The equation of a parabola is y=x2–10x+25. Write the equation in vertex form.

The equivalent Fahrenheit temperature for 20 degrees Celsius is 68 degrees Fahrenheit.

To convert Celsius to Fahrenheit, you can use the formula: F = (C × 9/5) + 32

Using this formula, we can calculate the equivalent Fahrenheit temperature for 20 degrees Celsius:

F = (20 × 9/5) + 32 = 68 degrees Fahrenheit

Answer:

27 trees in each row

Step-by-step explanation:

Abe is going to plant 54 oak trees and 27 pine trees

 greatest number of trees Abe can have in each row =?

54 = 2 x 27

27 = 1 x 27

Now 27 is the common in both numbers and also is the greatest number

So, there are 2 rows of oak trees and 1 row of pine trees and all the rows have 27 number of trees.

7 divided by 28 is 1/4 or 0.25.

To calculate 7 divided by 28.

What is simplification?

Simplification is defined as solving mathematical problems using arithmetic operators.

7 divided by 28 = 7/28
                           = 1/4
                           =  0.25

Thus, 7 divided by 28 is 1/4 or 0.25.

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To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.

To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2

Combine like terms: 171x + y = -733

Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2

Simplify: 171x + y + 7391/4 = 17113/4

Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4

Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4

If a school has 30 teachers and there is a 10% reduction, there will be 27 teachers remaining.

If a school employs 30 teachers and there is a 10% reduction, we can calculate the number of teachers after the reduction by multiplying the initial number of teachers by (100% - 10%) = 90%. So, there will be 30 * 0.90 = 27 teachers after the reduction.

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Let the short side be W

The half circumference of the semi-circle = .5 * pi *W

2Lengths + width + semicircle = 20 ft

2L + W + (.5*pi*W) = 20

2L + W + 1.57W = 20

Combine like terms

2L + 2.57W = 20

Simplify divide by 2

L + 1.285W = 10

L = (10 - 1.285W); for substitution:

Get the area equation:

Rectangle area + semicircle area

A = L * W + (.5*pi*(.5W) ^2)

A = LW + (1.57*.25W^2)

A = LW + .3925W^2

Replace L with (10-1.285W)

A = W(10-1.285W) + .3925W^2

A = -1.285W^2 + .3925W^2 + 10W

A = -.8925W^2 + 10W

Find W by finding the axis of symmetry of this equation a=-.8925, b=10

W = -10 / 2 * (-.8925)

W = -10 / -1.785

W = 5.60 is the width for max area

then we solve for the length

L = 10 - 1.285(5.60)

L = 10 – 7.20 = 2.8 ft is the length

Then, Check the perimeter

2(2.8) + 5.60 + 1.57(5.60) = 20ft

5.6 + 5.6 + 8.736 = 20ft

Rectangle: 2.8 by 5.60 has semicircle circumference 8.736 has a maximum area: (2.8*5.60) + (.5 * pi * 2.8 ^ 2)

=15.68 + 12.31

=28 sq/ft

Answer:

[tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]  

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{\cos (x - 1)}{x - 1}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

a = -15

Step-by-step explanation:

Let's rewrite the exercise in math language.

We have to subtract a-4 from 4a+16 to get -25, that is

4a+16 - (a-4) = -25

The minus sign that is just before the parenthesis changes all the signs inside it. Therefore, if we want to delete the parenthesis, we need to change the signs before.

4a + 16 - a + 4 = -25

Now we can associate the terms with an a between them and the terms without it from the left side of the equation.

3a + 20 = -25

Let's subtract 20 on both sides.

3a + 20 - 20 = -25 - 20

3a = -45

Finally, we divide by 3 on both sides

3a/3 = -45/3

a = -15

Answer:

  36

Step-by-step explanation:

36 is a factor of both numbers

_____

If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.

If there is a remainder, replace the larger number with that and repeat the process.

Step-by-step explanation:

We have been given that [tex]\frac{2}{3}a=16[/tex].

Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.

[tex]\frac{2}{3}\times \frac{3}{2} =1[/tex]

To solve for a let us divide 16 by [tex]\frac{2}{3}[/tex].

[tex]a=16\div \frac{2}{3}[/tex]

Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by [tex]\frac{3}{2}[/tex].

[tex]a=16\times\frac{3}{2}[/tex]

[tex]a=8\times 3[/tex]

[tex]a=24[/tex]

We can see that to solve for a we have multiplied 16 by [tex]\frac{3}{2}[/tex] and [tex]\frac{3}{2}[/tex] is reciprocal of [tex]\frac{2}{3}[/tex].

Let us verify our answer by substituting a=24 in our given equation.

[tex]\frac{2}{3}\times 24=16[/tex]

[tex]2\times 8=16[/tex]

[tex]16=16[/tex]

Hence, to find the value of a we used multiplicative inverse property.

multiply 4 by 9.99 for cost of the 4 dvd's

9.99 *4 = 39.96

20% discount is: 39.96 *0.20 = 7.99

39.96 - 7.99 = 31.97

now add the sales tax:

31.97 * 1.0675 = 34.13

 total cost is $34.13

Answer:

fdx = x-4 2

Step-by-step explanation:The test was right

The 6 in 600 has a value one tenth the value of the 6 in 34, 761.

The question asks in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761.

To find the answer, we need to compare the place value of the 6 in both numbers. In 34, 761, the 6 is in the thousands place, and its value is 6,000. To have a value that is one tenth of 6,000, the 6 would need to be in the hundreds place in the other number.

So, the number in which the 6 has a value one tenth the value of the 6 in 34, 761 would be 600.

Final answer:

The number 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.

Explanation:

The number 6 in 34,761 has a value that is one-tenth the value of the 6 in the number 2,001.06.

To find this, we can compare the place values of the two 6's. The 6 in 34,761 is in the ones place, while the 6 in 2,001.06 is in the tenths place.

Since the tenths place is one place to the right of the ones place, the value of the 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.