87. Which of the following is an equation of the line tangent to the graph of f(x) = x² + 2x² at the
point where f'(x)=1?
(A) y=8x-5
(B) y=x+7
(C) y=x+0.763
(D) y=x-0.122
(E) y=x-2.146

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

\(\huge\text{Hey there!}\)

\(\mathsf{2x^2}\\\\\mathsf{= 2(5)^2}\\\\\mathsf{= 2(5\times5)}\\\\\mathsf{= 2(25)}\\\\\mathsf{= 50}\\\\\\\huge\text{Thus, your answer is: \boxed{\mathsf{50}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

6

Step-by-step explanation:

24+(3+6)=33

(24+3)+6=33

Answer:

= 11/3

Step-by-step explanation:

1. COMBINE MULTIPLIED TERMS INTO A SINGLE FRACTION

- 7/3 (3x-2)= -21

-7 (3x-2) = -21

-----------------------

3

2. DISTRIBUTE

-7( 3x- 2) ➗ 3 =-21

3. MULTIPLY ALL TERMS BY THE SAME VALUE TO ELIMINATE FRACTION DENOMINATORS

-21x + 14 ➗ 3 = 3 (-21)

4. CANCEL MULTIPLIED TERMS THAT ARE IN THE DENOMINATOR

3 ( -21x + 14) ➗ 3 (-21)

5. MULIPLY THE NUMBERS

-21x + 14 = 3(-21)

6. SUBTRACT 14 FROM BOTH SIDES OF THE EQUATION

-21x + 14 = -63

7. SIMPLIFY

-21x = - 77

8. DIVIDE BOTH SIDES OF THE EQUATION BY THE SAME TERM

-21x/-21 = -77/-21

9. SIMPLIFY

x = 11/3

Answer:

1. 30

2. x = 0

3. x = 10

4. 11.7

5. 60

Step-by-step explanation:

There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

Step-by-step explanation:

b(9-3)

Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  \(y-\) axis

Horizontal translation is shifting the graph along  \(x-\) axis.

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Answer:

B. the points scored by a basketball player compared to his minutes played

Step-by-step explanation:

Answer:

180 degree rotation

Step-by-step explanation:

Answer:

Reflect across the y-axis

Translate horizontally 7 units right

Step-by-step explanation:

Alright I'll try to quickly answer this for you.

Firstly you could try reflecting figure P across the y axis. That would mean multiplying the whole function times -1.

So a point like (-2,3) would be come (-2,-3), and then visualize moving that point to where it would be on figure Q. It looks like it would be on (5,-3) on figure Q. So to take (-2,-3) to (5,-3) you translate it horizontally 7 units right.

The four angles in a quadrilateral always add up to 360 degrees. To divide the quadrilateral into two triangles, we can draw a diagonal that connects any two non-adjacent vertices of the quadrilateral. This diagonal splits the quadrilateral into two triangles, each with three angles. The sum of the angles in each triangle is always 180 degrees.

In the first triangle formed by the diagonal, let's denote the three angles as A, B, and C. In the second triangle, the angles will be D (the reflex angle), B, and C. Since angles B and C are common to both triangles, they cancel each other out when calculating the total sum.

Therefore, the sum of angles A, B, C, and D is equal to A + D. Since the sum of angles in each triangle is 180 degrees, the sum of the four angles in the quadrilateral is 2(180) = 360 degrees.

In conclusion, dividing a quadrilateral with a reflex angle into two triangles by drawing a diagonal helps demonstrate that the sum of the angles in the quadrilateral remains constant at 360 degrees.

This property holds true for all quadrilaterals, regardless of the size or shape of their angles.

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Using a calculator, we have that:

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that:

Hence the regression equation is:

y = -4.75x + 88.57143.

Also using a calculator, the correlation coefficient is of -0.906.

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The formula to find the surface area of a cylinder is:

In this case, we have:

B. 140π units²

Answer:

d

took the test

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

khan academy

Answer: 19

Step-by-Step explanation:

So I am assuming that you should divide 114 divided by 6 which will leave you with the answer of 19.

See below for the proof that the areas of the lune and the isosceles triangle are equal

The area of the isosceles triangle is:

\(A_1 = \frac 12r^2\sin(\theta)\)

Where r represents the radius.

From the figure, we have:

\(\theta = 90\)

So, the equation becomes

\(A_1 = \frac 12r^2\sin(90)\)

Evaluate

\(A_1 = \frac 12r^2\)

Next, we calculate the length (L) of the chord as follows:

\(\sin(45) = \frac{\frac 12L}{r}\)

Multiply both sides by r

\(r\sin(45) = \frac 12L\)

Multiply by 2

\(L = 2r\sin(45)\)

This gives

\(L = 2r\times \frac{\sqrt 2}{2}\)

\(L = r\sqrt 2\)

The area of the semicircle is then calculated as:

\(A_2 = \frac 12 \pi (\frac{L}{2})^2\)

This gives

\(A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2\)

Evaluate the square

\(A_2 = \frac 12 \pi (\frac{2r^2}{4})\)

Divide

\(A_2 = \frac{\pi r^2}{4}\)

Next, calculate the area of the chord using

\(A_3 = \frac 12r^2(\theta - \sin(\theta))\)

Recall that:

\(\theta = 90\)

Convert to radians

\(\theta = \frac{\pi}{2}\)

So, we have:

\(A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))\)

This gives

\(A_3 = \frac 12r^2(\frac{\pi}{2} - 1)\)

The area of the lune is then calculated as:

\(A = A_2 - A_3\)

This gives

\(A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)\)

Expand

\(A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2\)

Evaluate the difference

\(A = \frac 12r^2\)

Recall that the area of the isosceles triangle is

\(A_1 = \frac 12r^2\)

By comparison, we have:

\(A = A_1 = \frac 12r^2\)

This means that the areas of the lune and the isosceles triangle are equal

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a=1

Hope this helps

have a great day!

Step-by-step explanation:

Answer:

X=-7

Step-by-step explanation:

X*5-4=3(X*3+8)

5x-4=9x+24

-4=4x+24

-28=4x

-7=x

Answer:

11x11x11=11³

Step-by-step explanation:

11 to the third means 11 times itself 3 times

Answer:

11 × 11 × 11= 11 square becaus 11's three times means11×11×11=11 square

Answer:

3/5, 0.6, and 60%

Step-by-step explanation:

Answer:

3/5, 60%, 0.60

Step-by-step explanation:

3 ÷ 5 = 0.60

0.60 is 60% (0.60 x 100)

60% = 60%

Answer: 29152332 ≡ 0 (mod 3)

Step-by-step explanation:

In modular arithmetic, there is the form a ≡ b (mod m) where b is the remainder.

To solve this problem, we want to divide 29152332 by 3 and find the remainder.

29152332 ÷ 3 = 9717444

Since we get an integer with no remainder, we know the answer is 29152332 ≡ 0 (mod 3).

Answer: x= 1/2

Step-by-step explanation:

Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.

The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")

Using math operations one can relate x values with y values via an equation of the type:

y = 2 x - 5

where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.

For example, try the number x = 0

and see which y number connects with it:

y = 2 (0) - 5 = 0 - 5 = -5

Then you say that the number 0 in the Domain connects with the number -5 in the Range.

This relationship can also be given with coordinate pairs of the form:

(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.

The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.

I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.

Answer:

Lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:

\(y=a(x-h)^2+k\) and this will allow us to solve for the value of a:

\(6=a(6-4)^2+5\) and

\(6=a(2)^2+5\) and

6 = 4a + 5 and

1 = 4a so

\(a=\frac{1}{4}\) and the equation is

\(y=\frac{1}{4}(x-4)^2+5\)

Answer:b

Step-by-step explanation:

Answer:

The standard general equation for a straight line is:

y = mx + C. You said the slope of line is 2/3. m is always the slope in this context. So with the numerical value slope we have the line

Y = 2/3 X + C. You also said the line passes through the point (1, -4) that is the X value is 1 and the y value is -4. Substitute these value into the linear equation to find C, as follows

-4 = 2/3 + c. and so C = - 4 - 2/3 = -14/3 and so the equation of line is :

y = 2x/3 + 14/3 or if you like 3y = 2x + 14

It is important to remember that the convention of the bracketted numbers e.g. (1,-4) or ( 1, -4, z), say is that the first number in the brackets indicates the X value, the second the y value and the third, the z value in the case of 3 D coordinates.

Do you see the negative sign in front of the parentheses? That is -1.

Multiply each term inside the parentheses by -1.

Doing so, we get -8 -b.

Answer:

No

Step-by-step explanation:

When \(x=2\), \(y=-6(2)=-12\), not \(4\).