2. Rotate the following points 180°.

a.) B(-2,-5) →B'( )
b.) B(-4,1) B'( )

c.) In the graphs above connect the pre-image point B to the origin. Then connect
the origin to the image point B. What angle has been formed?

Answer:

D

Step-by-step explanation:

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

Polynomials can be expressed as a product of binomials of the form (x - r) multiplied by a leading coefficient. The least polynomial contain the number of roots presented in statement, whose factor form is shown below:

f(x) = 1 · (x + 3)³ · x³ · (x - 3)

f(x) = (x + 3)³ · (x⁴ - 3 · x³)

f(x) = (x³ + 9 · x² + 27 · x + 27) · (x⁴ - 3 · x³)

f(x) = x⁷ + 9 · x⁶  + 27 · x⁵ + 27 · x⁴ - 3 · x⁶ - 27 · x⁵ - 81 · x⁴ - 81 · x³

f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

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The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

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

The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:

y = ax² + bx + c

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

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Answer:

The correct answer is A:3

Step-by-step explanation:

Answer:

The solution for the expression is choice D 26√5 +2√10

Step-by-step explanation:

Hello!

First, apply distributive law: a(b+c)= ab+ac

The coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).

The midpoint of AB,  given any points A (x₁, y₁) and B(x₂, y₂) is given as point M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).

In the question, we are given that the midpoint of PQ is (-3, 1) and point Q is (7, 5).

We are asked to find the coordinates of point P.

We assume the coordinates of point P as (x, y).

Thus, the midpoint of PQ = ({(x + 7)/2}, {(y + 5)/2}),

that is, (-3, 1) = ({(x + 7)/2}, {(y + 5)/2}).

Thus, we can show that:

(x + 7)/2 = -3,

or, x + 7 = -6,

or, x = -6 - 7 = -13.

(y + 5)/2 = 1,

or, y + 5 = 2,

or, y = 2 - 5 = -3.

Thus, the coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).

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Step-by-step explanation:

since there are z fishes

the number of angelfish = 1 × z

4

= 1 z

4

The average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

a. Average force

Using  this formula

Force (F) = Mass ×Acceleration

Where:

Mass (m) = 57 g = 57 / 1000= 0.057 Kg

Acceleration (a) = u / t = 50 / 0.05 = 1000 m/s²

Let plug in the formula

Force (F) = 0.057 × 1000

Force (F) = 57 N

b. Resistive force

F = m(v – u) / t

Where:

Force (F) = ?

Mass (m) = 3000 Kg

Initial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/s

Final velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/s

Time (t) = 40s

Let plug in the formula

Force = 3000(5 – 20) / 40

Force = 3000(-15) / 40

Force=-45,000/40

Force = -1125 N

Therefore the average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.

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Answer: No solutions

Step-by-step explanation: there would be no solutions, because these equations have the same slope and different y-intercepts, so they would end up being parallel from each other, and would never intersect or be equivalent.

Answer:

No solution.

Explanation:

Given equations:

(1) y - 4x = -3

(2) y = 4x + 7

Substitute equation 2 into 1

y - 4x = -3

4x + 7 - 4x = -3

7 = -3

As L.H.S ≠ R.H.S, There are no solution.

The lines are parallel and do not intersect each other. Their slope is same.

All expressions whose sum represents the same vector as (r + s) + t. is Option b,c,e

Where

r= (2,3)

s= (5,-3)

t= (-8,6)

Generally, the equation for statement is  mathematically given as

(7,0)+(-8,6) ,(2,3)+(-3,3) and (-6,9)+(5,-3) are equal to (r+s)+t

Therefore

x=(2,3)+(5,-3)

x=(7,0)

Now we can calculate (r+s)+t as

(7,0)+(-8,6)

(7-8,0+6)

(-1,6)

For (b)

x=(7,0)+(-8,6)

x=(-1,6)

in this scenario x expressions is equal to (r+s)+t

For (c)

x=(2,3)+(-3,3,)

x=(-1,6)

in this scenario x expressions is equal to (r+s)+t

For (e)

[tex]x=(-6,9)+(5,-3)[/tex]

x=(-1,6)

in this scenario x expressions is equal to (r+s)+t

In conclusion, all expressions whose sum represents the same vector as (r + s) + t. is b,c,e

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Answer:

  (c)  0.18

Step-by-step explanation:

If the x-values are exhaustive, then the p(X=x) values must total 1.00.

  0.11 +? +0.62 +0.09 = 1.00

  0.82 +? = 1.00 . . . . . . . simplify

  ? = 0.18 . . . . . . . . . subtract 0.82

P(X=3) = 0.18

The price of shirt is $12 and the price of tie is $2.5.

According to the statement

We have given that:

Let money spent on shirt = X and money spent on tie is Y.

So, 6X + 3Y = $79.5 and 3X + 2Y = $41 then

We have to find the the cost of each shirts.

Here we use the Elimination method.

Now,

6X + 3Y = $79.5  -(1)

3X + 2Y = $41  -(2)

By elimination method

Multiply (1) by 3 and (2) by 6 then

18X + 9Y = $238.5

18X + 12Y = $246

Then solve it and equation become

-3Y = -$7.5

Y = 2.5

It means the cost of tie is $2.5 and now the cost of shirt is

6X + 3Y = $79.5  

6X + 3(2.5) = $79.5  

6X + 7.5 = $79.5  

6X = $72

X = $12.

So, The price of shirt is $12 and the price of tie is $2.5.

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Answer:

a) Height of the ledge is 1.6 m.

b) roots of the equation are: [tex]\bf d = 2[/tex] ,  [tex]\bf d = -1[/tex]

c) Maximum height reached = 1.8 m.

Step-by-step explanation:

a) The height of the ledge is the same as the height at which Jake is when he hasn't moved any horizontal distance from the ledge yet, that is, when d = 0:

[tex]h = -0.8(0)^2 + 0.8(0) + 1.6[/tex]

⇒ [tex]\bf h = 1.6 \space\ m[/tex]

∴ Height of the ledge is 1.6 m.

b) The x-intercepts occur where y = 0, that is when h = 0:

[tex]-0.8d^2 + 0.8d + 1.6 = 0[/tex]

Divide both sides of the equation by -0.8:

[tex]d^2 - d -2 = 0[/tex]

Factorizing:

⇒ [tex]d^2 -2d + d - 2 = 0[/tex]

⇒ [tex]d(d-2) +1 (d-2) = 0[/tex]

⇒ [tex](d-2)(d+1) = 0[/tex]

⇒ [tex]d - 2 = 0[/tex]    or    [tex]d + 1 = 0[/tex]

∴ roots are :  [tex]\bf d = 2[/tex]   ,   [tex]\bf d = -1[/tex]

c) To find the maximum value of a quadratic equation in the form

y = ax² + bx + c , use the formula:

max = c - (b² / 4a).

Using the formula for [tex]h = -0.8x^2 + 0.8x + 1.6[/tex] :

max h =  [tex]1.6 - ( \frac{0.8^2}{4(-0.8)} )[/tex]

       = 1.8

∴ Maximum height reached = 1.8 m.

Answer:

  a) 1.6 m

  b) -1, 2 meters

  c) 1.8 m

Step-by-step explanation:

Apparently, technology tools are allowed when solving this problem. They readily show you the x- and y-intercepts and the vertex of the graph.

The height of the ledge is the value of h when d=0. It is the constant in the given equation, and the y-intercept of the graph.

The height of the ledge is 1.6 meters.

The x-intercepts are the values of d that make h equal to zero. The graph shows them to be ...

 d = -1

  d = 2 . . . . meters

The maximum height is the "h" coordinate of the vertex (d, h).

The maximum height is 1.8 meters.

__

Additional comment

"x" is the generic independent variable. The horizontal axis of a graph is often called the "x-axis" and places where the graph crosses that axis are called "x-intercepts" even when the independent variable is named something else. Here, the independent variable is "d", not "x".

Similarly, "y" is the generic dependent variable, and the vertical axis of a graph is often called the "y-axis" even when the dependent variable is something else. This is why we refer to h when d=0 as the "y-intercept". It is the point where the graph crosses the vertical axis.

Answer:

[tex]a=22, b=11\sqrt{3}[/tex]

Step-by-step explanation:

Given a 30-60-90 triangle, the shortest side is always opposite of the smallest angle, in this case 11 is opposite the 30° angle. The largest side of a 30-60-90 triangle will always be twice the smallest, giving [tex]a[/tex] a measure of [tex]22[/tex]. To get the side across the 60° angle we multiply the smallest side by the square root of 3. Meaning [tex]b=11\sqrt{3}[/tex]

Using the Pythagorean theorem, the length of line segment FJ is: 42 ft.

To find the length of line segment FJ, we need to apply the Pythagorean theorem to find the length of the segment from F to the point, say point O, on FJ where a right triangle FOG will be gotten.

Thus, we have:

FO = √(GF² - GO²)

FO = √(30² - 24²)

FO = 18 ft.

FJ = FO + GH

Plug in the values

FJ = 18 + 24

FJ = 42 ft.

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Answer:

1/3

Step-by-step explanation:

The numbers are 1, 2, 3, 4, 5, and 6.

Both 3 and 6 are multiples of 3.

So, 2/6 is the probability since there is an equal change that the arrow will land on each section.

This simplifies to 1/3.

Brainliest, please :)

Answer:

P (multiple of 3) =  [tex]\bf \frac{1}{3}[/tex]

Step-by-step explanation:

Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6}    (6 elements)

Multiples of 3 = {3, 6}   (2 elements)

P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner

                          =  [tex]\frac{2}{6}[/tex]

                          =  [tex]\bf \frac{1}{3}[/tex]

The equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

The formula for finding the equation of a circle is expressed as:

(x-a)² + (y - b)² = r²

where

(a, b) is the centre

r is the radius

Given the following

(a, b) = (0, 0)

r = 12.5/2 = 6.25

Substitute

(x-0)² + (y - 0)² = 6.25²

x²+y²=39.0625

Hence the equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

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The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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Considering an inverse proportional relationship, you find k taking a point (x,y), and multiplying the values of x and y.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For an inverse relationship, the function is:

[tex]y = \frac{k}{x}[/tex].

Then:

k = xy.

Which means that to find k, you take a point (x,y), and multiply the values of x and y.

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Answer: B

Step-by-step explanation:

A) False. Rotations do not preserve parallelism.

B) True. Rotations are rigid motions and thus preserve angle measure.

C) False. A rotation that changes the location of every point except for the center of rotation.

These districts are best characterized as Proportional Representation districts.

What is Proportional Representation?

There are numerous types of proportional representation systems, but they all have two things in common. They start by using districts with multiple members.

Proportional Representation, abbreviated as PR, uses significantly bigger districts that elect multiple members at once, such as five or ten, rather than electing one member of the legislature in each local district. Second, the percentage of votes a party receives in these districts with several members determines which candidates gain the seats.

The Proportional Representation system of America overcomes the wide ranging drawbacks of single-district voting system like not representing the  large number of voters, discrimination against third parties, etc.

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Answer:

Domain: [0,∞)

Range: (-∞, 4]

Step-by-step explanation:

The required domain and range of the function shown in the graph are,
Domain = (0, ∞)
Range = (-∞, 4)

To calculate the domain and range of a function from its graph, you can follow these steps:

So, from the above definition, from the graph we have,
Domain = (0, ∞)
Range = (-∞, 4)

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Beau can wrap 32 inches of ribbon outside the mirror.

Area of Beau Thai's mirror is 60 sq. inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Given information:

Length of mirror = 6 inches

Width of mirror = 10 inches

To Find:

The amount of ribbon Beau could wrap around the outside of the mirror.

Perimeter of the mirror = 2(6+10)

                                       = 2(16)

                                       = 32 inches

The area of Beau Thai's mirror.

Area of the mirror = 6*10

                              = 60 sq. inches

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total expenses= 1/4 + 1/8

the denominators should be equal to add the values.

1/4×2(divide both the numerator and denominator by two)

=2/8

=2/8+1/8

3/8//

3/8(fraction of the salary he spent)

3/8 of the salary

3/8×50,000

R.s 6250

balance = 50,000-6,250

= R.s 43,750//

Answer:

x = 2 or x = -1/4

Step-by-step explanation:

Let's solve your equation step-by-step.

4x2−7x−2=0

For this equation: a=4, b=-7, c=-2

4x^2+−7x+−2=0

Step 1: Use quadratic formula with a=4, b=-7, c=-2.

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

[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-2)} }{2(4)}[/tex]

[tex]x=\frac{7\pm\sqrt{81} }{8}[/tex]

x = 2 or x = -1/4

Answer:

x = 2 or x = -1/4

Answer:

11.2 square meters

Step-by-step explanation:

This is a very simple question. Basically, it's the area of a rectangle with the area of a circle subtracted. The area of a circle is calculated with the following formula:

[tex]\pi \times r^{2} [/tex]

Where r is the radius. We know the diameter is 1m, so we can simply halve this value to find the radius of 0.5m. Substituting in this value, we find the area of the circle to be:

[tex]\pi \times {0.5}^{2} \approx0.78539816339744830961566[/tex]

Now let's calculate the area of the rectangle, which is simply 3x4=12. Subtracting our earlier value from 12, we are left with an answer of 11.2 (to 1 d.p)

It can be proved that Circles X and Y are similar.

We were told that circle Y have a  radius of s

And X have the  Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y  by making a division on the  radii of both circles.

Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are similar

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Based on the information in the table, an example of independent events is  the: P(policer officer and chooses car).

An independent event can be defined as an event that isn't dependent on other events. Thus, it isn't affected by any previous event.

Based on the information provided, we can infer and logically deduce that an example of independent events is  the probability of being a policer officer and chooses a car because they aren't overlapping probabilities.

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The value of angle CFE in the diagram attached is 51 degrees.

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

From the diagram:

∠AFB = ∠CFD; ∠BFC = ∠DFE

Hence:

∠AFC = ∠CFE

∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB

90 = ∠AFC + 31

∠AFC = 51° = ∠CFE

The value of angle CFE in the diagram attached is 51 degrees.

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