Instructions: Given the figure, what is the angle of rotational symmetry?

Answer: C) [tex]f^{-1}(x)=3-7x[/tex]

Step-by-step explanation:

When solving for an inverse of a function replace f(x) with x and replace the original x with y.

[tex]f(x) = \frac{3-x}{7} \\x=\frac{3-y}{7}[/tex]

Now solve for y

[tex]x=\frac{3-y}{7} \\(7)x=(\frac{3-y}{7}) (7)\\7x=3-y\\7x+y=3-y+y\\7x+y=3\\7x-7x+y=3-7x\\y=3-7x[/tex]

Replace y with the [tex]f^{-1}(x)[/tex]

Answer:

Yes.

Step-by-step explanation:

Yes. They are normal

keeping in mind that regular polygon has 12 sides

[tex]\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ans~~ \begin{cases} a=apothem\\ n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ A=214.14\\ a=8.3\\ n=12 \end{cases}\implies 214.14=\cfrac{1}{2}(8.3)(12)s \\\\\\ 214.14=49.8s\implies \cfrac{214.14}{49.8}=s\implies 4.3=s[/tex]

Answer:

1. (-3) and (-4)

2. (-5) and 6; vise versa

Answer:

Step-by-step explanation:

hello :

1)Two numbers have a product of 12 but their sum is -7 :

means :  xy=12 ....(*)

              x+y = -7 ....(**)

solve this system : use (**) you have   x = -y-7 put this value in (*)

so : (-y-7)y = 12

-y²-7y-12 = 0

y² +7y+12=0       a=1 b=7   and  c= 12

the discriminant  delta =b²-4ac        delta = 7²-4(1)(12) = 1

y1 = (-7-1)/2  = -4      and y2 =  (-7+1)/2 =-3

but x= -7-y

if :y =  - 4   x= -7-(-4) =-3

if : y=-3   x = -7-(-3) =-4

2) same method : xy=-30

                             x+y=1

The volume of the pyramid with a square base, where the perimeter of the base is 14 m and the height of the pyramid is 8.8 m is 35.9 m³

First, we shall determine the determine the area of the square base. This is shown below:

P = 4L

14 = 4L

Divide both sides by 4

L = 14 / 4

L = 3.5 m

Now, the area is obtained as follow

A = L²

A = 3.5²

A = 12.25 m²

Finally, we shall determine the volume of the pyramid. Details below:

V = ⅓Ah

V = ⅓ × 12.25 × 8.8

V = 35.9 m³

Thus, we can conclude that the volume of the pyramid is 35.9 m³

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Answer:

46784

Step-by-step explanation:

You would multiply all.the numbers and then your w

answer will be 46784

Answer:

The cost of one T-shirt is £4

The cost of a hat is £1

Step-by-step explanation:

Answer:

n

(

−

2

)

n

4

+

n

Step-by-step explanation:

Answer:

least common denominator=6

Step-by-step explanation:

For the fractions, 1/3 and 1/6th, 3*2=6. making the fraction 2/6 and leaving the other the same 1/6th.

Answer:

D.

Step-by-step explanation:

1) if the points (1;-1) and (4;0) belong to the line, then

2) the equation of this line is 3y-x=-4;

3) the inequality is 3y-x≤-4.

Answer:

Part A: No. Based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means pratically no corrlation, while the points on the graph are moderately correlatedPart B: you must describe a scenary where a variable is the cause of the number of strawberries picked. See below, the example of rainfall.

Explanation:

1. Part A:

Since the points in the scatter plot show a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.

The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to  1.

r = - 1 is  a perfect negative correlation: the points will adjust perfectly to a line with negative slope.r =  + 1 is a perfect positive correlation: the points will ajdust perfectrly to a line with positive slope.r = 0 means that the variables are not correlated at all.

Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows other thing.

Therefore, the calculated value of r = 0.01 is not accurate for t his scatter plot.

2. Part B.

A causal relationship means that the expllanatory variable (the independent variable) is the cause of the dependent variable.

Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.

I could imagine the amount of rainfall the week before of harvest.

Thus, the scenario could be:

Amout of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

        50                                                     40

        25                                                     80

        12.5                                                  160

        6.25                                                 320

The amount of rainfall is the cause of the number of strawberries picked, and you could find a model (function) that relates both variables.

Answer:

i believe the last one would be 9 for the number of hours kevin works.

Step-by-step explanation:

Answer:

While resting, his heart rate is at 60 bpm. After sprinting, his heart rate is at 130bmp. The difference is 130 - 60 = 70

Step-by-step explanation:

i hope this helps

The correlation coefficient of the given data about time and heart rates is 0.98.

A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable expect change to the value of another.

We have been given time and heart rates of students in Mrs. Anderson's health class and we have to find the value of correlation coefficient.

The formula by Karl Pearson to calculate correlation coefficient is as under:

Correlation coefficient=

=∑(x-x bar)(y-y bar)/[tex]\sqrt{sum(x-x bar)^{2} } \sqrt{sum(y-y bar)^{2} }[/tex]

We have to calculate figures required to fill in the formula which are:

∑(x-x bar)(y-y bar)=350

∑[tex](x-x bar)^{2}[/tex]=44.67

∑[tex](y-y bar)^{2}[/tex]=2872.25

Correlation coefficient=350/[tex]\sqrt{44.67} \sqrt{2872.25}[/tex]

=350/6.68*53.59

=350/357.98

=0.977

After rounding off to nearest hundred it will be 0.98.

Hence the correlation coefficient of the data about time and heart rate is 0.98.

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Answer:

y = 7x

Step-by-step explanation:

Every y is greater 7 times than x. It means that everytime you multiply X by 7, it will be equal to y

24

[tex]Convert\ the\ unit\ for\ \frac{12in}{1ft}:\\ \downarrow\\ 24[/tex]

I hope this helps you

:)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here's the solution :

[tex]\qquad \sf  \dashrightarrow \:(2 {x}^{2} + 5x - 7) + (3 - 4 {x}^{2} + 6x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2{x}^{2} + 5x - 7 + 3 - 4 {x}^{2} + 6x[/tex]

[tex]\qquad \sf  \dashrightarrow \:2 {x}^{2} - 4 {x}^{2} + 5x + 6x - 7 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 2 {x}^{2} + 11x - 4[/tex]

Answer:

Exact Form:3√2+6

Decimal Form:

10.24264068…

Step-by-step explanation:

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

the baseline (where the height hits at a 90° angle) is 4 m.

the height is 3.7 m.

so, the area is

4 × 3.7 / 2 = 2 × 3.7 = 7.4 m²

Answer:

15-5+38+8+595+2+8+6+9+7-5+29-8+8-5-5+2+8+3+9

Answer:

Below.

Step-by-step explanation:

To find the volume of the silo find the volum of the hemisphere with radius of 15 feet and add the volume of the cylinder with a radius of 15 feet and a height of (100 - 15) = 85 feet.

The total volume = 1/2 * 4/3 π (15)^3  + π (15)^2 * 85

= 67151.5 ft^3.

Step-by-step explanation:

find the volume of a sphere with a radius of 15 ft and divide by 2 (because there is only half a sphere on top of the silo).

then add the volume of a cylinder with a radius of 15 ft and a height of 85 ft (because we need to deduct the radius of the sphere from the total height to get the height of the cylinder itself).

[tex]\\ \rm\Rrightarrow -42z^2=14z[/tex]

[tex]\\ \rm\Rrightarrow 42z^2=-14z[/tex]

[tex]\\ \rm\Rrightarrow 3z^2=-z[/tex]

[tex]\\ \rm\Rrightarrow 3z=-1[/tex]

[tex]\\ \rm\Rrightarrow z=-1/3[/tex]

Answer:

[tex] - \frac{844}{29} z[/tex]

Step-by-step explanation:

I hope to help

Answer:

teacher's age: 30

student's age: 15

Step-by-step explanation:

T = 15 + S

from above,

(T+15)/(s+15) = 3/2

by substitution,

(15+S +15)/(S+15) = 3/2

cross multiply,

2(S+30) = 3(S+15)

2S + 60 = 3S + 45

60 = S + 45

s = 15

T = 30

Answer:

5050

Step-by-step explanation:

sum of first n natural num. = [n(n+1)]/2

sum of first 100 natural num. = (100x101)/2 = 5050

Answer : The sum of 1 to 101 positive integer is 5050

5052 will be sum of 1 to 101 only positive integer

Answer:

Option D

Step-by-step explanation:

Square:

     Side = 25 ft

    Area of square = side * side

                              = 25*25

                              = 625 square ft

Area of semicircle:

diameter = 25 ft

r = 25/2 = 12.5 ft

[tex]\boxed{\text{Area of semicircle =$ \dfrac{\pi r^{2}}{2} $}}[/tex]

                              [tex]=\dfrac{3.14 * 12.5*12.5}{2}\\\\\\= 245.3 \ square \ ft[/tex]

Area of the shaded region = area of square - area of semicircle

                                              = 625 - 245.3

                                              = 379.7 square ft