Aniela took 10 pages
of notes over the span of 4
classes. If Aniela worked at a
constant rate, how many notes
did she take in one class?

The equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).

Since the directrix y = 1, it shows it is vertical, so we use the equation of the parabola that opens up or down.

( x - h )² = 4p( y - k )

Given the data in the question;

First, we determine the vertex.

The vertex ( h,k ) is half way between the directrix and the focus.

Find the y-coordinate of the vertex using;

y = ( y-coordinate of focus + directrix )/2

y =  (7+1)/2 = 8/2 = 4

The x-coordinate of the vertex is the same as that of the focus 0

Hence, the vertex is ( 0,4 )

Next, we determine the distance p from the focus to the vertex.

p = y-coordinate of focus - y-coordinate of vertex

p = 7 - 4

p = 3

Now, plug the known values into the equation and simplify

( x - h )² = 4p( y - k )

( x - 0 )² = 4(3)( y - 4 )

x² = 12( y - 4 )

Therefore, the equation of the parabola with the given focus and directrix is x² = 12( y - 4 ).

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Answer:448

Step-by-step explanation:None

Answer:

448

Step-by-step explanation:

(-4 × 16)×(-7)

(-64)×(-7)

448

Answer:

60% increase

Step-by-step explanation:

First: subtract your final value by your starting value

136 - 85 = 51

Second: divide your product from the first step by your starting value

51 ÷ 85 = 0.6

Third: multiply your product from the second step by 100

0.6 x 100 = 60

The best description of range is (b) The y-values on a graph.

A graph is characterized by the following concepts:

The domain of a function is the set of input values of the graph

On the other hand, the range of a function is the set of output values of the graph

This in other word means that the range is the y-values on a graph.

Hence, the best description of range is (b) The y-values on a graph.

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Answer:

its B

Step-by-step explanation:

the y values on the graph

i did the quiz and got a 100

Answer:

$271

Step-by-step explanation:

$741-$199= $542

$542/2= $271

271=p

Irenes $271+ Rochelles $271+199 more than Irene= $741

Irene only raised $271 and rochelle raised 470$

Answer:

C 39

Step-by-step explanation:

took the test

Answer: R'=(6, -2)

S=(-6,9) ==> S'=(6, -9)

T=(-5,9) ==> T'=(5, -9)

U=(-5,2) ==> U'=(5, -2)

Step-by-step explanation:

When rotated around the origin by 180 degrees, the rectangle will have all its coordinates' x and y values negated.

R=(-6, 2) ==> R'=(6, -2)

S=(-6,9) ==> S'=(6, -9)

T=(-5,9) ==> T'=(5, -9)

U=(-5,2) ==> U'=(5, -2)

The temperature at 6000 meters would be -21.9°C.

The lapse Rate refers to the rate of decline in air temperature with relation to increase in altitude.

Here, the lapse Rate is given as follows-

for 0-1500 meters: 5.5 °C/1000m

for 1500-4000 meters: 12.1°C/1000m.

and above 4000 meters: normal lapse rate

The Normal lapse Rate is 6.5°C per 1000 meters.

Now,

surface temperature at sea level = 29.6°C

the decline in temperature up to 1500m would be-

5.5°C/1000×1500 = 8.25°C

So the temperature at 1500 meter is 29.6 - 8.25 = 21.35°C

Further, the decline in temperature up to 4000m would be-

12.1°C/1000×2500= 30.25°C

So Temperature at 4000 meters is 21.35 - 30.25 = -8.9°C

Now, above 4000 meters, decline in temperature would be-

6.5°C/1000×2000= 13°C

So temperature at 6000 meters would be

-8.9°C - 13°C = -21.9°C

Thus, the temperature at 6000 meters would be -21.9°C

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Answer:

20.02

Step-by-step explanation:

maths calc

The new data set is the {54,46,54,52,47}.

According to the statement

We have to find that the value of the data set.

So, For this purpose, we know that the

A data set is a collection of related, discrete items of related data that may be accessed individually or in combination or managed as a whole entity.

From the given information:

45 is added to the data set 9, 1, 9,7, 2

It means the data set is the

{ 9, 1, 9,7, 2}

Then the number 45 is added into the each elements of the data.

Then

9+45 = 54

1+45 = 46

9+45 = 54

7+45 = 52

2+45 = 47.

The new data set is the {54,46,54,52,47}

So, The new data set is the {54,46,54,52,47}.

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Answer:

(-6, -8)

Step-by-step explanation:

We have the following system of equations:
[tex]y = 2x+4[/tex]    (1)

and

[tex]y=x-2[/tex]      (2)

Set (1) = (2) since the LHS is y in both

We get

[tex]2x + 4 = x - 2[/tex]

Subtract x from both sides:

[tex]2x + 4 - x = x - 2 -x[/tex]

[tex]x + 4 = -2[/tex]

Subtract 4 from both sides

[tex]x + 4 - 4 = -2 -4[/tex]

[tex]x = -6[/tex]

Substitute for x in Equation (2) to get
[tex]y = -6 - 2 = -8[/tex]

So the solution is (-6, -8)

let x be the capital invested in the 9% account

let y be the capital invested in the 8% account

let j be the interest earned from the 9% account

let k be the interest earned from the 8% account

[tex]j = xi_{1}n \: \: \: (n = 1 \: year)\\ j = x( \frac{9}{100})(1) = 0.09x[/tex]

[tex]k =yi_{2}n \: \: \: \: (n = 1 \: year) \\ k = y( \frac{8}{100} )(1) = 0.08y[/tex]

But the total interest made is 2100 $, hence:

[tex] \: \: \: \: \: \: \: j + k = 2100 \\ 0.09x + 0.08y = 2100[/tex]

And the total capital invested is 25000 $

[tex]x + y = 25000[/tex]

System of 2 equations and two unknowns:

[tex]0.09x + 0.08y = 2100 \\ x + y = 25000 \\ \\ \: \: \: \: (x,y)=(10000,15000)[/tex]

The width of the rectangle is 14 units and the right option is b 14

Perimeter can be defined as the total distance around an object.

To calculate the width of the rectangle, we use the formula of perimeter.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the width of the rectangle is 14 units and the right option is b 14

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Laine will take 30 minutes to read 25 pages.

Given Laine reads 200 pages in 240 minutes.

We need to find the time taken to read 25 pages, if Laine reads at the same rate.

First, let us find out the time taken to read one page.

240 minutes are taken to read 200 pages

This implies that the time taken to read 1 page = 240/200 minutes

This implies that the time taken to read 1 page = 6/5 minutes

Therefore, the time taken for 25 pages = 25 ×(6/5) minutes

⇒ The time taken for 25 pages = 30 minutes

Hence, Laine will read 25 pages in 30 minutes, if she reads 200 pages in 240 minutes.

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Answer: 24, 26

Step-by-step explanation:

a=first even number. b=second even number

a=b-2

a*3=b*2+20

(b-2)*3=2b+20

3(b-2)=2b+20

3b-6=2b+20

b-6=20

b=26

a=b-2

a=26-2

a=24

24, 26

Answer:

mark me please

Explanation:

If the lesser of two consecutive even integers is tripled, the result is 20 more than twice the grater integer. find the two integers

let the numbers be x & x+2

3x=20+2(x+2)

3x=20+2x+4

3x-2x=24

x=24

The integers are 24 & 26

well, the carpet and table set are both 173.95 + 88.08 = 262.03, however Judy is so smashing she got an 18% discount on that, ,so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{18\% of 262.03}}{\left( \cfrac{18}{100} \right)262.03} ~~ \approx ~~ 47.17~\hfill \underset{discounted~price}{\stackrel{262.03~~ - ~~47.17}{\approx 214.86}}[/tex]

now, let's add the 8% tax to that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 214.86}}{\left( \cfrac{8}{100} \right)214.86} ~~ \approx ~~ 17.19~\hfill \underset{\textit{ total price}}{\stackrel{214.86~~ + ~~17.19}{\approx \text{\LARGE 232.05}}}[/tex]

I'm going to assume you meant 89/56 and not 8965 due to the fact you are asking for a mixed number answer.

[tex]=\frac{22}{1}\div \frac{89}{56}[/tex]
[tex]=\frac{22}{1}\times \frac{56}{89}[/tex] <- Apply the fraction rule [tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]\frac{22\times \:56}{1\times \:89}[/tex] <- Apply the fraction rule [tex]\frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]=\frac{1232}{1\times \:89}[/tex]
[tex]=\frac{1232}{89}[/tex]
[tex]13 \frac{75}{89}[/tex] <- Convert to mixed number and there is your final answer
____________________________________________________
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Answer: three seven and two

Step-by-step explanation:

Order of the given expression into smallest to largest are as follow:

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12} < \frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12}[/tex]

As given in the question,

Given expressions are as follow:

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12},\\\\\frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12}\\\\\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} \\ \\\frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)}[/tex]

Arrange them in the order of smallest to largest by simplifying them,

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12}= \frac{2+4}{24-12\\}[/tex]

          = 0.5

[tex]\frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12}= \frac{4+\sqrt{2} }{12}[/tex]

          =0.45

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} = \frac{2+4}{-48}[/tex]

           = -0.125

[tex]\frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)}= \frac{4+\sqrt{2} }{-48}[/tex]

            = -0.1128

-0.125 < -0.1128 < 0.45 < 0.5

Therefore, order of the given expression into smallest to largest are as follow:

[tex]\frac{ \sqrt{\frac{8}{2} } +4 }{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times (4-12)} < \frac{ \frac{\sqrt{8} }{2} +4}{6\times 4-12} < \frac{ \sqrt{\frac{8}{2} } +4 }{6\times 4-12}[/tex]

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Pete will earn $594.83 for one week that he worked for 51 hours

What is the normal hours of work per week?

The number of hours that Pete works normally in any week is 40 hours, beyond the 40 hours, it is regarded as overtime and the overtime hours are paid at one and a half of the normal hourly rate of $11.55

overtime=51.50-40

overtime=11.50

normal earnings=40*$11.55

normal earnings=$462.00

overtime pay=11.50*$11.55

overtime pay=$132.83

total weekly earnings=$462.00+$132.83

total weekly earnings=$594.83

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Answer:

Use 12 boxes of rice

Step-by-step explanation:

4/13 becomes x/39

to get from 13 to 39 you multiply 13 by 3 so you do the same to 4

3*4 is 12

Solution of the inequality is q> 1/4 and in interval notation is (1/4 , ∞ ).

According to the question we have been given the inequality that is

                3/4q - 2/3q < 5/12q - 1/12

Solving the equation step by step we get

First simplifying 3/4q - 2/3q which will get q/12

Therefore,         q/12 < 5/12q - 1/12

moving all the terms with q on the left hand side we get

                       q/12 - 5/12q < -1/12

                       (q-5q)/12 < -1/12

                          -4q/12 < -1/12

multiplying both sides by 12 we get

                            -4q/12 * 12 < -1/12*12

                                -4q < -1

multiplying -1 both sides we get

                                  4q>1

                                     q >1/4

Hence solution of the inequality we get

                  (1/4 , ∞ )

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by using inductive reasoning, we get the next 2 terms as 7 / 12 and 4 / 7.

We are given a sequence:

3 / 4, 2 / 3, 5 / 8, 3 / 5

We need to find the next two terms by using the inductive reasoning.

Now, we can also write this sequence as:

3 / 4, 4 / 6, 5 / 8, 6 / 10

Now, we can see that, in each term, the numerator is increasing by 1 and the denominator is increasing by 2 units.

So, the 5th term will be:

Numerator = 6+ 1 = 7

Denominator = 10 + 2 = 12

5th term = 7 / 12

And the 6th term will be:

Numerator = 7 + 1 = 8

Denominator = 12 + 2 = 14

6th term = 8 / 14 = 4 / 7

Therefore, by using inductive reasoning, we get the next 2 terms as 7 / 12 and 4 / 7.

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Answer: I'm sure it is just 1

Answer:

Addition and multiplication both use the associative property, while subtraction and division do not.

Step-by-step explanation:

Answer:

subtraction doesn't have the associative property. If we subtract the first two numbers, 10 minus 5, it gives us 5. If we move on to subtract 3, it gives us 2. However, if we subtract the last two numbers first, 5 minus 3 is 2.

Answer:

8/14

Step-by-step explanation:

All of the other ratios can be simplified to 2/3

Step-by-step explanation:

tan x = 1 / (cot x)

Tangent Formula Using Sin and Cos

We know that sin x = (opposite) / (hypotenuse), cos x = (adjacent) / (hypotenuse), and tan x = (opposite) / (adjacent). Now we will divide sin x by cos x.

(sin x) / (cos x) = [ (opposite) / (hypotenuse) ] / [ (adjacent) / (hypotenuse) ] = (opposite) / (adjacent) = tan x

Thus, the tangent formula in terms of sine and cosine is, 

tan x = (sin x) / (cos x)

Answer: 7.93

Step-by-step explanation: I am not sure if this is correct but I really hope it helps.