Triangle ABC is rotated 90° counterclockwise about the origin to produce triangle A'B'C'. Then, triangle A'B'C' is dilated by a scale factor of 1/2 with respect to the origin to produce A''B''C''.
Write coordinates of each vertex in the final image.
A"
B"
C"

If a point's preimage is P(x, y), then its image after a dilation with a scale factor of k and centered at the origin (0, 0) is P'(kx, ky).

The set of all points in a function's domain that correspond to a given point in the range is known as the preimage of a point in mathematics.

Formally, let f be a function that goes from a set A to a set B, and let y be a point in B. The preimage of y is the set of all points x in A where f(x) = y, or the set of all points in the domain that the function maps to the given point in the range.

If the preimage of the point P has facilitates (x, y), and the expansion focused at the beginning with a scale component of k is applied, then the directions of the picture point P' can be tracked down utilizing the accompanying recipe:

The x- and y-coordinates of P' are determined by multiplying the corresponding coordinates of the preimage point P by the scale factor k; consequently, the coordinates of the image point P' following the dilation with the origin centered on k would be (kx, ky).

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Complete question: If P(x,y) is the preimage Of a point, then it’s image after a dilation centered at the origin (0,0) with the scale factor k is the point P'.

What are the coordinates of point P'?

Answer:

I think it will help u (:

Step-by-step explanation:

Assuming the given measurement is the diameter of the sphere, we can find the radius as follows:Radius (r) = Diameter / 2 = 7.2 / 2 = 3.6 cmThe formula for the volume of a sphere is:V = (4/3) * π * r³Substituting the values, we get:V = (4/3) * 3.14 * (3.6)³

V = 4.19 * 46.656

V = 195.4 cm³Rounding this to the nearest tenth, we get:V ≈ 195.4 cm³Therefore, the volume of the sphere is approximately 195.4 cm³.

Step-by-step explanation:

Vertical angles are equal soooo   1 and  3 are equal = 102 degrees

 then    1 plus 2  forma straight line = 180 degrees

    so 2 = 78 degrees

       then vertical angles again, 2 and 4 are equal = 78 degrees

Answer:

Isabelle is taking a survey to find the most popular music group of students in her community. Which of these is not a way for her to get a representative sample of this information?

 ask every tenth student she sees ac a concert

 ask every fifth student entering her school in the morning

 ask every third student she encounters at the mall

 ask every student at a local movie theater

Step-by-step explanation:

Answer:

In the images

Hope this helps!

Step-by-step explanation:

Clockwise is the direction the arrow is pointing, counter-clockwise is the other direction.

Answer:

Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.

Answer:

1st option

Yes, Triangle CAB is congruent to triangle DAB by the SAS Congruence Theorem, so line segment BC is congruent to line segment BD. This means that line segment AB is a perpendicular bisector of line segment CD.

Answer:

For the binomial with a degree of 35 it would be 2x35+4

For the monomial with a degree of 100 would be 5y100

Step-by-step explanation:

Answer:

the value for p will be 162

The question that can be answered by finding 10 divided by 2 11/20 is "What is the simplified value of 10 divided by 2 11/20?" and the answer is "7 43/51".

A mixed number is a representation of both a whole integer and a legal fraction. In most cases, it denotes an integer that falls between any two whole numbers. Look at the illustration; it shows a fraction that is larger than 1 but less than 2 (see the given image). Therefore, it is a composite number.

The expression "10 divided by 2 11/20" can be simplified as a mixed number or fraction as follows:

10 divided by 2 11/20 = 10 ÷ (2 + 11/20)

= 10 ÷ (40/20 + 11/20)

= 10 ÷ (51/20)

= 10 × (20/51)

= 400/51

= 7 43/51 (in mixed number form)

Therefore, the question that can be answered by finding 10 divided by 2 11/20 is "What is the simplified value of 10 divided by 2 11/20?" and the answer is "7 43/51".

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Step-by-step explanation & Answer

f(x) = x² - 4x -5, factored is simply f(x) = (x - 5)(x + 1).

If you zero out f(x), namely 0=(x-5)(x+1), that simply gives you the zeros of 5 and -1.

Now, from ----- -1------0---------------------------------5,

Notice from -1 to 5, there are 6 units, and half of 6 is 3, so, the half-way is 3 units away from either zero.

We can get to the half-way point by -1 + 3, or 2, x = 2, that's where the vertex is at, but you already knew that, and of course the y-coordinate is at f(2) = (2)² - 4(2) - 5, which is -9, so the vertex is indeed at (2, -9).

Well, surely you can, simply use the zeros location, -1 and 5, and draw a bowl between them, with the bottom of the bowl at 2, -9.

The car wheel will make approximately 840 revolutions as the car travels a distance of one mile.

To calculate the number of revolutions that a car wheel of diameter 24 in. will make as the car travels a distance of one mile, we need to use the formula:

number of revolutions = distance traveled / distance per revolution

The distance traveled is given in miles, and we need to convert the diameter of the wheel, given in inches, to the distance per revolution in miles.

The diameter of the wheel is 24 in., which means the radius is 12 in. The distance per revolution is equal to the circumference of the wheel, which is given by the formula:

circumference = 2 * pi * radius

Substituting the values, we get:

circumference = 2 * pi * 12 in. = 75.4 in.

To convert this to miles, we divide by 63,360 inches per mile:

distance per revolution = 75.4 in. / 63,360 in./mi = 0.00119 mi/rev

Now, we can calculate the number of revolutions as:

number of revolutions = 1 mi / 0.00119 mi/rev ≈ 840 revolutions

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Answer:

the area of the trapezoid is (3/2)x^2 + 2x square units.

Step-by-step explanation:

Let's use "x" to represent the height of the trapezoid. According to the problem, one base measures 5 feet more than the height, so we can use "x + 5" to represent the length of that base. The other base is one foot less than twice the height, so we can use "2x - 1" to represent the length of that base.

The area of a trapezoid is given by the formula:

Area = (1/2)(sum of the bases)(height)

Substituting the expressions for the bases and the height, we get:

Area = (1/2)(x + 5 + 2x - 1)(x)

Simplifying the expression inside the parentheses, we get:

Area = (1/2)(3x + 4)(x)

Expanding the expression, we get:

Area = (3/2)x^2 + 2x

the area of the trapezoid is (3/2)x^2 + 2x square units.

Step-by-step explanation:

See image

The number of electoral votes does the state of nevada have in the electoral college is 6 electoral votes.

Nevada will be having a total of 6 electoral votes in the electoral college. The number of electoral votes for each state is equal to the total number of its members in Congress, which will be including its representatives in the House of Representatives and its two senators.

Therefore, since Nevada has 4 members in the House of Representatives and 2 senators, the state has a total of 6 members in Congress, and hence it can be concluded that a total of 6 electoral votes will be there in the Electoral College.

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Step-by-step explanation:

You will need to find  two lengths of corresponding sides

LH =  sqrt 5

L'H' = sqrt(20)    which is four times larger than sqrt5

scale factor 4

The minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).

Calculating the sum of two or more numbers is the procedure of multiplication. It is expressed as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.

The given values are:

A = 900 rounded to the nearest 10 = 900

B = 90.7 rounded to 1 decimal place = 90.7

We need to find the minimum value of AxB.

Multiplying A and B directly, we get:

AxB = 900 x 90.7 = 81,630

To find the minimum value of AxB, we can use the concept of AM-GM inequality which states that for two positive real numbers a and b, their arithmetic mean (AM) is greater than or equal to their geometric mean (GM):

AM ≥ GM

or

(a+b)/2 ≥ √(ab)

Applying this to our values of A and B, we get:

(A+B)/2 ≥ √(AxB)

Substituting the given values of A and B, we get:

(900 + 90.7)/2 ≥ √(AxB)

Simplifying this, we get:

495.35 ≥ √(AxB)

Squaring both sides, we get:

245,376.72 ≥ AxB

Therefore, the minimum value of multiplication of AxB is 245,376.72, which is obtained when A = 450 (rounded down from 495) and B = 545 (rounded up from 537.03).

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Complete question:

A = 900 rounded to the nearest 10

b = 90.7 rounded to 1 DP

Find the minimum of a x b​

the answer would be b.

Answer:

1/2 it’s like flipping a coin it can either come up heads or tails.

Step-by-step explanation:

The probability that the other child is a daughter is 1/2 or 50%.

The gender of each child is independent, and there are two equally likely outcomes for each child (male or female). Therefore, the probability of having a son is 1/2 and the probability of having a daughter is also 1/2. Since one child is already known to be a son, that does not affect the probability of the other child being a daughter. Thus, the probability of having a daughter as the other child is also 1/2 or 50%.

Therefore, the answer to the question is that the probability that the other child is a daughter is 1/2 or 50%

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Answer:

Here is the correct answer:

15 m, 20 m, 25 m

Answer:

It is 9 1/4

Step-by-step explanation:

This is because 9 stays the same as the whole number, and 25 divided by 100 is 4. To check our work we can multiply 25 by 4 to get 100. Now we know we have the right answer.

"The beautiful part of learning is that no one can take it away from you" (:

Answer:

(- 12, - 16 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

(- 12, 16 ) → (- 12, - 16 )

Answer:

x=2

Step-by-step explanation:

33=32x-31

64=32x

2=x

Answer:  [tex]x = 2[/tex]

Answer: To have infinitely many solutions, the equation must simplify to a true statement, such as 0=0.

So, let's simplify the given equation:

4(x-4) = 4x + ?

We need to choose a value for the constant on the right-hand side so that the equation simplifies to a true statement.

We can start by distributing the 4 on the left-hand side:

4x - 16 = 4x + ?

Now we can see that the 4x terms cancel out, leaving:

-16 = ?

We can choose any value for the constant on the right-hand side, and the equation will be true. For example:

-16 = -16

So the complete equation with infinitely many solutions is:

4(x-4) = 4x - 16

Step-by-step explanation:

The total surface area of the triangular prism is 200 square inches.

A triangular prism is a three-dimensional geometric shape that consists of two parallel triangular bases connected by three rectangular faces.

To find the surface area of the triangular prism using the net provided, we need to find the area of each face and then add them together.

Using formulas,

Area of rectangle= [tex]length\times width[/tex] square unit.

Area of triangle = [tex]\frac{1}{2}\times Base \times Height[/tex] square unit.

The blue rectangle has a length of 5 inches and a width of 4 inches, so its area is

=> 5 x 4 = 20 square inches.

The orange rectangle has a length of 12 inches and a width of 4 inches, so its area is

=> 12 x 4 = 48 square inches.

The red rectangle has a length of 13 inches and a width of 4 inches, so its area is

=> 13 x 4 = 52 square inches.

The green triangles have a base of 12 inches and a height of 5 inches, so each triangle's area is

=> [tex]\frac{1}{2}\times12\times5[/tex]=  30 square inches.

To find the total surface area, we add the area of each face:

=> 20 + 20 + 48 + 52 + 30 + 30 = 200 square inches.

Therefore, the surface area of the triangular prism is 200 square inches.

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The area of triangle PQR is 25/2 * √(5).

In geometry, a triangle is a two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and has many important properties and applications.

The sum of the interior angles of a triangle is always 180 degrees, and the exterior angles sum to 360 degrees. The three sides of a triangle can be classified according to their lengths and their angles.

To find the area of triangle PQR, we can use the formula:

Area = (1/2) * base * height

where the base and height are the lengths of two sides of the right triangle that meet at a 90-degree angle.

We can use the distance formula to find the lengths of the sides of triangle PQR:

PQ = √[(x_Q - x_P)² + (y_Q - y_P)²] = √[(-1 - (-6))² + ((-1) - 9)²] = √[25 + 100] = 5√(5)

PR = √[(x_R - x_P)² + (y_R - y_P)²] = √[(-9 - (-6))² + (5 - 9)²] = √[9 + 16] = 5

QR = √[(x_R - x_Q)² + (y_R - y_Q)²] = √[(-9 - (-1))² + (5 - (-1))²] = √[64 + 36] = 2√20) = 4√(5)

Since triangle PQR is a right triangle, the base and height are PQ and PR, respectively. Therefore, the area of triangle PQR is:

Area = (1/2) * PQ * PR = (1/2) * 5√(5) * 5 = 25/2 * √(5)

So the area of triangle PQR is 25/2 * √(5).

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Answer:

Step-by-step explanation:

125,000 x 16% = $20,000

(23%) 28,750 + (8%) 10,000 + (9%) 11,250 + (12%) 15,000 + (16%) 20,000 + (19%) 23,750 + (13%) 16,250 = $125,000

a) 1)  x=0 or x=-2 ,    2) x=0 or x=2    3)  x=0 or x=-2    4) x=0 or x=-2  

b) 1) x=0 or x=-5/3   2)x=0 or x=5/3   3) x=0 or x=5/3  4) x=0 or x=-5/3 .this equations can be solved by factorization and simplification.

what is factorization?

Factorization is the process of expressing a given number or algebraic expression as a product of two or more factors. The factors are the numbers or expressions that when multiplied together result in the original number or expression.

In the given question,

a) x²+2x=0:

x(x+2)=0

x=0 or x=-2

x²-2x=0:

x(x-2)=0

x=0 or x=2

x²+2x=0:

x(x+2)=0

x=0 or x=-2

-x²-2x=0:

-x(x+2)=0

x=0 or x=-2

b)

3x²+5x=0:

x(3x+5)=0

x=0 or x=-5/3

3x²-5x=0:

x(3x-5)=0

x=0 or x=5/3

-3x²+5x=0:

x(-3x+5)=0

x=0 or x=5/3

-3x²-5x=0:

x(-3x-5)=0

x=0 or x=-5/3

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After answering the presented question, we can conclude that As a expression result, the laptop costs $2500 without GST.

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To get the laptop's price without GST, divide the inclusive price by (1 + GST rate as a decimal).

As a result, the laptop's price without GST can be estimated as follows:

Price excluding GST = Price including GST / (1 + GST rate as a decimal)

Price excluding GST = 2675 / (1 + 0.07)

Without GST, the price is $2500.

As a result, the laptop costs $2500 without GST.

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