Find the angle of rotation about the center of the regular pentagon that maps A to D.

Answer:

M(2, −4), N(−2, 4)

Step-by-step explanation:

Transformation is the movement of a point from one place to another. If an object is transformed, all the points of the object are being changed. There are different types of transformation which are: Reflection, rotation, translation  and dilation.

Reflection of a point is the flipping of a point. If a point A(x, y) is reflected across the x axis, the new point is A'(x, -y). If a point B(x, y) is reflected across the y axis, the new point is A'(-x, y).

The coordinates of point L on a coordinate grid are (−2, −4), if Point L is reflected across the y-axis to obtain point M, the coordinates of M is at (2, -4).

if Point L is reflected across the x-axis to obtain point N, the coordinates of N is at (-2, 4).

Answer: M(2, −4), N(−2, 4) So D can i get branliest

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

[tex]3^2 + \frac{3}{3}-1\\\\=9+1-1\\\\=9[/tex]

Answer:

C: 40 teaspoons.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is a straight proportion question. Many things can be solved with a proportion. This is a good example of what is possible.

Formula

3 teaspoons       x

======              =========

36 cookies        480 cookies

Notice that in the end, the units of teaspoons will be left. Multiply both sides by 480

3 teaspoons * 480 cookies

=======================            =  X

36 cookies

Notice the cookies cancel

3 teaspoons * 480

===============     =  x

36

x = 1440/36 teaspoons.

x = 40 teaspoons

answer: C

Answer:

D.  y + 6 = -3(x - 2)

Step-by-step explanation:

To find the equation in point-slope form, you need to use the slope and a point from that line.  The slope is -3 and the point given is (2, -6).

Point-slope form is y - y₁ = m(x - x₁).  Plug in the slope and point.

y - (-6) = -3(x - 2)

y + 6 = -3(x - 2)

Answer:

D. [tex]y - 2 = -3(x+6 )[/tex]

Step-by-step explanation:

Well point slope form is,

[tex]y - y_{1} = m(x-x_{1} )[/tex]

So we already have slope meaning we can plug that in for m.

[tex]y - y_{1} = -3(x-x_{1} )[/tex]

And with the given point (2,-6),

we can create point slope form.

[tex]y - 2 = -3(x+6 )[/tex]

Therefore,

the answer is d. [tex]y - 2 = -3(x+6 )[/tex].

Hope this helps :)

Answer:

A.

Step-by-step explanation:

We need to find the equation where, if x is equal to 3, g(x) is equal to 1, because g(x) passes through the point (3,1)

Then, replacing x by 3 on every option we get:

[tex]g(x)=(\frac{1}{3}x)^2= (\frac{1}{3}3)^2=1\\g(x)=(\frac{1}{9}x)^2= (\frac{1}{9}3)^2=\frac{1}{9}\\g(x)= \frac{1}{3}x^2= \frac{1}{3}3^2=3\\g(x)=3x^2=3*3^2=27[/tex]

So, the answer is A. because g(x) is equal to 1

Answer:

your welcome and hope this helps

Answer:  D

Step-by-step explanation:

The solution of the two equations does not exist since they are parallel.

Slope of a line is the ratio of the change in y coordinates to the change in x coordinates of two points.

Equation of a line in slope intercept form is y = mx + b, where m is the slope and b is y intercept.

Given linear equation of a line in slope intercept form as,

y = 1/2 x + 1

Here slope = 1/2 and y intercept = 1

y intercept is the y value of a point where it touches the y axis.

A second linear equation is to be found by using the values in the table.

Taking two points (2, 7) and (0, 6).

Slope = (6 - 7) / (0 - 2) = (-1) / (-2) = 1/2

Since the point (0, 6) is given, 6 is the y coordinate when the line touches the Y axis.

y intercept = 6

Equation of the second line is,

y = 1/2 x + 6

Since the slopes of two lines are equal, they are parallel.

There is no solution for two parallel lines.

Hence there is no solution for the linear equations given.

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Answer:

The correct option is;

A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25

Please find attached the graphs of the table data

Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x,               -3,                 -1,                 2,                5,                10

y,              -4.5,              -3.0,             -1.5,             0.0,              1.5              

-4.5/-3  = 1.5 ≠ -3.0/-1 = 3

No direct variation

Table 2      

x,             -5.5,               -4.5,            -3.5,            -2.5,             -1.5

y,              10,                   8,                 6,              4,                  2

10/(-5.5) = -20/11  ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3              

x,              -5.5,               -5.5,             -5.5,           -5.5,            -5.5

y,              -3,                    -1,                 2,                5 ,              10                  

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x,              -3,                    -1,                2,                  5,             10

y,              -7.5,                 -2.5,            5.0 ,              12.5,         25  

 -7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists        

Answer:

so D

Step-by-step explanation:

Answer:

for exapmle:  (2, 5)          {5=2•2.5}

                       (8, 20)        {20=8•2.5}  

                       (-5,  -12.5}    {-12.5=-5•2.5}

Step-by-step explanation:

    -3y+3x    -3y+3x

            ÷2     ÷2

Answer:

neither

Step-by-step explanation:

Answer:

this. question is not clear please send clear question

We can conclude that -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have the following two functions -

y = -x

AND

y = x

Refer to the graphs attached for both the functions -

y = - x     and     y = x

The graphs as seen pass through the origin. One graph (y = x) has a slope of +1 while the other one (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.

We can conclude that -

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Answer:

B. y= -x^2+50x-300

Step-by-step explanation:

A. y^2=4x^2-100

B. y= -x^2+50x-300

C. x=-y^2-400

D. x^2=-6y^2+200

we are to find profits (y) when the company sells x items

Option A can be used to calculate the profit (y) squared

Option B can be used to calculate profits (y)

Option C can be used to calculate items sold(x)

Option D can be used to calculate items sold squared(x^2)

We are asked to find the weekly profit (y) function which eliminate options A, C and D leaving us with option B

Therefore, the weekly profits (y) function in thousands of dollars when the company sells x items is

B. y= -x^2+50x-300

Answer:

x ∈ R, x ≠ 9

Step-by-step explanation:

Given

f(x) = [tex]\frac{1}{x-9}[/tex]

The denominator of f(x) cannot be zero as this would make f(x) undefined.

To find the value that x cannot be, equate the denominator to zero and solve for x

x - 9 = 0 ⇒ x = 9 ← excluded value

Thus the domain is x ∈ R, x ≠ 9

Answer:

The domain is all values but x=4 and x=2

Step-by-step explanation:

f(x) = (x+1) / ( x^2-6x+8)

Factor the function

f(x) = (x+1) / ( (x-4) ( x-2))

The domain of the function is all values of x except where the function does not exist

This is where the denominator goes to zero

(x-4) ( x-2) =0

Using the zero product property

x-4 =0   x-2 =0

x=4   x=2

The domain is all values but x=4 and x=2

Answer:

Hey there!

This, is the graph of your function:

Thus the domain, or all the possible x values would be all real numbers except 2 and 4, because the lines will only reach 2 and 4 when y is infinity.

Hope this helps :)

Answer:

336m^2

Step-by-step explanation:

The triangle area is half of base times height so: 1/2*8*12=48m^2

There are 4 triangles so 48*4=192

Then the square base area is side times side so: 12*12=144m^2

Then surface area of model is 192m^2+144m^2=336m^2

Answer:

336 m²

Step-by-step explanation:

We can find the surface area of this pyramid by finding the surface area of one of the sides, multiplying it by 4 (as there are 4 sides to the pyramid) then adding it to the surface area of the base.

Each side of this (excluding the base) is a triangle, and to find the area of a triangle we use the equation [tex]\frac{b \cdot h}{2}[/tex].

[tex]\frac{12 \cdot 8}{2}[/tex]

[tex]\frac{96}{2}[/tex]

48.

So, one side of this is 48. Multiplying it by 4 gets us 192.

Now we have to add the area of the base. The area of the bass is a square with side lengths of 12, so we can square 12 to get the area of the bass. 12² = 144.

Now let's add these numbers:

192+144 = 336

So, 336 m² is what this comes out to.

Hope this helped!

Answer:

Step-by-step explanation:

Hello,

First of all, we know that the solution of the following equation

   [tex]ax^2+bx+c=0[/tex]

are

   [tex]\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \ \text{ when } \Delta=b^2-4ac \geq 0[/tex]

I would suggest that you try to apply this formula first and check the solution only after you try.

Let's apply it in this case, we have:

[tex]a=4\sqrt{5} \\ \\ b=-24 \\ \\ c= -9\sqrt{5}[/tex]

[tex]\Delta=b^2-4ac=24^2+4*9*5=1296 \\ \\ \sqrt{\Delta}=36 \ \text{ and the solutions are } \\ \\ \\ x_1=\dfrac{24-36}{8\sqrt{5}}=\dfrac{-12}{8\sqrt{5}}=\boxed{\dfrac{-3}{2\sqrt{5}}} \\ \\x_2=\dfrac{24+36}{8\sqrt{5}}=\dfrac{60}{8\sqrt{5}}=\boxed{\dfrac{15}{2\sqrt{5}}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Lines r and s are parallel as Corresponding Angles given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.

Step-by-step explanation

answer from haven

Answer:

0.75

Step-by-step explanation:

The average length is given as the sum of all the lengths given divided by the number of lengths (frequency).

Mathematically:

Average = (Sum of lengths) / frequency

The lengths given are -3, 3, -4, -3, 4, -2, 6, 5. There are 8 lengths there.

The average is therefore:

Average = (-3 + 3 + (-4) + (-3) + 4 + (-2) + 6 + 5) / 8

Average = 0.75

Answer: 81

Step-by-step explanation:

First digit  and    Second digit    and    Third digit    and    Fourth digit

3 choices  x       3 choices          x        3 choices      x       3 choices     = 81

Answer:

g = (h+a) - l

None of them

Step-by-step explanation:

Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them

Let

h = liters of oil in the morning

l= liters that has leaked

a= liters that were added during the day

g= amount of liters at the end of the evening

Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked

Substituting each variable into the formula, we have

g = (h+a) - l

Answer:

Step-by-step explanation:

Since we're given a time at which the height is maximum, we can use a cosine function for the model.

The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.

The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.

The period is given as 3 seconds, and the right shift is given as 1.31 seconds.

This gives us enough information to write the function as ...

  H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)

  H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm

Answer:

The bank offering simple interest at rate of 3% for four years

Step-by-step explanation:

Hello,

To find out which deal would be better, we have to find how much accrued on the simple and compound interest.

Data;

Principal (P) = $7,000

Time = 4 years

Simple interest rate = 3%

S.I = PRT / 100

S.I = (7000 × 3 × 4) / 100

S.I = $840

In four years, he would have $7000 + $840 = $7840.

For compound interest,

C.I = P(1 + r/n)^nt

Where n = number of time compounded = 1 (since it's annually)

rate = 2.5% = 2.5/ 100 = 0.025

C.I = 7000(1 + 0.025/1)⁽¹*⁴⁾

C.I = 7000 (1 + 0.025)⁴

C.I = 7000×(1.025)⁴

C.I = 7000 × 1.1038

C.I = $7726.6

In four years he would have $7,726.6

After calculating and evaluating both option, it's advisable for him to select the bank offering a simple interest of 3% for four years

Answer:

0.8

Step-by-step explanation:

because the template should be axr^n-1

where r is the common ratio

r=0.8

Answer:

0.8

Step-by-step explanation:

Answer:

work is shown and pictured

C, infinitely many solutions.

B, one solution.

C, infinitely many solution.

A system of linear equations is a collection of one or more linear equations involving the same variables.

A system of linear equation has

According to the given questions

the given system of equations

(1). 2x+2y=3 and 4x+4y=6

if we see the graph of the above system of linear equations, the graphs are the" exact at same line".

Hence, they have infinitely many solution.

(2). 7x+5y=8 and 7x+7y =8

if we see the graph of the above system of linear equations, the graphs are intersecting at a single point.

Hence, there is only one solution.

(3). -2x+3y=7 and 2x-3y=-7

if we see the graph of the above system of linear equations, the graphs are exact at same line.

Hence, there is infinitely many solutions.

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Answer:

Z = 0.87

Explanation:

Given the following data;

Sample 1:

n1 = 30

Mean, X = 2.36

Standard deviation, Ox = 0.96

Sample 2:

n2 = 60

Mean, Y = 2.19

Standard deviation, Oy = 0.66

The formula for test statistics for two population is;

[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]

Substituting the values, we have;

[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]

[tex]Z = \frac{0.17}{0.19488}[/tex]

Z = 0.8723

The test statistics to 2 d.p is 0.87

Therefore, Z = 0.87

Answer:

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

Step-by-step explanation:

The interior angle of a regular heptagon = = 900/7° = 128.57°

Therefore, angle DAB = 128.57°

The interior angle of the square = 90°

Therefore, angle DAC = 90°

Therefore, we have

angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))

Angle BAC = 360° - angle DAB - angle DAC =  360° - 900/7° - 90° = 990/7°

Angle BAC = 141.43°

Expressing 141.43° as a common fraction gives;

[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

 The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]

Given, A square and a regular heptagon are coplanar as shown in below figure attached.

We have find the exterior angle of BAC.

We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,

[tex]\frac{180(n-2)}{n}[/tex]  where n is the number of sides.  

Since the heptagon has 7 no. of sides.

So regular heptagon's interior angle measures,

[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]

Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.

We know that a square's interior angle is 90 degrees and a heptagon's interior angle is  128.57 degrees. We will subtract those from 360 degrees to find angle BAC.

[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]

[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]

Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].

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Answer:

A. 3

Step-by-step explanation:

ΔDEC is bigger than ΔABC by 5. For the hypotenuse, 25 is 5 times bigger than 5.

So, side DE on ΔDEC has to be 5 times bigger than side AB on ΔABC.

If side AB equals 3, side DE equals 18 - 3, which is 15.

15 is five times bigger than 3, so the answer is A. 3.

Hope that helps.

Answer:

SOLUTION SET ={a/a≥20}

Step-by-step explanation:

[tex]\frac{2a}{5}-2\geq\frac{a}{4}+1[/tex]

[tex]adding 2 on both sides[/tex]

[tex]\frac{2a}{5}-2+2\geq \frac{a}{4}+1+2[/tex]

[tex]now subtracting \frac{a}{4} on both sides[/tex]

[tex]\frac{2a}{5}-\frac{a}{4}\geq 3[/tex]

[tex]takig LCM as 20\\\frac{8a}{20}-\frac{5a}{20}\geq 3[/tex]

[tex]\frac{3a}{20}\geq 3[/tex]

[tex]by cross-multiplication[/tex]

3a≥3×20

3a≥60

dividing 3 on both sides

3a/3≥60/3

a≥20

SOLUTION SET ={a/a≥20} is the answer

i hope this will help you :)

Answer: rotate 180 degrees and reflection across the line y=2

Step-by-step explan

Answer:

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

2/9 * 9/10 = 2/10 = 1/5