If the graph of the function f, defined by f(x)= x2 + 5, is translated vertically upward by 2 units, it
becomes the graph of a function k. Find the expression for k(x).
A. k(x)=x2 + 3
B. k(x)=(x + 2)2 +5
C. k(x)=(x - 2)2 +5
D. k(x)= x2 +7

Answer: The chosen topic is not meant for use with this type of problem. Try the examples below.

x

=

2

,

y

=

1

x

=

9

,

y

=

10

x

=

9

,

y

=

4

The Area of rectangle is "[tex]30 \ unit^2[/tex]" and the equation of the semi circle is "[tex]y = \sqrt{36-x^2}[/tex]".

According to the question,

The vertices of rectangle,

(5, 0) and (-5, 0)

Length,

l = 10 unit

Breadth,

b = 3 unit

Radius of semi circle,

r = 6

Centre of origin,

(0, 0)

As we know,

→ The Area of rectangle is:

= [tex]Length\times Breadth[/tex]

= [tex]10\times 3[/tex]

= [tex]30 \ unit^2[/tex]

and,

→ The Equation of semi circle is,

[tex]y = \sqrt{r^2-x^2}[/tex]

by substituting the values, we get

  [tex]=\sqrt{(6)^2-x^2}[/tex]

  [tex]= \sqrt{36-x^2}[/tex]

Thus the above is the correct answers.

Learn more about Area of rectangle here:

https://brainly.com/question/14383947

Answer:

8+8 =16 not 0

Step-by-step explanation:

First she used associative property of addition. After that 8 + 8 = 16

but she wrote 0

she added them wrong

Answer:

4

Step-by-step explanation:

5-3x+4x^2

Write the terms from highest power to smallest power

4x^2 -3x +5

The leading coefficient is the term in front of the highest power

4

Answer:

4

Step-by-step explanation:

The first step here is to rearrange the terms of this polynomial in descending order:  x^2, then x, then x^0 (nothing that x^0 = 1):

4x^2 - 3x + 5

The "leading coefficient of the polynomial) is the coefficient of the highest x power, which here is x^2:  4.

Answer:

[tex]54\pi\ cm^2[/tex]

Step-by-step explanation:

1. Approach

In order to solve this problem, one needs to find the height of the cone. This can be done using the Pythagorean theorem. After finding the height of the cone, one can use the formula to find the surface area of a cone, to find the surface area of this particular cone.

2. Find the height of the cone

The Pythagorean theorem is a property that relates the sides of a right triangle. The radius (distance from the center to circumference (outer edge)) of the base, the height of the cone, and the slant of the cone forms a right triangle. Thus, one can use the Pythagorean theorem to solve for the height. The Pythagorean states the following:

[tex]a^2+b^2=c^2[/tex]

Please note that (a) and (b) represent the sides adjacent (next to) the right angle, (c) represents the hypotenuse (the side opposite the right angle). In this case (a) is the height, and (b) is the radius of the base. (c) is the diagonal of the cone. Substitute the given values in and solve for the height,

[tex]a^2+b^2=c^2[/tex]

[tex]a^2+3^3=15^2[/tex]

Simplify,

[tex]a^2+3^3=15^2[/tex]

[tex]a^2+9=225[/tex]

Inverse operations,

[tex]a^2+9=225[/tex]

[tex]a^2=216[/tex]

[tex]a=\sqrt{216}[/tex]

3. Find the surface area of the cone

The following formula can be used to find the surface area of a cone,

[tex]A_s=\pi r(r+\sqrt{h^2+r^2})[/tex]

Where (h) is the height of the cone, (r) is the radius of the base of the cone, and ([tex]\pi[/tex]) represents the value (3.1415...). Substitute the given values into the formula and solve for the surface area,

[tex]A_s=\pi r(r+\sqrt{h^2+r^2})[/tex]

[tex]A_s=\pi(3)(3}+\sqrt{\sqrt{216}^2+3^2}[/tex]

Simplify,

[tex]A_s=\pi(3)(3}+\sqrt{\sqrt{216}^2+3^2}[/tex]

[tex]A_s=\pi(3)(3}+\sqrt{216+9})[/tex]

[tex]A_s=\pi(3)(3}+\sqrt{225})[/tex]

[tex]A_s=\pi(3)(3}+15)[/tex]

[tex]A_s=\pi(3)(18)[/tex]

[tex]A_s=\pi(54)[/tex]

Answer:

perimeter=40m

Step-by-step explanation:

PERIMETER=(AREA ROOT)*4

                   =10*4=40m

Answer:

See below

Step-by-step explanation:

Okay so...I might be interpreting the question wrong-if I am please comment! I'll fix it to the best of my ability.

A) Plug in -5 to all x values

   f(-5)=10(-5)-3

          ==50-3

    f(-5)= -53

B) f(0)=10(0)-3

    f(0)= -3

C) f(7)=10(7)-3

         =70-3

    f(7)=67

D) f(t^2+2)=10(t^2+2)-3

                 =10t^2+20-3

     f(t^2+2)=10t^2+17

E) f(12-x)=10(12-x)-3

              =120-10x-3

    f(12-x)=117-10x

F) f(x+h)=10(x+h)-3

             =10x+10h-3

Answer:

Not enough infomation, you need to provide #12

Step-by-step explanation:

Step-by-step explanation:

Answer:

1/2 of his shirts are green or blue

Step-by-step explanation:

4+1 / 10 = 5 / 10 = 1 / 2

Answer:

No

Step-by-step explanation:

x^3• x^3•x^3

We add the exponents

x^(3+3+3) = x^9

x^3•3•3 x^3 *9

9x^3

These are not equal unless

x^9 = 9x^3

points are

[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{0-3}{1-0}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-3}{1}[/tex]

[tex]\\ \sf\longmapsto m=-3[/tex]

Answer:

loss of work and deficiency in progress

disturbance in schedule

Answer:

Shortage of gas

interruption in water supply for households that access piped water from the local municipality

Loss of profit for businesses

Step-by-step explanation:

Answer:

The x-intercepts are reflecting zero-profit: (0, 0) and (6, 0).

The maximum value of the graph is at vertex (3, 120): maximum profit when the price is $3.

The function is increasing until the vertex, between x-value of 0 to 3 and is decreasing once it reached the vertex, between x-value of 3 to 6.

In the first interval the sale and profit increases, in the second interval the sale and profit decreases.

Average rate of change from x = 3 to x = 5 is:

This represents the profit drop of $30 per $1 price increase when price changes from $3 to $5.

Answer:

Step-by-step explanation:

6x - 11 = 3x + 13

3x = 24

x = 8

Answer:

3√13

Step-by-step explanation:

3√13

This expression cannot be simplified because you cannot take any common factor outside the root.

Answer:

2(3x+4) = 11x-17

6x+8 = 11x-17

25=-5x

x=-5

11x-17

55-17

38

AC = 38

CD = 38

49-38 = 11

DE = 11

Let me know if this helps!

Answer:

1/6x = 9

x = 54

Step-by-step explanation:

Let x = number

1/6x = 9

Multiply each side by 6

1/6x * 6 = 9*6

x = 54

Answer:

1/6n = 9 ---> the equation

x = 54 ----> equation's answer

Step-by-step explanation:

The variable used can be either x or n, doesn't really matter.

It says 1/6th of a number is 9 --> write 1/6, n for the number, and then = 9

so, 1/6n = 9

Now, you are going to multiply each side by 6

1/6x * 6 = 9 * 6 --------> 54

x = 54

Step-by-step explanation:

here u have answer of your question dear

Answer:

13 and 17 units

Step-by-step explanation:

explaination is in pic.

The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.

The length between two given points (x₁, y₁) and (x₂, y₂) will be:

√[(x₂ - x₁)² + (y₂ - y₁)²] units

Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).

Therefore, the diagonals of the quadrilateral will be AC and BD.

The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).

Now, the length of the diagonal AC will be:

= √[(-8 - 4)² + (2 - (- 3))²] units

= √[(- 12)² + (5)²] units

= √[144 + 25] units

= √(169) units

= 13 units                                  (length can't be negative)

Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).

Now, the length of the diagonal BD will be:

= √[(-1 - 7)² + (- 5 - 10)²] units

= √[(- 8)² + (- 15)²] units

= √[64 + 225] units

= √(289) units

= 17 units                                  (length can't be negative)

Learn more about the length between two points on a plane here: https://brainly.com/question/14898312

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3rd step

Solution:-

[tex]\\ \sf\longmapsto -2x+8-3x=7[/tex]

[tex]\\ \sf\longmapsto -2x-3x+8=7[/tex]

[tex]\\ \sf\longmapsto -5x+8=7[/tex]

[tex]\\ \sf\longmapsto -5x=7-8[/tex]

[tex]\\ \sf\longmapsto -5x=-1[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-1}{-5}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1}{5}[/tex]

Answer

[ 1 by 2, -1 by 2 ]

Step-by-step explanation:

https://haygot.s3.amazonaws.com/questions/1118559_1200733_ans_2ec06a240d2240e49dc1c9fda7b41ef5.jpeg

Answer:

range { 1, ∞ }

Step-by-step explanation:

y = x² + 1

is a parabola with its vertex at (0, 1)

The range is { 1, ∞ }

Answer:

8

Step-by-step explanation:

-4(2)+8(-3)+12-8(2)-2(-3)+6=-8-24+12-16+6+6=8

Answer:

-24

Step-by-step explanation:

-4b + 8c + 12 - 8b - 2c + 6

Combine like terms

6c+18-12b

Let b=2  c=-3

6(-3) +18-12(2)

-18 +18 -24

-24

Step-by-step explanation:

2x+3y+5+4x-7y-8

2x+4x+3y-7y+5-8

6x-4y-3

Answer:

6x - 4y - 3

Step-by-step explanation:

They are basically telling you to sum both equations. So,

(2x + 3y + 5) + (4x - 7y - 8)

= 2x + 4x + 3y - 7y + 5 - 8

= 6x - 4y - 3

Answer:

TRUE

Step-by-step explanation:

The answer is TRUE.

Answer:

Original number = 38

Step-by-step explanation:

10*x + y

x   = y - 5

10y + x = 2 (10x + y) +  7

10y + y - 5 = 2(10(y - 5) + y) + 7

11y - 5 = 2(10y - 50 + y ) + 7

11y - 5 = 2(11y - 50) + 7

11y - 5 = 22y - 100 + 7

11y - 5 = 22y - 93

11y + 88 = 22y

88 = 11y

y = 8

x = y - 5

x = 8 - 5

x = 3

So the original number is 38. Does that work?

3 is 5 less than 8.

83 = 2*38 + 7

83 = 76 + 7

83 = 83.         Yes it works.

Answer:

Step-by-step explanation:

Taxable income = $ 91,307

Tax for $ 17,850 = 10% of 17850 = 0.1*17850 = $ 1785

Tax for $17,850 to $72,500 = 15% of (72,500-17850) = 0.15* 54650 = $ 8197.5

Tax  $72,500 to $91,307 = 25% of (91307-72500)=0.25*18807= $ 4701.75

Total tax = 1785 + 8197.5 + 4701.75 = 14684.25

Total tax = $14684

Step-by-step explanation:

here's the answer to your question

Answer:

Step-by-step explanation:

The number of terms:

Each term is greater than 1, so the expression is greater than 16:

It's easy to note each of the numbers getting smaller like 145/2005 > 144/2006 etc. Taking the smallest fraction.

The sum is:

So the largest integer not greater than S is 17.