Region R is bounded by the curves y = √x, y = 1, and x = 4. A solid has base R, and cross sections perpendicular to the x-axis are squares. The volume of this solid is
A. 4/3
B. 8
C. 7/6
D. 15/2

Answer:

-4

Step-by-step explanation:

Rate of Changes:

[tex]\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Pick two values of x and y from the given table:

Therefore:

[tex]\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{5-13}{1-(-1)}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{-8}{1+1}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=\dfrac{-8}{2}}\\\displaystyle \large{\dfrac{\Delta y}{\Delta x}=-4}[/tex]

Therefore, rate of change is -4

The correct statement about the congruent figures is,

⇒ a reflection across the x-axis, followed by a translation 3 units to the right.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Three congruent figures are shown in the coordinate plane.

Now, From figure A and figure B,

Figure B is reflection across the x-axis, followed by a translation 3 units to the right across the figure A.

Thus, The correct statement about the congruent figures is,

⇒ a reflection across the x-axis, followed by a translation 3 units to the right.

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Answer:

v=l×h×w

Step-by-step explanation:

that the furmula

The equation that illustrates the identity property of multiplication is (a+bi) × 1 = (a+bi).

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The identity property of multiplication states that when a factor is multiplied by 1 the result is the factor itself. Therefore, the equation that illustrates the identity property of multiplication is (a+bi) × 1 = (a+bi).

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Answer:

D

Step-by-step explanation:

duh

The value of the a, in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

The solution of the quadratic equation is the solution of the variable of the equation, for which the equation satisfies.

Nancy found that x=1 is one solution to the quadratic equation. The quadratic equation is,

[tex](x +2)^2=a[/tex]

For this equation, one solution is x=1. Put this value in the above equation to get the value of a,

[tex](1 +2)^2=a\\(3)^2=a\\9=a\\a=9[/tex]

Thus, the value of the a, in the provided quadratic equation for which Nancy found one solution as x=1 is 9.

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Answer:

D. 9

Step-by-step explanation:

Answer:

2 1/3 cups of onions

Step-by-step explanation:

3 2/3-1 1/3= 2 1/3 cups

Answer:

[tex]b^{2} -2b+5[/tex]

Step-by-step explanation:

Answer:

I think the answer is 3150 miles

I multiplied 1.50 by 21 and the answer I converted to miles

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Answer:

approximately 71.50215

Step-by-step explanation:

Answer:

C. 2

Step-by-step explanation:

h/6 + h/3 = 1

h/6 + 2h/6 = 1

3h/6 = 1

3h = 6

h = 2

Answer:

f'(0)= -2/5

Step-by-step explanation:

Answer:

40 in.^2

Step-by-step explanation:

Let's name the 2 shaded triangles: The left one is T1 and the right one is T2.

The area of a right triangle can be found using the equation (a*b)/2.


The 2 legs of T1 are 8 in. and 6 in. (from 10 - 4)
Area of T1 = [tex]\frac{8 * 6}{2}[/tex] = 24 in.^2

The 2 legs of T2 are 8 in. and 4 in.
Area of T2 = [tex]\frac{8 * 4}{2}[/tex] = 16 in.^2

Area of shaded region = 16 + 24 = 40 in.^2

Answer:

C-12

Step-by-step explanation:

The definition of a Vertex of a 3D shape is 'Where 3 lines meet to form an angle' which in this case would be 12.

Answer:

it's c12 first do the edge face vertical nameing polygon and then you can get your answers

Answer:

it would be +3

Step-by-step explanation:

This is he answer because +3 is equal to p+3 if pounds=p

The equation of the area of the rectangle is w(2w + 5) = 50. Then the correct option is C.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

A rectangle’s length is 5 inches more than twice its width. its area is 50 square inches.

Let the width of the rectangle be w, then the length of the rectangle will be (2w + 5).

Then the area of the rectangle is given as

Area = l × w

Then we have

w(2w + 5) = 50

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Answer:

7 to the left, and up 2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

See attached image.

1.  What would you use to graph the solution to an equation with one variable?      

I picked an example equation, y=2x+3, to demonstrate the impacts of changing condions.  It is the blue line.  I'm not sure how to answer the quesion "What would you use . . .", but my response would be "I would use DESMOS to graph the solution."  It is free, efficient, and very flexible.  It can handle multiple equations and a variety of functions.

2.  What would happen to the graph if all the y-values were increased by 1?

I added 1 to the right side of the equation to increase all the y values by 1.  It is the black line.  All points are raised by 1.

3.  What would happen to the graph if all the x-values were increased by 1?

I added +1 to each x value, shown as the red line.  All points are increased by 2 over the original line.

4.  What would happen to the graph if all the y-values were multiplied by 2 or by 1/2?

See Increeases2, attached.  The slopes of the lines are doubled when the y values are doubled, and decreased by (1/2) when they are multiplied by (1/2).  The y intercepts are also doubled or halved, respectively.

Answer:

Step-by-step explanation:

In similar triangles, the corresponding sides are in same proportion.

[tex]\sf \dfrac{4x}{3x+1}=\dfrac{15}{12}[/tex]

Cross multiply,

4x*12 = 15*(3x + 1)

48x    = 15*3x + 15*1

48x    = 45x + 15

48x -45x = 15

          3x = 15

           x = 15/3

x = 5

Answer:

x =(24-√596)/2=12-√ 149 = -0.207

x =(24+√596)/2=12+√ 149 = 24.207

Step-by-step explanation:

Factoring  x2-24x-5

The first term is,  x2  its coefficient is  1 .

The middle term is,  -24x  its coefficient is  -24 .

The last term, "the constant", is  -5

Multiply the coefficient of the first term by the constant   1 • -5 = -5

Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -24 .

     -5    +    1    =    -4

     -1    +    5    =    4

Two solutions were found :

x =(24-√596)/2=12-√ 149 = -0.207

x =(24+√596)/2=12+√ 149 = 24.207

Without buying points, the time that will be taken to break even will be 6 years.

The monthly mortgage payment will be $1,250. Buying 1 point at closing would reduce the payment to $1,236.

1 point= $1000

The time taken will be:

Monthly savings = 4250/1236 = 14

Time taken = 7

1000/14 = 71.4 months

71.4/12=5.95 years = ~6 years

Thus, The time that will be taken to break even will be 6 years.

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Answer: 6

Step-by-step explanation:

Answer:

a) AE and BC are parallel (as shown by the markings)

b) ED and CD are equal in length (as shown by the markings)

c) 3: AE is perpendicular AB, AB is perpendicular to AE/AC, AC is perpendicular to AB

Answer:

7.2

Step-by-step explanation:

We know that the radius is always the same throughout the entire circle. That is, any line going from the center of the circle to the edges = radius. In this problem, radius = 20.9 and so does the other 4 lines going from the center of the circle to the edge.

Since there is a right angle, we know that both triangles are right triangles where hypotenuse, c = 20.9 and b = 19.6. To solve for x, use pythagorean theorem:

a² + b² = c²

x² + 19.6² = 20.9²

x² + 384.16 = 436.81

x = √(436.81 - 384.16)

x = √52.65

x ≈ 7.256

Hope this helps!

He will pay $200,000.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Your homeowners policy has a premium of $150, a deductible of $5000, and a limit of $300,000.

And,  Your home suffers $500,000 in damages.

Now,

Since, Homeowners policy has a premium of $150, So we can pay the amount = 12 x 150

           = $1,800

And,  Homeowners policy has a deductible of $5000.

Then, The remain amount = $500,000 - $5,000

                                        = $495,000

Since, The limit of the policy = $300,000

Hence, The remain amount = $495,000 - $300,000

                                           = $195,000

After including the deductible amount we get;

Deductible amount = $195,000 + $5,000

                             = $200,000

Thus, He will pay $200,000.

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The surface area of a similar rectangular-prism-shaped skyscraper that has a scale factor of 1/800 would be equal to 1.7 meter.

Mathematically, the surface area of a rectangular-prism is given by this formula:

A = 2(wl + hl + hw)

Where:

Given the following data:

Surface area of rectangular prism = 1,115,000 m²

Scale factor = 1/800

The length, height and width of the similar model would be 1/800 the original rectangular-prism-shaped skyscraper.

Substituting the given parameters into the formula, we have;

Surface area = 1,115,000 × 1/800 × 1/800

Surface area = 1.7 meter.

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By taking the quotient between the number of calls and the number of phone numbers, we see that each number was called 76 times.

We need to find the quotient between the total number of calls and the total number of phone numbers called.

We know that the total number of calls is 836, while it is equally distributed between 11 phone numbers.

The number of times that each of these numbers was called is given by:

N = 836/11 = 76

This means that he calls each number 76 times.

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Answer:

16pi ft^2

(the first answer)

Step-by-step explanation:

Answer:

p =1

q = 9

Step-by-step explanation:

f(x) = 2x³ - px² + 2qx + q

(x - 3) is a factor of f(x)

⇒f(3)  = 0

2(3)³ - p*3² - 2q*3 +q = 0

2*27 - 9p - 6q + q = 0

    54 - 9p - 5q = 0

            -9p - 5q = -54 -------------------(I)

(2x - 1) is a factor of f(x)

2x - 1 = 0

      2x = 1

        [tex]\st x = \dfrac{1}{2}[/tex]

f(1/2) = 0

[tex]2*(\dfrac{1}{2})^{3}-p*(\dfrac{1}{2})^{2}-2q*\dfrac{1}{2}+q=0\\\\2*\dfrac{1}{8}-p*\dfrac{1}{4}-q+q = 0\\\\\dfrac{1}{4}-\dfrac{1}{4}p =0\\\\[Multiply the entire equation by 4]\\\\4*\dfrac{1}{4}-4*\dfrac{1}{4}p=0\\\\[/tex]

1 - p = 0

    -p = -1

p = 1

Substitute p =1 in equation (I)

-9*1 - 5q = -54

 -9 - 5q = -54

      -5q = -54 + 9

      -5q = -45

           q = -45/(-5)

q = 9

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.