Demonstrate your knowledge by giving clear, concise solutions to each problem. Be sure to include all relevant drawings and justify your answers (show all your work). You may show your solution in more than one way to investigate beyond the requirements of the problem. 1. Some important formulas are given below Area of a circle is A=πR^2 where r is the radius of the circle.
A)Write a formula for the area of the figure below. (5pts)

Explanation:

Because point A is the center of dilation, it will stay fixed. It never moves. Everything else around it will move. Specifically, every point but A will move inward closer to A.

To get from A to B, we move 9 spaces. The scale factor 1/2 means we'll move half that amount and 9/2 = 4.5 spaces will be between A' and B'. Relabel A' as point E, and change the name of B' to F.

To go from A to D, we do the following steps

Cut each of those values in half to get 9/2 = 4.5 and 6/2 = 3. The results 4.5 and 3 are the horizontal and vertical distances we must travel when going from A' to D'. We'll relabel point D' as point H.

To go from D to C, we move 3 spaces. This cuts in half (again because of the scale factor) to get 3/2 = 1.5 spaces which is the distance from D' to C', aka from H to G.

Everything is marked in the diagram below.

Answer:

17.5 Ounces

Step-by-step explanation:

14/100=.14                 .14x25=3.5              14+3.5=17.5

Answer:

The balance in Mary's account at the end of the month is $14.09

Step-by-step explanation:

Step 1: 50+25.62=75.62

Step 2: 75.62+19.76=95.38

Step 3: 95.38-56.29=39.09

Step 4: 39.09-25= $14.09

Answer:

1. Hence, the answer is $74.50

2. Hence, the answer is 16.

Step-by-step explanation:

1. Given: Natalie and her friends decide to rent 4 lanes at regular cost for a party. Ten people need to rent shoes, adn 4 people are members.

To find: What is the total cost for the party?

Solution:

Since Natalie and her friends wanted to rent four lanes, we need to calculate this at REGULAR cost.

4 * 9 .75 = 39

Now since 10 people want to rent shoes, and 4 people are members, we subtract.

10 - 4 = 6

6 nonmembers

4 members

6 times the amount of shoe rental for 6 * 3.95 - 23.70

non members

4 times the number of members shoe rental 4* 2.95

11. 80

Now add the quantities

39 + 11.80 + 23.70 += 50.80 + 23.70 =

74.50

Now, our answer is 74.50

2.

Solution:

20 / 1.25 = 16

So the possible amount that can be bought is 16 medium sodas.

Answer:

2) x = -4; y = 0; z = -2

4) x = 4; y = 2; z = 0

Step-by-step explanation:

2)

-4x - 5y - z = 18

-2x - 5y - 2z = 12

-2x + 5y + 2z = 4

Add the 2nd and 3rd equations to eliminate y and z.

-4x = 16

x = -4

Substitute x = -4 in first and second equations.

(-4)(-4) - 5y - z = 18

(-2)(-4) - 5y - 2z = 12

-5y - z = 2

-5y - 2z = 4

Multiply first equation by -1 and add to second equation.

       5y + z = -2

(+)   -5y - 2z = 4

----------------------

               -z = 2

z = -2

Substitute x = -4 and z = -2 in first original equation and solve for y.

-4(-4) - 5y - (-2) = 18

16 - 5y + 2 = 18

-5y = 0

y = 0

Answer: x = -4; y = 0; z = -2

4)

4x + 4y + z = 24

2x - 4y + z = 0

5x - 4y - 5z = 12

Add equations 1 and 3 to eliminate y.

9x - 4z = 36    Eq. 1

Add equations 1 and 2 to eliminate y.

6x + 2z = 24    Eq. 2

Multiply Eq. 2 by 2 and add to Eq. 1.

       12x + 4z = 48

(+)      9x - 4z = 36

----------------------------

        21x       = 84

x = 4

Substitute x = 4 into Eq. 1 to solve for z.

9x - 4z = 36

9(4) - 4z = 36

-4z = 0

z = 0

Substitute x = 4 and z = 0 into the first original equation to solve for y.

4x + 4y + z = 24

4(4) + 4y + 0 = 24

4y = 8

y = 2

Answer: x = 4; y = 2; z = 0

Answer:

120 minutes

Step-by-step explanation:

find the LCM

first find the GCF using prime factorization

15=3*5 12=2*2*3 10=2*5

GCF is 5 and 2 respectively

remove from each and multiply

3*2*2*2*5=120

If you flip a coin one time, the probability to get a Head is

p = 1/2

The probability of not getting a head in a single toss is :

q = 1 - 1/2 = 1/2

Thus there is only one unique situation to get the same number of heads and tails : in 10 toss you need to get exactly five heads, it will means that the rest is the tails.

Now using Binomial theorem of probability, the probability of getting exactly x = 5 heads in a total of n = 10 tosses is :

P(X = 5) = [tex]\frac{10!}{5!*5!} *(\frac{1}{2})^{5} *(\frac{1}{2})^{5}[/tex]≈ 0.246

So the probability of that is 24,6 %

Good Luck

Answer:

2y+x+9=0

Step-by-step explanation:

eqn is given by

[tex]m = \frac{y - y1}{x - x1} [/tex]

given

[tex] - \frac{1}{2} \: as \: m[/tex]

and

[tex]{3 \: and \: - 6} \: as \: x \: and \: y \: respectively[/tex]

subtitute values into the formula

[tex] - \frac{1}{2} = \frac{y - - 6}{x - 3} [/tex]

cross multiply giving

[tex] - 1{x - 3}= 2{y + 6[/tex]

[tex] - x + 3 = 2y + 12 \\ 2y + 12 + x - 3 = 0 \\ 2y + x + 9 = 0[/tex]

Answer:

1%

Step-by-step explanation:

0.4X2.5=1

Refer the attachment please

Hope it helps

Best of luck

Answer:

21

Step-by-step explanation:

1) Simplify 1 + 2 to 3.

1 + 2 + 3 ×  ( 3 + 3 )

2) Simplify 3 + 3 to 6.

1 + 2 + 3 × 6

3) Simplify 3 × 6 to 18.

1 + 2 + 18

4) Simplify 1 + 2 to 3.

3 + 18

5) Simplify.

21

Answer:

tan 72 = 6/x

OR

cos 72 = x/15

Step-by-step explanation:

A good way to remember trig ratios is this

SOH CAH TOA -

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

You can find x in a few different ways.

If you did tangent, it would be

tan 72 = 6/x (because tangent is opposite over adjacent)

Or, there's also the pythagorean theorem...

Work Shown:

[tex]t = \frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\\\\t = \frac{113-117}{\frac{11}{\sqrt{28}}}\\\\t \approx \frac{-4}{\frac{11}{5.291503}}\\\\t \approx \frac{-4}{2.078804}\\\\t \approx -1.924183\\\\t \approx -1.924\\\\[/tex]

In the intermediate steps, I rounded to 6 decimal places. The final answer is rounded to 3 decimal places (to the nearest thousandth).

Step-by-step explanation:

the factor of x : 20 or 20/1

that means with each additional videotaping (number of tapings goes up by +1) the cost goes up by +20.

Answer:

4.9 inches

Step-by-step explanation:

78.4 diveded by 4

19.6 divided by 4

=4.9

=》The answer is -61/3 = -20.333

Steps are in the attachment.

Note :-

=》The LCM is 3.

_______

Hope it helps ⚜ :))

Answer:

12 weeks

Step-by-step explanation:

I will use x to describe the amount of weeks.

200.39 (amount already have) + 80.10x (amount per week) = 1161.59 (total amount needed)

Now, just solve for x.

80.10x = 961.2

x = 12

Answer:

11

Step-by-step explanation:

2x - 6 = 16 (Based on similarity)

2x = 16 + 6

2x = 22

x = 22/2

x = 11

Answer:

0

Step-by-step explanation:

-5/6 - (-5/6)

Negative times a negative is a possitive

-5/6 + 5/6

0

Hopes this answers your question. :)

Answer: 0

Step-by-step explanation:

-5/6 - -5/6 =

-5/6 + 5/6 =

-5 + 5

   6

= 0/6

=0

Answer:

77

Step-by-step explanation:

Hope this helps..

Good luck.

Answer: x=-5

Step-by-step explanation:

Graph has no y intercept, thus has to be equal to x, and since its -5... x=-5 is your answer

Answer: X= -5

Step By-Step explantation:

Answer: X = 7/2 or 3.5

Answer:

D: assets.

Step-by-step explanation:

point A will represent the input-output values of the function.

What is number line ?

Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.

In the graph of y = f(x),

For every x-value (input value), value of the function is the y-value (output value).

For the input value x = 2,

Output value of the function will be,

y = f(2)

Therefore, point A will represent the input-output values of the function.

check and know more about function here :

https://brainly.com/question/12431044

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