A recipe for lemonade requires 10 parts of water to every 6 parts of lemon juice. How many cups of water should be added to 30 cups of lemon juice to make the lemonade? I dont understand how many "parts" of water = 1 cup

Answer: Initial height before launch

Step-by-step explanation:

Given

The equation [tex]y=-9.8t+109.7t+7.4[/tex]  the height of toy rocket after t sec

when the rocket is launched, time is [tex]t=0[/tex]

Substituting 0 for [tex]t[/tex] in the equation

[tex]\Rightarrow y(0)=-9.8(0)+109.7(0)+7.4\\\Rightarrow y(0)=7.4[/tex]

Here, [tex]7.4[/tex] represents that rocket is already at a height of [tex]7.4[/tex] m before the launch.

Answer:

(x + 8)

Step-by-step explanation:

If you factor x2 + 5x – 24 using the AC method, it equals (x - 3) and (x + 8).

Answer:

D on edge :)

Step-by-step explanation:

Answer:

18 cm^3

Step-by-step explanation:

To find the volume, count the number of cubes, since each cube has a side length of 1 cm

The volume of 1 cube is 1*1*1 = 1 cm^3

There are 6 rows of 3 cubes each or 18 cubes

18 cubes of 1 cm^3 = 18 cm^3

Answer: 18 cubic cm

Step-by-step explanation:

Answer 18 :D !!!

As the name implies, there are 3 parts or conditions that must be held true in order for the function to be continuous at x = a.

Those three conditions are:

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

In this case, a = -1 as this is where the junction happens. It's where f(x) swaps identity from the first piece x^2-3 to the second piece 3x+1

To compute f(a), aka f(-1), we'll use the second piece

f(x) = 3x+1

f(-1) = 3(-1)+1

f(-1) = -2

We see that f(a) does indeed exist, so condition (1) is held true.

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

To compute the limit, we'll need the left hand limit (LHL) and right hand limit (RHL)

The LHL is found by having x approach -1 from the left. So you'll start with something like x = -2, then move to x = -1.5 then to x = -1.1 then to x = -1.01, and so on, getting steadily closer to x = -1. We won't actually arrive at x = -1 itself.

But because x^2-3 is a polynomial, and all polynomials are continuous, we can simply plug x = -1 into this to find that...

y = x^2-3

y = (-1)^2 - 3

y = -2

The input x = -1 leads to the output y = -2 for the first piece. This is the LHL.

We found earlier that x = -1 lead to y = -2 for the second piece. This is the RHL.

Because LHL = RHL, we have proven condition (2) is true. It also means condition (3) is true because f(a) is part of the RHL, more or less.

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

In layman's terms, we can think of the two curves as roads. For the function to be continuous, the road cannot have any jumps, gaps, or potholes. Condition (1) says that the point must exist, aka there isn't a pothole there. Condition (2) says that the two pieces of the road, on either side of the point in question, must connect together. Hence there are no gaps or jumps. Condition (3) effectively ties everything together.

You might be asking if condition (3) is a bit redundant. Surely if f(a) exists and the limit exists, then that's enough to prove continuity, right? Unfortunately no that's not the case. Consider the situation where the limit exists, but f(a) was some other value. That means we have a removable discontinuity. That point in the road is a pothole but the two roads do connect.

One could argue that conditions (2) and (3) are sufficient, and condition (1) isn't really needed. This is because if condition (3) was the case, then we automatically have shown that f(a) must exist. This is of course assuming we found that the limit exists as well, and it's not plus/minus infinity.

Answer:

triangular prism

Step-by-step explanation:

Answer:

1.6 ft.

Step-by-step explanation:

Given that the conical pylons had a radius (r) of 1 foot and a height (h) of 2 foot. The volume of the conical pylons is:

Volume = πr²h/3

Therefore substituting gives:

Volume = π(1)²(2)/3 = 2π/3 ft³

Since the same amount of concrete is used to construct a spherical barrier, hence the volume of the sphere would be the same as the volume of the conical pylon.

Volume of sphere = 4πr³/3

4πr³/3 = 2π/3

2r³ = 1

r³ = 1/2 = 0.5

r = ∛0.5 = 0.8 ft.

Therefore the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.

Square root of 9340 = 96.64

nearby number = 96

square of 96 = 9216

9340- 9216= 124

the smallest number 124 should be subtracted from 9340 so as to get a perfect square.

Answer: A

Step-by-step explanation:

Answer:

[tex]n = -3[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

-5-2n=8n+25

-5-25=8n+2n

-30=10n

-30/10=n

-3=n

Step-by-step explanation:

therefore n=-3

Hope this helps u!!

Answer:

1 1/4 mile/hr (Answer B)

Step-by-step explanation:

Distance traveled:  1/4 mile; elapsed time:  1/5 hour.  Then:

 1/4 mile

--------------- = 5/4 mile/hr, or 1 1/4 mile/hr (Answer B)

  1/5 hour

Step-by-step explanation:

Hey there!

Here;

Diameter (d) = 13 ft

Radius (r) = 13/2 = 6.5 ft

Now,

Area of a circle= πr²

= (22/7)*(6.5)²

= 132.78 ft²

Therefore, the area is 133 ft².

Hope it helps!

Step-by-step explanation:

Hey there!

Here;

Diameter (d) = 13 ft

Radius (r) = 13/2 = 6.5 ft

Now,

Area of a circle= πr²

= (22/7)*(6.5)²

= 132.78 ft²

Therefore, the area is 133 ft².

Hope it helps!

Answer:

[tex]21(2-x)+12x=44[/tex]

[tex]42-21x+12x=44[/tex]

[tex]42-9x=44[/tex]

[tex]42-9x-42=44-42[/tex]

[tex]-9x=2[/tex]

[tex]-9x=2\\-9 ~~-9[/tex]

[tex]x=-2/9[/tex]

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

hope it helps..

have a great day!!

Answer:

Step-by-step explanation:

Formula for total surface area of of the triangular prism is:

Total Surface area (S) = Ph+ 2B

P = Perimeter of the triangular base

P = 6 + 8 + 10

P = 24 cm

h = height of the prism = 10 cm

B = area of the base

B = ½*bh = ½*8*6

B = 24 cm

S = 24*10 + 2(24)

S = 240 + 48

S = 288 cm²

Total surface area = 288 cm²

Answer:

system has 1 solution at (2.5, -1.5)

Step-by-step explanation:

y = x - 4     this equation has a slope of 1 and a y-intercept of -4

3y - x = -7   this equation has a slope of 1/3 and a y-intercept of -7/3

Answer:

The correct answer is - 3 hours.

Step-by-step explanation:

Given:

Price of parts: $200

Price of labor: $75/hour

Total cost: $425

Solution:

Let x = x of hours work done on the car

The inequality can be represented as:

425 = 75x + 200

Solving this inequality, we find that

225 =75x

or

x = 3

Thus, It means that the mechanic will take at least 3 hrs to work on his car.

Answer:

3/8 tablespoons

Step-by-step explanation:

When we add fractions, we have to make each fraction a common denominator.

So we get 1/4 into 2/8 and we have 1/8

So we add and get 3/8

Answer:

The answer would be 96

Step-by-step explanation:

Because 20/2=10x2=20

                         19x4=76

20+76=96

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

Explanation:

For now, let's focus on the probability of getting one "5".

There are 4 of these cards (one of each suit) and 52 total. The probability of getting the card we're after is 4/52 = 1/13.

We can think of it like saying "if we focus on one suit only, then there's a 1 in 13 chance of getting a '5' from this pile".

The probability of getting two "5"s in a row is (1/13)*(1/13) = 1/169 assuming we put the first card back. If the first card is not put back, then we would compute it like so: (4/52)*(3/51). I'll leave it unevaluated for you to try out as practice.

Side note: 1/169 = 0.0059 = 0.59% approximately

Answer:

option 4

Step-by-step explanation:

[tex]perpendicular means = slope_1 \times sope_2 = -1\\[/tex]

                                [tex]-2 \times slope_2 = -1\\\\slope_2 = \frac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

The slopes of perpendicular lines are negative reciproclas. That means their product equals -1.

If you know the slope of a line, to find the slope of a perpendicular line, flip the slope and change the sign.

Given line: slope = -2

-2 is the same as -2/1

Flip it: -1/2

Change the sign: 1/2

Answer: 1/2

Answer:

4.8 slices each

Step-by-step explanation:

8*3= 24

24/5= 4.8

Answer: [tex]518.4\ cm^3[/tex]

Step-by-step explanation:

Given

The volume of the small block is [tex]300\ cm^3[/tex]

The ratio of the surface area of small to large block is [tex]25:36[/tex]

Suppose the length of the small and large box is a and b

[tex]\therefore \left(\dfrac{6a^2}{6b^2}\right)=\dfrac{25}{36}\\\\\Rightarrow \left(\dfrac{a}{b}\right)^2=\dfrac{25}{36}\\\\\Rightarrow \left(\dfrac{a}{b}\right)=\dfrac{5}{6}\\\\\therefore \text{Ratio of the volumes of two is }\\\\\Rightarrow \dfrac{a^3}{b^3}=\dfrac{5^3}{6^3}\\\\\Rightarrow \dfrac{V_s}{V_l}=\dfrac{125}{216}\\\\\Rightarrow V_l=300\times \dfrac{216}{125}\\\\\Rightarrow V_l=518.4\ cm^3[/tex]

Answer:

288 pages

Step-by-step explanation:

Step 1: Set up a fraction (Since 75% is 216, 100% is x. We don't need the percent (%).)

[tex]\frac{216}{75} = \frac{x}{100}\\\\[/tex]

Step 2: Solve; Divide the given values (All we are doing is finding what is between those values.)

[tex]\frac{216}{75}\\\\216 \div 75\\\\= 2.88[/tex]

Step 3: Multiply the result to the value (Now we multiply the result to 100 because that would make it equal.)

[tex]100\\\\2.88 \times 100\\\\= 288[/tex]

Therefore, the book is 288 pages long.

Answer:

v = 2c

Step-by-step explanation:

Answer:

Logan played for 22 minutes during the second half.

Step-by-step explanation:

Since Keith played the first 22 minutes of a soccer game and Logan then replaced him for the rest of the half, and Logan started the second half and was replaced by Wilson with 18 minutes left in the game, if each half is 40 minutes long To determine how long did Logan play during the second half, the following calculation must be performed:

Second Half Total - Time Played by Wilson = Time Played by Logan

40 - 18 = X

22 = X

Therefore, Logan played for 22 minutes during the second half.

Answer:

I don't know how to explain it well but i got part of my notes and i solved it and i got D. 144 and i got it checked and it was correct

Step-by-step explanation:

Sorry for not helping sooner

Answer:

D

Step-by-step explanation:

y - 4 = 7(x - 6)                    Remove the brackets

y - 4 = 7x - 42                    Add 4 to both sides

y = 7x - 42 + 4

y = 7x - 38                  

Note when you put this in slope, y intercept form, the ordered pair is easier to find.

Let x = 5

y = 7*5 - 38

y = 35 - 38

y = -3          (5,4) isn't right

Let x = 6

y = 7*6 - 38

y = 42 - 38

y = 4                 That does not work either.

The answer is D