The equilateral triangle shown is rotated about line a. each side of the triangle measures 20 mm. an equilateral triangle is shown. line of rotation a goes through one point and the midpoint of the opposite side. what shape is created by the rotation and what is the approximate circumference of the base? circumference of a circle: c = 2πr a cylinder with a circumference of about 63 mm a cylinder with a circumference of about 126 mm a cone with a base circumference of about 63 mm a cone with a base circumference of about 126 mm

The sides length of the square is 3 units, then the perimeter of the square is 12 units.

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

If (-1, 2) and (2, -1) are two opposite vertices of a square, then the perimeter of the square will be

The other two vertices of the square will be

(-1, -1) and (2, 2)

Then the distance between the points (2, 2) and (2, -1) will be

[tex]\rm D = \sqrt{(2-2)^2+ (-1-2)^2}\\\\D = \sqrt{3^2}\\\\D = 3[/tex]

Then the perimeter of the square will be

Perimeter = 4 × 3

Perimeter = 12 units

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Answer: [tex]\displaystyle d=3\sqrt{5}[/tex]

Step-by-step explanation:

     First, we will find the coordinate placement of each point. See attached.

     Now, we can use the distance formula.

[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

[tex]d=\sqrt{(6-3)^2 +(-3-3)^2}[/tex]

[tex]d=\sqrt{(3)^2 +(-6)^2}[/tex]

[tex]d=\sqrt{9+36}[/tex]

[tex]d=\sqrt{45}[/tex]

[tex]d=\sqrt{9*5}[/tex]

[tex]\displaystyle d=3\sqrt{5}[/tex]

Answer:

42.5° East of South

Step-by-step explanation:

Hope this helps :)

Answer:

48.89

Hope this helps!!

Answer: 48.89

Step-by-step explanation:

     The proportion for tangent is the opposite side over the adjacent side.

[tex]\displaystyle \frac{\text{opposite \;side}}{\text{adjacent \;side}} =\frac{55}{48}[/tex]

Given:

tan(E) = [tex]\frac{55}{48}[/tex]

Inverse:

[tex]\displaystyle tan^{-1} (tan(E)) = (\frac{55}{48} ) tan^{-1}[/tex]

Simplify:

≈ 48.8879

Round:

≈ 48.89

Answer:

If the children divide evenly onto 3 buses, there will be 11 children on each bus

Step-by-step explanation:

Add all 3 classes to ind total amount of students

Ms. Noels class has 10 students

Mr. Grubbs class has 9 students

Ms. Ackerman's class has 14 students

Total Students: 10 students + 9 students + 14 students

33 total students

Dividing 33 students in 3 busses is 33 / 3 which equals 11

Answer:

[tex]x =\dfrac 47[/tex]

Step-by-step explanation:

[tex]~~~~~9x-1 = 2x+3\\\\\implies 9x -2x = 3+1\\\\\implies 7x = 4\\\\\implies x =\dfrac 47[/tex]

Answer:

254.47 in²(rounded to nearest hundredth)

_________________________________________________________

[tex]A = \pi r^2[/tex]

tiny r means radius

² means multiply the number by itself twice

[tex]\pi r^2 = \pi * 9^2 = 81\pi(254.47~in^2)[/tex]

_________________________________________________________

Since the radius of a circle is 9 inches, the circle's area is equal to 254.34 square inches.

In Mathematics and Geometry, the area of a circle can be calculated by using this mathematical equation (formula):

Area = πr²

Where:

r represents the radius of a circle.

By substituting the given parameters into the formula for the area of a circle, we have the following;

Area of circle = 3.14 × 9²

Area of circle = 3.14 × 81

Area of circle = 254.34 square inches.

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Answer: B, C, D, E

Step-by-step explanation:

The coordinates of four points on the line are (0,-5), (3,-3), (6,-1) and (9,1)

The given parameters are given as:

The equation is represented as:

y = mx + c

So, we have:

y = 2/3x -5

When x = 0, we have;

y = 2/3 * 0 -5 = -5

When x = 3, we have;

y = 2/3 * 3 -5 = -3

When x = 6, we have;

y = 2/3 * 6 -5 = -1

When x = 9, we have;

y = 2/3 * 9 -5 = 1

Hence, the coordinates of four points on the line are (0,-5), (3,-3), (6,-1) and (9,1)

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The option first ΔXYZ≅ΔLMN, option second ∠Y = ∠M = 86°, option third ∠X =∠L = 38°, and option sixth XZ ≅ LN are correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a triangle XYZ shown in the diagram, and triangle LMN is the reflection of the triangle XYZ.

∠Z = 180 - 86-38 = 56°

Similarly,

∠L = 38°

From this, two triangles XYZ and LMN

We can say:

ΔXYZ≅ΔLMN

∠Y = ∠M = 86°

∠X =∠L = 38°

XZ ≅ LN

Thus, the option first ΔXYZ≅ΔLMN, option second ∠Y = ∠M = 86°, option third ∠X =∠L = 38°, and option sixth XZ ≅ LN are correct.

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Answer:

the answer is 97.5%

Step-by-step explanation:

Answer:

1,260

Step-by-step explanation:

you have too do 2 by 3 by 5 by 6 by 7 so you get

1,260

Answer:

The expected number of blue tiles is 20 blue tiles.

Step-by-step explanation:

You can easily do 80% x 25 or

0.8 x 25 = 20

OR (other method)
Turn the 80% into a fraction
80        x
----  =  -----
100     25

100 / 4 gives us 25, so 80 / 4 will give 20.

So the answer is 20 blue tiles.

Answer:

x = the quantity of 3 plus or minus the square root of 37 all over 2

Step-by-step explanation:

Given/To Find:

What are the exact solutions of x2 − 3x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a?

Answer choices:

x = the quantity of 3 plus or minus the square root of 37 all over 2

x = the quantity of negative 3 plus or minus the square root of 37 all over 2 x = the quantity of 3 plus or minus the square root of 19 all over 2

x = the quantity of negative 3 plus or minus the square root of 19 all over 2

Solve:

By using the quadratic formula, the solutions are

[tex]x=\frac{-(-3)±\sqrt{(-3)^2-4\times1\times(-7)}}{2\times1}[/tex]

[tex]x=\frac{3±\sqrt{37}}{2}[/tex]

Hence, the answer is :

x = the quantity of 3 plus or minus the square root of 37 all over 2

Kavinsky

Answer:

The exact solution is:

x = the quantity of 3 plus or minus the square root of 37 all over 2

Step-by-step explanation:

We are asked to find the exact solution of the polynomial equation which is given by:

[tex]x^2 - 3x - 7 = 0[/tex]

We know that the solution of the equation are the possible value of x which is obtained on solving the equation and hence satisfy the equation.

Now, on solving the quadratic equation i.e.  degree 2 polynomial equation using the quadratic formula:

That is any polynomial equation of the type:

[tex]ax^2+bx+c=0[/tex]

is solved by using the formula:

[tex]x=\frac{-b±\sqrt{x} b^2-4ac}{2a}[/tex]

Here we have:

a=1, b=-3 and c=-7.

Hence, the solution of the equation is:

[tex]x=\frac{-(-3)±\sqrt{(-3)^2-4*(-7)*1} }{2*1}[/tex]

[tex]x=\frac{3±\sqrt{9+28} }{2}[/tex]

[tex]x=\frac{3±\sqrt{37} }{2}[/tex]

Hence, the solution is:

x = the quantity of 3 plus or minus the square root of 37 all over 2

( i.e.

[tex]x=\frac{3±\sqrt{37} }{2}[/tex] )

The horizontal ground distance between the person and the plane is 6174.5 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let d represent the horizontal ground distance between the person and the plane.

tan(39) = 5000 / d

d = 6174.5 feet

The horizontal ground distance between the person and the plane is 6174.5 feet

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The percent of the purchase price for Julio’s down payment was C. 18%

This refers to the amount of money that is added to a loan collected by a person, for when he makes repayment.

Hence,

Given that

We use the formula Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]

Pv= 1,558.09×((1−(1+0.05875÷12)^(−12×20))÷(0.05875÷12))

=219,684.92

Next thing to do is make a subtraction to get the down payment:

267,900−219,684.92=48,215.08

Then the percentage would be:

48,215.08÷267,900= 18% approx.

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Answer:

option A is the mostly likely to be population distribution

The distribution (A) is a distribution that is most likely to be from this population distribution option (A) is correct.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

It is given that:

The normal distribution or bell curve is shown in the picture.

As we can see in the picture the distribution is distributed 50 - 50 % along the median line or mean line.

The distribution is most likely to be from this population distribution is shown in option (A).

Thus, the distribution (A) is a distribution that is most likely to be from this population distribution option (A) is correct.

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Answer:

9(7p) is the expression.

Step-by-step explanation:

Let's multiply 7p and 9 to get product,

→ 7p × 9

→ 9(7p)

So, the product is 9(7p).

Answer:

  40 quarts

Step-by-step explanation:

The amount of additional 50% acid solution can be found by writing an equation for the amount of acid in the mix.

__

Let x represent the number of quarts of 50% acid solution that need to be added. The total number of quarts of acid in the 40% mix is ...

  0.50x +0.20(20) = 0.40(x +20)

  0.10x = 0.20(20) . . . . . . . subtract 0.40x +0.20(20)

  x = 40 . . . . . . . . . . . . divide by 0.10

40 quarts of 50% solution must be added.

_____

Additional comment

That will make a total of 60 quarts of solution, of which 24 quarts (40%) are acid.

Step-by-step explanation:

while the other answer is correct, let me try to explain this in a different optical way :

50% means 50/100 = 1/2 = 5/10 of the substance is acid.

20% means 20/100 = 1/5 = 2/10 of the substance is acid.

40% means 40/100 = 2/5 = 4/10 of the substance is acid.

now, we want to find the quantity of x quarts that satisfies the desired balance :

x × 50% + 20 × 20% = (x + 20) × 40%

x × 5/10 + 20 × 2/10 = (x + 20) × 4/10

5x/10 + 4 = 4x/10 + 8

x/10 = 4

x = 40

so, yes, we need to add 40 quarts of the 50% solution.

that gives us 60 quarts, with 40% = 40/100 = 4/10 = 2/5 = being acid : 60 × 2/5 = 120/5 = 24 quarts

Answer:

Reflection over the y-axis followed by a translation to the left by 2 units

Step-by-step explanation:

From inspection of the graph, the y-values of figure ABCD and the y-values of figure A'B'C'D' have not changed, yet the x-values have changed from positive to negative.

(x, y) →  (-x, y)

This indicates a reflection in the y-axis.

To reflect figure ABCD in the y-axis, simply change the x-values to negative:

A (1, 3)  →  (-1, 3)

B (3, 4)  →  (-3, 4)

C (2, 1)  →  (-2, 1)

D (1, 1)  →  ( -1, 1)

Comparing the x-values of the figure reflected in the y-axis to the x-values of the final translated figure, the reflected figure needs to be translated to the left by 2 units.

So the total transformation is: (x, y) → (-x - 2, y)

A (1, 3)  →  A' (-3, 3)

B (3, 4)  →  B' (-5, 4)

C (2, 1)  →  C' (-4, 1)

D (1, 1)  →  D' ( -3, 1)

Answer:

4,8

Step-by-step explanation:

because the lins equation goes through in 6

Answer:

28.27

Step-by-step explanation:

π x 6^2 x 90/360 = 28.27

[tex]2x+y-2z=-1\\\\x+0\cdot y-2z=-4\\\\0\cdot x -5y + 2z=-23\\\\\text{In}~ AX =B~ \text{form,}\\\\\begin{bmatrix} 2 & 1&-2\\ 1&0&-2\\ 0&-5&2\end{bmatrix} \begin{bmatrix} x\\y\\z\end{bmatrix}= \begin{bmatrix} -1\\-4\\-23\end{bmatrix}[/tex]

Answer:

a

.6666666 has been rounded up to .6666667

b

0.3333333 = 1/3

0.8333333 = 5/6

2.1666667 = 13/6

0.6666667 = 2/3

0.1428571429 = 1/7

1.6666667 = 5/3

Step-by-step explanation:

a

7 appears at the end of 3 of the decimals because it has been rounded up from 6.66666 recurring.

b

I will go through how to convert one decimal to a fraction:

0.833333333 = x

8.333333333 = 10x

83.33333333 = 100x

100x - 10x = 75

90x = 75

x = 75/90 = 5/6

Answer:

(see attachment)

To approximate the square root of 13:

Working from the top down...

Enter the number you are trying to approximate in the top box: [tex]\boxed{\sf \sqrt{13}}[/tex]

Find the perfect squares directly below and above 13.

Perfect squares:  1, 4, 9, 16, 25, 36, ...

Therefore, the perfect squares below and above 13 are: 9 and 16

Enter these with square root signs in the next two boxes: [tex]\boxed{\sf \sqrt{9}}[/tex] and  [tex]\boxed{\sf \sqrt{16}}[/tex]  

Carry out the operation and enter  [tex]\boxed{\sf 3}[/tex] and [tex]\boxed{\sf 4}[/tex] in the next two boxes.

Enter the number you are trying to square root (13) in the top left box, the perfect square above it (16) in the box below, then the perfect square below it (9) in the two boxes to the right of these. Carry out the subtractions and place the numbers in the boxes to the right.

[tex]\dfrac{\boxed{\sf 13}-\boxed{\sf 9}}{\boxed{\sf 16}-\boxed{\sf 9}}=\dfrac{\boxed{\sf 4}}{\boxed{\sf 7}}[/tex]

Now enter the number you are trying to square root (13) under the square root sign.  Place the square root of the perfect square below it (3) in the box to the right.  Copy the fraction from above (4/7).  Finally, enter this mixed number into a calculator and round to the nearest hundredth.

[tex]\sf \sqrt{13}=\boxed{\sf3}\dfrac{\boxed{\sf 4}}{\boxed{\sf 7}}=\boxed{\sf3.57}[/tex]

Using the combination formula, it is found that the probability that she will choose one by each composer is given by:

144/1365.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, she will pick 4 CDs from a set of 4 + 6 + 3 + 2 = 15, hence the total number of options is given by:

[tex]C_{15,4} = \frac{15!}{4!11!} = 1365[/tex]

The number of options that include one from each is given by:

N = 4 x 6 x 3 x 2 = 144.

Hence the probability is given by:

p = 144/1365.

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Answer:

73008 views

Step-by-step explanation:

find 27% of 35100:

35100*27/100

=9477

so, you start with 35100 which means;

35100 + (9477*4)

35100 + 37908

= 73008 views

Answer: 91,311

Step-by-step explanation:

This is what it shows as correct on ixl.

Answer:

D) A triangle where there is a 90 degree angle

Step-by-step explanation:

Answer:

2 and 5/11

Step-by-step explanation:

first we find how many times 11 goes into 27. It goes in twice, which gives us our whole number, 2. Then we need to find the fraction part, which is whatever's left over. 27-22 is 5, giving us 2 and 5/11