Find the distance (d) from the point (4,-4,1) to the plane x+5 y+2 z=6 d=

Answer:

3 tiles

because 1/4+1/4+1/4=3/4

I hope this helps you!

Answer:

Step-by-step explanation:

The logarithmic form of an exponential equation is:

y = log(base b)(x)

if and only if

x = b^y

In this case, we have the exponential equation:

e^(5x) = 1,298

To write this in logarithmic form, we can take the natural logarithm (ln) of both sides:

ln(e^(5x)) = ln(1,298)

Using the rule that ln(e^y) = y, we can simplify the left-hand side:

5x = ln(1,298)

Finally, we can divide both sides by 5 to solve for x:

x = ln(1,298) / 5

Therefore, the logarithmic form of the equation e^(5x) = 1,298 is:

x = ln(1,298) / 5, or equivalently,

log(base e)(1,298) / 5

Responder:

2n

Explicación paso a paso:

Dado 2, 4, 6, 8

Enésimo término de una progresión aritmética:

Tn = a + (n - 1) d

d = diferencia común

n = enésimo término

a = primer término

Tn = 2 + (n - 1) * 2

Tn = 2 + 2n - 2

Tn = 2n

The robot moves in the positive direction along a straight line so that after t minutes its distance is s=6t^4 feet from the origin. (a) Find the average velocity of the robot over intervals 2, 4. We have the following data: Initial time, t₁ = 2 min.

Final time, t₂ = 4 min.The distance from the origin is given by s = 6t^4Therefore, s₁ = s(2) = 6(2^4) = 6(16) = 96 feet s₂ = s(4) = 6(4^4) = 6(256) = 1536 feet

We can find the average velocity of the robot over the interval 2, 4 as follows: Average velocity = (s₂ - s₁) / (t₂ - t₁)Average velocity = (1536 - 96) / (4 - 2)Average velocity = 1440 / 2Average velocity = 720 feet per minute(b) Find the instantaneous velocity at t=2.To find the instantaneous velocity at t = 2 min, we need to take the derivative of the distance function with respect to time. We have the distance function as:s = 6t^4 Taking derivative of s with respect to t gives the velocity function:v = ds / dt Therefore,v = 24t³At t = 2, the instantaneous velocity is:v(2) = 24(2)³v(2) = 24(8)v(2) = 192 feet per minute Therefore, the instantaneous velocity at t = 2 min is 192 feet per minute.

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a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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Answer:

5+3w

Step-by-step explanation:

make it braintliest please

Answer:

w^3+5

Step-by-step explanation:

I am pretty sure you would just combine like terms and then add them together.

I hope this helps u out...

The annual percentage rate on Leigh's loan is 14.48%.

Leigh bought herself a set of new bedroom furniture. The total cost, including tax and delivery, was. The furniture store required down, and Leigh financed the rest for months at per month. The first step in calculating the annual percentage rate on a loan is to determine the monthly interest rate. Leigh financed the remainder of the furniture after making the down payment for months at $per month. The amount of money Leigh financed is the purchase price minus the down payment. If we let P be the purchase price and D be the down payment, we can express the amount financed as P - D. We can then determine the monthly interest rate using the following formula:r = (2 / n) * (F / (P - D) - 1)where n is the number of months in the loan and F is the total amount of finance charges paid over the life of the loan. The finance charges paid can be determined by subtracting the amount financed from the total amount paid and then subtracting any taxes, delivery fees, or other charges that are not part of the interest on the loan. In this case, we have:F = (payments per month) * n - P + D + (taxes and fees not part of interest)Substituting the values given in the problem, we get:F = $1,970.00 - P + DTo determine the annual percentage rate, we need to convert the monthly interest rate to an annual rate by multiplying by 12. The formula for this conversion is:APR = (1 + r/2)^12 - 1where r is the monthly interest rate. Substituting the values we calculated, we get:r = (2 / 36) * ($1,970.00 - $ - 1) = 0.01222APR = (1 + 0.01222)^12 - 1 = 0.1448 = 14.48%Therefore, the annual percentage rate on Leigh's loan is 14.48%.

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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Answer:

I'm going to say that there is one girl in the class

The year it will take Mussman to reach a population of 27,000 resident is 10.7 years

Population growth is the increase in the number of people in a population or dispersed group.

We use exponential function when calculating increase in population per time

p(t) =p(o) e^kt

27000 = 13500 e^0.065t

e^0.065t = 27000/13500

0.065t = ln 2

0.065t = 0.693

t = 0.693/0.065

t = 10.7 years

therefore it will take 10.7years for the resident of Mussman to reach a population of 27000

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Answer:

Step-by-step explanation:

In mathematics, every integer is a rational number, hence a whole number 6 can be written as 6/1. 1/3 ÷ 6 = 1/18 in fraction form. 1/3 ÷ 6 = 0.0556 in decimal form.

Answer:

1/18 or 18 is your answer.

Step-by-step explanation:

Since 1/3 is already in fraction form, we will now turn 6 into fraction form.  Which is 1/6. Now we will put it into the equation 1/3 x 1/6 = 1/18.  The fraction 1/18 can also be 18.  Therefore, 18 or 1/18 is our answer.

Answer:

768 in²

Step-by-step explanation:

Surface Area = 2(15*14) + 2(15*6) + 2(14*6)

Surface Area = 2(210 + 90 + 84)

Surface Area = 2(384)

Surface Area = 768

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

768 in²

Step-by-step explanation:

i got it right on the test

To find the area between two z-scores on the TI-84, use the "normalcdf" function with the lower and upper z-scores as the first two arguments, and the mean (if not 0) as the third argument.

To find the area between two z-scores on the TI-84 calculator, you can use the "normalcdf" function. First, you need to determine the lower and upper z-scores that define the area you want to find.  For example, if you want to find the area between z=-1.5 and z=1.5, you would enter "normalcdf(-1.5, 1.5)" into the calculator. The answer will give you the area between those two z-scores. It's important to note that the "normalcdf" function requires three arguments: the lower z-score, the upper z-score, and the mean (which is assumed to be 0 if not specified). Therefore, when using this function, make sure to include all three values.

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The cost of each apple is $0.56 while the cost of each banana is $0.8

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Let a represent the cost of each apples and b represent the cost of each bananas. Four apples and three bananas cost £4.48:

4a + 3b = 4.48      (1)

Also, three apples and four bananas cost £4.76, hence:

3a + 4b = 4.76    (2)

Solving both equations simultaneously gives:

a = 0.56, b = 0.8

The cost of apple is $0.56 while the cost of banana is $0.8

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The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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Answer:

16. 33° and 57°

17. 10x+20= mEBC

18. 92°

Answer:

4.2 units

Step-by-step explanation:

To find the length of the arc, we can use the relationship between the length of an arc, the radius of the circle and the measure of the angle in radians. This relationship is:

arc length = (angle in radians) * (radius)

In this case, the radius is 2 and the angle in radians is 2.1. So we can substitute these values into the equation:

arc length = (2.1) * (2)

arc length = 4.2

So the length of the arc is 4.2 units to the nearest 10th

The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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Answer:

Step-by-step explanation:

f(5a) = (\(5a)^{2}\) + 3× 5a - 4

When a 10% increase in income causes a 4% increase in quantity demanded of a good is income inelastic.

More specifically, the income elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in income. In this case, we have:

Income elasticity of demand = (% change in quantity demanded) / (% change in income)

= 4% / 10%

= 0.4

Since the income elasticity of demand is less than one, we say that the good is income inelastic. we can say that the income elasticity of demand for the good is positive and less than one. This means that the quantity demanded of the good does not increase proportionally as income increases. Instead, the increase in quantity demanded is less than the increase in income.

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The length of the side is 5/3 meters when the area is 225/81 square meters.

To determine the length of the side when the area is given as 225/81 square meters, we can use the formula for the area of a square:

Area = side^2

Given that the area is 225/81 square meters, we can set up the equation as follows:

225/81 = side^2

To find the length of the side, we need to solve for side. The square root of each side of the equation can be used as a starting point:

√(225/81) = √(side^2)

Simplifying,

15/9 = side

By dividing the numerator and denominator by their greatest common divisor, which is three, we may further reduce the fraction:

15/9 = (15/3) / (9/3) = 5/3

Therefore, the length of the side is 5/3 meters when the area is 225/81 square meters.

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For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

\(C = \frac{5}{9} (F- 32)\)

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

The equations to an equivalent equation with a perfect square on one side are below: x² + 8x = 2 ⇒ (x + 4)² = 18, x² + 10x = -13 ⇒  (x + 5)² = 12, x² - 14x = 5  ⇒ (x - 7)² = 54, x² + 2x = 0  ⇒ (x + 1)² = 1, x² + 4x -5 = 0  ⇒ (x + 2)² = 9 and x² -20x = -9  ⇒ (x - 10)² = 91.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

According to the given question, the required solution would be as:

x² + 8x = 2

x² + 2 × 4 × x = 2

Add both sides 16 in the above equation,

x² + 2 × 4 × x + 16 = 2 + 16

x² + 2 × 4 × x + 4² = 2 + 16

As per the formula : (a + b)² = a² + 2 × a × b + b²

(x + 4)² = 18

x² + 8x = 2 ⇒ (x + 4)² = 18

Evaluation each equation similarly, then we get

x² + 10x = -13 ⇒  (x + 5)² = 12

x² - 14x = 5  ⇒ (x - 7)² = 54

x² + 2x = 0  ⇒ (x + 1)² = 1

x² + 4x -5 = 0  ⇒ (x + 2)² = 9

x² -20x = -9  ⇒ (x - 10)² = 91

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Answer:

2048

Step-by-step explanation:

Formula for volume of a sphere is given:

V = 4/3πr^3

Where r = radius

The sphere shown has a given radius of 8

All we have to do to find the volume of the sphere is simply plug in the given value of the radius (8) into the volume of a sphere formula

(Note it says use 3 for π )

V = 4/3(3)r^3

Substitute 8 for r

V = 4/3(3)(8)^3

Plug this into a calculator and you get that the volume is 2048

Answer:

2,048in³

Step-by-step explanation:

The formula to find the volume of the sphere is already given to you in the problem. All we need to do is substitute and solve.

V = 4/3π(8)³

V = 4/3π(512)

V ≈ 682.67(3)

V ≈ 2,048

Best of Luck!