Rae wants to poll the students in her school to find out their favorite subject.

The school has 600 students.


Choose the statement below that describes the best way for Rae to survey the students in her school without asking all 600 of them.

well, we know the directrix is at y = 4 and the focus point is down below it at (-6 , -3), meaning is a downward opening vertical parabola, like the one you see in the picture below.

keeping in mind that the vertex is equidistant from the directrix and focus point by a distance "P", that puts this vertex at ( -6 , 1/2 ), and since the parabola is opening downwards, P is negative.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex][tex]\begin{cases} h=-6\\ k=\frac{1}{2}\\[1em] P=-\frac{7}{2} \end{cases}\implies 4\left( -\cfrac{7}{2} \right)\left(y-\cfrac{1}{2} \right)=[x-(-6)]^2 \\\\\\ -14\left(y-\cfrac{1}{2} \right)=(x+6)^2\implies y-\cfrac{1}{2}=-\cfrac{1}{14}(x+6)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{14}(x+6)^2+\cfrac{1}{2}~\hfill[/tex]

Answer:

(-4, 4)

(6, 2)

(0, -2)

(-∞, -4), (0, 6)

(-4, 0), (6, ∞)

Step-by-step explanation:

(-4, 4)

(6, 2)

(0, -2)

(-∞, -4), (0, 6)

(-4, 0), (6, ∞)

Answer: 20

Step-by-step explanation:

log 5x^3 - log x^2 = 2

log 5x = 2

5x = 100

x = 20

Answer:

x=20

Step-by-step explanation:

keep smiling

Answer:

9 numbers

Step-by-step explanation:

10^2 + 10 = 110. This is also greater than 100.

Highest value of x is 9.

9^2 + 9 = 90.

Not sure if zero counts, but if it does, it'll be 10 numbers instead.

Hope this helps!

There are 9 positive integers x satisfy the inequality x² + x < 100.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have the inequality

x² + x < 100.

First take x= 1 then

1² + 1 = 2 < 100

Take x= 2

2² + 2 = 6 <100

Take x= 3

3² + 3 = 12 < 100

Take x = 4

4² + 4 = 20 < 100

Take x= 5

5² + 5 = 30 < 100

Take x =6, 7, 8, 9, 10 and 11

6² + 6<100

7² + 7<100

8² + 8<100

9² + 9 <100

10² + 10 > 100

So, there are 9 possible digits.

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#SPJ2

The amount left by Diana is percent part of total food cost. The 15% tip of $44 total cost given by Diana is : Option D: $6.60

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Since the total food cost was $44 and the tip was 15% of the total cost, thus,

[tex]\text{Tip amount} = \dfrac{44}{100} \times 15 = 6.6 \text{\:dollars}[/tex]

Thus,

The 15% tip of $44 total cost given by Diana is : Option D: $6.60

Learn more about percentage here:

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Answer:

  9

Step-by-step explanation:

Ron can deliver 300t pounds of mulch in t trips. The number of trips needed to deliver at least 2700 pounds is ...

  300t ≥ 2700

  t ≥ 9 . . . . . . . . divide by 300

Ron needs to make at least 9 trips to deliver at least 2700 pounds of mulch.

Answer:

    2

Step-by-step explanation:

   1 + 1 = 2

Answer:

1 + 1 = 2

Step-by-step explanation:

1 + 1 = 2

basic addition as

2 + 2 = 4

or like

3 + 2 = 5

or

2 + 1 = 3

Answer:

2091.9

Step-by-step explanation:

multiply 4580 by 243 and then divide your answer by 532.

Rhombus can have harmonious diagonals provided that this is true we talk about the square unique instance of rhombus which additionally has four equivalent length sides and its diagonals are opposite and divide each other with respect to a square shape rhombus doesn't constantly need to be a square shape since it doesn't must have 4 right points

Answer:

S4, E17 (Judgement)

Step-by-step explanation:

Hope that helps!

Answer:

24°

Step-by-step explanation:

Let x = one complementary angle

Let y = the other complementary angle

As the sum of two complementary angles is 90°:

x + y = 90

If one angle is 18° more than two times the other angle:

y = 18 + 2x

Rewrite x + y = 90 to make x the subject:

x = 90 - y

Now substitute x = 90 - y into y = 18 + 2x and solve for y:

y = 18 + 2(90 - y)

⇒ y = 18 + 180 - 2y

⇒ 3y = 198

⇒ y = 198 ÷ 3 = 66

Now substitute found value of y = 66 into x + y = 90 and solve for x:

x + 66 = 90

⇒ x = 90 - 66 = 24

Therefore, the larger angle = 66° and the smaller angle = 24°

Product of polynomials can be done by distribution of multiplication over addition. The product of  [tex](2x - 3)(2x^2 + 7x - 1)[/tex] is [tex]4x^3 + 8x^2 -23x + 3[/tex]

Suppose a, b and c are three numbers. Then we have:

[tex]a(b + c) = a\times b + a\times c[/tex]

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

The product result of the given expression is

[tex](2x - 3)(2x^2 + 7x - 1) = 2x(2x^2 + 7x - 1) -3(2x^2 + 7x - 1) \\(2x - 3)(2x^2 + 7x - 1) = 4x^{1+2} + 14x^2 -2x - 6x^2 - 21x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + (14 -6)x^2 + (-2 -21)x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + 8x^2 -23x + 3[/tex]

It is because when bases are same and there is multiplication, then powers add up, so we have: [tex]a^b \times a^c = a^{b+c}[/tex]

Also, we've

[tex](-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve[/tex]

where -ve, +ve are sign of operands and result.

That's why [tex]2 \times -1 = -2[/tex]

Thus,

The product of   [tex](2x - 3)(2x^2 + 7x - 1)[/tex]  is [tex]4x^3 + 8x^2 -23x + 3[/tex]

Learn more about product of polynomials here:

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Answer:

slope = 9/4

Step-by-step explanation:

Slope is a ratio (looks like a fraction) It tells you the steepness or flatness of a line.

To find slope you subtract the y's (that's the second number in the ordered pairs; here it's 10 and 1) put that on top. Then subtract the x's and put that on the bottom (here 9 and 5)

Slope = 10-1 / 9-5

=9/4

Now, parallel lines have the same slope, so if one of the lines has slope 9/4, then the other line does too!

Answer:

steps below

Step-by-step explanation:

volume of rock : 16 * 12 * 12 = 2304

height will take when it was threw into tank: 2304 / (32*24) = 3

Original water height + rock height: 12 + 3 = 15 cm

10k^3 , 6k^3

k^3 ( 10, 6 )

2k^3 (5, 3)

so 2k^3 is the greatest common factor of both the numbers .

Answer:

greatest common factor: 2k³

Step-by-step explanation:

given 10k³ and 6k³

for gcf just simply break them down:

10k³ = 2 * 5 * k * k * k

6k³ =  2 * 3 * k * k * k

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

Analyse both of them and find similarities:

the similarities are: 2 * k * k * k

so the greatest common factor is 2k³

Answer:

So for number 1 and 2

Step-by-step explanation:

Perimeter is = 2(L+W)

L=2w as it said on the problem above.

60=2 (2w+w)

60= 2 (3w)

60 = 6w

w= 10 , L=20 P=60

Area of rectangle = L x W

20 x 10 = 200

2)You would have twice as many hot dogs and 24 is two times 12 and if you add them you get 36.

Answer:

36, 44, 52

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

You move the decimal point twice to the right because 100 has two zeros. But if it was 7.20÷100 it would be 0.072 because you move the point to the left.

Answer:

-30.44

Step-by-step explanation:

50.54 - 20.10 = 30.44

Answer:

Step-by-step explanation:

Given:

Angles QPR and TPR both are:

Verify if the remaining angles are same.

This is not same as ∠PTS:

This makes ∠PST ≠ ∠PRQ

Since corresponding angles are different, the triangles are not similar

Given two right triangles.

Verify the corresponding sides have same ratio.

Find the ratio of longer legs:

Find JN:

Find the ratio of shorter legs:

The triangles are similar by SAS since we have two sides similar and included angle is same (right angle)

Answer:

y= 2 x - 7/3

Step-by-step explanation:

Answer:

  24.5 mi

Step-by-step explanation:

Each cm represents 9.8 miles, so 2.5 cm will represent a distance 2.5 times as far:

  (2.5)(9.8 mi) = 24.5 mi

From Old Faithful to West Thumb is 24.5 miles.

Answer:

  15

Step-by-step explanation:

Let 'a' represent Artaud's age. He notices the relationship ...

  -a +39 = 24

If we add a-24 to both sides, we get ...

  15 = a

Artaud is 15 years old.

Answer: 15 years old

Step-by-step explanation:

Let x be Artaud's age. Let the opposite of his age be -x

-x + 39 = 24

-x = 24-39

-x = -15 (multiply both sides by -1)

x = 15 years old

Answer:

I believe the answer is B. 15/5 = n/12

Step-by-step explanation:

Once again same method as I've explained before. However, this one tricked me a little bit and still is because of the appearance of the smaller triangle. However, If I don't focus on that I believe this answer is correct. This is because in order to find the missing side we need to find the factor of which the triangle was expanded. So we must divide a given side of the bigger triangle by the same similar side of the little triangle, like 15/5. Then we must divide n by its similar side which the appearance made me think 13 which is not an option so I believe it is 12 and it was just trying to throw me off. So n/12. Therefore that is why I believe B is correct.

Answer:

35v

Step-by-step explanation:

5(6v)+5v

[tex]5 \times 6v + 5v \\ 30v + 5 \\ combine \: the \: terms \\ = 35v[/tex]

Answer:

35v

Step-by-step explanation:

5 times 6v = 30v, then you add 5v which gives you 35v. Hope that helps :)

Answer: B

Step-by-step explanation:

Answer:

B) 9/3 * 2/3

Step-by-step explanation:

B is correct since 9/3 * 2/3 = 18/9 = 2

If you check the other answer choices, they will not be between 2 and 3

Answer:

a)c=20

b)b=16

c)a=-3

d)c=2•5

e)a=0•8