Anita is eating popcorn at the movies. She eats 24 kernels in 10 minutes and 72 kernels in 30 minutes. Which TWO other ratios can represent the rate at which she is eating popcorn?

Answer:

see explanation

Step-by-step explanation:

(13)

v² - 11v + 18 = 0 ← in standard form

(v - 2)(v - 9) = 0 ← in factored form

Equate each factor to zero and solve for v

v - 2 = 0 ⇒ v = 2

v - 9 = 0 ⇒ v = 9

solutions are v = 2, v = 9

(14)

5x² - 12x + 7 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × 7 = 35 and sum = - 12

The factors are - 5 and - 7

Use these factors to split the x- term

5x² - 5x - 7x + 7 = 0 ( factor the first/second and third/fourth terms )

5x(x - 1) - 7(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(5x - 7) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

5x - 7 = 0 ⇒ 5x = 7 ⇒ x = [tex]\frac{7}{5}[/tex]

solutions are x = 1, x = [tex]\frac{7}{5}[/tex]

Answer:

A. The slope is  [tex]\frac{3}{2}[/tex]

B.  the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point.

Step-by-step explanation:

PART A: Slope

Given tangent line;

[tex]y = \frac{3x}{2} + \frac{9}{2}[/tex]

The slope of the tangent line is equal to the derivative of the function;

[tex]\frac{dy}{dx} =\frac{3}{2}[/tex]

the slope = [tex]\frac{3}{2}[/tex]

PART B: Correct statement that describe the slope of a tangent line:

A secant line is a straight line joining two points on a function and the slope of the function is equal to average rate of change of the function between the two points.

A tangent line is a straight line that touches a function at only one point, and the slope of the function is equal to the instantaneous rate of change of the function at that one point.

Thus, the correct statement is " the slope of the tangent line at x = 1 is also the instantaneous rate of change at that point".

Answer:

$40 and $72, see below :)

Step-by-step explanation:

One way we can do this is to add the total ratios and then divide that from 112.

10x + 18x = 28x = 112

28x = 112

x = 4

That means, for every ratio, you just have to multiply the amount by 4.

so for example, 10 is just 10 * 4 = 40

So, your answer would be you share the money into $40 and $72

Answer:

2/11 is your slope

Step-by-step explanation:

If you use the point slope form: y2-y1/x2-x1, then you should be able to find your slope with two given coordinates

Answer:2/11

Step-by-step explanation: I am super good at math

Step-by-step explanation:

coordinate of A is -3,-1

Answer:

-3,-1 is answer hope you like

Answer:

y = -2x + 5

Step-by-step explanation:

The slope is -2/1 and the y intercept is 5.  

Answer:

y=−3

Step-by-step explanation:

(−2)(5)−7y=11

−10+−7y=11

−7y−10=11

Step 2: Add 10 to both sides.

−7y−10+10=11+10

−7y=21

Step 3: Divide both sides by -7.

−7y

−7

=

21

−7

Answer:

Really hope this helps

Step-by-step explanation:

Tom= £149.40

Ben= £522.90

Answer:

a)

x      -3         -2         -1         0          1            2         3

y       0          8          6         0         -4           0        18

b)

see in the table, at x = {-3; 0; 2}, y = 0

=> x = {-3; 0; 2} is the solutions of the equation x³ + x² - 6x = 0

Step-by-step explanation:

a) 0 and 6  will be written in the given blank spaces.

b) The value of x for the given equation is 0, -3 and 2.

It is a method for finding the values of variable, by substituting the value of one variable to get the another.

To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero.

a). We have, an equation

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

so, at x = -3

[tex]y = -3^{3} +(-3)^{2} -6(-3)[/tex] =  -27+9+18 = 0   (substitute x = -3 in the given equation)

at x = -1

y = [tex]-1^{3} +(-1)^{2} -6(-1) = -1+1+6 = 6[/tex]

Hence, 0 and 6 will we written the blank spaces of the given table.

b). We have an equation

[tex]x^{3} +x^{2}-6x = 0[/tex]

⇒ [tex]x(x^{2} +x-6)=0[/tex]

⇒ [tex]x (x^{2} +3x-2x-6)=0[/tex]

⇒ [tex]x(x(x+3)-2(x+3))=0[/tex]

⇒ [tex]x(x+3)(x-2)=0[/tex]

⇒ [tex]x = 0,-3 and 2[/tex]

Hence, 0, -3 and 2 are the solutions of the given equation.

Learn more about substitution method  here:

https://brainly.com/question/14619835

#SPJ2

Answer:

y = [tex]\frac{7}{4}[/tex] x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

7x - 4y = 28 ( subtract 7x from both sides )

- 4y = - 7x + 28 ( divide all terms by - 4 )

y = [tex]\frac{7}{4}[/tex] x - 7 ← in slope- intercept form

Answer:

I think it's 6 or 0.6

Answer:

1

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define Expression

2x - 2x + 4 - 3

Step 2: Simplify

Step-by-step explanation:

2x + (-2x) + 4 + (-3)

With this, you subtract -2x from 2x leaving the answer as 0.

And you would also have to subtract 3 from 4 leaving your answer as 1

2x-2x+4-3

=1

Answer:

42:14

42 cats and 14 fish

Answer:

3:1

Step-by-step explanation:

42 : 14 ---> 42/14 = 21/7 = 3/1 ---> 3 : 1

Denominators= 4 and 6

LCM of 4 and 6 => 12

So, the least common denominator of the given fractions is 12.

Hope it helps!

Answer:

12

Step-by-step explanation:

1/4 and 5/6

4, 8, 12

6, 12

Answer:

The top right corner

Step-by-step explanation:

I hope you have a good day

Answer:

2nd One

Step-by-step explanation:

The answer is the 2nd one because it is not a line, and the rest are functions. This line is curved. Non-linear functions mean the graph is not a straight line, which would perfectly describe this one because it starts straight and curves up.

Step-by-step explanation:

cot0=1/tan0

cot0=1/0.5=2

Answer:

27.4%

Step-by-step explanation:

Step one:

given

original cost $69

seling price $52

Required

The percent reduction

Step two:

% reduction= change in price/original price*100

% reduction= 69-52/62*100

% reduction=17/62*100

% reduction= 0.274*100

% reduction= 27.4%

Answer:

1.

1) The area of the sector is 168.8π mi²

2) The area of the sector is 529.9 mi²

2.

1) The area of the sector is 42.3π in²

2) The area of the sector is 132.7 in²

Step-by-step explanation:

The formula of the area of a sector in a circle is A = [tex]\frac{x}{360}[/tex] × π r², where

1.

∵ The central angle subtended by the arc of the circle is 270°

∴ x = 270°

∵ The radius of the circle is 15 mi.

∴ r = 15

→ Substitute them in the formula of the area above

∵ A = [tex]\frac{270}{360}[/tex] × π (15)²

∴ A = 168.75π mi²

→ Round it to the nearest tenth

∴ A = 168.8π mi²

1) The area of the sector is 168.8π mi²

∵ π = 3.14

∴ A = 168.75 × 3.14

∴ A = 529.875 mi²

→ Round it to the nearest tenth

∴ A = 529.9 mi²

2) The area of the sector is 529.9 mi²

2.

∵ The central angle subtended by the arc of the circle is 90°

∴ x = 90°

∵ The radius of the circle is 13 in

∴ r = 13

→ Substitute them in the formula of the area above

∵ A = [tex]\frac{90}{360}[/tex] × π (13)²

∴ A = 42.25π in²

→ Round it to the nearest tenth

∴ A = 42.3π in²

1) The area of the sector is 42.3π in²

∵ π = 3.14

∴ A = 42.25 × 3.14

∴ A = 132.665 in²

→ Round it to the nearest tenth

∴ A = 132.7 in²

2) The area of the sector is 132.7 in²

Answer:

she got back 63 times

Step-by-step explanation:

Here, we want to know the number of times she is at bat

from the question, we are made to know that she strikes out twice after 9 times

So striking out 14 times, the number of times she has got back will be ;

14/2 * 9 = 63 times

Answer:

16. this would be "base" but that isn't an option...

17.  R, exponent

24. F, term

Answer:

formula:

A=(A+B/2)H

Step-by-step explanation:

Hope I helped and good luck :)

Answer:

x > 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Inequality

5x > 20

Step 2: Solve for x

Here we see that any value x greater than 4 would work as a solution to the inequality.

2x-227 je pense,r éonse siplifié

Answer:

(12157)/(1000(-20x-2))

Step-by-step explanation:

Answer:

a) (i) 1200

b) (ii) 3750

c) (i) [tex]\frac{3}{20}[/tex]

Step-by-step explanation:

a) Total number of students = 5000

Ratio of teachers to students = 6 : 25

i) Number of teachers = ?

By the given ratio, we can let the number of teachers = 6[tex]x[/tex]

and we can let the number of students = 25[tex]x[/tex]

[tex]25x = 5000\\\Rightarrow x = 200[/tex]

Therefore, number of teachers = 6 [tex]\times[/tex] 200 = 1200

b) A Quarter of the students own i-phone classic 20.

ii) Number of students who do not own an i-phone classic?

As per question statement,

Number of students who own i-phone classic 20 = [tex]\frac{1}{4}\times 5000[/tex] = 1250

Number of students who do not own i-phone classic 20 = 5000 - 1250 = 3750

c) Number of students who own samsung galaxy a80s = 60% of students who own i-phone classic 20 = [tex]\frac{60}{100}\times 1250[/tex] = 750

Fraction of students who own samsung galaxy a80s = Number of students having samsung a80s divided by total number of students

[tex]\dfrac{750}{5000} = \dfrac{3}{20}[/tex]

Answer:

No solutions

Step-by-step explanation:

As it's parallel line

Answer:

To write 65/100 as a decimal you to divide numerator by the denominator of the fraction.

We divide now 65 by 100 what we write down as 65/100 and we get 0.65.

And finally we have:

65/100 as a decimal equals 0.65

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

x+8=5

subtract 8 from 5 to get x on its own

x=-3