3. Bob has 8 pieces of square index cards that each measures 8 inches per side. Using a pair of scissors, he cuts each piece in half (so the resulting size is 8” x 4”) and then places all the resulting card pieces in a new stack. If he repeats this procedure 4 more times, how many pieces of card stock will he have and what will be the measure of each piece? (Note: All cuts will be made along the longer edge of the piece if the piece of index card is not square.)

The length of the radius of a circle exists 41 units.

Given: The center exists at -7+2i and a point in the circle at 33+11i.

The radius of the circle exists given by the following formula;

The radius of the circle [tex]$=\sqrt{x^{2}+y^{2}}$[/tex]

The center exists at -7 + 2i and a point in the circle at 33 + 11i.

[tex]$&x(33-(-7)), y(2 \mathrm{i}-11 \mathrm{i}) \\[/tex]

simplifying the equation, we get

[tex]$&\mathrm{x}(33+7), \mathrm{y}(-9 \mathrm{i}) \\[/tex]

[tex]$&\mathrm{x}(40), \mathrm{y}(-9(-1)) \\[/tex]

[tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex]

The center of the circle exists at [tex]$&\mathrm{x}(33+7), \mathrm{y}(9)[/tex].

The length of the radius of a circle exists,

Radius [tex]$}=\sqrt{x^{2}+y^{2}} \\[/tex]

substituting the values of x and y, we get

Radius[tex]$}=\sqrt{40^{2}+9^{2}} \\[/tex]

Radius [tex]$}=\sqrt{1600+81} \\[/tex]

Radius [tex]$=\sqrt{1681} \\[/tex]

Radius = 41 unit

Therefore, the length of the radius of a circle exists 41 unit.

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13.1 = 13.10

---> 13.1 > 13.01

---> 13.01 < 13.1

The correct answer is <

ADG is an equilateral triangle, then, line AD is equivalent to line AG.

From the information given, we have to prove that;

AD=AG

It is important to note that the triangle ADG is an equilateral triangle.

The properties of an equilateral triangle are;

Since ADG is an equilateral triangle, then, line AD is equivalent to line AG

Thus, since ADG is an equilateral triangle, then, line AD is equivalent to line AG.

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The answer is.........

25.99

The equation for the plane through the points p(0, 1, 1), q(1, 0, 1) and r(1, 1, 0) is x + y + z = 2

Given,

Three points :- p(0, 1, 1), q(1, 0, 1), r(1, 1, 0)

We can take this as ([tex](x_{1} ,y _{1}, z_{1} ), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] respectively.

Thus,

The equation for the plane through the points

Here,

The formula of equation of the plane passing through three non collinear points

[tex]x-x_{1} y-y_{1} z-z_{1} \\x_{2} -x_{1} y_{2} -y_{1} z_{2} -z_{1} = 0\\x_{3} -x_{2} y_{3} -y_{2} z_{3} -z_{2}[/tex]

by substituting the values in the formula of equation of the plane

x-0  y-1  z-1

1-0  0-1  1-1    = 0

1-0  1-1  0-1

x  y  z

1  -1  0   =  0

1  0  -1

x(1) - (y-1)(-1) - (z-1)(-1) = 0

x + y - 1 + z - 1 = 0

x + y + z + 2 = 0

x + y + z = 2

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

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The equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

For given question,

We have been given three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)

We need to find an equation for the plane through the given three points.

We know that the equation of the plane through the points [tex](x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)[/tex] is,

[tex]\begin{vmatrix}x-x_1 & y-y_1 & z-z_1\\x_2-x_1 & y_2-y_1 & z_2-z_1\\x_3-x_1 & y_3-y_1 & z_3-z_1\end{vmatrix}=0[/tex]

Assume that for given points,

[tex](x_1,y_1,z_1)=(0, 1, 1)\\\\(x_1,y_1,z_1)=(1, 0, 1)\\\\(x_1,y_1,z_1)=(1, 1, 0)[/tex]

So, the equation of the plane passing though given points would be,

[tex]\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1-0 & 0-1 & 1-1\\1-0 & 1-1 & 0-1\end{vmatrix}=0\\\\\\\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1 & -1 & 0\\1 & 0 & -1\end{vmatrix}=0\\\\\\\Rightarrow x(1-0)-(y-1)(-1-0)+(z-1)(1-0)=0\\\\\Rightarrow x+y-1+z-1=0\\\\\Rightarrow x+y+z=2[/tex]

Therefore, the equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

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Answer:

20 percent

40 percent

20 percent

20(.008) percent

Step-by-step explanation:

6) 54 - 45 = 9

45 / 9 = 5

100 / 5 = 20

20 percent

7) 60 - 36 = 24

60 / 24 = 2.5

100 / 2.5 = 40

40 percent

8) 30 - 24 = 6

30 / 6 = 5

100 / 5 = 20

20 percent

9) 24.99 - 19.99 = 5

24.99 / 5 = 4.998

100 / 4.998 approx. = 20.008

20.008 percent (or rounded 20 percent)

Answer:

D is correct

Step-by-step explanation:

Since you have 2 parallel lines cut by a transversal, <BAC and <BDE are corresponding angels.  Corresponding angles are congruent.  You are able to prove that 2 pairs of angles are congruent so the triangles are similar.  All of the answers show that the 2 triangles share angle B as the first part of the answer.

Answer:

0

Step-by-step explanation:

In cartesian graphs, the slope or a gradient of a fully horizontal line will always be 0.

Answer:

  s = -24

Step-by-step explanation:

This is a 2-step linear equation, so can be solved the way all 2-step equations are solved.

Step 1

Identify the constant term on the side of the equation with the variable term, and add its opposite to both sides.

  [tex]7 = \dfrac{1}{6}s+11\qquad\text{given}\\\\7-11=\dfrac{1}{6}s+11-11\qquad\text{add $-11$ to both sides}\\\\-4=\dfrac{1}{6}s\qquad\text{simplify}[/tex]

Step 2

Multiply both sides by the inverse of the coefficient of the variable.

  [tex](6)(-4)=(6)\left(\dfrac{1}{6}s\right)\qquad\text{multiply both sides by 6}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

Often, when equations contain fractions, you are advised to "eliminate fractions" as a first step. That generally means you multiply both sides of the equation by a suitable common denominator.

Here, the only denominator is 6, so the fraction can be eliminated by multiplying both sides of the equation by 6.

  [tex]7=\dfrac{1}{6}s+11\qquad\text{given}\\\\6(7)=6\left(\dfrac{1}{6}s+11\right)\qquad\text{multiply both sides by 6}\\\\42=s+66\qquad\text{simplify}\\\\42-66=s+66-66\qquad\text{add the opposite of 66 to both sides}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]

You will note this requires the same number of steps, but you don't have to mess with fractions after the first step.

The value we found for the variable can be checked in the original equation.

  [tex]7=\dfrac{1}{6}(-24)+11\\\\7=-4+11\qquad\text{true}[/tex]

Using the normal distribution, the z-score that separates the bottom​ 70% from the top​ 30% is z = 0.525.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score that separates the bottom​ 70% from the top​ 30% is z with a p-value of 0.7, hence z = 0.525.

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In the given diagram, the measure of arc QS is 168°

From the question, we are to determine the measure of arc QS

The measure of the arc is the angle subtended by the arc at the center of the circle.

From one of the circle theorems, we have that

The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference

In the given diagram,

The angle subtended by arc at the circumference of the circle = 84°

∴ The angle subtended by the arc QS at the center = 2 × 84°

The angle subtended by the arc QS at the center = 168°

Hence, in the given diagram, the measure of arc QS is 168°

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Answer:  168°

Step-by-step explanation:  TRUST ME!!!  Answer is correct in Edge!  :)

Answer:

109x

Step-by-step explanation:

We know that there are 109 students in the fourth grade, who each have x cupcakes. In order to find the total amount of cupcakes, we could add all of the cupcakes together to get:

x + x + x + x + .... x

109 times because there are 109 students.

This can be simplified to become 109x.

The correct unscrambling of whyrot is worthy.

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The number of ways people can get off the elevator is 604800 ways.

In this question,

Number of people, n = 7

Number of floors, r = 10

The first person can leave elevator in one of 10 ways. Then second person has to choose from one of remaining 9 floors. Then third person in 8, fourth in 7 ways and so on.

Number of ways people can get off the elevator can be calculated as

⇒ [tex]nP_r=\frac{n!}{(n-r)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(10-7)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(3)!}[/tex]

⇒ [tex]10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}[/tex]

⇒ [tex]10P_{7}=(10)(9)(8)(7)(6)(5)(4)[/tex]

⇒ 604800 ways.

Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.

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Answer:

A: (4,7)

B: (2,1)

C: (6,1)

Step-by-step explanation:

To plot the points, go along the x-axis (the horizontal line with the x on the end) and stop where the dot is. Whatever number the dot is above is the   x-coordinate. Then, however many numbers you go up by to reach the dot is your y-coordinate.

hope this helps :)

The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

According to the statement

We have given that the sin(x) = 5/13 , x in quadrant iii

And we have to Find the value of cos x using the following:

So, For this purpose, we know that the trigonometry terms are:

sin2(x) + cos2(x) = 1;  

or cos2(x) = 1-sin2(x)

And

cos2(x) = 1-(-5/13)2 =

cos2(x) = 144/169;  

We know that the

In quadrant III both the sin and cos are negative so

cos(x) = -12/13 (after taking square roots).

And

Then tan(x) = sin(x)/cos(x) = (-5/13)/(-12/13) = 5/12.

Now you can use the angle addition formulas to find sin(2x), cos(2x), and tan(2x).

Now

sin(x + x) = sinx * cosx + cosx * sinx

              = (-5/13)*(-12/13) + (-12/13)(-5/13) = 120/169

And

cos(x + x) = cosX * cos(x) - sinx*sinx

               = (-12/13)(-12/13) - (-5/13)(-5/13)

               =  119/169

So,

You could use the tan double angle formula, but it is easiest to use  

tan(2x) = sin(2x)/cos(2x)  = (120/169) / (119/169)

          = 120/119.

So, The value of trigonometry terms sin(2x) is 120/169 and cos(2x) is 119/169 and tan(2x) is 120/119.

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Answer: 1.71, 1 3/4, 16/9, pie

Step-by-step explanation: We convert all the numbers to improper fractions. 1.71 = 171/100. 1 3/4 = 175/100 because 3/4 is 0.75. pi is 3.14... which is larger than all of the other numbers. So, pi is the largest. For 16/9, we can just divide to find the solution. Once you divide, you will notice that the answer is 1.77777777... This means that it is larger than 1.71 and 1.75 so 16/9 is the second largest. 1.71 is smaller than 1.75 so the order is 1.71, 1 3/4, pie, 16/9

The size of the largest angle of the pentagon will be 150°.

A pentagon is the polygon that has five sides. It should be noted that the interior angle of a regular pentagon is 540°.

The given ratio is 2:3:4:4:5. Therefore, the size of the largest angle of the pentagon will be:

= 5/(2+3+4+4+5) × 540

= 5/18 × 540

= 150°

In this case, the size of the largest angle of the pentagon will be 150°.

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The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.

Given data set: {1,2,3,4,5,6}

Median of the given data set =3.5

The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.

Thus, the first quartile is 2.

The quarter divides the distribution into four groups and calculates the range of values above and below the mean.

A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.

The interquartile range, a measurement of variation around the median, is calculated using quartiles.

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Answer: 8π mm (in terms of π)

Step-by-step explanation:

1) The formulas for solving the circumference of a circle is πd (π times diameter).

2) 8 times π equals 8π mm.

Hopes this helps!

Answer:

12.56 [tex]mm^{2}[/tex]

Step-by-step explanation:

c = 2[tex]\pi[/tex]r

or c =[tex]\pi[/tex]D

The diameter is the measure of a line segment going from one side the circle to the other and going through the middle of the circle.  A radius is a line 1/2 a diameter.  It is a line segment that goes from the center of a circle to a point on the edge of the circle.

C = (3.14)(4)

C = 12.56

Answer:

1: Linear

2: Linear

Step-by-step explanation:

Scenario 1:

Equation: y=8x  (where x represents # of hours worked)

The graph would be linear.

Scenario2:

Equation: y=5x (where x is the # of boxes of donuts purchased)

The graph would be linear. ( I assumed that each box is $5 since 5/1=10/2 )

A similar situation could be: In an art shop, crayons are sold. It costs $7 for 1 box of crayons.

- The graph would be linear, and it would be constant as long as the price for each box of crayons is not changed. Equation is: y=7x

I'm not sure if this is exactly what the last question asked, pretty sure this would be an okay example.

Please see the picture below

Answer:

The second choice is correct.

Step-by-step explanation:

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

The second choice that is B≥ C is correct.

The basics of this question requires us to read the number line perfectly

As we go right on the number line, we are getting to larger and larger values.

D is greater than C because it is to the right of C, so the first choice is not correct.

The third choice is showing absolute value.  This is saying that the letters C and D are both the same distance from zero. They are not.

The last choice says that A is to the right of B and it is not.

Thus option 2) is correct

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Each side of equilateral triangle will have the length equals to 42.7 cm.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.

You should find the perimeter of the rectangle.

2P=23+23+41+41= 128 cm

The equilateral triangle will have the same perimeter of the rectangle. An equilateral triangle presents the equal three sides, thus,

128= 3L

L=128/3=42.7 cm

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Answer:

A) f(x) = x^2 +8(x+2)

Step-by-step explanation:

We will start by putting y=0

0 = x^2+8(x+2) -Apply distributive property

0 = x^2+8x+16

0=(x+4)(x+4)

0=x+4, 0=x+4

x=-4

There is only one zero, and that is x=-4

Brainiest would be appreciated.

First one

Because

If we solve for x

Option A

In the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.

In trigonometry, for a right triangle, the sine (sin) of any angle θ is given as the ratio of its opposite side to the hypotenuse of the triangle, that is, sin θ = (opposite side)/(hypotenuse).

In the question, we are asked to find the trigonometric ratio, sin J, for the given right triangle JKL.

The side opposite to angle J is KL, which has a value of 3 units.

The hypotenuse of the given right triangle is JK, which has a value of 7.8 units.

Thus, sin J can be calculated as:

sin J = KL/JK = 3/7.8 = 5/13 = 0.39.

Thus, in the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.

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The concept exhibited by the thirteen year old who was unsure of one of her responses. she decided to go with the answer that felt the ""most right."" is an example of; Intuitive thought.

It follows from the task content that the thirteen year old was unsure of one of her responses. she decided to go with the answer that felt the ""most right."".

Such concept may be attributed to Intuitive thought.

This follows from the fact that the internal impulse which prompts individuals to make decisions is termed; Intuition.

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Answer:

  (c)  f(g(3)) > g(f(3))

Step-by-step explanation:

The relationship between the function values can be found by evaluating the functions.

The order of operations tells us we must first evaluate g(3).

  g(x) = -3x +15

  g(3) = -3(3) +15 = 6

Then we can evaluate f(x) for x=6:

  f(x) = 7x

  f(6) = 7(6) = 42

So, the composition is ...

  f(g(3)) = 42

As above, we must first evaluate f(3):

  f(3) = 7(3) = 21

Then we can evaluate g(x) for x=21:

  g(21) = -3(21) +15 = -63 +15 = -48

That means the composition is ...

  g(f(3)) = -48

The first is greater than the second.

  42 > -48

  f(g(3)) > g(f(3))