12. What is the equation of the following parabola?
A y = 2(x + 1)2 - 4
B y = 3(x - 1)2 - 4
C y = 3(x + 1)2 - 4
Dy=2(x - 1)2 - 4

Answer: x = -5

New Equation (after substituting) 4x = 3x - 5

Subtract 3x from both sides

x = -5

Answer:

find the answer of the rectangle (7×3=21)

than find the area if one triangle and do 7/2 to get base then multiply 1/2base×height. because there are two triangles add the area to itself then add it to the area of the rectangle. the two triangles shoukd equal 21 together and 21 plus 21 equals 42.

Step-by-step explanation:

im sorry if this is incorrect but it should be right

yah it's not probably it's not 2 mmmm

Answer:

49

Step-by-step explanation:

7^2 mean 7x7 which is 49

Answer:

The first term is 10.

The second term is 16

The third term is 22.

We can see that the first term plus 6, is:

10 + 6 = 16

Then the first term plus 6 is equal to the second term.

And the second term plus 6 is:

16 + 6 = 22

Then the second term plus 6 is equal to the third term.

A) As we already found, the recursive rule is:

Aₙ = Aₙ₋₁ + 6

B) The explicit rule is:

Aₙ = A₁ + (n - 1)*6

Such that A1 is the first term, in this case A₁ = 10

Then:

Aₙ = 10 + (n - 1)*6

C)

Now we want to find A₅, then:

A₅ = 10 + (5 - 1)*6 = 34

There are 34 chairs in row 5.

D)

Here we have 17 rows, then we can have 17 terms, this means that the total number of chairs will be:

C = A₀ + A₁ + ... + A₁₆

This summation can be written as:

∑ 10 + (n - 1)*6        such that n goes from 0 to 16.

The formula  for the sum of the first N terms of a sum like this is:

S(N) = (N)*(A₁ + Aₙ)/2

Then the sum of the 17 rows gives:

S(17) = 17*(10 + (10 + (17 - 1)*6)/2 = 986 chairs.

There are total 986 chairs in the considered auditorium and there are 34 chairs in the fifth row.

A rule defined such that its definition includes itself.

Example: [tex]F(x) = F(x-1) + c[/tex] is one such recursive rule.

For this case, we're provided that:

Seats in rows are 10 in front, 16 in second, 22 in third, and so on.

10 , 16 , 22 , .....

16 - 10 = 6

22 - 16 = 6

...

So consecutive difference is 6

If we take [tex]T_i[/tex] as ith term of the series then:

[tex]T_2 - T_1 = 6\\T_3 - T_2 = 6\\T_4 - T_3 = 6 \\T_5 - T_4 = 6\\\cdots\\T_{n} - T_{n-1} = 6[/tex]

Thus, the recursive rule for the given series is [tex]T_{n} - T_{n-1} = 6[/tex] or [tex]T_n = T_{n-1} + 6[/tex]

From this recursive rule, we can deduce the explicit formula as:
[tex]T_n = T_{n-1} + 6\\T_n = T_{n-2} + 6 + 6\\\cdots\\T_n = T_{n-k} + k \times 6\\T_n = T_1 + 6(n-1)\\T_n = 10 + 6(n-1) \: \rm (as \: T_1 = 10)\\[/tex]

Thus, the explicit rule for this series is [tex]T_n = 10 + 6(n-1)[/tex]

For 5th row, putting n = 5 gives us:

[tex]T_n = 10 + 6(n-1) = 6n + 4\\T_5 = 6(5) + 4 = 34[/tex]

If the auditorium has 17 rows, then total chairs are:

[tex]T = T_1 + T_2 + \cdots + T_{17} = \sum_{n=1}^{17} T_n\\\\T = \sum_{n=1}^{17} (10 + 6(n-1))\\\\T = \sum_{n=1}^{17} (6n + 4)\\\\T = 6\sum_{n=1}^{17} n + \sum_{n=1}^{17}4 = 6\sum_{n=1}^{17} n + 4 \times 17\\\\T = 6\left( \dfrac{17(18)}{2}\right) + 68 = 918 + 68\\\\T = 986[/tex]

(it is because [tex]\sum_{k=1}^n k = 1 + 2 + \cdots + n = \dfrac{n(n+1)}{2}[/tex] )

Thus, there are total 986 chairs in the considered auditorium. There are 34 chairs in the fifth row. The recursive rule for this series is: [tex]T_n = T_{n-1} + 6[/tex] The explicit rule for this series is: [tex]T_n = 6n + 4[/tex].

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Answer:

-822

Step-by-step explanation:

i just typed it in the calculator

but if you're doing it by hand, 1st multiply 4*12*3*6 and then subtract 42 from it

Answer:

sin 105 = sin (45 + 60) = sin 45 cos 60 + cos 45 sin 60, or

                                    = (1 / √2)(1 / 2)        + (1 / √2)(√3 / 2)

                                         1 + √3

                                    = -------------

                                           2√2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

10 days

Step-by-step explanation:

Mogaka and Ondiso working together can do a piece of job in 6 days. Mogaka working alone takes 5 days longer than Ondiso. How many days does it take Ondiso to do the work alone?

Let us represent :

The number of days

Mogaka worked alone = x

Ondiso worked alone = y

Total days worked together = T

Mogaka and Ondiso working together can do a piece of job in 6 days.

Hence,

1/x + 1/y = 1/T

Mogaka working alone takes 5 days longer than Ondiso.

x = y + 5

Therefore:

1/y + 5 + 1/y = 1/6

Multiply all through by (y+5)(y)

= y + y + 5 = (y+5)(y)/6

= 2y + 5/1 = (y+5)(y)/6

Cross Multiply

6( 2y + 5) = (y+5)(y)

12y + 30 = y² + 5y

= y² + 5y - 12y - 30 = 0

= y² - 7y - 30 = 0

Factorise

= y² +3y - 10y - 30 = 0

y(y + 3) - 10(y + 3) = 0

(y + 3)(y -10)= 0

y + 3 = 0, y = -3

y - 10 = 0

y = 10 days

Note that

The number of days Ondiso worked alone = y

Hence, it takes 10 days for Ondiso to work alone

Answer:

50 units

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

a = 48

b = 14

c = ?

Step 2: Solve for c

Answer:

150.72

Step-by-step explanation:

C = 2*pi * r

C = 2* 3.14 * 6

C = 37.68

1 revolution = 37.68

4 revolutions = 4 * 37.68

4 revolutions = 150.72

Answer:

The probability of getting a white or green gumball is 35.64%.

Step-by-step explanation:

1. calculate the total number of gumballs in the gumball machine

35 + 22 + 30 + 14 = 101 gumballs

2. calculate the number of white and green gumballs combined

22 + 14 = 36 w/g gumballs

3. divide the number of white and green gumballs combined by the total number of gumballs in the gumball machine

36 / 101 = 0.3564

Answer: the probability of getting a white or green gumball is 35.64% (0.3564).

Probability is the chance of occurring an event from the total possible outcomes.

The probability of getting a white or a green gumball is 57/101.

It is the chance of occurring an event from the total possible outcomes.

We have,

Green gumballs = 35

White gumballs = 22

Purple gumballs = 30

Blue gumballs = 14

Total gumballs = 35 + 22 + 30 + 14 = 101

The combination is given by:

= [tex]^nC_{r}[/tex]

= n! / r! (n-r)!

The probability of choosing a white gumball:

= [tex]\frac{^{22}C_{1}}{^{101}C_{1} }[/tex]

= 22 / 101

The probability of choosing a green gumball:

= [tex]\frac{^{35}C_{1}}{^{101}C_{1} }[/tex]

= 35 / 101

The probability of getting a white or a green gumball:

= 22/101 + 35 / 101

= (22 +35) / 101

= 57 / 101

Thus the probability of getting a white or a green gumball is 57/101.

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Answer:

[tex]y=0.01(4)^x[/tex]

Step-by-step explanation:

Answer:

16. Right isosceles

17. D

Step-by-step explanation:

The triangle has a right angle this makes it a right trangle. Also all parallelograms are not squares, all rectangles aren't squares and all parallelograms aren't rhombuses.

16. right isosceles

17. C: all rectangles are squares

Answer:

= $88.7429

Step-by-step explanation:

Regular price: $124.99

Total off: $124.99 x 20% + 15% = 43.7465%

Tax: $124.99 x 6% = 7.4994

So he should pay: 124.99 - 43.7465 +7.4994

The total cost of her meal would be amount of $88.74.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Misha obtained a score of 57% on her exam, that corresponds to 67 out of 100.

As per the given information, the required solution would be as

Regular price of dinner = $124.99

Total off =  $124.99 × 20% + 15% = 43.7465%

Total tax = $124.99 × 6% = 7.4994

The total cost of her meal = Regular price of dinner - Total off + Total tax

The total cost of her meal = 124.99 - 43.7465 +7.4994

Apply the arithmetic operation to get the cost

The total cost of her meal = 88.74

Therefore, the total cost of her meal would be amount of $88.74.

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I think the answer would be B. The range is then total price of the tickets purchased and includes all whole numbers from 1 to 4.

Answer:

1

Step-by-step explanation:

Answer:

x= 114, y= 66

Step-by-step explanation:

Opposite angles of a parallelogram are equal

Answer:

P(-3) = -1

Step-by-step explanation:

So just substitute the value of x in the equation:

Value of x is (-3)

So:

P(x) = -2(1 - x)2 +5

P(-3) = -2(1-(-3)) 2 + 5

P(-3) = -2(4) 2 + 5

P(-3) = -8 + 2 + 5

P(-3) = -6 + 5

P(-3) = -1

Answer:

if its not a fraction or a number that can be written as a fraction, its an irrational

Answer:

2 6/7 units

Step-by-step explanation:

You substitute 5/7 in for x

4(5/7) = 20/7 = 2 6/7 units

You can also add 5/7 + 5/7 + 5/7 + 5/7 to check your work

Answer:

C - 18 pi

Step-by-step explanation:

edge

Answer:

5/18

108

A sector has an area of 30π in.2. The radii containing the sector form an angle of 100°. What is the area of the circle?

The ratio of the angle of the sector to the entire circle is

✔ 5/18

.

Area of the sector = StartFraction n degrees over 360 degrees EndFraction (pi) (r squared). 30 pi = StartFraction 100 degrees over 360 degrees EndFraction (pi) (r squared). (StartFraction 18 over 5 EndFraction) 30 pi = (pi) r squared.

The area of the entire circle is

✔ 108

Pi in.2

Answer:

[tex] {x}^{3} {y}^{3} [/tex]

Step-by-step explanation:

Given,

Width of the rectangular prism

= x

Length of the rectangular prism

[tex] = {x}^{2} y[/tex]

Height of the rectangular prism

[tex] = {y}^{2} [/tex]

Therefore,

Volume of the rectangular prism

= Width × Length × Height

[tex] = x \times {x}^{2} y \times {y}^{2} [/tex]

[tex] = {x}^{3} {y}^{3} [/tex]

Hence,

The required volume of the rectangular prism is

Option J:

[tex] {x}^{3} {y}^{3} [/tex]

Answer:

C. 2:5

Step-by-step explanation:

Find perimeter of each...

a. 10+25+21.5=56.5

b. 4+10+8.6=22.6

b:a

22.6:56.6

simplify

11.3 will go into both for..

2:5

Answer:

39°

Step-by-step explanation:

The sum of AXE, AXC and CXF will be 180 because they together span a straight line (EF).

So: y + 90 + y - 12 = 180, which is an equation you can solve by simplifying it:

y + 90 + y - 12 = 180

2y + 78 = 180

y + 39 = 90

y = 90 - 39 = 51

So AXE = 51

AXC = 90

CXF = 51-12 = 39 (the answer)

Check: 51+90+39 = 180

Answer:

The real answer is (-20, 8).

Step-by-step explanation:

I just did the unit test practice or whatever and used the answer above and got it wrong. This is the correct answer.