what is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet? the total surface area is about square feet.

Function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

How do you find the maximum and minimum value of the function?

Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.

Given function:

[tex]-3x^2+18x+3[/tex]

To find the maximum and minimum value of the function use second derivative test.

On differentiating the above function we get,

-6x + 18

Now, find critical point

-6x + 18 = 0

-6x = - 18

x = - 18/-6 = 3

x = 3

Here, x = 3 is the critical point. Now again differentiate the above function we get,

-6

As , [tex]f^{''}(x)[/tex] < 0 , therefore x = 3 will given a maximum value of function and maximum value is

f(3) = [tex]-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30[/tex]

Hence , function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

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Answer:

x = 19/2 or 9.5

Step-by-step explanation:

a) Distribute.

(4)(x) + (4)(−5) = 18

4x + −20 = 18

4x − 20 = 18

b) Add 20 to both sides.

4x − 20 + 20 = 18 + 20

4x = 38

c) Divide both sides by 4.

4x/4 = 38/4

x = 19/2 or 9.5

Answer:

9.5 or 19/2

Step-by-step explanation:

4 ( x - 5 ) = 18

Step 1 : Divide 4 on both sides.

x - 5 = 18/4

x - 5 = 4.5

Step 2 : Add 5 on both sides.

x = 4.5 + 5

x = 9.5

Value of x in fraction = 95/10 = 19/2

Value of x in decimal = 9.5

a. The ramp dimensions of 15 feet away and 3 feet above do not meet the ADA guidelines.

b. A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.

The verification if the ramp meets the guidelines is made with the slope of the ramp, which is the ratio of the vertical distance of the ramp by the horizontal distance of the ramp, obtained dividing these two measures.

The measures are given as follows:

Hence the ratio is given as follows:

3/15 = 1/5.

The ratio is greater than the threshold of 1/12, hence the ramp does not meet the guideline.

Keeping the vertical distance, the adequate horizontal distance is obtained multiplying the vertical distance by 13, as the ratio would be of 1/13, hence:

13 x 3 = 39 feet.

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Answer:

a = 4.52 km

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (7.2)² = a² + (5.6)²

→ 51.84 = a² + 31.36

→ a² = 51.84 - 31.36

→ a = √20.48

→ [ a = 4.52 km ]

Hence, value of a is 4.52 km.

The answers are as follows -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

Given are the following relations -

3y = x

{(2,6),(3,9),(5,15)}

{(1,16),(2,8),(4,4)}

We can write -

x = 3y

as

y = (1/3)x

m = 1/3

Relation 3y=x represents direct variation.

For the relation - {(2,6),(3,9),(5,15)}, we can write -

We can write it as -

y = 3x

Relation {(2,6),(3,9),(5,15)} represents direct variation.

For the relation - {(1,16),(2,8),(4,4)} , as [x] increases, [y] decreases, so it is a inverse relation.

Therefore -

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Answer:

See below

Step-by-step explanation:

The equations are in form   y = mx + b  where m = slope

  if the lines are parallel then the slopes are equal :

3/K  = H/2      Done.

Answer:

14

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Miguel drove at a speed of 60 mph in the first part of the trip and at a speed of 50 mph in the second part of the trip.

Let the speed while dropping his son to college be x mph

Therefore speed while returning is (x - 10) mph

The distance is 300 mi

Speed = Distance/Tie

or, Time = Distance/Speed

Hence the time taken during the first part of the journey = 300/x hrs

and,

Time taken for the next part of the journey

= 300/(x - 10) hrs

It is given that the total time taken was 11 hrs

Hence we get

300/x + 300/(x - 10) = 11

or, (300x - 3000 + 300x) / x(x - 10) = 11

or, (600x - 3000) / (x² - 10x) = 11

or, 600x - 3000 = 11x² - 110x

or, 11x² -710x + 3000 = 0

Applying the shreedharacharya rule gives us

x =  (710 ± √(710² -132000)/22)

x = 50/11 or x = 60

If x = 50/11 then x - 10 will be negative.

hence x = 60

Therefore Miguel drove at a speed of 60 mph in first half and 50 mph in second half.

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Answer:

24%

Step-by-step explanation:

6/25 is also the same as 24/100 because

(6/25)*(4/4)=24/100

Since the denominator is 100, the numerator is the percentage.

6/25=24%

Answer:

24%

Step-by-step explanation:

One way to figure this out is to multiply the denominator by 4 so that it becomes 100. This makes it easy to see what the percentage will be.

6/25 x 4/4 = 24/100

6/25 = 24%

Answer:

5 11/16 as a decimal = 5.6875

7 24/25 as a decimal is 7.96

Step-by-step explanation:

Answer:

5 11/16 = 5.6875

7 24/25 = 7.97

Step-by-step explanation:

you keep the whole numbers then you turn the fractions into decimals so to do that you divide 100 by the denominator and whatever the answer is you multiply it by the numerator to get your answer, 100 divided by 16 is 6.25 and 6.25 multiplied by 11 is 68.75 but since the 5 is already the whole number you basically just forget the decimal in 68.75 ( I hope that makes sense)

And for 7 24/25 you do 100 divided by 25 and that’s 4 so now you multiply 24 by 4 and that’s 96 so that goes after the decimal so it’s 7.96 (I hope that helped and all made sense.)

The value of test statistic is  -1.14

Define Standard error.

The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).

Null Hypothesis

P = 0.54

Alternate Hypothesis

P < 0.54

For 0.05 level , the value of Z = 1.645

Decision rule ,

reject null Hypothesis if test statistic Z < -1.645

sample size (n) = 200

sample success (x) = 100

Standard error SE = √(p * (1 - p) / n

                         = √0.54 * (1 - 0.54) / 200

Standard error SE= 0.0352

Sample proportion (р)  = x/n

                               = 100 / 200 ⇒ 0.5

test statistic  Z = (р - P) / SE

                         = (0.5 - 0.54) / 0.0352

test statistic  Z = -1.136 or -1.14

Therefore, the value of test statistic is  -1.14

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Answer: m=0

Step-by-step explanation: (-10,17) & (-9, 17) are 2 points away from each other on the x-axis, there is no difference in y. Therefore the answer is zero.

The sum of the reciprocal of the two numbers is 44.

Let a and b be the two number

It is given that the sum of the number is equal to 44 times their product.

So from this, we get an equation:

a + b = 44 ab -------(1)

Now we have to find the sum of the reciprocal of the two numbers.

1/a + 1/b = b + a/ ab

            = a + b / ab -------(2)

As from equation (1) we have

a + b/ ab = 44

Now put this value in equation (2) we get

1/a + 1/ b = 44

Therefore the sum of the reciprocal of the two numbers is 44.

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After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.

Exponent:

Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.

Given,

Here we have the expression 8√(x²y⁴).

Now, we need to simplify the fractional exponents.

When we rewritten the expression like the following,

=> 8√(x²y⁴)

While we looking at these expression we know that, the number 8 can be written as the multiple of 2,

So, it can be written as,

=> 8√(x²y⁴) = 2³√(x²y⁴).

So, in the simplified form it can be written as,

=>8√(x²y⁴) =  2³(x²y⁴)¹/₂.

Therefore, the simplified form is 2³(x²y⁴)¹/₂.

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Answer:

y=2x+8

Step-by-step explanation:

The slope must be the same so the equation so far is y=2x+b

To find b, you have to multiply the given x value (-1 is the given x value) and then see how much you have to add to reach the given y value (aka 6)

-1*2=-2

6--2=8

b=8

That means that the equation is y=2x+8

Answer:

C

Step-by-step explanation:

In the graph, you can see an asymptote is happening for x=-5, so look for an equation that divides by 0 for x=-5. That is clearly C, for x=-5 the denominator is 0.

In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

What is area of circle?

 For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. We can determine the boundary length, or the circle's circumference, using the area formula.

Here area of circle

=> A= π[tex]r^2[/tex]--------> 1

Differentiating 1 with respect to to time then

=> [tex]\frac{dA}{dt}= 2\pi r\frac{dr}{dt}[/tex]

If the radius is  increasing at a constant rate 3.3ft/sec then after 6.4 seconds, radius is

=> 6.4*3.3=21.12 ft.

We know [tex]\frac{dr}{dt}= \frac{3.3ft}{sec}[/tex] and so ,

=> [tex]\frac{dA}{dt}[/tex] = 2*[tex]\pi[/tex]*21.12*3.3=139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec.

Hence In 139.4 [tex]\pi[/tex] [tex]ft^2[/tex]sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

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There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.

Take into account the details offered.

43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.

Consequently, p= 8/43.

If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.

q= 35/43

Let X represent how many presidents have passed away while in office.

The probaility that at least one student will choose a president who passed away in office is:

P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)

P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸

By using  Combinations Formula,

By solving we get,

P(X[tex]\geq[/tex]1 ) = 0.97541

As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.

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The worth of the book after 10 years is $1061.1

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

First edition book worth = $262

Rate of increase per year = 15%

The worth of the book after t years can be given by the expression.

= 262 x [tex]1.15^{t}[/tex]

Now,

The worth of the book when t = 10.

= 262 x [tex]1.15^{10}[/tex]

= 262 x 4.05

= $1061.1

Thus,

The book is worth $1061.1 after 10 years.

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The commission earned by selling the merchandise worth $3000 is $270

The percentage of the commission earned by the salesman is 9%

The worth of the merchandise is $3000

A sales commission is typically an amount paid to an employee upon completion of a task for the sale of a specified quantity of goods or services.

Therefore, the commission earned can be found using the formula,

              Commission = SP x CP

where SP is the selling price and

          CP is the commission percentage.

Let us substitute the known values in the above equation, we get

              Commission = 3000 x 9%

                                    = 3000 x 9/100

                                    = 30 x 9

                                    = $270

Therefore, the commission earned is $270

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Answer:

  14 square units

Step-by-step explanation:

You want the area of the triangle whose vertices are the points A(-11, 4), B(-7, 8), C(-4, 4).

The area of a triangle is given by the formula ...

  A = 1/2bh

where b is the base of the triangle, and h is the height, the1 perpendicular distance to the opposite vertex.

The diagram shows one side is the horizontal line AC. The length of that is the difference of the x-coordinates of the end points:

  b = -4 -(-11) = 7

The opposite vertex, B, has a y-coordinate of 8, so the height of the triangle is ...

  h = 8 -4 = 4

We now have the information we need to use the area formula:

  A = 1/2(7)(4) = 14 . . . . square units

The area of ∆ABC is 14 square units.

__

Additional comment

You can use the diagram and count grid squares to find the dimensions of the triangle.

Answer:

The rocket reaches its maximum height at 2.25 seconds.

It’s maximum height is 88 feet.

This can be found by finding the derivative of the function and setting it to zero.

-16x² +72x + 7

Taking first derivative and setting to zero:

-32x + 72 = 0

x = -72/-32=2.25

Find the height when x is 2 seconds by substituting this value into the original function:

-16 * (2.25)² + 72 * 2.25 + 7 = 88

Therefore the maximum turning point of the parabola will be (2.25, 88)

Answer: 11 months

Step-by-step explanation:

You do this by 73 times 11 equals 803

Then 49 times 11 equals 539 then add on the registration fee and it equals to 779 which is less than 803

Answer:

The solution is (-2, 4).

Answer:

Step-by-step explanation:

so you just have to round where it came from

Answer:

d = 3h - 6

Step-by-step explanation:

h = [tex]\frac{d}{3}[/tex] + 2 ( multiply through by 3 to clear the fraction )

3h = d + 6 ( subtract 6 from both sides )

3h - 6 = d

The missing base for the expression x² = 100 is given by:

± x = 10.

The expression in this problem is given as follows:

x² = 100.

The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.

To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:

x = plus/minus square root of 100.

The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:

x = ± 10.

Plus/minus 10 because both of these statements are true:

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