30 POINTS! Explanation too, please!
Point A' prime is the image of point A under a rotation about point P. Determine the angles of rotation. Choose all answers that apply: (Choice A) 90 degrees clockwise (Choice B) 90 degrees counterclockwise (Choice C) 180 degrees (Choice D) 270 degrees clockwise (Choice E) 270 degrees counterclockwise

Answer:

[tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]

Step-by-step explanation:

The equation of hyperbola is given by:

[tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} }[/tex]

Where [tex]c^{2} =a^{2} +b^{2}[/tex]

∵ [tex]a=8,c=20[/tex]

∴ [tex]b^{2} =c^{2} -a^{2}[/tex]

⇒ [tex]b= \sqrt{20^{2} -8^{2} } =4\sqrt{21}[/tex]

Now, [tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1[/tex]

⇒ [tex]\frac{x^{2} }{8^{2} } -\frac{y^{2} }{y(4\sqrt{21} )^{2} } =1[/tex]

⇒ [tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]

Hence, equation is [tex]\frac{x^{2} }{64} -\frac{y^{2} }{336} =1[/tex]

Hope this helps,

ROR

Answer:

x = 3 ± 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

x² - 6x + 1 = 0 ( subtract 1 from both sides )

x² - 6x = - 1

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = - 1 + 9

(x - 3)² = 8 ( take square root of both sides )

x - 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( add 3 to both sides )

x = 3 ± 2[tex]\sqrt{2}[/tex]

Answer:

(-4, 1)

Step-by-step explanation:

Coordinates on the plane are written (x, y), meaning you write where the point is located on the x-axis (across) and then you write where the point is located on the y-axis (up and down).

You can see that A's location on the x-axis is -4, so now we have (-4, y). We can also see that A's location on the y-axis is 1, so we have (-4, 1) as our coordinates of A.

I hope this helps! Have a lovely day!! :)

Answer: 2d+3<=9

Step-by-step explanation:2 times a number is 2d plus 3 is +3 less than or equal to is <=

Answer:

that is 4.6 m that the answer

Answer:

Angles x and y measure 115°. Angle Z measures 65°.

Step-by-step explanation:

Since a rhombus is a parallelogram, opposite angles are congruent, and consecutive angles are supplementary.

The measure of the angles x, y, and z will be 115°, 115°, and 65°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The adjecent angle of the rhombus is supplementary. Then the value of 'x' is given as,

65° + ∠x = 180°

∠x = 180° - 65°

∠x = 115°

The opposite angle of the rhombus is congruent to each other.

∠y = ∠x

∠y = 115°

∠z = 65°

The measure of the angles x, y, and z will be 115°, 115°, and 65°, respectively.

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Answer:

Step-by-step explanation:

Answer:

1 solution

Step-by-step explanation:

3(2x-7)=9

dustribute: (3)(2)+(3)(-7x)=9

6+-21x=9

subtract 6 from both sides: -21x=3

Divide both sides by -21: x=-1/7

so your 1 solution is x = - 1/7

Answer:

Step-by-step explanation:

Solve each inequality in the system:

The solution is:

The integer solution set is:

[tex]\\ \rm\rightarrowtail 3-2a<13[/tex]

[tex]\\ \rm\rightarrowtail -2a<10[/tex]

[tex]\\ \rm\rightarrowtail -a<5[/tex]

[tex]\\ \rm\rightarrowtail a>-5[/tex]

And

[tex]\\ \rm\rightarrowtail 5a<17[/tex]

[tex]\\ \rm\rightarrowtail a<17/5[/tex]

[tex]\\ \rm\rightarrowtail a<3\dfrac{2}{5}[/tex]

So

solution set

[tex]\\ \rm\rightarrowtail a\in\left(-5,3\dfrac{2}{5}\right)[/tex]

So

Answer:

D. 15(4a + 3)

Step-by-step explanation:

15 is the least possible factorisation for both sides, therefore D is the most efficient on of all of them

Using the GCF and Distributive property, the expression can be factorized as, d. 15 (4a + 3).

GCF is the abbreviated form for Greatest Common Factor.

As the name suggests, GCF of two or more numbers or expressions is the greatest of all the common factors of them.

The given expression is 60a + 45.

Distributive property for 3 numbers, a, b and c states that,

a (b + c) = ab + ac

There are two terms here 60a and 45.

We can find the GCF using Prime factorization.

60 = 2 × 30

     = 2 × 2 × 15

     = 2 × 2 × 3 × 5

45 = 3 × 15

    = 3 × 3 × 5

Common factors are 3 and 5.

GCF = 3 × 5 = 15

60a + 45 = (15 × 4a) + (15 × 3)

               = 15 (4a + 3)    [Using the distributive property]

Hence the factorized form is 15 (4a + 3)  

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The equivalent value of the sum for any value of "x" is 12x - 6

Given the sum of the expression as:

3

∑ k(2x-1)

k=0

We need to take the sum of the function at the point where k = 0 to 3

3

∑ k(2x-1) = 0(2x-1) + 1(2x - 1) + 2(2x-1) + 3(2x - 1)

k=0

3

∑ k(2x-1) = 2x-1+4x-2+6x-3

k=0

3

∑ k(2x-1) = 12x - 6

k=0

Hence the equivalent value of the sum for any value of "x" is 12x - 6

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Answer:

The answer is 8x-3y hope this helps!

The function y = √(x + 2) + 3 is a quadratic function. Then the correct optin is A.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The equation is given below.

[tex]y = (x+2)^{1/2} + 3[/tex]

The equation can be written as

[tex]y - 3= (x+2)^{1/2}[/tex]

Square on both sides, we have

[tex]\begin{aligned} (y - 3)^2 &= [(x+2)^{1/2}]^2 \\\\x + 2 &= y^2 + 9 -6y \\\\x &= y^2 -6y +7 \end{aligned}[/tex]

The equation is a quadratic equation.

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Answer:

A) Quadratic

Explanation:

Hope you have a great day!

Answer:

4.23 x 10 to the 4, 2 x 10 to the 3, 9.2 x 10 to the 6, 4 x 10 to the 3, 8 x 10 to the 7, and 3.2 x 10 to the 10.

Step-by-step explanation:

I will explain in the comments to this response

The Scientific notation of the number 42300 is 4.23×10⁴.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 42300 in Scientific notation as 4.23×10⁴.

2000 in Scientific notation as 2×10³.

9200000 in Scientific notation as 9.2×10⁶.

42300 in Scientific notation as 4.23×10⁴.

4000 in Scientific notation as 4×10³.

80 million=80000000 in Scientific notation as 8×10⁷.

32 billion=32,000,000,000 in Scientific notation as 3.2×10¹⁰.

Therefore, the Scientific notation of the number 42300 is 4.23×10⁴.

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Answer: 297 in.^2

Step-by-step explanation:

Area of a triangle: b*h/2 ---> (9*12)/2=544 triangles--->4*54(area of triangle)= 216Area of square: b*h ----> 9*9 = 81Add area of all four triangles plus are of square-----> 216+81 = 297 in.^2

Answer:

39

Step-by-step explanation:

You find the area by multiplying the length times the height which is what I did 13 x 3 = 39

Answer - 25.761-17.49=?

Then,

the answer is 8.271

The magnitude of the total velocity of the boat is 38 knots, and the direction is 32°, so the correct option is d.

First, we need to write need to find the component of the two given velocities.

For the boat, the magnitude is 28 knots and the angle is 36°, then the components are:

For the wind, the components are:

Adding these, the total components of the boat's velocity are:

Then the magnitude of the velocity is:

|V| = √( (31.92 knots)^2 + (20.21 knots)^2)  =37.78 knots

That can be rounded to 38 knots

To get the angle, we take the arctangent of the quotient between the y-component and the x-component:

a = Atan(20.21 knots/31.92 knots) = 32.34°

Then the correct option is d) 38 knots and 32°

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Answer:

It is 38 knots; 32 degrees

Step-by-step explanation:

The answer below is right

I took the test

Answer:

42

Step-by-step explanation:

If you add all the number in the stem and leaf plot it equals 336 and you divide by how many numbers there are and there are 8 numbers so 336/8=42

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Answer:

1) 18b - 3c - 10

2) [tex]1\frac{3}{4}[/tex]g + 7

3) 0.3y

4) -4n - 5

Step-by-step explanation:

1) 16b + 5c - 10 - 8c + 2b

like terms: 16b + 2b = 18b

like terms: 5c - 8c = -3c

like terms: -10

simplified: 18b - 3c - 10

____________

2) 1/2g + 2g - 3/4 g + 7

like terms: 1/2g + 2g - 3/4g

2 1/2 - 3/4

improper fraction > 5/2 > same denom > 10/4

10/4 - 3/4 = 7/4 > mixed number> 1 3/4g

like terms: +7

simplified: 1 3/4g + 7

____________

3) -0.9y + 4.4y - 3.2y

like terms:  -0.9y + 4.4y - 3.2y

simplified: 0.3y

____________

4) 4 - 8n + 7n - 3n - 9

like terms: -8n + 7n - 3n = -4n

like terms: 4 - 9 = -5

simplified: -4n - 5

____________

Answer:

40 and 67

Step-by-step explanation:

Answer:

4.3< 4.1

Step-by-step explanation:

its 4.1 because 4 is the same and three is greater than one

Answer:

Mean = 8 gerbils

MAD = 4.29 gerbils

Step-by-step explanation:

Find the mean:

Mean= 0+3+6+9+11+13+14 ÷ 7

Mean = 56 ÷ 7

Mean = 8 gerbils

you have to find the distance of each value of gerbil from the mean

8,5,2,1,3,5,6

MAD = 9+6+3+0+2+4+5 ÷ 7

MAD = 30 ÷ 7

MAD = 4.29  gerbils

Answer:

Step-by-step explanation:

is the sign that you mean ÷ ?

if so:

-3×7÷5×1/7

= -21÷5×1/7

=-21/5 × 1/7

= (-21×1) / (5×7)

= -21/35

=-3/5

=-0.6

Answer:

3 hrs and 15 minutes :)

Step-by-step explanation:

We can solve this by multiplying :)

39 x 5 = 195 minutes

195/60 = 3 hrs and 15 minutes :)

Have an amazing day!!

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Answer: 195 minutes or 3 hours and 15 mintues

Step-by-step explanation:

     We will multiply the number of tests by the amount of time it takes to do each test.

     39 total tests * 5 minutes = 195 minutes

           195 minutes or 3 hours and 15 mintues

The height of the trapezoidal is 4.33 feet. Then the area of the tarp to cover the pool is 51.96 square feet.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoidal, one pair of opposite sides are parallel.

A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use.

Then the area of the trapezoidal will be

Area = 0.5(sum of parallel sides) height

Then the height of the trapezoidal will be

[tex]\rm h = 5 \times \sin 60 \\\\h = 4.33 \ ft[/tex]

Then the area of the trapezoidal will be

Area = 0.5 × (10 + 12) × 4.33

Area = 51.96 ft²

The area of the tarp to cover the pool is 51.96 square feet.

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Answer:

1. 120 degrees

2. 4.3

3. 47.3

Step-by-step explanation:

PLATO/EDMENTUM

Answer:

b) angle bisector of angle ABC

One lily is $9

One shrub is $11

Step-by-step explanation:

Let the lillies be x

Let the shrub be y

2x + 6y= 84.........i

6x + 6y = 120..........ii

Lets make x the subject formula in eq(I)

2x= 84- 6y

x = 42 - 3y........iii

Put the value of x into eq (ii)

6(42-3y) + 6y = 120

252 - 18y + 6y= 120

252 - 12y= 120

12y= 252-120

12y= 132

Y= 11

Put the value of Y into eq (I)

2x + 6(11)= 84

2x + 66= 84

2x= 18

X= 9

Therefore,the cost of one day lily is $9 and the cost of one shrub is $11.

Answer:

try using a protractor

Step-by-step explanation:

when you use a protractor it can be easier and collect all like terms together