 = 4(25) - 12 = 100 - 12 = 88

Answer:

-51 months

Step-by-step explanation:

To solve, we can use the second model since we're told the money is compounded monthly

\(A=P(1+r/n)^n^t\\\\1000=4000(1+0.027/12)^1^2^t\\\\1/4=(4009/4000)^1^2^t\\\\log(1/4)=log(4009/4000)^1^2^t\\\\log(1/4)=12t*log(4009/4000)\\\\log(1/4)/log(4009/4000)=12t\\\\1/12*(log(1/4)/log(4009/4000))=t\\\\-51.40197623=t\\-51=t\)

To solve this problem, we'll use the formula A=P(1+r/n)^nt, where A is the future value, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

In this case, we know that P=$4000, r=2.7%, and n=12 (since interest is compounded monthly). We're trying to find the time required for the account to earn $1000, so A=P+$1000=$5000.

Plugging these values into the formula, we get:

$5000=$4000(1+0.027/12)^(12t)

Simplifying, we can divide both sides by $4000 and take the natural logarithm of both sides:

ln(1.25)=ln(1+0.027/12)^(12t)

Using the properties of logarithms, we can bring the exponent down:

ln(1.25)=12t*ln(1+0.027/12)

Dividing both sides by 12ln(1+0.027/12), we get:

t=ln(1.25)/(12ln(1+0.027/12))

Using a calculator, we find that t is approximately 3.5 years. Rounded to the nearest month, this is 42 months.

Therefore, it would take approximately 42 months (or 3 years and 6 months) for the account to earn $1000 with an initial investment of $4000 at an interest rate of 2.7% compounded monthly.

Learn more about compound interest here:

https://brainly.com/question/29335425

#SPJ11

Answer:

1/8

Step-by-step explanation:

Simplify the following:

(1 + 3/4)/(1/2) - (1/2 + 1)^3

Hint: | Write (1 + 3/4)/(1/2) as a single fraction.

Multiply the numerator of (1 + 3/4)/(1/2) by the reciprocal of the denominator. (1 + 3/4)/(1/2) = ((1 + 3/4)×2)/1:

(3/4 + 1) 2 - (1/2 + 1)^3

Hint: | Put the fractions in 1 + 1/2 over a common denominator.

Put 1 + 1/2 over the common denominator 2. 1 + 1/2 = 2/2 + 1/2:

(1 + 3/4) 2 - (2/2 + 1/2)^3

Hint: | Add the fractions over a common denominator to a single fraction.

2/2 + 1/2 = (2 + 1)/2:

(1 + 3/4) 2 - ((2 + 1)/2)^3

Hint: | Evaluate 2 + 1.

2 + 1 = 3:

(1 + 3/4) 2 - (3/2)^3

Hint: | Put the fractions in 1 + 3/4 over a common denominator.

Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:

4/4 + 3/4 2 - (3/2)^3

Hint: | Add the fractions over a common denominator to a single fraction.

4/4 + 3/4 = (4 + 3)/4:

(4 + 3)/4×2 - (3/2)^3

Hint: | Evaluate 4 + 3.

4 + 3 = 7:

7/4×2 - (3/2)^3

Hint: | Express 7/4×2 as a single fraction.

7/4×2 = (7×2)/4:

(7×2)/4 - (3/2)^3

Hint: | In (7×2)/4, divide 4 in the denominator by 2 in the numerator.

2/4 = 2/(2×2) = 1/2:

7/2 - (3/2)^3

Hint: | Simplify (3/2)^3 using the rule (p/q)^n = p^n/q^n.

(3/2)^3 = 3^3/2^3:

7/2 - 3^3/2^3

Hint: | In order to evaluate 3^3 express 3^3 as 3×3^2.

3^3 = 3×3^2:

7/2 - (3×3^2)/2^3

Hint: | In order to evaluate 2^3 express 2^3 as 2×2^2.

2^3 = 2×2^2:

7/2 - (3×3^2)/(2×2^2)

Hint: | Evaluate 2^2.

2^2 = 4:

7/2 - (3×3^2)/(2×4)

Hint: | Evaluate 3^2.

3^2 = 9:

7/2 - (3×9)/(2×4)

Hint: | Multiply 2 and 4 together.

2×4 = 8:

7/2 - (3×9)/8

Hint: | Multiply 3 and 9 together.

3×9 = 27:

7/2 - 27/8

Hint: | Put the fractions in 7/2 - 27/8 over a common denominator.

Put 7/2 - 27/8 over the common denominator 8. 7/2 - 27/8 = (4×7)/8 - 27/8:

(4×7)/8 - 27/8

Hint: | Multiply 4 and 7 together.

4×7 = 28:

28/8 - 27/8

Hint: | Subtract the fractions over a common denominator to a single fraction.

28/8 - 27/8 = (28 - 27)/8:

(28 - 27)/8

Hint: | Subtract 27 from 28.

| 2 | 8

- | 2 | 7

| 0 | 1:

Answer: 1/8

The race result will not be disqualified due to an illegal wind.

In order to determine whether the wind velocity during the race was legal, we need to compare the wind velocity w to the legal wind speed limit of 5 km/hr. In this case, the wind velocity is given as 5ij km/h, which is purely vertical wind. The direction of the wind is not relevant in this case, since the race is run in the direction of the vector v, which is a purely horizontal direction. Since the wind velocity w is purely vertical and the race is run in a purely horizontal direction, the wind velocity w has no effect on the race result. Therefore, the race result will not be disqualified due to an illegal wind.

To learn more about velocity, visit:

brainly.com/question/18084516

#SPJ4

Answer:

a) 26

b) 14

Step-by-step explanation:

Given Formula:

\(\frac{1}{2}(\frac{b1+b2}{2})\) x h

Steps for A:

\(\frac{1}{2}(\frac{5+8}{2})\) x 4

5+8=13

13÷2=6.5

6.5 x 4

= 26

Steps for B:

\(\frac{1}{2}(\frac{1+6}{2})\) x 4

1+6=7

7÷2=3.5

3.5 x 4

= 14

To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

Learn more about coefficient here: brainly.com/question/13431100

#SPJ11

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

Learn more about volume here:

https://brainly.com/question/13338592

#SPJ11

Answer:

133.78684807256

Step-by-step explanation:

step 1: We need the assumption that 44.1 is 100% since it is our output value

step 2: We need to represent the value we seek in x

step 3: From step 1, it follows that 100% = 44.1

step 4: In the same vein x% = 59

step 5: This give us a pair of simple equations:

100% = 44.1 (1)

x% = 59 (2)

step 6: by simplify dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have

\( \frac{100}{x} = \frac{44.1}{59} \)

step 7: Taking the inverse (or reciprocal) of both sides yields

\( \frac{x}{100 } = \frac{59}{44.1} \)

= x = 133.78684807256

Therefore, 59 is 133.78684807256% of 44.1

Answer:

median is not a measure of variability

Answer:

D.median

Step-by-step explanation:

Answer:

1] x=4.21

2] 52.5

3] 3.82

4] 38.73

5] 32.005

6] 31.21

Step-by-step explanation: