If the area of the circle is 97.9 units squared, what is the radius?

Answer:

3.75 in.

Step-by-step explanation:

Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in.

3 regular hexagons are connected at their sides. A dotted line is drawn through the middle of the 3 hexagons. The top image is a reflection of the bottom image. The dotted line is the length of one side and the distance from one point of the hexagon to the opposite point.

What is the length of the dotted line? Round to the nearest hundredth.

2.50 in.

3.75 in.

5.00 in.

6.25 in.

The length of the dotted line in the hexagon is 3.75 cm.

A polygon with 6 sides is called a hexagon.

Finding the length across one entire hexagon :-

We can draw 6 small triangles from the center of the hexagon. The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360.

The sum of the measures of the angles in a triangle is 180°; taking out the top angle, we have 180-60 = 120°.  

Since the triangle is isosceles, the base angles will be equal to 120/2 = 60

The bottom two angles will also be 60°.  

This makes the triangle equiangular, which also makes it equilateral; all 3 sides will be 1.25.

Hence,

This means across the dotted line we have 1.25+1.25+1.25 = 3.75.

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Answer:

4 = x

Step-by-step explanation:

x³ - 5 = 59     Add five to both sides of the equation.

x³ = 64          Now find the cubed root of 64

∛64 = 4

x = 4

Answer:

B

Step-by-step explanation:

I also took a test

The correct answer is that neither prism has a greater volume  they must have the same volume.

Let denote the volume of prism A as [tex]\( V_A \)[/tex] and the volume of prism B as [tex]\( V_B \).[/tex] According to the problem statement, we have the following relationships:

1. Prism A has 17 more cubic units of volume than prism B:

[tex]\[ V_A = V_B + 17 \][/tex]

2. Prism B has 3 more cubic units of volume than prism A:

[tex]\[ V_B = V_A + 3 \][/tex]

3. Prism B has 8 more cubic units of volume than prism A:

[tex]\[ V_B = V_A + 8 \][/tex]

However there is a contradiction in the last two statements. Prism B cannot have both 3 more cubic units and 8 more cubic units than prism A. This suggests there might be a typographical error in the problem statement.

Assuming there is a mistake and we only consider the first two statements, we can solve for the volumes by setting the two equations equal to each other since both right-hand sides are equal to [tex]\( V_B \):[/tex]

[tex]\[ V_B + 17 = V_A + 3 \][/tex]

Now, we can solve for [tex]\( V_A \)[/tex]in terms of[tex]\( V_B \)[/tex] using the first equation:

[tex]\[ V_A = V_B + 17 \][/tex]

Substitute \( V_A \) into the second equation:

[tex]\[ V_B = (V_B + 17) + 3 \][/tex]

Simplify the equation

[tex]\[ V_B = V_B + 20 \][/tex]

This simplifies to:

[tex]\[ 0 = 20 \][/tex]

This is not possible, which means our initial assumption that the two statements could be true simultaneously is incorrect. The only logical conclusion, given the contradictory information, is that neither prism has a greater volume; they must have the same volume. This is the only way to satisfy the condition that each prism has more volume than the other by different amounts.

Therefore, the volumes of prism A and prism B are equal:

[tex]\[ V_A = V_B \][/tex]

This resolves the contradiction in the problem statement. The volumes of the two prisms must be the same for the given conditions to hold true.

Answer:

23 1/3   or 70/3 =p

Step-by-step explanation:

7/p = 3/10

Using cross products

7*10 = 3p

70 = 3p

Divide each side by 3

70/3 = 3p/3

70/3 =p

or as a mixed number

23 1/3 =p

Your answer would be 900m².

We can find this by finding the area of each of the shapes that make up the surface of this prism.

First there is the bottom of the prism, which would be 11 × 24 = 264m².

Then you have the two triangles on the sides of the prism, which are both (10 × 24)/2 each, which equals 120m² for each triangle. This means that the area for both triangles is 120 × 2 = 240m².

Next we have the area of the back of the prism, which is 11 × 10 = 110m².

Finally we need to find the area of the rectangle on top of the prism, which is 11 × 26 = 286m²

This means your final answer would be the sum of all of these, which is 264 + 240 + 110 + 286 = 900m².

I hope this helps!

D. Graph D. A graph that shows a quadratic function with a discriminant value of 0 is graph D.

In Mathemeatics, the number of zeros for any quadratic function by using the discriminant formula as follows;

Discriminant, D = b² - 4ac

where:

a, b, and c are constants.

Note:

If D equals 0, the quadratic equation has only one real solution.

If D is greater than 0, the quadratic equation has two real solutions.

If D is less than 0, the quadratic equation has two complex solutions

In this context, we can logically deduce that only graph D shows a quadratic function with a discriminant value of 0 because it has only one real solution (x = 1).

Answer: B. 105

Step-by-step explanation:

      180 - 75 = 105

Hope this helps!

Answer:

Let x be the number of chips.

\frac{8}{x}=\frac{1}{5}

x = 40

The answer is: There are 40 chips in

Answer:

b^2-4ac

Step-by-step explanation:

By looking at that part after substituting and calculating, you can tell these things about the solution

Step-by-step explanation:

The following match

* a² + 2ab + b² and (a + b)²

* a² - b² and (a - b)(a + b)

* a² - 2ab + b² and (a - b)²

* a³ - b³ and (a - b)(a² + ab + b²)

* a³ + b³ and (a + b)(a² - ab + b²)

* y = 10x Direct variation

* xy = 18 Algorithm

* y = 4xz Joint variation

* y = 4x/z Inverse variation

Answer:

438.86

Step-by-step explanation:

1. 457 x 0.99 = 452.43 - Decreased by 1%

2. We need to decrease 452.43 again but this time by 3% - 452.43 x 0.97

3. This gives us an answer of 438.8571

4. Finally we need to round this to 2DP, the 7 (438.8571) rounds up so the number to the left increases. This leaves an answer of 438.86

Hope this helps :D

Answer:

x2-16x+100=0  

Two solutions were found :

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-16x+100  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -16x  its coefficient is  -16 .

The last term, "the constant", is  +100  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100  

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -16 .

     -100    +    -1    =    -101  

     -50    +    -2    =    -52  

     -25    +    -4    =    -29  

     -20    +    -5    =    -25  

     -10    +    -10    =    -20  

     -5    +    -20    =    -25  

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  1  :

 x2 - 16x + 100  = 0  

Step  2  :

Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-16x+100

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.  

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.  

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   8.0000  

Plugging into the parabola formula   8.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 8.00 * 8.00 - 16.0 * 8.00 + 100.0

or   y = 36.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-16x+100

Axis of Symmetry (dashed)  {x}={ 8.00}  

Vertex at  {x,y} = { 8.00,36.00}  

Function has no real roots

Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-16x+100 = 0 by Completing The Square .

Subtract  100  from both side of the equation :

  x2-16x = -100

Now the clever bit: Take the coefficient of  x , which is  16 , divide by two, giving  8 , and finally square it giving  64  

Add  64  to both sides of the equation :

 On the right hand side we have :

  -100  +  64    or,  (-100/1)+(64/1)  

 The common denominator of the two fractions is  1   Adding  (-100/1)+(64/1)  gives  -36/1  

 So adding to both sides we finally get :

  x2-16x+64 = -36

Adding  64  has completed the left hand side into a perfect square :

  x2-16x+64  =

  (x-8) • (x-8)  =

 (x-8)2

Things which are equal to the same thing are also equal to one another. Since

  x2-16x+64 = -36 and

  x2-16x+64 = (x-8)2

then, according to the law of transitivity,

  (x-8)2 = -36

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-8)2   is

  (x-8)2/2 =

 (x-8)1 =

  x-8

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x-8 = √ -36

Add  8  to both sides to obtain:

  x = 8 + √ -36

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1  

Since a square root has two values, one positive and the other negative

  x2 - 16x + 100 = 0

  has two solutions:

 x = 8 + √ 36 •  i  

  or

 x = 8 - √ 36 •  i  

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-16x+100 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =   -16

                     C   =  100

Accordingly,  B2  -  4AC   =

                    256 - 400 =

                    -144

Applying the quadratic formula :

              16 ± √ -144

  x  =    ——————

                     2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)  

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -144  =  

                   √ 144 • (-1)  =

                   √ 144  • √ -1   =

                   ±  √ 144  • i

Can  √ 144 be simplified ?

Yes!   The prime factorization of  144   is

  2•2•2•2•3•3  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 144   =  √ 2•2•2•2•3•3   =2•2•3•√ 1   =

               ±  12 • √ 1   =

               ±  12

So now we are looking at:

          x  =  ( 16 ± 12i ) / 2

Two imaginary solutions :

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

 or:  

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

Two solutions were found :

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

Step-by-step explanation:

Answer:

=A$2, =A$2, =A$2

Step-by-step explanation:

Autofill is used in excel to fill a series of cells automatically. If the formula in cell B1 is =A$2. On using autofill by dragging B1's autofill box across to C1, D1, and E1, =A$2, =A$2, =A$2 appear in C1, D1, and E1, respectively. Excel tries to guess and insert next values on the basis of selected data.

Answer:

Step-by-step explanation:

A$2 A$3 A$4

Answer:

V = 77 m^3

Step-by-step explanation:

We want the volume of the cylinder

V = pi r^2 h

We know the diameter not the radius

r = d/2 = 7/2 = 3.5

V = 3.14 * (3.5)^2 (2)

V = 76.93 m^3

To the nearest cubic meter

V = 77 m^3

The answer is 77 m^3

Quick question though... Why say "easy" and ask for an answer?

Answer:

90

Solution:

The 1st choice is 1 of 10.

The 2nd is one of 9.

Therefore, 10 times 9= 90

B

Step-by-step explanation:

I hoped this helped

Based on the provided box and whisker plot, the lower quartile (Q1) represents the 25th percentile of the data, which means 25% of the data points are below this value. To find the lower quartile weight of Frank's classmates, we need to identify the middle value of the lower half of the data.

The box and whisker plot separates the data into four quartiles: the lower whisker, the box (which contains Q1), the median (Q2), and the upper whisker. The box covers the interquartile range (IQR), which contains the middle 50% of the data.

Let's find the lower quartile (Q1) based on the provided data:

Weights of Frank's Classmates (in lbs.): 50, 75, 100, 125, 150

Step 1: Arrange the data in ascending order: 50, 75, 100, 125, 150

Step 2: Find the position of Q1:

Position of Q1 = (25/100) * (Total number of data points + 1)

Position of Q1 = (25/100) * (5 + 1)

Position of Q1 = (25/100) * 6

Position of Q1 = 1.5

Since the position is not a whole number, we need to take the average of the data points at positions 1 and 2.

Step 3: Calculate Q1:

Q1 = (Data at position 1) + [(Position of Q1 - Integer part of Position of Q1) * (Data at position 2 - Data at position 1)]

Q1 = 50 + [(1.5 - 1) * (75 - 50)]

Q1 = 50 + [0.5 * 25]

Q1 = 50 + 12.5

Q1 = 62.5

So, the lower quartile weight of Frank's classmates is 62.5 lbs.

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Answer:

14inches farenheight

Step-by-step explanation:

Answer:

14 inches farenheit

Step-by-step explanation:

Answer: 72

72/8 will get you 9. To see if the answer is correct Multiply 9*8.

Answer:

72

Step-by-step explanation:

c/8 = 9

Multiply each side by 8

c/8 * 8 =9*8

c = 72

Answer:

x=8

A = 192

Step-by-step explanation:

The perimeter is the sum of the outer lengths

17.9 + 22.6 + 3x = 64.5

Combine like terms

40.5 +3x = 64.5

Subtract 40.5 from each side

40.5 +3x -40.5 = 64.5 - 40.5

3x =24

Divide each side by 3

3x/3 = 24/3

x = 8

The area of a triangle is given by

A = 1/2 bh

The base is 3x = 3(8) =24

and the height is 2x = 2(8) =16

A = 1/2 (24) * 16

A =192

Answer: 24 days

Step-by-step explanation:

Sandy plays tennis once every 6 six days while Jim plays tennis once every 8 eight days.

To get the number of days they will play on the same day again, we find the lowest common multiple for the numbers.

The lowest common multiple is the smallest positive integer which is evenly divisible by both 6 and 8.

6 = 6, 12, 24, 30

8 = 8, 16, 24, 32

The lowest common multiple is 24.

In 24 days, they will play on the same day again

Answer:

5 dollars

Step-by-step explanation:

Answer:

5 dollars

Step-by-step explanation:

Answer:

B. 7 inches

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

56 = 8*w

Divide each side by 8

56/8 = 8w/8

7 =w

Answer: 7 inches

Step-by-step-Explanation: The formula for the area of a rectangle is below shown below.

Area = length · width

Since we know that the area of the rectangle is 56 in² and the length of the rectangle is 8 inches, we have 56 = 8 · w.

Now to find w or the width of the rectangle, we divide

both sides of the equation by 8 to get 7 = w.

So the width of the rectangle is 7 inches.

Notice that we include inches in our final answer because we were given inches as units in the original problem.

Also notice that we don't ever have to draw a picture of the rectangle in this problem. We can find our answer by simply using the formula for the area of a rectangle.

Answer:

47

Step-by-step explanation:

add all the numbers and divide them by however many numbers there are.

Answer: The mean is 47.

There are 5 numbers.

To find the mean of them we add them and divide the sum by 5.

Mean = [tex]\frac{\left(40+40+52+41+62\right)}{5}=\frac{235}{5}=47[/tex]

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Answer:

adbbcbaca

Step-by-step explanation:

Answer:

55 words per minute

Step-by-step explanation:

165/3

Final answer:

The ratio of words typed per minute for Kale who typed 165 words in 3 minutes is calculated by dividing the number of words by the number of minutes, resulting in 55 words per minute.

Explanation:

To calculate the number of words typed per minute, you take the total number of words typed and divide it by the number of minutes it took to type them. In this case, Kale typed 165 words in 3 minutes, so the ratio of words to minutes is:

165 words / 3 minutes = 55 words per minute

This ratio indicates the typing speed, measured in words per minute (wpm), which is a common way to express typing efficiency.

Answer:B

Step-by-step explanation:

Edge2021

Answer: 7/8 pounds of cheese

Step-by-step explanation:

Add the two numbers.

4/8 + 3/8 = 7/8.

That is your answer.

Answer:

The inverse of the function is ±sqrt( (x+4)/2

Step-by-step explanation:

Set the function equal to y

y = 2x^2 -4

Exchange x and y

x = 2y^2 -4

Solve for y

Add 4 to each side

x+4 = 2y^2 -4+4

x+4 = 2y^2

Divide each side by 2

(x+4)/2 = 2/2y^2

(x+4)/2 = y^2

Take the square root of each side

±sqrt( (x+4)/2 )= sqrt(y^2)

±sqrt( (x+4)/2 )= y

The inverse of the function is ±sqrt( (x+4)/2