What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`? A. `y = -(49)/(16)` B. `x = -(49)/(16)` C. `y = (47)/(16)` D. `x = (47)/(16)`

Follow this as an example

An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of

10 m

and a depth of

1.4 m

. Suppose water is pumped into the pool at a rate of

11 m3

per hour. How many hours will it take to fill the empty pool?

Use the value

3.14

for

π

, and round your answer to the nearest hour. Do not round any intermediate computations.

The formula for the volume of a cylinder is  ∏r2h.  The problem gives d=10m, so r=5m.

The pool holds  (3.14)*52*1.4 m3 = 109.9 m3 of water.

At a rate of 11 m3 per hour:

            ( 109.9 m3 ) / (11 m3/hr)  = 9.990909 hr.

              rounding to the nearest hour, this is 10 hours

The pool has a volume of approximately 47.97 cubic meters. The pump can fill 11 cubic meters per hour. Therefore, rounding up, it will take roughly 5 hours to fill the pool.

The volume of the swimming pool shaped like a cylinder can be calculated using the formula for the volume of a cylinder which is V = πr2h, where r is the radius, h is the height (or depth in this case) and π is a constant whose value we'll take as 3.14. Therefore, the volume of the pool is V = 3.14 * (6/2)2 * 1.7.

Once we have the volume, we can divide this by the rate of water being pumped in, in terms of how many cubic meters it pumps per hour, to find out how many hours it would take. So the time taken to fill the pool, in hours, is Time = Volume / Rate.

By substituting the numbers we have into these formulas, we get V = 3.14 * 9 * 1.7 = 47.97 m3, and Time = 47.97 m3 / 11 m3/hour = approximately 4.36 hours. Since we need to round up to the nearest hour, the pool will take about 5 hours to fill.

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Answer:

The measure of angle ABC = The measure of angle A prime B prime C prime

Step-by-step explanation:

we know that

The transformation of the figure is a reflection, so after the transformation  the shape still has the same size, area, angles and line lengths.

the triangles ABC and A'B'C' are congruent

therefore

the corresponding sides and corresponding angles are equal

so

The relationship between the measures of the angles of the two triangles is

[tex]m<ABC=m<A'B'C'[/tex]

[tex]m<BCA=m<B'C'A'[/tex]

[tex]m<BAC=m<B'A'C'[/tex]

Answer: 4

Step-by-step explanation:

Find all of the factor pairs of 120, then look for the ones that are even-odd

         120

           ∧

      120   1     even-odd

        60   2    even-even

        40   3    even-odd

         30   4    even-even

         24   5    even-odd

         20   6    even-even

          8    15    even-odd

           10  12    even-even

There are 4 even-odd factors pairs for 120.

Let's find out how much tax was paid. Subtract the amounts: 1800 - 1683 = 117

So $117 was paid in tax. Divide this over the initial amount 1800 and we get 117/1800 = 0.065

To convert from decimal form to percent form, you multiply by 100. This is basically moving the decimal point 2 spots to the right. So we go from 0.065 to 6.5%

Therefore the answer is 6.5%

I believe it is A.  I did this awhile ago.

we are given

system of equations

First equation is

[tex]3x-2y=31[/tex]

Second equation is

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

now, we can find augmented matrix

[tex]A=\begin{pmatrix}3&-2&31\\ 3&2&-1\end{pmatrix}[/tex]

now, we can change it into reduced row echelon form

step-1: multiply the 1st row by 1/3

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 3&2&-1\end{pmatrix}[/tex]

step-2:add -3 times the 1st row to the 2nd row

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&4&-32\end{pmatrix}[/tex]

step-3:multiply the 2nd row by 1/4

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&1&-8\end{pmatrix}[/tex]

step-4: add 2/3 times the 2nd row to the 1st row

[tex]A=\begin{pmatrix}1&0&5\\ 0&1&-8\end{pmatrix}[/tex]

so, we get

[tex]x=5,y=-8[/tex]

Answer is (5,-8)

Solution is (5,-8)

3x – 2y = 31

3x + 2y = -1

first we write it in matrix form

3  -2   | 31   -------------> Row 1

3   2   | -1  -------------> Row 2

We use row operations and get matrix in 1   0    and 0  1  form

Subtract Row 2 by row 1.  R2 -> R2 - R1. So R1 remains the same

3  -2   | 31   -------------> Row 1

0   4   | -32  -------------> Row 2

Divide row 1 by 3, R1-> R1/3. So R2 remains the same

1   [tex]\frac{-2}{3}[/tex]   | [tex]\frac{31}{3}[/tex]    -------------> Row 1

0   4   | -32  -------------> Row 2

Divide row 2 by 4. R2 -> R2/4

1   [tex]\frac{-2}{3}[/tex]   | [tex]\frac{31}{3}[/tex]    -------------> Row 1

0   1   | -8  -------------> Row 2

Now we need to get 0 in the place of -2/3

Multiply Row 2 by 2/3  and add it with Row 1. R1 --> 2/3 times R2 + R1

1   [tex]1*\frac{2}{3}+\frac{-2}{3}[/tex]   | [tex]-8*\frac{-2}{3}\frac{31}{3}[/tex]    -------------> Row 1

0   1   | -8  -------------> Row 2

Now simplify the fraction

1   0   | 5    -------------> Row 1

0   1   | -8  -------------> Row 2

So from this we can see that x=5  and y = -8

Solution is (5,-8)

Answer:

x = 1; y = 1; z = 0

Step-by-step explanation:

First problem:

First equation minus second equation: 3y + 2z = 3      Eq. A

Second equation plus third equation: 2y + 4z = 2        Eq. B

-2 times Eq. A plus Eq. B: -4y = -4

y = 1

Substitute y = 1 in Eq. A: 3 + 2z = 3

2z = 0

z = 0

Substitute z = 0 and y = 1 in original first equation:

-2x + 2 + 0 = 0

-2x = -2

x = 1

Answer: x = 1; y = 1; z = 0

Answer:

-1075

Step-by-step explanation:

The other person was right they forgot to make it a negative

There are two sequence in mathematics, one is arithmetic and other is geometric sequence. Therefore, the 64th term of the arithmetic sequence is -1075.

In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same. Another sequence is the geometric sequence.

The nth term of an arithmetic sequence is given by:

[tex]a_{n}[/tex]=a₁+(n-1)d

In which  is the first term from−4,−21,−38 is a₁  -4

Common difference between two consecutive terms is d=-38-(-21)=-17

substituting in the above equation an=a1+(n-1)d

[tex]a_{n}[/tex]=-4+(n-1)(-17)

Since we have to find the 64th term of the arithmetic sequence we have to put n=64

[tex]a_{n}[/tex]=-4+(64-1)(-17)

 [tex]a_{n}[/tex]   =-4+(63)(-17)

[tex]a_{n}[/tex] =-1075

Therefore, the  64th term in the arithmetic sequence -4, -21, -38 is -1075.

To know more about Arithmetic sequence, here:

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you said times and sum, sum is addition and times is multiplication so im confused. can you copy the exact question so i can help?

Its not correct because the answer would be 1,440 (rounded) this is no where near as close as 222.3.

117 * 19

= 120 * 20  to the nearest 10

=  2400   which indicates that 2223 is a reasonable answer.

10 units

calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 5, 8 )

d = √(- 5 - 3 )² + (8 - 2 )²

  = √(64 + 36 ) = √100 = 10

Answer:

Anything that does not cost more than $2,560.00

Step-by-step explanation:

Provided that Nikita is spending money that she had invested and the amount  she collected over the period of 7 years. She can buy any item that costs no more than $2,560.00 but how?

It is a problem of simple interest:

Here the principal amount (P) = $2,000.00

Interest rate (r) = 4%

Time period (t) = 7 years

So, total amount that she would get by the end of 7 years is:

[tex]A=P+SI[/tex]

[tex]SI=\frac{P\times r\times t}{100}[/tex]

Plugging the values we get:

[tex]SI=\frac{2000\times 4\times 7}{100}=560.00[/tex]

So the interest collected over 7 years is $560.00

Therefore, the total amount after 7 years is:

[tex]\$2000.00+\$560.00=\$2,560.00[/tex]

If Nikita is using this money then the most expensive item that she could buy will cost no more than $2,560.00.

Answer:

The answer is B (a mountain bike priced at $2,500) in Plato

Step-by-step explanation:

The standard form of the number 5.871x10⁻⁷ is 0.0000005871 after using the properties of the integer exponent.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The number is:

= 5.871x10⁻⁷

After using the properties of the integer exponent:

= 5.871x(1/10⁷)

= 5.871x(1/10000000)

= 5.871x0.0000001

= 0.0000005871

Thus, the standard form of the number 5.871x10⁻⁷ is 0.0000005871 after using the properties of the integer exponent.

Learn more about the integer exponent here:

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In order to answer this question, you must do some multiplication!

So, in order to have a pair of shoes, you must have 2 shoes. There are 42 PAIRS of shoes. So if you wanna find the number of ALL of the shoes, you have to multiply da numbers.

42 × 2 = 84

There are 84 shoes altogether.

If you need anymore help, just let me know!

The number of shoes in one pair is two thus there will be 84 in the office.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given,

Number of pairs of shoes = 42

Number of shoes in one pair of shoes = 2

Total number of individual shoes = 42 x 2 = 84

Hence "The number of shoes in one pair is two thus there will be 84 in the office".

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This is a more difficult one to explain. Let's start with the line to the right.  It has a slope (m) of [tex]\frac{-2}{2}[/tex] = -1 and a y-intercept of +3 (continue the line to see where it crosses the y-axis). So, the equation of that line is: y = -x + 3 when x ≥ 2. This can also be written as y = 3 - x when x ≥ 2.  The only option that has that equation is A.

Answer: A

First of all, you can see that this is a piecewise polynomial, since it is shaped like a parabola before [tex] x = 2 [/tex], and is a line after [tex] x = 2 [/tex] So, option C is surely wrong, because it uses [tex] x = 3 [/tex] as splitting point.

Moreover, the way the parabola "bounces" on the x axis, avoiding its negative part, tells us that there is an absolute value. This excludes options B and D, and the answer is thus A.

Answer:

45mins ÷ 15pages = 3

so she reads 3pages per minute

3pages × 60minutes = 180

she read 180pages in 60minutes

hope this helps

Step-by-step explanation:

10 units up means to add 10 to the y-coordinate of the vertex (h, k).

p(x) = 0.005(x - 40)² + 60

p(x) shifted up 10 units = 0.005(x - 40)² + (60 + 10)

                                q(x) =  0.005(x - 40)² + 70  

dude its b thats easy and yes im sure 4 units down and sense its not reflection then thats the answer

the answer is 39.9 %

The answer to this question is A

ANSWER

The set of the intersection  of {[tex]2,3,5,7[/tex]} and {[tex]2,5,11,13[/tex]} is

{[tex]2,5[/tex]}

EXPLANATION

Let [tex]A=[/tex]{[tex]2,3,5,7[/tex]}

and

[tex]B=[/tex]{[tex]2,5,11,13[/tex]}.

The intersection of the two sets are the elements that are in both set A and set B.

The elements that are common to both sets are 2 and 5. So, we write;

[tex]A \cap B=[/tex]{[tex]2,5[/tex]}

Therefore the correct answer is C

The intersection of the sets {2,3,5,7} and {2,5,11,13} is the set {2,5}, which has the elements common to both sets. Therefore option c is correct

The intersection of two sets is the set of elements common to both sets. In the provided sets {2,3,5,7} and {2,5,11,13}, the common elements are 2 and 5. Therefore, the intersection of these two sets is {2,5}. So, the correct answer is C. {2,5}.

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To arrange numbers from least to greatest:

First write them down in decimal form. Now it will be easy to determine which value is greater than the other.

Arrange the decimal numbers from least to greatest.

Finally revert the decimal values to their fraction form having arranged them from one with least value to one with greatest value.

Dan will earn £59.40 for 6 hours of work.

To calculate Dan's earnings for 6 hours of work, we can multiply his hourly rate (£9.90) by the number of hours (6).

So, Dan will earn £9.90 x 6 = £59.40 for 6 hours of work.

Therefore, Dan will earn £59.40 for 6 hours of work.

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(2.99×c)+(50×s) this is the equation for the word problem