AOC and BOD are diameters of a circle, centre O.
Prove that triangle ABD and triangle DCA are congruent by RHS.

The translation is of 5 units to the right and 3 units down, it can also be written as:

(x, y) ---> (x + 5, y - 3)

To study the translation, just look at some vertex in both figures.

The top left vertex of F is at (2, 7)

And the top left vertex at G is (7, 4)

Taking the difference between these, we will get:

(7, 4) - (2, 7) = (5,, - 3)

Then the translation from F to G can be defined as:

(x, y) ---> (x + 5, y - 3)

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The length of segment EC is 24 in the given triangle

A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.

3x=2(x+4)

Apply distributive property on RHS

3x=2x+8

Subtract 2x from both sides

x=8

The segment EC =3x

=3(8)

=24

Hence, the length of EC is 24 in the given triangle

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The value of the function f(1/2) for the f(x) = 2 / 5 x- 5 / 2 is equal to -2.3.

Function is equal to,

f(x) = 2 / 5 x- 5 / 2

To get the value of f ( 1 / 2 ) .

Substitute the value of x equals to ( 1 / 2 ) we get,

f(x) = (2 / 5 ) x- ( 5 / 2 )

This implies,

f ( 1 / 2 ) = ( 2 /5 ) × ( 1 / 2 ) - ( 5 / 2 )

⇒ f ( 1 / 2 ) = ( 1 / 5 ) - ( 5 / 2 )

Take the least common multiple of 5 and 2 we get,

least common multiple of 5 and 2 is 10.

⇒ f ( 1 / 2 ) = ( 2  - 25 ) / 10

⇒ f ( 1 / 2 ) = -23 /10

⇒ f ( 1 / 2 ) = -2.3

Therefore, the value of f(1/2) for the given function is equal to -2.3.

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The above question is incomplete, the complete question is:

Consider the function: ƒ(x) = 2/5 x- 5/2 find the value of f( 1/2)?

Don would take 1500 minutes to fill the 1000-gallon water tank using the 2-gallon bucket.

If the capacity of the water tank is 1000 gallons and Don uses a bucket that can hold 2 gallons to fill the tank, we can calculate the number of buckets Don needs to fill the tank.

Let's assume the number of buckets Don needs to fill the tank is represented by 'n'.

Capacity of the tank = 1000 gallons

Capacity of each bucket = 2 gallons

Number of buckets needed to fill the tank, n = Capacity of the tank / Capacity of each bucket

n = 1000 gallons / 2 gallons

n = 500

So, Don needs 500 buckets, each holding 2 gallons, to fill the 1000-gallon water tank.

Given that it takes Don 3 minutes to fill the bucket with water and pour it into the tank, the total time taken by Don to fill the tank would be the product of the number of buckets (500) and the time taken to fill each bucket (3 minutes).

Total time taken to fill the tank = Number of buckets × Time taken to fill each bucket

Total time taken = 500 × 3 minutes

Total time taken = 1500 minutes

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Answer:

B 2

Step-by-step explanation:because a quart is 0.25 of a gallon

The requried class average is 83.2 points.

To find the class average, we need to calculate the total number of points earned by all the students and divide by the total number of students.

The 12 students who scored 80 points earned a total of 12 × 80 = 960 points.

The 8 students who scored 88 points earned a total of 8 × 88 = 704 points.

The total number of points earned by all the students is 960 + 704 = 1664 points.

The total number of students is 12 + 8 = 20.

To find the class average, we divide the total number of points by the total number of students:

average = total points / total students

average = 1664 / 20

average = 83.2

Therefore, the class average is 83.2 points.

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Answer: x = -5, 5 y= 0

Step-by-step explanation:

vertical asymptotes = x= -5, 5

horizontal asymptotes = y= 0

The number of residents Town A used to have is 1400, and the number of residents Town B used to have is 3600, as shown by the simple equation below.

Let x be the number of residents Town A used to have. The number of residents in Town B is:

5000 - x

We know that Town A had 12% whites and Town B had 10% whites. After the merge, the percentage of whites is 10.56%. With that in mind:

12%x+10%(5000-x) = 10.56%(5000)

0,12x + 500 - 0,1x = 528

0.02x = 28

x = 1400

Therefore, the number of residents Town A used to have is 1400. Now, the number of residents town B used to have is:

5000 - 1400 = 3600

With that in mind, we can conclude our answer is correct.

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The contrapositive statement is option D

If the hypothesis and conclusion of an earlier conditional statement are reversed, a contrapositive statement is produced.

Technically speaking, the contrapositive of a conditional statement that starts with "If p, then q" is "If not q, then not p." The initial assertion and its contrapositive, then, are both true because they are logically equivalent.

Thus the contrapositive statement as shown is the statement ~q ~p

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(-35z⁴x + 32z⁴x⁶) divided by  -4z³x⁵ gives {(35z - 32zx⁵)/ (4x⁴)} by applying simple rule of division of polynomials.

Let the given polynomial be written as,

f(z,x) = -35z⁴x + 32z⁴x⁶

g(z,x) = -4z³x⁵

Here the functions of the given polynomial are composed of two variables, namely x and z, so the functions are denotes likewise.

We can divide the polynomial f(x) by g(x) by the division method as,

[tex]\frac{f(z,x)}{g(z,x)}[/tex] = (-35z⁴x + 32z⁴x⁶) / ( -4z³x⁵)

= { (-35z⁴x)/ ( -4z³x⁵) } + {(32z⁴x⁶)/ ( -4z³x⁵)}

= [tex]\frac{35z}{4x^4}[/tex] + [tex]\frac{-8zx}{1}[/tex]

= [tex]\frac{35z - 32zx^5}{4x^4}[/tex]

or, =  {(35z - 32zx⁵)/ (4x⁴)}

Thus the required value of (-35z⁴x + 32z⁴x⁶) divided by  -4z³x⁵ is {(35z - 32zx⁵)/ (4x⁴)}

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The expanded form of 12³ is given as follows:

12³ = 12 x 12 x 12 = 1728 cubic feet.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

This expression is equivalent to multiplying the side length of the object by itself twice, as follows:

V(a) = a x a x a.

The side length for this problem is given as follows:

a = 12 feet.

Hence the volume of the cube is given as follows:

V = 12³ = 1728 feet³.

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Answer: the last option is correct

Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:

r = √((-7√3/2)^2 + (7/2)^2)

θ = atan2(7/2, -7√3/2)

Simplifying the expressions:

r = √(147/4 + 49/4) = √(196/4) = √49 = 7

θ = atan2(7/2, -7√3/2)

Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:

θ ≈ 5π/6

So the correct answer is: (7, 5π/6), which is option (6).

The length of the base of the right-angle triangle will be 1 / 2 inches.

Since, We know that;

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

So, The area of the right-angle triangle is given as

A = 1/2 x B x H

Where B is the base and H is the height of the right triangle.

The area of the triangle below is 1/8 square inches. And the length of the perpendicular will be 1/2 inches.

Then the length of the base will be;

A = 1/2 x B x H

1/8 = 1/2 x B x 1/2

1/8 = 1/4 x B

B = 1/2

Thus, The length of the base of the right-angle triangle will be 1/2 inches.

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The requried, justification for the given function has been shown below.

(a) Yes, R₁ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is 0 in this case.

(b) No, R₂ does not define a function. For some values of n, there may be multiple animals with n legs, so there is no unique output for each input.

(c) Yes, R₃ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is the remainder of n divided by 5.

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The slope of f(x) is less than the slope of g(x).

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know two points on a line, then the slope is equal to the quotient between the difference of the y-values and the difference of the x-values.

So the slope of f(x) is:

a = (3 - 0)/(0 + 2) = 3/2

And g(x) = (4/5)*x - 2

So here the slope is 4/5

We can see that clearly the slope of g(x) is larger.

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The side length ZW is 6 units and the side length WX is 10.392 units. Then the area of the rectangle is 62.352 square units.

Given that:

Diagonal, d = 12

Angle, α = 30°

The rectangle's area will be given as,

Area of the rectangle = L × W square units

The measure of the side length ZW is calculated as,

sin 30° = ZW / 12

ZW = 6 units

The measure of the side length WX is calculated as,

cos 30° = WX / 12

ZW = 10.392 units

The area of the rectangle is calculated as,

A = 6 x 10.392

A = 62.352 square units

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Answer:

Step-by-step explanation:

no higher than 4

Answer: option b

Step-by-step explanation:

Answer:

18q + 27

Step-by-step explanation:

9(2q + 3)

9 x 2q = 18q

9 x 3 = 27

18q + 27

: )

Answer:

Step-by-step explanation:

The new mixture contains 34% peanuts. The correct option is A

The idea of weighted averages can be applied.

First, let's determine the mixture's entire weight:

Total weight = 4 kg + 12 kg = 16 kg

We can now calculate how many peanuts there are overall in the mixture:

Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Finally, we can find the percentage of peanuts in the mixture:

Percent of peanuts = (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

   = 34%

Therefore, the new mixture contains 34% peanuts, which is option A.

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The ordered pair that would best represent the location of point E' is (8z, 4z).

A graph of the vertices of the dilated image is shown in the image below.

The rule that best represent the dilation of quadrilateral WXYZ to quadrilateral W'X'Y'Z'.

In Mathematics and Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 5/2 centered at the origin as follows:

Ordered pair W (-2, 1) → Ordered pair W' (-2 × 5/2, 1 × 5/2) = W' (-5, 5/2).

Ordered pair X (2, 2) → Ordered pair X' (2 × 5/2, 2 × 5/2) = X' (10, 10).

Ordered pair Y (1, -1) → Ordered pair Y' (1 × 5/2, -1 × 5/2) = Y' (5/2, -5/2).

Ordered pair Z (-2, -2) → Ordered pair Z' (-2 × 5/2, -2 × 5/2) = Z' (-5, -5).

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Answer:

b)

Step-by-step explanation:

a) y = 4x +1 y= -4x + 1

Different slopes; same y-intercept; lines intersect at 1 point; there is 1 solution.

b) y= 2x + 7 y= 2x - 7

Same slopes; different y-intercepts; parallel lines do not intersect; no solution.

c) 3x + y =1 6x + 2y =2

Equations are the same; infinite number of solutions.

d) 5x + y =3 x + 5y = 15

Different slopes; lines intersect at 1 point; there is 1 solution.

Answer: b)

The distance between the points (1, 2) and (10,-10) is 15 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, we have the following;

Distance = √[(10 - 1)² + (-10 - 2)²]

Distance = √[(9)² + (-12)²]

Distance = √[81 + 144]

Distance = √225

Distance = 15 units.

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Answer:

28(17) + π(7^2)

= 476 + 49π square meters

= 629.94 square meters

The value of x is, x = 6 ft

Now, We can formulate;

Area of the polygon = area of the square + 2(area of the triangle)

Here, We have;

Area of the polygon = 176 ft²

So, Area of the square = length × width

                                   = 16 × 8

                                  = 128

And, Area of the two triangles = 2( 1/2 x base x height)

                                               = 2(1/2 × x × 8)

                                               = 8x

Now, Plug in the above values into the equation for area of the polygon.

Thus: We get;

176 = 128 + 8x

Subtract 128 from each side

176 - 128 = 8x

48 = 8x

Divide both sides by 8

6 = x

x = 6 ft

Thus, The value of x is, x = 6 ft

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The triangle triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Triangle ∆BCD is not similar to the triangle ∆BTS, BT does not correspond to BC, and BS does not correspond to BD. Also, the angle m∠SBT does not correspond to m∠DBC.

Therefore, the triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

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