A 20-oz bottle of soda costs $2.98.What is the cost per ounce?

Answer:

y < 1/2x -5

Step-by-step explanation:

1/2 is the slope

-5 is the y intercept

Answer:

B: (2, -1)

Step-by-step explanation:

Answer:

(x,y)=(-4/5,10/19)

Step-by-step explanation:

x+2y=3

x-8y=-16

x+2y=3

-x+8y=16 (multiply both sides by-1)

10y=16

y=16/10

x+2(16/10)=3

x=-4/5

Answer:

b. 29°

Step-by-step explanation:

In the given diagram, the smallest angle in the diagram is ∠FLG = 29°.

When to lines are meeting at a point, then the geometrical figure is formed called an angle.

Given, four lines extend from point L.

They are lines LF, LG, LH, and LI.

∠FLI = 106°, ∠FLG = (2x - 1)°, ∠GLH = (x + 17)°, ∠HLI = (4x - 15)°

Here, ∠FLI = ∠FLG + ∠GLH + ∠HLI

106°  = (2x - 1)° + (x + 17)° + (4x - 15)°

⇒ (2x - 1)° + (x + 17)° + (4x - 15)° = 106°

⇒ (7x + 1)° = 106°

⇒ 7x = 105

⇒ x = 15

Now, ∠FLG = (2x - 1)° = (2 × 15 - 1)° = 29°

GLH = (x + 17)° = (15 + 17)° = 32°

∠HLI = (4x - 15)° = (4 × 15 - 15)° = 45°

Therefore, the smallest angle in the diagram is ∠FLG = 29°.

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Answer:

2nd option.............................................

Answer:

you're question is complicated

Step-by-step explanation:

Answer:

u

Step-by-step explanation:

hb

Answer:

(x−1)(6x2+1)

Step-by-step explanation:

x^3-6x^2+x-1

(x−1)(6x^2+1)

Answe: (

( − 1 ) ( 6 ^ 2 + 1 )

Answer:

9

Step-by-step explanation:

13*3=39

48-39=9

Answer:

48-39=9

        ^

(13 x 3=39)

Answer:

A

Step-by-step explanation:

If you were to dilate a point by a scale factor of 2, then if you have the point (-4,0), both the x value and the y value would be multiplied by 2, giving a coordinate of (-8,0). If you do this to the other point, you get (0,4).

Now graph it out, and you get a parallel line that is not right on top, eliminating answer B. It's not C because it is parallel, not intersecting. And it's not D because they are related, they're parallel.

Hope this helps!

Answer:

i think 7

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

9 1, 3 9

67 1 and 67

so just enjoy ur day and have a great Christmas and new year

Answer:

Percent of occurrences= (Numbers of behavior/Numbers of opportunities)*100

Step-by-step explanation:

Based on the information given if a child is to put his/her plate in the sink everyday after having dinner the formula that will be use to calculates percent of occurrences is :

Percent of occurrences=( Numbers of behavior/Numbers of opportunities)*100

Where:

Numbers of behavior represent the Numbers of times the plate was put in the sink by child everday

Numbers of opportunities represent the Numbers of dinners the child had everyday

Answer:

I think it might be d

Step-by-step explanation:

Im not completely sure, BUT YOU GOT THIS

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

[tex]A=\frac{\sqrt{3} }{4} a^{2}[/tex]

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

[tex]A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}[/tex]

[tex]A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}[/tex]

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

[tex]A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}[/tex]

[tex]A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}[/tex]

Now, comparing areas:

[tex]\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )[/tex]

[tex]\frac{A_{1}}{A_{2}} =[/tex] 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

Answer:

24 i can be rong

Step-by-step explanation:

Answer:

B - 9

Step-by-step explanation:

5 x 9 = 45 or 45 divided 5

Step-by-step explanation:

u should:

7t = t + 48 » 7t - t = 48 » 6t = 48 » t = 8

and another one is:

2u + t + 13 = 10t + u - 44» 2u + 8 + 13 = 80 + u - 44»

» 2u + 21 = u + 36 » 2u - u = 36 - 21 » u = 15

Answer:

Solved only ticked ones

Answer:

use the formula:

[tex]a {}^{2} + {b}^{2} = (a + b) {}^{2} - 2ab[/tex]

1) 4a² + 49b²

= 2²a² + 7²b²

= (2a)² + (7b)²

based on the formula above, a = 2a and b = 7b

= ( 2a + 7b )² - 2(2a)(7b)

substitute 2a+7b = 11 into the equation

= 11² - 2( 14ab )

= 121 - 28ab

substitute ab = 2 into the equation

= 121 - 28(2)

= 121 - 56

= 65

2) 4x² + 9y²

= 2²x² + 3²y²

= (2x)² + (3y)²

based on the formula, a = 2x and b = 3y

= ( 2x + 3y )² - 2(2x)(3y)

substitute 2x+3y = 12 into the equation

= 12² - 2(2x)(3y)

= 144 -2(6xy)

= 144 - 12xy

substitute xy = 6 into the equation

= 144 - 12(6)

= 144 - 72

= 72

3) 4x² + 9y²

= 2²x² + 3²y²

= (2x)² + (3y)²

= (2x)² - (-3y)²

based on the formula, a=2x and b=-3y

= ( 2x-3y )²- 2(2x)(-3y)

substitute 2x-3y = 2 into the equation

= (2)² - 2(2x)(-3y)

= 4 - 2( -6xy )

= 4 + 12xy

substitute xy = 8 into the equation

= 4 + 12(8)

= 4 + 96

= 100

4) 16x² + 25y²

= 4²x² + 5²y²

= (4x)² + (5y)²

= (4x)² - (-5y)²

based on the formula, a = 4x and b = -5y

= (4x-5y)² - 2(4x)(-5y)

substitute 4x-5y = 6

= (6)² -2(4x)(-5y)

= 36 -2(-20xy)

= 36 + 40xy

substitute xy = 8 into the equation

= 36 + 40(8)

= 36 + 320

= 356

Answer:

Step-by-step explanation:

[tex]x-5=2\qquad|\text{add 5 to both sides}\\\\x-5+5=2+5\\\\x=7\\\\\text{Substitute to}\ 6x-20:\\\\6\cdot7-20=42-20=22[/tex]

Answer:

Out of

Step-by-step explanation:

A two-word phrase used to show division in a word problem.

Out of is a two-word phrase which is used to show division in a word problem.

Word problems in mathematics often use words such as divided by, per, average, split into, cut into, quotient of, ratio of to denote division (÷)

Answer:

b=56

Step-by-step explanation:

Try

Answer:

a burger

Step-by-step explanation:

because the cow is made into a burger lol

Answer:

it takes her 1/10 of an hour

Step-by-step explanation:

math

3 Answers: x = 0, x = 1, or x = 2

==================================================

Explanation:

The relation

{(0, 5) (1, 5) (2, 6) (x, 7)}

has points with x coordinates of: 0, 1, 2, and x.

If we repeated any of the x values listed so far, then we will not have a function.

So if we had the points (0,5) and (0,7), then the input x = 0 leads to multiple outputs. A function is only possible when any input x leads to exactly one output y.

This means that if x = 0, 1, or 2, then we won't have a function.

Side note: The y values can repeat, but if they do, then we won't have a one-to-one function. In this case, y = 5 repeats, so this function is not one-to-one (assuming x is not 0, not 1, and not 2).

Answer:

a) [tex]\frac{dA}{dt} = 48 \pi\frac{in^{2}}{min}[/tex]

b) [tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]

c) [tex]\frac{dh}{dt} = - 2\frac{h}{r} \frac {dr}{dt}[/tex]

Step-by-step explanation:

In order to solve this problem, we must first picture a cylinder of height h and radius r (see attached picture).

a) So, in order to find the rate at which the area of the circular surface of the dough is increasing with respect to time, we need to start by using the are formula for a circle:

[tex]A=\pi r^{2}[/tex]

So, to find the rate of change of the area, we can now take the derivative of this formula with respect to the radius r:

[tex]dA = \pi(2) r dr[/tex]

and divide both sides into dt so we get:

[tex]\frac{dA}{dr} = 2\pi r \frac{dr}{dt}[/tex]

and now we can substitute:

[tex]\frac{dA}{dr} = 2\pi(12in)(2\frac{in}{min})[/tex]

[tex]\frac{dA}{dt} = 48\pi\frac{in^{2}}{min}[/tex]

b) In order to solve part b, we can start with the formula for the volume:

[tex]V=\pi r^{2} h[/tex]

and solve the equation for h, so we get:

[tex]h=\frac{V}{\pi r^{2}}[/tex]

So now we can rewrite the equation so we get:

[tex]h=\frac{V}{\pi}r^{-2}[/tex]

and now we can take its derivative so we get:

[tex]dh=\frac{V}{\pi} (-2) r^{-3} dr[/tex]

we can rewrite the derivative so we get:

[tex]\frac{dh}{dt}=-2\frac{V}{\pi r^{3}}\frac{dr}{dt}[/tex]

we can take the original volume formula and substitute it into our current derivative, so we get:

[tex]\frac{dh}{dt}= -2\frac{\pi r^{2} h}{\pi r^{3}} \frac{dr}{dt}[/tex]

and simplify:

[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]

so now we can go ahead and substitute the values  provided by the problem:

[tex]\frac{dh}{dt} =-2\frac{13in}{12in} (2\frac{in}{min})[/tex]

Which simplifies to:

[tex] \frac{dh}{dt} = - \frac{13}{3} \frac{in}{min}[/tex]

c)

Part c was explained as part of part b where we got the expression for the rate of change of the height of the dough with respect to the radius of the dough in terms of the height h and the radius r:

[tex]\frac{dh}{dt} =-2\frac{h}{r} \frac{dr}{dt}[/tex]

The rate of change of the height of the pizza with respect to (w.r.t.) time

can be found given that the volume of the pizza is constant.

Reasons:

The height of the dough when t = k is 13 inches

Radius of the dough = 12 inches

Rate at which the radius of the dough is increasing, [tex]\dfrac{dr}{dt}[/tex] = 2 in.²/min

(a) Required: The rate of increase of the surface area with time

Solution:

The circular surface area, A = π·r²

By chain rule of differentiation, we have;

[tex]\dfrac{dA}{dt} = \mathbf{\dfrac{dA}{dr} \times \dfrac{dr}{dt}}[/tex]

[tex]\dfrac{dA}{dt} = \dfrac{d ( \pi \cdot r^2)}{dr} \times \dfrac{dr}{dt} = 2 \cdot \pi \times 2 = 4 \cdot \pi[/tex]

The rate of increase of the surface area with time, [tex]\mathbf{\dfrac{dA}{dt}}[/tex] = 4·π in.²/min.

(b) Required: The rate of decrease of the height with respect to time

The volume of the pizza is constant, given by; V = π·r² ·h

Therefore;

[tex]h = \mathbf{ \dfrac{V}{\pi \cdot r^2}}[/tex]

[tex]\dfrac{dh}{dt} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} \times \dfrac{dr}{dt} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} \times \dfrac{dr}{dt} = \mathbf{-2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt}}[/tex]

[tex]\dfrac{dh}{dt} = -2 \cdot \dfrac{h}{r} \times \dfrac{dr}{dt} = -2 \times \dfrac{13}{12} \times 2 = \dfrac{13}{3} = 4. \overline 3[/tex]

The rate at which the height of the dough is decreasing, [tex]\mathbf{\dfrac{dh}{dt}}[/tex]= [tex]\underline{4.\overline 3 \ in./min}[/tex]

(c) Required:]The expression for the rate of change the height of the dough with respect to the radius of the cone.

Solution:

[tex]\dfrac{dh}{dr} = \dfrac{d \left( \dfrac{V}{\pi \cdot r^2} \right)}{dr} = \dfrac{-2 \cdot V}{\pi \cdot r^3} = \dfrac{-2 \cdot \pi \cdot r^2 \cdot h}{\pi \cdot r^3} = -2 \cdot \dfrac{h}{r}[/tex]

[tex]\dfrac{dh}{dr} = \mathbf{ -2 \cdot \dfrac{h}{r}}[/tex]

The rate of change the height of the dough w.r.t. the radius is [tex]\underline{\dfrac{dh}{dr} = -2 \cdot \dfrac{h}{r}}[/tex]

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Answer:

9/50

Step-by-step explanation:

There are nine single digit numbers from integers 1-50 so in order to calculate the probability of getting 3 random numbers from 1-50 to be single digits:

Probability = number of favorable outcomes /total number of outcomes

Therefore Probability of getting 3 single digits randomly from 1-50 = 9/50

Answer:

A point on the line is m=1/2

A point on the line is (1,4)

Step-by-step explanation: